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• Problem Solving in STEM

Solving problems is a key component of many science, math, and engineering classes.  If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems.  Problem solving during section or class allows students to develop their confidence in these skills under your guidance, better preparing them to succeed on their homework and exams. This page offers advice about strategies for facilitating problem solving during class.

How do I decide which problems to cover in section or class?

In-class problem solving should reinforce the major concepts from the class and provide the opportunity for theoretical concepts to become more concrete. If students have a problem set for homework, then in-class problem solving should prepare students for the types of problems that they will see on their homework. You may wish to include some simpler problems both in the interest of time and to help students gain confidence, but it is ideal if the complexity of at least some of the in-class problems mirrors the level of difficulty of the homework. You may also want to ask your students ahead of time which skills or concepts they find confusing, and include some problems that are directly targeted to their concerns.

You have given your students a problem to solve in class. What are some strategies to work through it?

• Try to give your students a chance to grapple with the problems as much as possible.  Offering them the chance to do the problem themselves allows them to learn from their mistakes in the presence of your expertise as their teacher. (If time is limited, they may not be able to get all the way through multi-step problems, in which case it can help to prioritize giving them a chance to tackle the most challenging steps.)
• When you do want to teach by solving the problem yourself at the board, talk through the logic of how you choose to apply certain approaches to solve certain problems.  This way you can externalize the type of thinking you hope your students internalize when they solve similar problems themselves.
• Start by setting up the problem on the board (e.g you might write down key variables and equations; draw a figure illustrating the question).  Ask students to start solving the problem, either independently or in small groups.  As they are working on the problem, walk around to hear what they are saying and see what they are writing down. If several students seem stuck, it might be a good to collect the whole class again to clarify any confusion.  After students have made progress, bring the everyone back together and have students guide you as to what to write on the board.
• It can help to first ask students to work on the problem by themselves for a minute, and then get into small groups to work on the problem collaboratively.
• If you have ample board space, have students work in small groups at the board while solving the problem.  That way you can monitor their progress by standing back and watching what they put up on the board.
• If you have several problems you would like to have the students practice, but not enough time for everyone to do all of them, you can assign different groups of students to work on different – but related - problems.

When do you want students to work in groups to solve problems?

• Don’t ask students to work in groups for straightforward problems that most students could solve independently in a short amount of time.
• Do have students work in groups for thought-provoking problems, where students will benefit from meaningful collaboration.
• Even in cases where you plan to have students work in groups, it can be useful to give students some time to work on their own before collaborating with others.  This ensures that every student engages with the problem and is ready to contribute to a discussion.

What are some benefits of having students work in groups?

• Students bring different strengths, different knowledge, and different ideas for how to solve a problem; collaboration can help students work through problems that are more challenging than they might be able to tackle on their own.
• In working in a group, students might consider multiple ways to approach a problem, thus enriching their repertoire of strategies.
• Students who think they understand the material will gain a deeper understanding by explaining concepts to their peers.

What are some strategies for helping students to form groups?  

• Instruct students to work with the person (or people) sitting next to them.
• Count off.  (e.g. 1, 2, 3, 4; all the 1’s find each other and form a group, etc)
• Hand out playing cards; students need to find the person with the same number card. (There are many variants to this.  For example, you can print pictures of images that go together [rain and umbrella]; each person gets a card and needs to find their partner[s].)
• Based on what you know about the students, assign groups in advance. List the groups on the board.
• Note: Always have students take the time to introduce themselves to each other in a new group.

What should you do while your students are working on problems?

• Walk around and talk to students. Observing their work gives you a sense of what people understand and what they are struggling with. Answer students’ questions, and ask them questions that lead in a productive direction if they are stuck.
• If you discover that many people have the same question—or that someone has a misunderstanding that others might have—you might stop everyone and discuss a key idea with the entire class.

After students work on a problem during class, what are strategies to have them share their answers and their thinking?

• Ask for volunteers to share answers. Depending on the nature of the problem, student might provide answers verbally or by writing on the board. As a variant, for questions where a variety of answers are relevant, ask for at least three volunteers before anyone shares their ideas.
• Use online polling software for students to respond to a multiple-choice question anonymously.
• If students are working in groups, assign reporters ahead of time. For example, the person with the next birthday could be responsible for sharing their group’s work with the class.
• Cold call. To reduce student anxiety about cold calling, it can help to identify students who seem to have the correct answer as you were walking around the class and checking in on their progress solving the assigned problem. You may even want to warn the student ahead of time: "This is a great answer! Do you mind if I call on you when we come back together as a class?"
• Have students write an answer on a notecard that they turn in to you.  If your goal is to understand whether students in general solved a problem correctly, the notecards could be submitted anonymously; if you wish to assess individual students’ work, you would want to ask students to put their names on their notecard.  
• Use a jigsaw strategy, where you rearrange groups such that each new group is comprised of people who came from different initial groups and had solved different problems.  Students now are responsible for teaching the other students in their new group how to solve their problem.
• Have a representative from each group explain their problem to the class.
• Have a representative from each group draw or write the answer on the board.

What happens if a student gives a wrong answer?

• Ask for their reasoning so that you can understand where they went wrong.
• Ask if anyone else has other ideas. You can also ask this sometimes when an answer is right.
• Cultivate an environment where it’s okay to be wrong. Emphasize that you are all learning together, and that you learn through making mistakes.
• Do make sure that you clarify what the correct answer is before moving on.
• Once the correct answer is given, go through some answer-checking techniques that can distinguish between correct and incorrect answers. This can help prepare students to verify their future work.

How can you make your classroom inclusive?

• The goal is that everyone is thinking, talking, and sharing their ideas, and that everyone feels valued and respected. Use a variety of teaching strategies (independent work and group work; allow students to talk to each other before they talk to the class). Create an environment where it is normal to struggle and make mistakes.
• See Kimberly Tanner’s article on strategies to promoste student engagement and cultivate classroom equity. 

A few final notes…

• Make sure that you have worked all of the problems and also thought about alternative approaches to solving them.
• Board work matters. You should have a plan beforehand of what you will write on the board, where, when, what needs to be added, and what can be erased when. If students are going to write their answers on the board, you need to also have a plan for making sure that everyone gets to the correct answer. Students will copy what is on the board and use it as their notes for later study, so correct and logical information must be written there.

For more information...

Tipsheet: Problem Solving in STEM Sections

Tanner, K. D. (2013). Structure matters: twenty-one teaching strategies to promote student engagement and cultivate classroom equity . CBE-Life Sciences Education, 12(3), 322-331.

• Designing Your Course
• A Teaching Timeline: From Pre-Term Planning to the Final Exam
• The First Day of Class
• Group Agreements
• Classroom Debate
• Flipped Classrooms
• Leading Discussions
• Polling & Clickers
• Teaching with Cases
• Engaged Scholarship
• Devices in the Classroom
• Beyond the Classroom
• On Professionalism
• Getting Feedback
• Equitable & Inclusive Teaching
• Advising and Mentoring
• Teaching and Your Career
• Teaching Remotely
• Tools and Platforms
• The Science of Learning
• Bok Publications
• Other Resources Around Campus

April 11, 2017

The Science of Problem-Solving

It turns out practices that might seem a little odd—like talking to yourself—can be pretty effective

By Ulrich Boser

justgrimes Flickr   (CC BY-SA 2.0)   

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American

For Gurpreet Dhaliwal, just about every decision is a potential opportunity for effective problem solving. What route should he take into the office? Should Dhaliwal write his research paper today or next week? "We all do problem solving all day long," Dhaliwal told me.

An emergency medicine physician, Dhaliwal is one of the leaders in a field known as clinical reasoning , a type of applied problem solving. In recent years, Dhaliwal has mapped out a better way to solve thorny issues, and he believes that his problem solving approach can be applied to just about any field from knitting to chemistry.

For most of us, problem solving is one of those everyday activities that we do without much thought. But it turns out that many common approaches like brainstorming don’t have much research behind them. In contrast, practices that might seem a little odd—like talking to yourself —can be pretty effective.

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I came across the new research on problem solving as part of my reporting on a book on the science of learning, and it was mathematician George Polya who first established the field, detailing a four-step approach to cracking enduring riddles.

Credit: Ulrich Boser

For Polya, the first phase of problem solving is “understanding.” In this phase, people should look to find the core idea behind a problem. “You have to understand the problem,” Polya argued. “What is the unknown? What are the data?”

The second phase is “devising a plan,” in which people map out how they’d address the problem. “Find the connection between the data and the unknown,” Polya counseled. 

The third phase of problem solving is “carrying out the plan.” This is a matter of doing—and vetting: “Can you prove that it is correct?”

The final phase for Polya is “looking back.” Or learning from the solution: People should "consolidate their knowledge.”

While Dhaliwal broadly follows this four-step method, he stresses that procedures are not enough. While a focused method is helpful, thorny issues don’t always fit nicely into categories.

This idea is clear in medicine. After all, symptoms rarely match up perfectly with an illness. Dizziness can be the signal of something serious—or a symptom of a lack of sleep. “What is tricky is to figure out what’s signal and what’s noise,” Dhaliwal told me.

In this regard, Dhaliwal argues that what’s at the heart of effective problem solving is making a robust connection between the problem and the solution. "Problem solving is part craft and part science, " Dhaliwal says, a type of "matching exercise. "

To get a sense of Dhaliwal’s approach, I once watched him solve a perplexing case. It was at a medical conference, and Dhaliwal stood at a dais as a fellow doctor explained the case: Basically, a man came into ER one day—let’s call him Andreas—and he spat up blood, could not breath very well, and had a slight fever.

At the start of the process, Dhaliwal recommends developing a one-sentence description of the problem. "It’s like a good Google search,” he said. “You want a concise summary,” and in this case, it was: Sixty-eight-year-old man with hemoptysis, or coughing up blood.

Dhaliwal also makes a few early generalizations, and he thought that Andreas might have a lung infection or an autoimmune problem. There wasn’t enough data to offer any sort of reliable conclusion, though, and really Dhaliwal was just gathering information.

Then came an x-ray, an HIV test, and as each bit of evidence rolled in, Dhaliwal detailed various scenarios, assembling the data in different ways. “To diagnosis, sometimes we are trying to lump, and sometimes trying to split,” he said.

Dhaliwal’s eyes flashed, for instance, when it became apparent that Andreas had worked in a fertilizer factory. It meant that Andreas was exposed to noxious chemicals, and for a while, it seemed like a toxic substance was at the root of Andreas’s illness.

Dhaliwal had a few strong pieces of evidence that supported the theory including some odd-looking red blood cells. But Dhaliwal wasn't comfortable with the level of proof. “I'm like an attorney presenting in a court of law,” Dhaliwal told me. “I want evidence.”

As the case progressed, Dhaliwal came across a new detail, and there was a growth in the heart. This shifted the diagnosis, knocking out the toxic chemical angle because it doesn't spark tumors.

Eventually, Dhaliwal uncovered a robust pattern, diagnosing Andreas with a cardiac angiosarcoma, or heart cancer. The pattern best explained the problem. “Diagnosing often comes down the ability to pull things together,” he said.

Dhaliwal doesn’t always get the right answer. But at the same time, it was clear that a more focused approach to problem solving can make a clear difference. If we’re more aware of how we approach an issue, we are better able to resolve the issue.

This idea explains why people who talk to themselves are more effective at problem solving. Self-queries—like is there enough evidence? —help us think through an issue.

As for Dhaliwal, he had yet another problem to solve after his diagnosis of Andreas: Should he take an Uber to the airport? Or should he grab a cab? After a little thought, Dhaliwal decided on an Uber. It was likely to be cheaper and equally comfortable. In other words, it was the solution that best matched the problem.

Why Science?

• Posted November 13, 2015
• By Leah Shafer

The push for STEM initiatives — coding workshops for elementary school children, or extended-day science experiments for middle school students — reigns at the forefront of the education conversation today. But anyone in the classroom knows that science can be a tough subject to teach, with educators at times overwhelmed with the amount of material to cover, and students simultaneously discouraged with the amount to master.

As STEM enthusiasm percolates, the teaching of science — its importance, its challenges — isn’t always part of the conversation. Usable Knowledge spoke with two Harvard faculty members, one an experienced high school teacher and the other a philosopher of science, whose thoughts may help to reframe and revitalize the mission of science education. Both argue that science should be much more than the rote memorization of theories, formulas, and vocabulary. It should be an education in problem solving and collaboration.

Science as Skill Building

HGSE Lecturer Victor Pereira , who taught high school science for more than a decade before becoming the master teacher in residence (science) in the new Harvard Teacher Fellows Program , knows the challenges firsthand. Classes can vary hugely in terms of students’ prior knowledge, experiences, and interest in the subject, he says. By the time they reach high school, many students are wary of science, thinking the material is boring and useless, or that they themselves are incapable of learning it. And building an understanding of science depends on acquiring a new and complicated vocabulary, which can be odious to teach and to learn. 

To confront these obstacles, educators should help their students approach science as more than an academic subject, Pereira says. “The nature of science itself is: make observations of the natural world, try and identify patterns, ask questions, find answers, ask more questions,” he explains. “It’s solving. It’s a way of thinking.” He argues that educators should portray science as acquiring skills, rather than memorizing facts. If the classroom focuses on the scientific process of discovery, more students will be engaged in the subject matter.

Collaborative Search for Truth

To uncover new knowledge and advance their fields, scientists have to be trustworthy themselves. After all, they want their findings to contribute to the discovery of truth — an underlying goal of any scientific inquiry. What’s more, scientists know that the public depends on them to publish accurate research that will lead to necessary advances in health and technology. To meet these expectations, findings must be honestly and meticulously recorded. Because this trustworthiness is a moral attribute, Elgin maintains, scientific inquiry is a moral activity.

But how does this connect to science education?

Elgin explains that the process of learning science reinforces these attributes. Chemistry majors cannot become chemists — and high schoolers cannot pass their chemistry labs — if, as students, they do not work together, double–check their assignments, and remain honest in their reports.

“Science does not happen on an island or in isolation,” Pereira says. It’s the science teacher’s responsibility to make sure that students understand the importance of collaborating, along with staying organized and paying attention to detail.

Fostering Engaged Learners

These interrelated characteristics of science education — the process of discovery and the collaboration on trustworthy results — are not mutually exclusive. Pereira believes that science teachers should encourage their students to look at scientific advancements through an ethical lens, looking for patterns and asking questions about scientific developments. Science teachers should help students think critically about current technologies made possible by science, and reflect on whether future technologies will be morally acceptable.

The payoff of stepping back to consider the purpose of science education? Increased student engagement, Pereira says. Like all of us, students want to learn what’s important. “The science teacher has to make sure that the class is relevant to what’s happening in students’ lives, and that they know how they can apply it,” he says.

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Why STEM? Success Starts With Critical Thinking, Problem-Solving Skills

• Partner Content
• Author: Stephen F. DeAngelis, Enterra Solutions. Stephen F. DeAngelis, Enterra Solutions

Our educational system is tasked with preparing the next-generation to succeed in life. That’s a tall order and it will substantially fail if it doesn’t teach children how to think critically and solve problems. In a post entitled “ STEM Education: Why All the Fuss? ,” I wrote, “Educating students in STEM subjects (if taught correctly) prepares students for life, regardless of the profession they choose to follow. Those subjects teach students how to think critically and how to solve problems — skills that can be used throughout life to help them get through tough times and take advantage of opportunities whenever they appear.”

I’m not alone in making this assessment. Vince Bertram, President and CEO of Project Lead The Way, Inc., feels the same way. “The United States can no longer excuse its poor academic performance by asserting that students in other nations excel in rote learning, while ours are better at problem solving. Recent test results clearly tell a different story.” [“ We Have to Get Serious About Creativity and Problem Solving ,” Huffington Post The Blog , 7 May 2014] Naveen Jain, Entrepreneur and Founder of the World Innovation Institute, adds, “Please don’t get me started on ‘No Child Left Behind.’ It might as well be called ‘All Children Left Behind.’ This system of standardized, rote learning that teaches to a test is exactly the type of education our children don’t need in this world that is plagued by systemic, pervasive and confounding global challenges. Today’s education system does not focus enough on teaching children to solve real world problems and is not interdisciplinary, nor collaborative enough in its approach.” [“ School’s Out for Summer: Rethinking Education for the 21st Century ,” Wall Street Journal , 27 June 2013] He continues:

“Imagine education that is as entertaining and addictive as video games. Sound far-fetched? I believe that this is exactly the idea — driven by dynamic innovation and entrepreneurism — that will help bring our education system out of the stone ages.”

There a numerous examples of how teachers have involved students in problem-solving activities and, as a result, have excited them about education while teaching them how to better cope with the world around them. As Bertram noted above, Americans can no longer boast that we are teaching our children how to solve problems better than the rest of the world. He explains:

“The latest round of international standardized test results showed American students are lagging behind the rest of the developed world not just in math, science and reading , but in problem solving as well. The 2012 Program for International Student Assessment (PISA) test examined 44 countries’ students’ problem-solving abilities — American students landed just above the average, but they still scored below many other developed countries, including Britain, Singapore, Korea, Japan, China and Canada.”

Jeevan Vasagar insists that the data shows that countries that teach their children how to solve problems are more successful than those who don’t. It sounds both obvious and sensible; yet, America seems to have turned its back on that approach. “Education is under pressure to respond to a changing world,” writes Vasagar. “As repetitive tasks are eroded by technology and outsourcing, the ability to solve novel problems has become increasingly vital.” [“ Countries that excel at problem-solving encourage critical thinking ,” Financial Times , 19 May 2014] He continues:

“Students from the main western European countries — England, France, Germany, Italy, the Netherlands and Belgium — all performed above the average, as did pupils from the Czech Republic and Estonia. In the rest of the rich world, the US, Canada and Australia also performed above average. But the laurels were taken by east Asian territories; Singapore and South Korea performed best, followed by Japan, and the Chinese regions of Macau and Hong Kong. That result poses a challenge to schools in the west. Critics of east Asian education systems attribute their success at maths and science to rote learning. But the OECD’s assessment suggests that schools in east Asia are developing thinking skills as well as providing a solid grounding in core subjects. Across the world, the OECD study found a strong and positive correlation between performance in problem solving and performance in maths, reading and science. In general, the high-performing students were also the ones best able to cope with unfamiliar situations.”

The lesson that needs to be learned here is that, if you want your child to succeed in life, teach him or her how to think critically and solve problems. The best way to do that is to provide them with a good foundation in science, technology, engineering, and mathematics (STEM). As I noted at the beginning of this article, grounding student in STEM subjects doesn’t mean that other social or liberal arts subjects aren’t important , only that STEM subjects teach life-skills that other disciplines don’t. Bertram explains:

“In America, we must make core subjects like math and science relevant for students, and at the same time, foster creativity, curiosity and a passion for problem solving. That’s what STEM education does. STEM is about using math and science to solve real-world challenges and problems. This applied, project-based way of teaching and learning allows students to understand and appreciate the relevancy of their work to their own lives and the world around them. Once they grasp core concepts, students are able to choose a problem and use their own creativity and curiosity to research, design, test and improve a viable solution.”

One of the reasons that I, along with a few colleagues, founded The Project for STEM Competitiveness , was to help get a project-based, problem-solving approach into schools. As an employer of people with technical skills, I am naturally interested in ensuring that, in the future, I will have an adequate employee pool from which to draw; but, as a parent, I want to ensure that our children are equipped to succeed in a changing world. As I’ve noted in previous articles, many of the jobs our children will asked to fill don’t even exist today. Daisy Christodoulou, an educationalist and the author of Seven Myths about Education , explains that students need exposure to a broad array of disciplines so that they are exposed to the problem-solving skills required in each area. She “argues that such skills are domain specific – they cannot be transferred to an area where our knowledge is limited.” She also believes this will help teach students to think more critically. Vasagar explains:

“Critical thinking is a skill that is impossible to teach directly but must be intertwined with content, Christodoulou argues. … Some argue that placing too strong an emphasis on children acquiring knowledge alone leaves them struggling when faced with more complex problems. Tim Taylor, a former primary school teacher who now trains teachers, says: ‘If you front-load knowledge and leave all the thinking and critical questioning until later, children don’t develop as effective learners.’ There are some generic tools that transfer across disciplines, Taylor argues. ‘What is reading if not a cognitive tool? And that is clearly “transferable”.’ … The way to teach generic skills is to be ‘mindful of it as a teacher’, Taylor suggests. ‘You create opportunities to keep that in the forefront of what you are doing – how is this helping us? How can we use this in another context? That is the point of education, to develop a “growth mindset”,’ he states.”

I agree with Bertram that we must foster educational approaches that appeal to a child’s natural sense of curiosity. He explains:

“Children are born with a natural curiosity. Give a child a toy and watch him or her play for hours. Listen to the questions a child asks. Children have a thirst to understand things. But then they go to school. They are taught how to take tests, how to respond to questions — how to do school. At our own peril, we teach them compliance. We teach them that school isn’t a place for creativity. That must change.”

We are all familiar with the adage “give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime.” Too often we are feeding our students instead of teaching them how to feed themselves. The disciplines that do that best are STEM-related.

Stephen F. DeAngelis is President and CEO of the cognitive computing firm Enterra Solutions.

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October 1, 2018

To Solve Real-World Problems, We Need Interdisciplinary Science

Solving today’s complex, global problems will take interdisciplinary science

By Graham A. J. Worthy & Cherie L. Yestrebsky

T he Indian River Lagoon, a shallow estuary that stretches for 156 miles along Florida's eastern coast, is suffering from the activities of human society. Poor water quality and toxic algal blooms have resulted in fish kills, manatee and dolphin die-offs, and takeovers by invasive species. But the humans who live here have needs, too: the eastern side of the lagoon is buffered by a stretch of barrier islands that are critical to Florida's economy, tourism and agriculture, as well as for launching NASA missions into space.

As in Florida, many of the world's coastlines are in serious trouble as a result of population growth and the pollution it produces. Moreover, the effects of climate change are accelerating both environmental and economic decline. Given what is at risk, scientists like us—a biologist and a chemist at the University of Central Florida—feel an urgent need to do research that can inform policy that will increase the resiliency and sustainability of coastal communities. How can our research best help balance environmental and social needs within the confines of our political and economic systems? This is the level of complexity that scientists must enter into instead of shying away from.

Although new technologies will surely play a role in tackling issues such as climate change, rising seas and coastal flooding, we cannot rely on innovation alone. Technology generally does not take into consideration the complex interactions between people and the environment. That is why coming up with solutions will require scientists to engage in an interdisciplinary team approach—something that is common in the business world but is relatively rare in universities.

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Universities are a tremendous source of intellectual power, of course. But students and faculty are typically organized within departments, or academic silos. Scientists are trained in the tools and language of their respective disciplines and learn to communicate their findings to one another using specific jargon.

When the goal of research is a fundamental understanding of a physical or biological system within a niche community, this setup makes a lot of sense. But when the problem the research is trying to solve extends beyond a closed system and includes its effects on society, silos create a variety of barriers. They can limit creativity, flexibility and nimbleness and actually discourage scientists from working across disciplines. As professors, we tend to train our students in our own image, inadvertently producing specialists who have difficulty communicating with the scientist in the next building—let alone with the broader public. This makes research silos ineffective at responding to developing issues in policy and planning, such as how coastal communities and ecosystems worldwide will adapt to rising seas.

Science for the Bigger Picture

As scientists who live and work in Florida, we realized that we needed to play a bigger role in helping our state—and country—make evidence-based choices when it comes to vulnerable coastlines. We wanted to make a more comprehensive assessment of both natural and human-related impacts to the health, restoration and sustainability of our coastal systems and to conduct long-term, integrated research.

At first, we focused on expanding research capacity in our biology, chemistry and engineering programs because each already had a strong coastal research presence. Then, our university announced a Faculty Cluster Initiative, with a goal of developing interdisciplinary academic teams focused on solving tomorrow's most challenging societal problems. While putting together our proposal, we discovered that there were already 35 faculty members on the Orlando campus who studied coastal issues. They belonged to 12 departments in seven colleges, and many of them had never even met. It became clear that simply working on the same campus was insufficient for collaboration.

So we set out to build a team of people from a wide mix of backgrounds who would work in close proximity to one another on a daily basis. These core members would also serve as a link to the disciplinary strengths of their tenure home departments. Initially, finding experts who truly wanted to embrace the team aspect was more difficult than we thought. Although the notion of interdisciplinary research is not new, it has not always been encouraged in academia. Some faculty who go in that direction still worry about whether it will threaten their recognition when applying for grants, seeking promotions or submitting papers to high-impact journals. We are not suggesting that traditional academic departments should be disbanded. On the contrary, they give the required depth to the research, whereas the interdisciplinary team gives breadth to the overall effort.

Our cluster proposal was a success, and in 2019 the National Center for Integrated Coastal Research (UCF Coastal) was born. Our goal is to guide more effective economic development, environmental stewardship, hazard-mitigation planning and public policy for coastal communities. To better integrate science with societal needs, we have brought together biologists, chemists, engineers and biomedical researchers with anthropologists, sociologists, political scientists, planners, emergency managers and economists. It seems that the most creative perspectives on old problems have arisen when people with different training and life experiences are talking through issues over cups of coffee. After all, "interdisciplinary" must mean more than just different flavors of STEM. In academia, tackling the effects of climate change demands more rigorous inclusion of the social sciences—an area that has been frequently overlooked.

The National Science Foundation, as well as other groups, requires that all research proposals incorporate a social sciences component, as an attempt to assess the broader implications of projects. Unfortunately, in many cases, a social scientist is simply added to a proposal only to check a box rather than to make a true commitment to allowing that discipline to inform the project. Instead social, economic and policy needs must be considered at the outset of research design, not as an afterthought. Otherwise our work might fail at the implementation stage, which means we will not be as effective as we could be in solving real-world problems. As a result, the public might become skeptical about how much scientists can contribute toward solutions.

Connecting with the Public

The reality is that communicating research findings to the public is an increasingly critical responsibility of scientists. Doing so has a measurable effect on how politicians prioritize policy, funding and regulations. UCF Coastal was brought into a world where science is not always respected—sometimes it is even portrayed as the enemy. There has been a significant erosion of trust in science over recent years, and we must work more deliberately to regain it. The public, we have found, wants to see quality academic research that is grounded in the societal challenges we are facing. That is why we are melding pure academic research with applied research to focus on issues that are immediate—helping a town or business recovering from a hurricane, for example—as well as long term, such as directly advising a community on how to build resiliency as flooding becomes more frequent.

As scientists, we cannot expect to explain the implications of our research to the wider public if we cannot first understand one another. A benefit of regularly working side by side is that we are crafting a common language, reconciling the radically different meanings that the same words can have to a variety of specialists. Finally, we are learning to speak to one another with more clarity and understand more explicitly how our niches fit into the bigger picture. We are also more aware of culture and industry as driving forces in shaping consensus and policy. Rather than handing city planners a stack of research papers and walking away, UCF Coastal sees itself as a collaborator that listens instead of just lecturing.

This style of academic mission is not only relevant to issues around climate change. It relates to every aspect of modern society, including genetic engineering, automation, artificial intelligence, and so on. The launch of UCF Coastal garnered positive attention from industry, government agencies, local communities and academics. We think that is because people do want to come together to solve problems, but they need a better mechanism for doing so. We hope to be that conduit while inspiring other academic institutions to do the same.

After all, we have been told for years to "think globally, act locally" and that "all politics is local." Florida's Indian River Lagoon will be restored only if there is engagement among residents, local industries, academics, government agencies and nonprofit organizations. As scientists, it is our responsibility to help everyone involved understand that problems that took decades to create will take decades to fix. We need to present the most helpful solutions while explaining the intricacies of the trade-offs for each one. Doing so is possible only if we see ourselves as part of an interdisciplinary, whole-community approach. By listening and responding to fears and concerns, we can make a stronger case for why scientifically driven decisions will be more effective in the long run.

Graham A. J. Worthy is founder and director of the National Center for Integrated Coastal Research at the University of Central Florida (UCF Coastal) and chairs the university's department of biology. His research focuses on how marine ecosystems respond to natural and anthropogenic perturbations.

Cherie L. Yestrebsky is a professor in the University of Central Florida's department of chemistry. Her research expertise is in environmental chemistry and remediation of pollutants in the environment.

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Using the Scientific Method to Solve Problems

How the scientific method and reasoning can help simplify processes and solve problems.

By the Mind Tools Content Team

The processes of problem-solving and decision-making can be complicated and drawn out. In this article we look at how the scientific method, along with deductive and inductive reasoning can help simplify these processes.

‘It is a capital mistake to theorize before one has information. Insensibly one begins to twist facts to suit our theories, instead of theories to suit facts.’ Sherlock Holmes

The Scientific Method

The scientific method is a process used to explore observations and answer questions. Originally used by scientists looking to prove new theories, its use has spread into many other areas, including that of problem-solving and decision-making.

The scientific method is designed to eliminate the influences of bias, prejudice and personal beliefs when testing a hypothesis or theory. It has developed alongside science itself, with origins going back to the 13th century. The scientific method is generally described as a series of steps.

• observations/theory
• explanation/conclusion

The first step is to develop a theory about the particular area of interest. A theory, in the context of logic or problem-solving, is a conjecture or speculation about something that is not necessarily fact, often based on a series of observations.

Once a theory has been devised, it can be questioned and refined into more specific hypotheses that can be tested. The hypotheses are potential explanations for the theory.

The testing, and subsequent analysis, of these hypotheses will eventually lead to a conclus ion which can prove or disprove the original theory.

Applying the Scientific Method to Problem-Solving

How can the scientific method be used to solve a problem, such as the color printer is not working?

1. Use observations to develop a theory.

In order to solve the problem, it must first be clear what the problem is. Observations made about the problem should be used to develop a theory. In this particular problem the theory might be that the color printer has run out of ink. This theory is developed as the result of observing the increasingly faded output from the printer.

2. Form a hypothesis.

Note down all the possible reasons for the problem. In this situation they might include:

• The printer is set up as the default printer for all 40 people in the department and so is used more frequently than necessary.
• There has been increased usage of the printer due to non-work related printing.
• In an attempt to reduce costs, poor quality ink cartridges with limited amounts of ink in them have been purchased.
• The printer is faulty.

All these possible reasons are hypotheses.

3. Test the hypothesis.

Once as many hypotheses (or reasons) as possible have been thought of, then each one can be tested to discern if it is the cause of the problem. An appropriate test needs to be devised for each hypothesis. For example, it is fairly quick to ask everyone to check the default settings of the printer on each PC, or to check if the cartridge supplier has changed.

4. Analyze the test results.

Once all the hypotheses have been tested, the results can be analyzed. The type and depth of analysis will be dependant on each individual problem, and the tests appropriate to it. In many cases the analysis will be a very quick thought process. In others, where considerable information has been collated, a more structured approach, such as the use of graphs, tables or spreadsheets, may be required.

5. Draw a conclusion.

Based on the results of the tests, a conclusion can then be drawn about exactly what is causing the problem. The appropriate remedial action can then be taken, such as asking everyone to amend their default print settings, or changing the cartridge supplier.

Inductive and Deductive Reasoning

The scientific method involves the use of two basic types of reasoning, inductive and deductive.

Inductive reasoning makes a conclusion based on a set of empirical results. Empirical results are the product of the collection of evidence from observations. For example:

‘Every time it rains the pavement gets wet, therefore rain must be water’.

There has been no scientific determination in the hypothesis that rain is water, it is purely based on observation. The formation of a hypothesis in this manner is sometimes referred to as an educated guess. An educated guess, whilst not based on hard facts, must still be plausible, and consistent with what we already know, in order to present a reasonable argument.

Deductive reasoning can be thought of most simply in terms of ‘If A and B, then C’. For example:

• if the window is above the desk, and
• the desk is above the floor, then
• the window must be above the floor

It works by building on a series of conclusions, which results in one final answer.

Social Sciences and the Scientific Method

The scientific method can be used to address any situation or problem where a theory can be developed. Although more often associated with natural sciences, it can also be used to develop theories in social sciences (such as psychology, sociology and linguistics), using both quantitative and qualitative methods.

Quantitative information is information that can be measured, and tends to focus on numbers and frequencies. Typically quantitative information might be gathered by experiments, questionnaires or psychometric tests. Qualitative information, on the other hand, is based on information describing meaning, such as human behavior, and the reasons behind it. Qualitative information is gathered by way of interviews and case studies, which are possibly not as statistically accurate as quantitative methods, but provide a more in-depth and rich description.

The resultant information can then be used to prove, or disprove, a hypothesis. Using a mix of quantitative and qualitative information is more likely to produce a rounded result based on the factual, quantitative information enriched and backed up by actual experience and qualitative information.

In terms of problem-solving or decision-making, for example, the qualitative information is that gained by looking at the ‘how’ and ‘why’ , whereas quantitative information would come from the ‘where’, ‘what’ and ‘when’.

It may seem easy to come up with a brilliant idea, or to suspect what the cause of a problem may be. However things can get more complicated when the idea needs to be evaluated, or when there may be more than one potential cause of a problem. In these situations, the use of the scientific method, and its associated reasoning, can help the user come to a decision, or reach a solution, secure in the knowledge that all options have been considered.

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Biology library

Course: biology library   >   unit 1, the scientific method.

• Controlled experiments
• The scientific method and experimental design

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation..

• Observation: the toaster won't toast.

2. Ask a question.

• Question: Why won't my toaster toast?

3. Propose a hypothesis.

• Hypothesis: Maybe the outlet is broken.

4. Make predictions.

• Prediction: If I plug the toaster into a different outlet, then it will toast the bread.

5. Test the predictions.

• Test of prediction: Plug the toaster into a different outlet and try again.
• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• Iteration time!
• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

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Teaching Creativity and Inventive Problem Solving in Science

• Robert L. DeHaan

Division of Educational Studies, Emory University, Atlanta, GA 30322

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Engaging learners in the excitement of science, helping them discover the value of evidence-based reasoning and higher-order cognitive skills, and teaching them to become creative problem solvers have long been goals of science education reformers. But the means to achieve these goals, especially methods to promote creative thinking in scientific problem solving, have not become widely known or used. In this essay, I review the evidence that creativity is not a single hard-to-measure property. The creative process can be explained by reference to increasingly well-understood cognitive skills such as cognitive flexibility and inhibitory control that are widely distributed in the population. I explore the relationship between creativity and the higher-order cognitive skills, review assessment methods, and describe several instructional strategies for enhancing creative problem solving in the college classroom. Evidence suggests that instruction to support the development of creativity requires inquiry-based teaching that includes explicit strategies to promote cognitive flexibility. Students need to be repeatedly reminded and shown how to be creative, to integrate material across subject areas, to question their own assumptions, and to imagine other viewpoints and possibilities. Further research is required to determine whether college students' learning will be enhanced by these measures.

INTRODUCTION

Dr. Dunne paces in front of his section of first-year college students, today not as their Bio 110 teacher but in the role of facilitator in their monthly “invention session.” For this meeting, the topic is stem cell therapy in heart disease. Members of each team of four students have primed themselves on the topic by reading selected articles from accessible sources such as Science, Nature, and Scientific American, and searching the World Wide Web, triangulating for up-to-date, accurate, background information. Each team knows that their first goal is to define a set of problems or limitations to overcome within the topic and to begin to think of possible solutions. Dr. Dunne starts the conversation by reminding the group of the few ground rules: one speaker at a time, listen carefully and have respect for others' ideas, question your own and others' assumptions, focus on alternative paths or solutions, maintain an atmosphere of collaboration and mutual support. He then sparks the discussion by asking one of the teams to describe a problem in need of solution.

Science in the United States is widely credited as a major source of discovery and economic development. According to the 2005 TAP Report produced by a prominent group of corporate leaders, “To maintain our country's competitiveness in the twenty-first century, we must cultivate the skilled scientists and engineers needed to create tomorrow's innovations.” ( www.tap2015.org/about/TAP_report2.pdf ). A panel of scientists, engineers, educators, and policy makers convened by the National Research Council (NRC) concurred with this view, reporting that the vitality of the nation “is derived in large part from the productivity of well-trained people and the steady stream of scientific and technical innovations they produce” ( NRC, 2007 ).

For many decades, science education reformers have promoted the idea that learners should be engaged in the excitement of science; they should be helped to discover the value of evidence-based reasoning and higher-order cognitive skills, and be taught to become innovative problem solvers (for reviews, see DeHaan, 2005 ; Hake, 2005 ; Nelson, 2008 ; Perkins and Wieman, 2008 ). But the means to achieve these goals, especially methods to promote creative thinking in scientific problem solving, are not widely known or used. An invention session such as that led by the fictional Dr. Dunne, described above, may seem fanciful as a means of teaching students to think about science as something more than a body of facts and terms to memorize. In recent years, however, models for promoting creative problem solving were developed for classroom use, as detailed by Treffinger and Isaksen (2005) , and such techniques are often used in the real world of high technology. To promote imaginative thinking, the advertising executive Alex F. Osborn invented brainstorming ( Osborn, 1948 , 1979 ), a technique that has since been successful in stimulating inventiveness among engineers and scientists. Could such strategies be transferred to a class for college students? Could they serve as a supplement to a high-quality, scientific teaching curriculum that helps students learn the facts and conceptual frameworks of science and make progress along the novice–expert continuum? Could brainstorming or other instructional strategies that are specifically designed to promote creativity teach students to be more adaptive in their growing expertise, more innovative in their problem-solving abilities? To begin to answer those questions, we first need to understand what is meant by “creativity.”

What Is Creativity? Big-C versus Mini-C Creativity

How to define creativity is an age-old question. Justice Potter Stewart's famous dictum regarding obscenity “I know it when I see it” has also long been an accepted test of creativity. But this is not an adequate criterion for developing an instructional approach. A scientist colleague of mine recently noted that “Many of us [in the scientific community] rarely give the creative process a second thought, imagining one either ‘has it’ or doesn't.” We often think of inventiveness or creativity in scientific fields as the kind of gift associated with a Michelangelo or Einstein. This is what Kaufman and Beghetto (2008) call big-C creativity, borrowing the term that earlier workers applied to the talents of experts in various fields who were identified as particularly creative by their expert colleagues ( MacKinnon, 1978 ). In this sense, creativity is seen as the ability of individuals to generate new ideas that contribute substantially to an intellectual domain. Howard Gardner defined such a creative person as one who “regularly solves problems, fashions products, or defines new questions in a domain in a way that is initially considered novel but that ultimately comes to be accepted in a particular cultural setting” ( Gardner, 1993 , p. 35).

But there is another level of inventiveness termed by various authors as “little-c” ( Craft, 2000 ) or “mini-c” ( Kaufman and Beghetto, 2008 ) creativity that is widespread among all populations. This would be consistent with the workplace definition of creativity offered by Amabile and her coworkers: “coming up with fresh ideas for changing products, services and processes so as to better achieve the organization's goals” ( Amabile et al. , 2005 ). Mini-c creativity is based on what Craft calls “possibility thinking” ( Craft, 2000 , pp. 3–4), as experienced when a worker suddenly has the insight to visualize a new, improved way to accomplish a task; it is represented by the “aha” moment when a student first sees two previously disparate concepts or facts in a new relationship, an example of what Arthur Koestler identified as bisociation: “perceiving a situation or event in two habitually incompatible associative contexts” ( Koestler, 1964 , p. 95).

In this essay, I maintain that mini-c creativity is not a mysterious, innate endowment of rare individuals. Instead, I argue that creative thinking is a multicomponent process, mediated through social interactions, that can be explained by reference to increasingly well-understood mental abilities such as cognitive flexibility and cognitive control that are widely distributed in the population. Moreover, I explore some of the recent research evidence (though with no effort at a comprehensive literature review) showing that these mental abilities are teachable; like other higher-order cognitive skills (HOCS), they can be enhanced by explicit instruction.

Creativity Is a Multicomponent Process

Efforts to define creativity in psychological terms go back to J. P. Guilford ( Guilford, 1950 ) and E. P. Torrance ( Torrance, 1974 ), both of whom recognized that underlying the construct were other cognitive variables such as ideational fluency, originality of ideas, and sensitivity to missing elements. Many authors since then have extended the argument that a creative act is not a singular event but a process, an interplay among several interactive cognitive and affective elements. In this view, the creative act has two phases, a generative and an exploratory or evaluative phase ( Finke et al. , 1996 ). During the generative process, the creative mind pictures a set of novel mental models as potential solutions to a problem. In the exploratory phase, we evaluate the multiple options and select the best one. Early scholars of creativity, such as J. P. Guilford, characterized the two phases as divergent thinking and convergent thinking ( Guilford, 1950 ). Guilford defined divergent thinking as the ability to produce a broad range of associations to a given stimulus or to arrive at many solutions to a problem (for overviews of the field from different perspectives, see Amabile, 1996 ; Banaji et al. , 2006 ; Sawyer, 2006 ). In neurocognitive terms, divergent thinking is referred to as associative richness ( Gabora, 2002 ; Simonton, 2004 ), which is often measured experimentally by comparing the number of words that an individual generates from memory in response to stimulus words on a word association test. In contrast, convergent thinking refers to the capacity to quickly focus on the one best solution to a problem.

The idea that there are two stages to the creative process is consistent with results from cognition research indicating that there are two distinct modes of thought, associative and analytical ( Neisser, 1963 ; Sloman, 1996 ). In the associative mode, thinking is defocused, suggestive, and intuitive, revealing remote or subtle connections between items that may be correlated, or may not, and are usually not causally related ( Burton, 2008 ). In the analytical mode, thought is focused and evaluative, more conducive to analyzing relationships of cause and effect (for a review of other cognitive aspects of creativity, see Runco, 2004 ). Science educators associate the analytical mode with the upper levels (analysis, synthesis, and evaluation) of Bloom's taxonomy (e.g., Crowe et al. , 2008 ), or with “critical thinking,” the process that underlies the “purposeful, self-regulatory judgment that drives problem-solving and decision-making” ( Quitadamo et al. , 2008 , p. 328). These modes of thinking are under cognitive control through the executive functions of the brain. The core executive functions, which are thought to underlie all planning, problem solving, and reasoning, are defined ( Blair and Razza, 2007 ) as working memory control (mentally holding and retrieving information), cognitive flexibility (considering multiple ideas and seeing different perspectives), and inhibitory control (resisting several thoughts or actions to focus on one). Readers wishing to delve further into the neuroscience of the creative process can refer to the cerebrocerebellar theory of creativity ( Vandervert et al. , 2007 ) in which these mental activities are described neurophysiologically as arising through interactions among different parts of the brain.

The main point from all of these works is that creativity is not some single hard-to-measure property or act. There is ample evidence that the creative process requires both divergent and convergent thinking and that it can be explained by reference to increasingly well-understood underlying mental abilities ( Haring-Smith, 2006 ; Kim, 2006 ; Sawyer, 2006 ; Kaufman and Sternberg, 2007 ) and cognitive processes ( Simonton, 2004 ; Diamond et al. , 2007 ; Vandervert et al. , 2007 ).

Creativity Is Widely Distributed and Occurs in a Social Context

Although it is understandable to speak of an aha moment as a creative act by the person who experiences it, authorities in the field have long recognized (e.g., Simonton, 1975 ) that creative thinking is not so much an individual trait but rather a social phenomenon involving interactions among people within their specific group or cultural settings. “Creativity isn't just a property of individuals, it is also a property of social groups” ( Sawyer, 2006 , p. 305). Indeed, Osborn introduced his brainstorming method because he was convinced that group creativity is always superior to individual creativity. He drew evidence for this conclusion from activities that demand collaborative output, for example, the improvisations of a jazz ensemble. Although each musician is individually creative during a performance, the novelty and inventiveness of each performer's playing is clearly influenced, and often enhanced, by “social and interactional processes” among the musicians ( Sawyer, 2006 , p. 120). Recently, Brophy (2006) offered evidence that for problem solving, the situation may be more nuanced. He confirmed that groups of interacting individuals were better at solving complex, multipart problems than single individuals. However, when dealing with certain kinds of single-issue problems, individual problem solvers produced a greater number of solutions than interacting groups, and those solutions were judged to be more original and useful.

Consistent with the findings of Brophy (2006) , many scholars acknowledge that creative discoveries in the real world such as solving the problems of cutting-edge science—which are usually complex and multipart—are influenced or even stimulated by social interaction among experts. The common image of the lone scientist in the laboratory experiencing a flash of creative inspiration is probably a myth from earlier days. As a case in point, the science historian Mara Beller analyzed the social processes that underlay some of the major discoveries of early twentieth-century quantum physics. Close examination of successive drafts of publications by members of the Copenhagen group revealed a remarkable degree of influence and collaboration among 10 or more colleagues, although many of these papers were published under the name of a single author ( Beller, 1999 ). Sociologists Bruno Latour and Steve Woolgar's study ( Latour and Woolgar, 1986 ) of a neuroendocrinology laboratory at the Salk Institute for Biological Studies make the related point that social interactions among the participating scientists determined to a remarkable degree what discoveries were made and how they were interpreted. In the laboratory, researchers studied the chemical structure of substances released by the brain. By analysis of the Salk scientists' verbalizations of concepts, theories, formulas, and results of their investigations, Latour and Woolgar showed that the structures and interpretations that were agreed upon, that is, the discoveries announced by the laboratory, were mediated by social interactions and power relationships among members of the laboratory group. By studying the discovery process in other fields of the natural sciences, sociologists and anthropologists have provided more cases that further illustrate how social and cultural dimensions affect scientific insights (for a thoughtful review, see Knorr Cetina, 1995 ).

In sum, when an individual experiences an aha moment that feels like a singular creative act, it may rather have resulted from a multicomponent process, under the influence of group interactions and social context. The process that led up to what may be sensed as a sudden insight will probably have included at least three diverse, but testable elements: 1) divergent thinking, including ideational fluency or cognitive flexibility, which is the cognitive executive function that underlies the ability to visualize and accept many ideas related to a problem; 2) convergent thinking or the application of inhibitory control to focus and mentally evaluate ideas; and 3) analogical thinking, the ability to understand a novel idea in terms of one that is already familiar.

LITERATURE REVIEW

What do we know about how to teach creativity.

The possibility of teaching for creative problem solving gained credence in the 1960s with the studies of Jerome Bruner, who argued that children should be encouraged to “treat a task as a problem for which one invents an answer, rather than finding one out there in a book or on the blackboard” ( Bruner, 1965 , pp. 1013–1014). Since that time, educators and psychologists have devised programs of instruction designed to promote creativity and inventiveness in virtually every student population: pre–K, elementary, high school, and college, as well as in disadvantaged students, athletes, and students in a variety of specific disciplines (for review, see Scott et al. , 2004 ). Smith (1998) identified 172 instructional approaches that have been applied at one time or another to develop divergent thinking skills.

Some of the most convincing evidence that elements of creativity can be enhanced by instruction comes from work with young children. Bodrova and Leong (2001) developed the Tools of the Mind (Tools) curriculum to improve all of the three core mental executive functions involved in creative problem solving: cognitive flexibility, working memory, and inhibitory control. In a year-long randomized study of 5-yr-olds from low-income families in 21 preschool classrooms, half of the teachers applied the districts' balanced literacy curriculum (literacy), whereas the experimenters trained the other half to teach the same academic content by using the Tools curriculum ( Diamond et al. , 2007 ). At the end of the year, when the children were tested with a battery of neurocognitive tests including a test for cognitive flexibility ( Durston et al. , 2003 ; Davidson et al. , 2006 ), those exposed to the Tools curriculum outperformed the literacy children by as much as 25% ( Diamond et al. , 2007 ). Although the Tools curriculum and literacy program were similar in academic content and in many other ways, they differed primarily in that Tools teachers spent 80% of their time explicitly reminding the children to think of alternative ways to solve a problem and building their executive function skills.

Teaching older students to be innovative also demands instruction that explicitly promotes creativity but is rigorously content-rich as well. A large body of research on the differences between novice and expert cognition indicates that creative thinking requires at least a minimal level of expertise and fluency within a knowledge domain ( Bransford et al. , 2000 ; Crawford and Brophy, 2006 ). What distinguishes experts from novices, in addition to their deeper knowledge of the subject, is their recognition of patterns in information, their ability to see relationships among disparate facts and concepts, and their capacity for organizing content into conceptual frameworks or schemata ( Bransford et al. , 2000 ; Sawyer, 2005 ).

Such expertise is often lacking in the traditional classroom. For students attempting to grapple with new subject matter, many kinds of problems that are presented in high school or college courses or that arise in the real world can be solved merely by applying newly learned algorithms or procedural knowledge. With practice, problem solving of this kind can become routine and is often considered to represent mastery of a subject, producing what Sternberg refers to as “pseudoexperts” ( Sternberg, 2003 ). But beyond such routine use of content knowledge the instructor's goal must be to produce students who have gained the HOCS needed to apply, analyze, synthesize, and evaluate knowledge ( Crowe et al. , 2008 ). The aim is to produce students who know enough about a field to grasp meaningful patterns of information, who can readily retrieve relevant knowledge from memory, and who can apply such knowledge effectively to novel problems. This condition is referred to as adaptive expertise ( Hatano and Ouro, 2003 ; Schwartz et al. , 2005 ). Instead of applying already mastered procedures, adaptive experts are able to draw on their knowledge to invent or adapt strategies for solving unique or novel problems within a knowledge domain. They are also able, ideally, to transfer conceptual frameworks and schemata from one domain to another (e.g., Schwartz et al. , 2005 ). Such flexible, innovative application of knowledge is what results in inventive or creative solutions to problems ( Crawford and Brophy, 2006 ; Crawford, 2007 ).

Promoting Creative Problem Solving in the College Classroom

In most college courses, instructors teach science primarily through lectures and textbooks that are dominated by facts and algorithmic processing rather than by concepts, principles, and evidence-based ways of thinking. This is despite ample evidence that many students gain little new knowledge from traditional lectures ( Hrepic et al. , 2007 ). Moreover, it is well documented that these methods engender passive learning rather than active engagement, boredom instead of intellectual excitement, and linear thinking rather than cognitive flexibility (e.g., Halpern and Hakel, 2003 ; Nelson, 2008 ; Perkins and Wieman, 2008 ). Cognitive flexibility, as noted, is one of the three core mental executive functions involved in creative problem solving ( Ausubel, 1963 , 2000 ). The capacity to apply ideas creatively in new contexts, referred to as the ability to “transfer” knowledge (see Mestre, 2005 ), requires that learners have opportunities to actively develop their own representations of information to convert it to a usable form. Especially when a knowledge domain is complex and fraught with ill-structured information, as in a typical introductory college biology course, instruction that emphasizes active-learning strategies is demonstrably more effective than traditional linear teaching in reducing failure rates and in promoting learning and transfer (e.g., Freeman et al. , 2007 ). Furthermore, there is already some evidence that inclusion of creativity training as part of a college curriculum can have positive effects. Hunsaker (2005) has reviewed a number of such studies. He cites work by McGregor (2001) , for example, showing that various creativity training programs including brainstorming and creative problem solving increase student scores on tests of creative-thinking abilities.

Model creativity—students develop creativity when instructors model creative thinking and inventiveness.

Repeatedly encourage idea generation—students need to be reminded to generate their own ideas and solutions in an environment free of criticism.

Cross-fertilize ideas—where possible, avoid teaching in subject-area boxes: a math box, a social studies box, etc; students' creative ideas and insights often result from learning to integrate material across subject areas.

Build self-efficacy—all students have the capacity to create and to experience the joy of having new ideas, but they must be helped to believe in their own capacity to be creative.

Constantly question assumptions—make questioning a part of the daily classroom exchange; it is more important for students to learn what questions to ask and how to ask them than to learn the answers.

Imagine other viewpoints—students broaden their perspectives by learning to reflect upon ideas and concepts from different points of view.

How Is Creativity Related to Critical Thinking and the Higher-Order Cognitive Skills?

It is not uncommon to associate creativity and ingenuity with scientific reasoning ( Sawyer, 2005 ; 2006 ). When instructors apply scientific teaching strategies ( Handelsman et al. , 2004 ; DeHaan, 2005 ; Wood, 2009 ) by using instructional methods based on learning research, according to Ebert-May and Hodder ( 2008 ), “we see students actively engaged in the thinking, creativity, rigor, and experimentation we associate with the practice of science—in much the same way we see students learn in the field and in laboratories” (p. 2). Perkins and Wieman (2008) note that “To be successful innovators in science and engineering, students must develop a deep conceptual understanding of the underlying science ideas, an ability to apply these ideas and concepts broadly in different contexts, and a vision to see their relevance and usefulness in real-world applications … An innovator is able to perceive and realize potential connections and opportunities better than others” (pp. 181–182). The results of Scott et al. (2004) suggest that nontraditional courses in science that are based on constructivist principles and that use strategies of scientific teaching to promote the HOCS and enhance content mastery and dexterity in scientific thinking ( Handelsman et al. , 2007 ; Nelson, 2008 ) also should be effective in promoting creativity and cognitive flexibility if students are explicitly guided to learn these skills.

Creativity is an essential element of problem solving ( Mumford et al. , 1991 ; Runco, 2004 ) and of critical thinking ( Abrami et al. , 2008 ). As such, it is common to think of applications of creativity such as inventiveness and ingenuity among the HOCS as defined in Bloom's taxonomy ( Crowe et al. , 2008 ). Thus, it should come as no surprise that creativity, like other elements of the HOCS, can be taught most effectively through inquiry-based instruction, informed by constructivist theory ( Ausubel, 1963 , 2000 ; Duch et al. , 2001 ; Nelson, 2008 ). In a survey of 103 instructors who taught college courses that included creativity instruction, Bull et al. (1995) asked respondents to rate the importance of various course characteristics for enhancing student creativity. Items ranking high on the list were: providing a social climate in which students feels safe, an open classroom environment that promotes tolerance for ambiguity and independence, the use of humor, metaphorical thinking, and problem defining. Many of the responses emphasized the same strategies as those advanced to promote creative problem solving (e.g., Mumford et al. , 1991 ; McFadzean, 2002 ; Treffinger and Isaksen, 2005 ) and critical thinking ( Abrami et al. , 2008 ).

In a careful meta-analysis, Scott et al. (2004) examined 70 instructional interventions designed to enhance and measure creative performance. The results were striking. Courses that stressed techniques such as critical thinking, convergent thinking, and constraint identification produced the largest positive effect sizes. More open techniques that provided less guidance in strategic approaches had less impact on the instructional outcomes. A striking finding was the effectiveness of being explicit; approaches that clearly informed students about the nature of creativity and offered clear strategies for creative thinking were most effective. Approaches such as social modeling, cooperative learning, and case-based (project-based) techniques that required the application of newly acquired knowledge were found to be positively correlated to high effect sizes. The most clear-cut result to emerge from the Scott et al. (2004) study was simply to confirm that creativity instruction can be highly successful in enhancing divergent thinking, problem solving, and imaginative performance. Most importantly, of the various cognitive processes examined, those linked to the generation of new ideas such as problem finding, conceptual combination, and idea generation showed the greatest improvement. The success of creativity instruction, the authors concluded, can be attributed to “developing and providing guidance concerning the application of requisite cognitive capacities … [and] a set of heuristics or strategies for working with already available knowledge” (p. 382).

Many of the scientific teaching practices that have been shown by research to foster content mastery and HOCS, and that are coming more widely into use, also would be consistent with promoting creativity. Wood (2009) has recently reviewed examples of such practices and how to apply them. These include relatively small modifications of the traditional lecture to engender more active learning, such as the use of concept tests and peer instruction ( Mazur, 1996 ), Just-in-Time-Teaching techniques ( Novak et al. , 1999 ), and student response systems known as “clickers” ( Knight and Wood, 2005 ; Crossgrove and Curran, 2008 ), all designed to allow the instructor to frequently and effortlessly elicit and respond to student thinking. Other strategies can transform the lecture hall into a workshop or studio classroom ( Gaffney et al. , 2008 ) where the teaching curriculum may emphasize problem-based (also known as project-based or case-based) learning strategies ( Duch et al. , 2001 ; Ebert-May and Hodder, 2008 ) or “community-based inquiry” in which students engage in research that enhances their critical-thinking skills ( Quitadamo et al. , 2008 ).

Another important approach that could readily subserve explicit creativity instruction is the use of computer-based interactive simulations, or “sims” ( Perkins and Wieman, 2008 ) to facilitate inquiry learning and effective, easy self-assessment. An example in the biological sciences would be Neurons in Action ( http://neuronsinaction.com/home/main ). In such educational environments, students gain conceptual understanding of scientific ideas through interactive engagement with materials (real or virtual), with each other, and with instructors. Following the tenets of scientific teaching, students are encouraged to pose and answer their own questions, to make sense of the materials, and to construct their own understanding. The question I pose here is whether an additional focus—guiding students to meet these challenges in a context that explicitly promotes creativity—would enhance learning and advance students' progress toward adaptive expertise?

Assessment of Creativity

To teach creativity, there must be measurable indicators to judge how much students have gained from instruction. Educational programs intended to teach creativity became popular after the Torrance Tests of Creative Thinking (TTCT) was introduced in the 1960s ( Torrance, 1974 ). But it soon became apparent that there were major problems in devising tests for creativity, both because of the difficulty of defining the construct and because of the number and complexity of elements that underlie it. Tests of intelligence and other personality characteristics on creative individuals revealed a host of related traits such as verbal fluency, metaphorical thinking, flexible decision making, tolerance of ambiguity, willingness to take risks, autonomy, divergent thinking, self-confidence, problem finding, ideational fluency, and belief in oneself as being “creative” ( Barron and Harrington, 1981 ; Tardif and Sternberg, 1988 ; Runco and Nemiro, 1994 ; Snyder et al. , 2004 ). Many of these traits have been the focus of extensive research of recent decades, but, as noted above, creativity is not defined by any one trait; there is now reason to believe that it is the interplay among the cognitive and affective processes that underlie inventiveness and the ability to find novel solutions to a problem.

Although the early creativity researchers recognized that assessing divergent thinking as a measure of creativity required tests for other underlying capacities ( Guilford, 1950 ; Torrance, 1974 ), these workers and their colleagues nonetheless believed that a high score for divergent thinking alone would correlate with real creative output. Unfortunately, no such correlation was shown ( Barron and Harrington, 1981 ). Results produced by many of the instruments initially designed to measure various aspects of creative thinking proved to be highly dependent on the test itself. A review of several hundred early studies showed that an individual's creativity score could be affected by simple test variables, for example, how the verbal pretest instructions were worded ( Barron and Harrington, 1981 , pp. 442–443). Most scholars now agree that divergent thinking, as originally defined, was not an adequate measure of creativity. The process of creative thinking requires a complex combination of elements that include cognitive flexibility, memory control, inhibitory control, and analogical thinking, enabling the mind to free-range and analogize, as well as to focus and test.

More recently, numerous psychometric measures have been developed and empirically tested (see Plucker and Renzulli, 1999 ) that allow more reliable and valid assessment of specific aspects of creativity. For example, the creativity quotient devised by Snyder et al. (2004) tests the ability of individuals to link different ideas and different categories of ideas into a novel synthesis. The Wallach–Kogan creativity test ( Wallach and Kogan, 1965 ) explores the uniqueness of ideas associated with a stimulus. For a more complete list and discussion, see the Creativity Tests website ( www.indiana.edu/∼bobweb/Handout/cretv_6.html ).

The most widely used measure of creativity is the TTCT, which has been modified four times since its original version in 1966 to take into account subsequent research. The TTCT-Verbal and the TTCT-Figural are two versions ( Torrance, 1998 ; see http://ststesting.com/2005giftttct.html ). The TTCT-Verbal consists of five tasks; the “stimulus” for each task is a picture to which the test-taker responds briefly in writing. A sample task that can be viewed from the TTCT Demonstrator website asks, “Suppose that people could transport themselves from place to place with just a wink of the eye or a twitch of the nose. What might be some things that would happen as a result? You have 3 min.” ( www.indiana.edu/∼bobweb/Handout/d3.ttct.htm ).

In the TTCT-Figural, participants are asked to construct a picture from a stimulus in the form of a partial line drawing given on the test sheet (see example below; Figure 1 ). Specific instructions are to “Add lines to the incomplete figures below to make pictures out of them. Try to tell complete stories with your pictures. Give your pictures titles. You have 3 min.” In the introductory materials, test-takers are urged to “… think of a picture or object that no one else will think of. Try to make it tell as complete and as interesting a story as you can …” ( Torrance et al. , 2008 , p. 2).

Figure 1. Sample figural test item from the TTCT Demonstrator website ( www.indiana.edu/∼bobweb/Handout/d3.ttct.htm ).

How would an instructor in a biology course judge the creativity of students' responses to such an item? To assist in this task, the TTCT has scoring and norming guides ( Torrance, 1998 ; Torrance et al. , 2008 ) with numerous samples and responses representing different levels of creativity. The guides show sample evaluations based upon specific indicators such as fluency, originality, elaboration (or complexity), unusual visualization, extending or breaking boundaries, humor, and imagery. These examples are easy to use and provide a high degree of validity and generalizability to the tests. The TTCT has been more intensively researched and analyzed than any other creativity instrument, and the norming samples have longitudinal validations and high predictive validity over a wide age range. In addition to global creativity scores, the TTCT is designed to provide outcome measures in various domains and thematic areas to allow for more insightful analysis ( Kaufman and Baer, 2006 ). Kim (2006) has examined the characteristics of the TTCT, including norms, reliability, and validity, and concludes that the test is an accurate measure of creativity. When properly used, it has been shown to be fair in terms of gender, race, community status, and language background. According to Kim (2006) and other authorities in the field ( McIntyre et al. , 2003 ; Scott et al. , 2004 ), Torrance's research and the development of the TTCT have provided groundwork for the idea that creative levels can be measured and then increased through instruction and practice.

SCIENTIFIC TEACHING TO PROMOTE CREATIVITY

How could creativity instruction be integrated into scientific teaching.

Guidelines for designing specific course units that emphasize HOCS by using strategies of scientific teaching are now available from the current literature. As an example, Karen Cloud-Hansen and colleagues ( Cloud-Hansen et al. , 2008 ) describe a course titled, “Ciprofloxacin Resistance in Neisseria gonorrhoeae .” They developed this undergraduate seminar to introduce college freshmen to important concepts in biology within a real-world context and to increase their content knowledge and critical-thinking skills. The centerpiece of the unit is a case study in which teams of students are challenged to take the role of a director of a local public health clinic. One of the county commissioners overseeing the clinic is an epidemiologist who wants to know “how you plan to address the emergence of ciprofloxacin resistance in Neisseria gonorrhoeae ” (p. 304). State budget cuts limit availability of expensive antibiotics and some laboratory tests to patients. Student teams are challenged to 1) develop a plan to address the medical, economic, and political questions such a clinic director would face in dealing with ciprofloxacin-resistant N. gonorrhoeae ; 2) provide scientific data to support their conclusions; and 3) describe their clinic plan in a one- to two-page referenced written report.

Throughout the 3-wk unit, in accordance with the principles of problem-based instruction ( Duch et al. , 2001 ), course instructors encourage students to seek, interpret, and synthesize their own information to the extent possible. Students have access to a variety of instructional formats, and active-learning experiences are incorporated throughout the unit. These activities are interspersed among minilectures and give the students opportunities to apply new information to their existing base of knowledge. The active-learning activities emphasize the key concepts of the minilectures and directly confront common misconceptions about antibiotic resistance, gene expression, and evolution. Weekly classes include question/answer/discussion sessions to address student misconceptions and 20-min minilectures on such topics as antibiotic resistance, evolution, and the central dogma of molecular biology. Students gather information about antibiotic resistance in N. gonorrhoeae , epidemiology of gonorrhea, and treatment options for the disease, and each team is expected to formulate a plan to address ciprofloxacin resistance in N. gonorrhoeae .

In this project, the authors assessed student gains in terms of content knowledge regarding topics covered such as the role of evolution in antibiotic resistance, mechanisms of gene expression, and the role of oncogenes in human disease. They also measured HOCS as gains in problem solving, according to a rubric that assessed self-reported abilities to communicate ideas logically, solve difficult problems about microbiology, propose hypotheses, analyze data, and draw conclusions. Comparing the pre- and posttests, students reported significant learning of scientific content. Among the thinking skill categories, students demonstrated measurable gains in their ability to solve problems about microbiology but the unit seemed to have little impact on their more general perceived problem-solving skills ( Cloud-Hansen et al. , 2008 ).

What would such a class look like with the addition of explicit creativity-promoting approaches? Would the gains in problem-solving abilities have been greater if during the minilectures and other activities, students had been introduced explicitly to elements of creative thinking from the Sternberg and Williams (1998) list described above? Would the students have reported greater gains if their instructors had encouraged idea generation with weekly brainstorming sessions; if they had reminded students to cross-fertilize ideas by integrating material across subject areas; built self-efficacy by helping students believe in their own capacity to be creative; helped students question their own assumptions; and encouraged students to imagine other viewpoints and possibilities? Of most relevance, could the authors have been more explicit in assessing the originality of the student plans? In an experiment that required college students to develop plans of a different, but comparable, type, Osborn and Mumford (2006) created an originality rubric ( Figure 2 ) that could apply equally to assist instructors in judging student plans in any course. With such modifications, would student gains in problem-solving abilities or other HOCS have been greater? Would their plans have been measurably more imaginative?

Figure 2. Originality rubric (adapted from Osburn and Mumford, 2006 , p. 183).

Answers to these questions can only be obtained when a course like that described by Cloud-Hansen et al. (2008) is taught with explicit instruction in creativity of the type I described above. But, such answers could be based upon more than subjective impressions of the course instructors. For example, students could be pretested with items from the TTCT-Verbal or TTCT-Figural like those shown. If, during minilectures and at every contact with instructors, students were repeatedly reminded and shown how to be as creative as possible, to integrate material across subject areas, to question their own assumptions and imagine other viewpoints and possibilities, would their scores on TTCT posttest items improve? Would the plans they formulated to address ciprofloxacin resistance become more imaginative?

Recall that in their meta-analysis, Scott et al. (2004) found that explicitly informing students about the nature of creativity and offering strategies for creative thinking were the most effective components of instruction. From their careful examination of 70 experimental studies, they concluded that approaches such as social modeling, cooperative learning, and case-based (project-based) techniques that required the application of newly acquired knowledge were positively correlated with high effect sizes. The study was clear in confirming that explicit creativity instruction can be successful in enhancing divergent thinking and problem solving. Would the same strategies work for courses in ecology and environmental biology, as detailed by Ebert-May and Hodder (2008) , or for a unit elaborated by Knight and Wood (2005) that applies classroom response clickers?

Finally, I return to my opening question with the fictional Dr. Dunne. Could a weekly brainstorming “invention session” included in a course like those described here serve as the site where students are introduced to concepts and strategies of creative problem solving? As frequently applied in schools of engineering ( Paulus and Nijstad, 2003 ), brainstorming provides an opportunity for the instructor to pose a problem and to ask the students to suggest as many solutions as possible in a brief period, thus enhancing ideational fluency. Here, students can be encouraged explicitly to build on the ideas of others and to think flexibly. Would brainstorming enhance students' divergent thinking or creative abilities as measured by TTCT items or an originality rubric? Many studies have demonstrated that group interactions such as brainstorming, under the right conditions, can indeed enhance creativity ( Paulus and Nijstad, 2003 ; Scott et al. , 2004 ), but there is little information from an undergraduate science classroom setting. Intellectual Ventures, a firm founded by Nathan Myhrvold, the creator of Microsoft's Research Division, has gathered groups of engineers and scientists around a table for day-long sessions to brainstorm about a prearranged topic. Here, the method seems to work. Since it was founded in 2000, Intellectual Ventures has filed hundreds of patent applications in more than 30 technology areas, applying the “invention session” strategy ( Gladwell, 2008 ). Currently, the company ranks among the top 50 worldwide in number of patent applications filed annually. Whether such a technique could be applied successfully in a college science course will only be revealed by future research.

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Submitted: 31 December 2008 Revised: 14 May 2009 Accepted: 28 May 2009

© 2009 by The American Society for Cell Biology

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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A Problem-Solving Experiment

Using Beer’s Law to Find the Concentration of Tartrazine

The Science Teacher—January/February 2022 (Volume 89, Issue 3)

By Kevin Mason, Steve Schieffer, Tara Rose, and Greg Matthias

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A problem-solving experiment is a learning activity that uses experimental design to solve an authentic problem. It combines two evidence-based teaching strategies: problem-based learning and inquiry-based learning. The use of problem-based learning and scientific inquiry as an effective pedagogical tool in the science classroom has been well established and strongly supported by research ( Akinoglu and Tandogan 2007 ; Areepattamannil 2012 ; Furtak, Seidel, and Iverson 2012 ; Inel and Balim 2010 ; Merritt et al. 2017 ; Panasan and Nuangchalerm 2010 ; Wilson, Taylor, and Kowalski 2010 ).

Floyd James Rutherford, the founder of the American Association for the Advancement of Science (AAAS) Project 2061 once stated, “To separate conceptually scientific content from scientific inquiry,” he underscored, “is to make it highly probable that the student will properly understand neither” (1964, p. 84). A more recent study using randomized control trials showed that teachers that used an inquiry and problem-based pedagogy for seven months improved student performance in math and science ( Bando, Nashlund-Hadley, and Gertler 2019 ). A problem-solving experiment uses problem-based learning by posing an authentic or meaningful problem for students to solve and inquiry-based learning by requiring students to design an experiment to collect and analyze data to solve the problem.

In the problem-solving experiment described in this article, students used Beer’s Law to collect and analyze data to determine if a person consumed a hazardous amount of tartrazine (Yellow Dye #5) for their body weight. The students used their knowledge of solutions, molarity, dilutions, and Beer’s Law to design their own experiment and calculate the amount of tartrazine in a yellow sports drink (or citrus-flavored soda).

According to the Next Generation Science Standards, energy is defined as “a quantitative property of a system that depends on the motion and interactions of matter and radiation with that system” ( NGSS Lead States 2013 ). Interactions of matter and radiation can be some of the most challenging for students to observe, investigate, and conceptually understand. As a result, students need opportunities to observe and investigate the interactions of matter and radiation. Light is one example of radiation that interacts with matter.

Light is electromagnetic radiation that is detectable to the human eye and exhibits properties of both a wave and a particle. When light interacts with matter, light can be reflected at the surface, absorbed by the matter, or transmitted through the matter ( Figure 1 ). When a single beam of light enters a substance at a perpendicularly (at a 90 ° angle to the surface), the amount of reflection is minimal. Therefore, the light will either be absorbed by the substance or be transmitted through the substance. When a given wavelength of light shines into a solution, the amount of light that is absorbed will depend on the identity of the substance, the thickness of the container, and the concentration of the solution.

Light interacting with matter.

(Retrieved from https://etorgerson.files.wordpress.com/2011/05/light-reflect-refract-absorb-label.jpg ).

Beer’s Law states the amount of light absorbed is directly proportional to the thickness and concentration of a solution. Beer’s Law is also sometimes known as the Beer-Lambert Law. A solution of a higher concentration will absorb more light and transmit less light ( Figure 2 ). Similarly, if the solution is placed in a thicker container that requires the light to pass through a greater distance, then the solution will absorb more light and transmit less light.

Light transmitted through a solution.

(Retrieved from https://media.springernature.com/original/springer-static/image/chp%3A10.1007%2F978-3-319-57330-4_13/MediaObjects/432946_1_En_13_Fig4_HTML.jpg ).

Definitions of key terms.

Absorbance (A) – the process of light energy being captured by a substance

Beer’s Law (Beer-Lambert Law) – the absorbance (A) of light is directly proportional to the molar absorptivity (ε), thickness (b), and concentration (C) of the solution (A = εbC)

Concentration (C) – the amount of solute dissolved per amount of solution

Cuvette – a container used to hold a sample to be tested in a spectrophotometer

Energy (E) – a quantitative property of a system that depends on motion and interactions of matter and radiation with that system (NGSS Lead States 2013).

Intensity (I) – the amount or brightness of light

Light – electromagnetic radiation that is detectable to the human eye and exhibits properties of both a wave and a particle

Molar Absorptivity (ε) – a property that represents the amount of light absorbed by a given substance per molarity of the solution and per centimeter of thickness (M-1 cm-1)

Molarity (M) – the number of moles of solute per liters of solution (Mol/L)

Reflection – the process of light energy bouncing off the surface of a substance

Spectrophotometer – a device used to measure the absorbance of light by a substance

Tartrazine – widely used food and liquid dye

Transmittance (T) – the process of light energy passing through a substance

The amount of light absorbed by a solution can be measured using a spectrophotometer. The solution of a given concentration is placed in a small container called a cuvette. The cuvette has a known thickness that can be held constant during the experiment. It is also possible to obtain cuvettes of different thicknesses to study the effect of thickness on the absorption of light. The key definitions of the terms related to Beer’s Law and the learning activity presented in this article are provided in Figure 3 .

Overview of the problem-solving experiment

In the problem presented to students, a 140-pound athlete drinks two bottles of yellow sports drink every day ( Figure 4 ; see Online Connections). When she starts to notice a rash on her skin, she reads the label of the sports drink and notices that it contains a yellow dye known as tartrazine. While tartrazine is safe to drink, it may produce some potential side effects in large amounts, including rashes, hives, or swelling. The students must design an experiment to determine the concentration of tartrazine in the yellow sports drink and the number of milligrams of tartrazine in two bottles of the sports drink.

While a sports drink may have many ingredients, the vast majority of ingredients—such as sugar or electrolytes—are colorless when dissolved in water solution. The dyes added to the sports drink are responsible for the color of the sports drink. Food manufacturers may use different dyes to color sports drinks to the desired color. Red dye #40 (allura red), blue dye #1 (brilliant blue), yellow dye #5 (tartrazine), and yellow dye #6 (sunset yellow) are the four most common dyes or colorants in sports drinks and many other commercial food products ( Stevens et al. 2015 ). The concentration of the dye in the sports drink affects the amount of light absorbed.

In this problem-solving experiment, the students used the previously studied concept of Beer’s Law—using serial dilutions and absorbance—to find the concentration (molarity) of tartrazine in the sports drink. Based on the evidence, the students then determined if the person had exceeded the maximum recommended daily allowance of tartrazine, given in mg/kg of body mass. The learning targets for this problem-solving experiment are shown in Figure 5 (see Online Connections).

Pre-laboratory experiences

A problem-solving experiment is a form of guided inquiry, which will generally require some prerequisite knowledge and experience. In this activity, the students needed prior knowledge and experience with Beer’s Law and the techniques in using Beer’s Law to determine an unknown concentration. Prior to the activity, students learned how Beer’s Law is used to relate absorbance to concentration as well as how to use the equation M 1 V 1 = M 2 V 2 to determine concentrations of dilutions. The students had a general understanding of molarity and using dimensional analysis to change units in measurements.

The techniques for using Beer’s Law were introduced in part through a laboratory experiment using various concentrations of copper sulfate. A known concentration of copper sulfate was provided and the students followed a procedure to prepare dilutions. Students learned the technique for choosing the wavelength that provided the maximum absorbance for the solution to be tested ( λ max ), which is important for Beer’s Law to create a linear relationship between absorbance and solution concentration. Students graphed the absorbance of each concentration in a spreadsheet as a scatterplot and added a linear trend line. Through class discussion, the teacher checked for understanding in using the equation of the line to determine the concentration of an unknown copper sulfate solution.

After the students graphed the data, they discussed how the R2 value related to the data set used to construct the graph. After completing this experiment, the students were comfortable making dilutions from a stock solution, calculating concentrations, and using the spectrophotometer to use Beer’s Law to determine an unknown concentration.

Introducing the problem

After the initial experiment on Beer’s Law, the problem-solving experiment was introduced. The problem presented to students is shown in Figure 4 (see Online Connections). A problem-solving experiment provides students with a valuable opportunity to collaborate with other students in designing an experiment and solving a problem. For this activity, the students were assigned to heterogeneous or mixed-ability laboratory groups. Groups should be diversified based on gender; research has shown that gender diversity among groups improves academic performance, while racial diversity has no significant effect ( Hansen, Owan, and Pan 2015 ). It is also important to support students with special needs when assigning groups. The mixed-ability groups were assigned intentionally to place students with special needs with a peer who has the academic ability and disposition to provide support. In addition, some students may need additional accommodations or modifications for this learning activity, such as an outlined lab report, a shortened lab report format, or extended time to complete the analysis. All students were required to wear chemical-splash goggles and gloves, and use caution when handling solutions and glass apparatuses.

Designing the experiment

During this activity, students worked in lab groups to design their own experiment to solve a problem. The teacher used small-group and whole-class discussions to help students understand the problem. Students discussed what information was provided and what they need to know and do to solve the problem. In planning the experiment, the teacher did not provide a procedure and intentionally provided only minimal support to the students as needed. The students designed their own experimental procedure, which encouraged critical thinking and problem solving. The students needed to be allowed to struggle to some extent. The teacher provided some direction and guidance by posing questions for students to consider and answer for themselves. Students were also frequently reminded to review their notes and the previous experiment on Beer’s Law to help them better use their resources to solve the problem. The use of heterogeneous or mixed-ability groups also helped each group be more self-sufficient and successful in designing and conducting the experiment.

Students created a procedure for their experiment with the teacher providing suggestions or posing questions to enhance the experimental design, if needed. Safety was addressed during this consultation to correct safety concerns in the experimental design or provide safety precautions for the experiment. Students needed to wear splash-proof goggles and gloves throughout the experiment. In a few cases, students realized some opportunities to improve their experimental design during the experiment. This was allowed with the teacher’s approval, and the changes to the procedure were documented for the final lab report.

Conducting the experiment

A sample of the sports drink and a stock solution of 0.01 M stock solution of tartrazine were provided to the students. There are many choices of sports drinks available, but it is recommended that the ingredients are checked to verify that tartrazine (yellow dye #5) is the only colorant added. This will prevent other colorants from affecting the spectroscopy results in the experiment. A citrus-flavored soda could also be used as an alternative because many sodas have tartrazine added as well. It is important to note that tartrazine is considered safe to drink, but it may produce some potential side effects in large amounts, including rashes, hives, or swelling. A list of the materials needed for this problem-solving experiment is shown in Figure 6 (see Online Connections).

This problem-solving experiment required students to create dilutions of known concentrations of tartrazine as a reference to determine the unknown concentration of tartrazine in a sports drink. To create the dilutions, the students were provided with a 0.01 M stock solution of tartrazine. The teacher purchased powdered tartrazine, available from numerous vendors, to create the stock solution. The 0.01 M stock solution was prepared by weighing 0.534 g of tartrazine and dissolving it in enough distilled water to make a 100 ml solution. Yellow food coloring could be used as an alternative, but it would take some research to determine its concentration. Since students have previously explored the experimental techniques, they should know to prepare dilutions that are somewhat darker and somewhat lighter in color than the yellow sports drink sample. Students should use five dilutions for best results.

Typically, a good range for the yellow sports drink is standard dilutions ranging from 1 × 10-3 M to 1 × 10-5 M. The teacher may need to caution the students that if a dilution is too dark, it will not yield good results and lower the R2 value. Students that used very dark dilutions often realized that eliminating that data point created a better linear trendline, as long as it didn’t reduce the number of data points to fewer than four data points. Some students even tried to use the 0.01 M stock solution without any dilution. This was much too dark. The students needed to do substantial dilutions to get the solutions in the range of the sports drink.

After the dilutions are created, the absorbance of each dilution was measured using a spectrophotometer. A Vernier SpectroVis (~$400) spectrophotometer was used to measure the absorbance of the prepared dilutions with known concentrations. The students adjusted the spectrophotometer to use different wavelengths of light and selected the wavelength with the highest absorbance reading. The same wavelength was then used for each measurement of absorbance. A wavelength of 650 nanometers (nm) provided an accurate measurement and good linear relationship. After measuring the absorbance of the dilutions of known concentrations, the students measured the absorbance of the sports drink with an unknown concentration of tartrazine using the spectrophotometer at the same wavelength. If a spectrophotometer is not available, a color comparison can be used as a low-cost alternative for completing this problem-solving experiment ( Figure 7 ; see Online Connections).

Analyzing the results

After completing the experiment, the students graphed the absorbance and known tartrazine concentrations of the dilutions on a scatter-plot to create a linear trendline. In this experiment, absorbance was the dependent variable, which should be graphed on the y -axis. Some students mistakenly reversed the axes on the scatter-plot. Next, the students used the graph to find the equation for the line. Then, the students solve for the unknown concentration (molarity) of tartrazine in the sports drink given the linear equation and the absorbance of the sports drink measured experimentally.

To answer the question posed in the problem, the students also calculated the maximum amount of tartrazine that could be safely consumed by a 140 lb. person, using the information given in the problem. A common error in solving the problem was not converting the units of volume given in the problem from ounces to liters. With the molarity and volume in liters, the students then calculated the mass of tartrazine consumed per day in milligrams. A sample of the graph and calculations from one student group are shown in Figure 8 . Finally, based on their calculations, the students answered the question posed in the original problem and determined if the person’s daily consumption of tartrazine exceeded the threshold for safe consumption. In this case, the students concluded that the person did NOT consume more than the allowable daily limit of tartrazine.

Sample graph and calculations from a student group.

Communicating the results

After conducting the experiment, students reported their results in a written laboratory report that included the following sections: title, purpose, introduction, hypothesis, materials and methods, data and calculations, conclusion, and discussion. The laboratory report was assessed using the scoring rubric shown in Figure 9 (see Online Connections). In general, the students did very well on this problem-solving experiment. Students typically scored a three or higher on each criteria of the rubric. Throughout the activity, the students successfully demonstrated their ability to design an experiment, collect data, perform calculations, solve a problem, and effectively communicate those results.

This activity is authentic problem-based learning in science as the true concentration of tartrazine in the sports drink was not provided by the teacher or known by the students. The students were generally somewhat biased as they assumed the experiment would result in exceeding the recommended maximum consumption of tartrazine. Some students struggled with reporting that the recommended limit was far higher than the two sports drinks consumed by the person each day. This allows for a great discussion about the use of scientific methods and evidence to provide unbiased answers to meaningful questions and problems.

The most common errors in this problem-solving experiment were calculation errors, with the most common being calculating the concentrations of the dilutions (perhaps due to the use of very small concentrations). There were also several common errors in communicating the results in the laboratory report. In some cases, students did not provide enough background information in the introduction of the report. When the students communicated the results, some students also failed to reference specific data from the experiment. Finally, in the discussion section, some students expressed concern or doubts in the results, not because there was an obvious error, but because they did not believe the level consumed could be so much less than the recommended consumption limit of tartrazine.

The scientific study and investigation of energy and matter are salient topics addressed in the Next Generation Science Standards ( Figure 10 ; see Online Connections). In a chemistry classroom, students should have multiple opportunities to observe and investigate the interaction of energy and matter. In this problem-solving experiment students used Beer’s Law to collect and analyze data to determine if a person consumed an amount of tartrazine that exceeded the maximum recommended daily allowance. The students correctly concluded that the person in the problem did not consume more than the recommended daily amount of tartrazine for their body weight.

In this activity students learned to work collaboratively to design an experiment, collect and analyze data, and solve a problem. These skills extend beyond any one science subject or class. Through this activity, students had the opportunity to do real-world science to solve a problem without a previously known result. The process of designing an experiment may be difficult for some students that are often accustomed to being given an experimental procedure in their previous science classroom experiences. However, because students sometimes struggled to design their own experiment and perform the calculations, students also learned to persevere in collecting and analyzing data to solve a problem, which is a valuable life lesson for all students. ■

Online Connections

The Beer-Lambert Law at Chemistry LibreTexts: https://bit.ly/3lNpPEi

Beer’s Law – Theoretical Principles: https://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/beers1.htm

Beer’s Law at Illustrated Glossary of Organic Chemistry: http://www.chem.ucla.edu/~harding/IGOC/B/beers_law.html

Beer Lambert Law at Edinburgh Instruments: https://www.edinst.com/blog/the-beer-lambert-law/

Beer’s Law Lab at PhET Interactive Simulations: https://phet.colorado.edu/en/simulation/beers-law-lab

Figure 4. Problem-solving experiment problem statement: https://bit.ly/3pAYHtj

Figure 5. Learning targets: https://bit.ly/307BHtb

Figure 6. Materials list: https://bit.ly/308a57h

Figure 7. The use of color comparison as a low-cost alternative: https://bit.ly/3du1uyO

Figure 9. Summative performance-based assessment rubric: https://bit.ly/31KoZRj

Figure 10. Connecting to the Next Generation Science Standards : https://bit.ly/3GlJnY0

Kevin Mason ( [email protected] ) is Professor of Education at the University of Wisconsin–Stout, Menomonie, WI; Steve Schieffer is a chemistry teacher at Amery High School, Amery, WI; Tara Rose is a chemistry teacher at Amery High School, Amery, WI; and Greg Matthias is Assistant Professor of Education at the University of Wisconsin–Stout, Menomonie, WI.

Akinoglu, O., and R. Tandogan. 2007. The effects of problem-based active learning in science education on students’ academic achievement, attitude and concept learning. Eurasia Journal of Mathematics, Science, and Technology Education 3 (1): 77–81.

Areepattamannil, S. 2012. Effects of inquiry-based science instruction on science achievement and interest in science: Evidence from Qatar. The Journal of Educational Research 105 (2): 134–146.

Bando R., E. Nashlund-Hadley, and P. Gertler. 2019. Effect of inquiry and problem-based pedagogy on learning: Evidence from 10 field experiments in four countries. The National Bureau of Economic Research 26280.

Furtak, E., T. Seidel, and H. Iverson. 2012. Experimental and quasi-experimental studies of inquiry-based science teaching: A meta-analysis. Review of Educational Research 82 (3): 300–329.

Hansen, Z., H. Owan, and J. Pan. 2015. The impact of group diversity on class performance. Education Economics 23 (2): 238–258.

Inel, D., and A. Balim. 2010. The effects of using problem-based learning in science and technology teaching upon students’ academic achievement and levels of structuring concepts. Pacific Forum on Science Learning and Teaching 11 (2): 1–23.

Merritt, J., M. Lee, P. Rillero, and B. Kinach. 2017. Problem-based learning in K–8 mathematics and science education: A literature review. The Interdisciplinary Journal of Problem-based Learning 11 (2).

NGSS Lead States. 2013. Next Generation Science Standards: For states, by states. Washington, DC: National Academies Press.

Panasan, M., and P. Nuangchalerm. 2010. Learning outcomes of project-based and inquiry-based learning activities. Journal of Social Sciences 6 (2): 252–255.

Rutherford, F.J. 1964. The role of inquiry in science teaching. Journal of Research in Science Teaching 2 (2): 80–84.

Stevens, L.J., J.R. Burgess, M.A. Stochelski, and T. Kuczek. 2015. Amounts of artificial food dyes and added sugars in foods and sweets commonly consumed by children. Clinical Pediatrics 54 (4): 309–321.

Wilson, C., J. Taylor, and S. Kowalski. 2010. The relative effects and equity of inquiry-based and commonplace science teaching on students’ knowledge, reasoning, and argumentation. Journal of Research in Science Teaching 47 (3): 276–301.

Chemistry Crosscutting Concepts Curriculum Disciplinary Core Ideas General Science Inquiry Instructional Materials Labs Lesson Plans Mathematics NGSS Pedagogy Science and Engineering Practices STEM Teaching Strategies Technology Three-Dimensional Learning High School

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What Is Problem Solving? How Software Engineers Approach Complex Challenges

From debugging an existing system to designing an entirely new software application, a day in the life of a software engineer is filled with various challenges and complexities. The one skill that glues these disparate tasks together and makes them manageable? Problem solving . 

Throughout this blog post, we’ll explore why problem-solving skills are so critical for software engineers, delve into the techniques they use to address complex challenges, and discuss how hiring managers can identify these skills during the hiring process. 

What Is Problem Solving?

But what exactly is problem solving in the context of software engineering? How does it work, and why is it so important?

Problem solving, in the simplest terms, is the process of identifying a problem, analyzing it, and finding the most effective solution to overcome it. For software engineers, this process is deeply embedded in their daily workflow. It could be something as simple as figuring out why a piece of code isn’t working as expected, or something as complex as designing the architecture for a new software system. 

In a world where technology is evolving at a blistering pace, the complexity and volume of problems that software engineers face are also growing. As such, the ability to tackle these issues head-on and find innovative solutions is not only a handy skill — it’s a necessity. 

The Importance of Problem-Solving Skills for Software Engineers

Problem-solving isn’t just another ability that software engineers pull out of their toolkits when they encounter a bug or a system failure. It’s a constant, ongoing process that’s intrinsic to every aspect of their work. Let’s break down why this skill is so critical.

Driving Development Forward

Without problem solving, software development would hit a standstill. Every new feature, every optimization, and every bug fix is a problem that needs solving. Whether it’s a performance issue that needs diagnosing or a user interface that needs improving, the capacity to tackle and solve these problems is what keeps the wheels of development turning.

It’s estimated that 60% of software development lifecycle costs are related to maintenance tasks, including debugging and problem solving. This highlights how pivotal this skill is to the everyday functioning and advancement of software systems.

Innovation and Optimization

The importance of problem solving isn’t confined to reactive scenarios; it also plays a major role in proactive, innovative initiatives . Software engineers often need to think outside the box to come up with creative solutions, whether it’s optimizing an algorithm to run faster or designing a new feature to meet customer needs. These are all forms of problem solving.

Consider the development of the modern smartphone. It wasn’t born out of a pre-existing issue but was a solution to a problem people didn’t realize they had — a device that combined communication, entertainment, and productivity into one handheld tool.

Increasing Efficiency and Productivity

Good problem-solving skills can save a lot of time and resources. Effective problem-solvers are adept at dissecting an issue to understand its root cause, thus reducing the time spent on trial and error. This efficiency means projects move faster, releases happen sooner, and businesses stay ahead of their competition.

Improving Software Quality

Problem solving also plays a significant role in enhancing the quality of the end product. By tackling the root causes of bugs and system failures, software engineers can deliver reliable, high-performing software. This is critical because, according to the Consortium for Information and Software Quality, poor quality software in the U.S. in 2022 cost at least $2.41 trillion in operational issues, wasted developer time, and other related problems.

Problem-Solving Techniques in Software Engineering

So how do software engineers go about tackling these complex challenges? Let’s explore some of the key problem-solving techniques, theories, and processes they commonly use.

Decomposition

Breaking down a problem into smaller, manageable parts is one of the first steps in the problem-solving process. It’s like dealing with a complicated puzzle. You don’t try to solve it all at once. Instead, you separate the pieces, group them based on similarities, and then start working on the smaller sets. This method allows software engineers to handle complex issues without being overwhelmed and makes it easier to identify where things might be going wrong.

Abstraction

In the realm of software engineering, abstraction means focusing on the necessary information only and ignoring irrelevant details. It is a way of simplifying complex systems to make them easier to understand and manage. For instance, a software engineer might ignore the details of how a database works to focus on the information it holds and how to retrieve or modify that information.

Algorithmic Thinking

At its core, software engineering is about creating algorithms — step-by-step procedures to solve a problem or accomplish a goal. Algorithmic thinking involves conceiving and expressing these procedures clearly and accurately and viewing every problem through an algorithmic lens. A well-designed algorithm not only solves the problem at hand but also does so efficiently, saving computational resources.

Parallel Thinking

Parallel thinking is a structured process where team members think in the same direction at the same time, allowing for more organized discussion and collaboration. It’s an approach popularized by Edward de Bono with the “ Six Thinking Hats ” technique, where each “hat” represents a different style of thinking.

In the context of software engineering, parallel thinking can be highly effective for problem solving. For instance, when dealing with a complex issue, the team can use the “White Hat” to focus solely on the data and facts about the problem, then the “Black Hat” to consider potential problems with a proposed solution, and so on. This structured approach can lead to more comprehensive analysis and more effective solutions, and it ensures that everyone’s perspectives are considered.

This is the process of identifying and fixing errors in code . Debugging involves carefully reviewing the code, reproducing and analyzing the error, and then making necessary modifications to rectify the problem. It’s a key part of maintaining and improving software quality.

Testing and Validation

Testing is an essential part of problem solving in software engineering. Engineers use a variety of tests to verify that their code works as expected and to uncover any potential issues. These range from unit tests that check individual components of the code to integration tests that ensure the pieces work well together. Validation, on the other hand, ensures that the solution not only works but also fulfills the intended requirements and objectives.

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Evaluating Problem-Solving Skills

We’ve examined the importance of problem-solving in the work of a software engineer and explored various techniques software engineers employ to approach complex challenges. Now, let’s delve into how hiring teams can identify and evaluate problem-solving skills during the hiring process.

Recognizing Problem-Solving Skills in Candidates

How can you tell if a candidate is a good problem solver? Look for these indicators:

• Previous Experience: A history of dealing with complex, challenging projects is often a good sign. Ask the candidate to discuss a difficult problem they faced in a previous role and how they solved it.
• Problem-Solving Questions: During interviews, pose hypothetical scenarios or present real problems your company has faced. Ask candidates to explain how they would tackle these issues. You’re not just looking for a correct solution but the thought process that led them there.
• Technical Tests: Coding challenges and other technical tests can provide insight into a candidate’s problem-solving abilities. Consider leveraging a platform for assessing these skills in a realistic, job-related context.

Assessing Problem-Solving Skills

Once you’ve identified potential problem solvers, here are a few ways you can assess their skills:

• Solution Effectiveness: Did the candidate solve the problem? How efficient and effective is their solution?
• Approach and Process: Go beyond whether or not they solved the problem and examine how they arrived at their solution. Did they break the problem down into manageable parts? Did they consider different perspectives and possibilities?
• Communication: A good problem solver can explain their thought process clearly. Can the candidate effectively communicate how they arrived at their solution and why they chose it?
• Adaptability: Problem-solving often involves a degree of trial and error. How does the candidate handle roadblocks? Do they adapt their approach based on new information or feedback?

Hiring managers play a crucial role in identifying and fostering problem-solving skills within their teams. By focusing on these abilities during the hiring process, companies can build teams that are more capable, innovative, and resilient.

Key Takeaways

As you can see, problem solving plays a pivotal role in software engineering. Far from being an occasional requirement, it is the lifeblood that drives development forward, catalyzes innovation, and delivers of quality software. 

By leveraging problem-solving techniques, software engineers employ a powerful suite of strategies to overcome complex challenges. But mastering these techniques isn’t simple feat. It requires a learning mindset, regular practice, collaboration, reflective thinking, resilience, and a commitment to staying updated with industry trends. 

For hiring managers and team leads, recognizing these skills and fostering a culture that values and nurtures problem solving is key. It’s this emphasis on problem solving that can differentiate an average team from a high-performing one and an ordinary product from an industry-leading one.

At the end of the day, software engineering is fundamentally about solving problems — problems that matter to businesses, to users, and to the wider society. And it’s the proficient problem solvers who stand at the forefront of this dynamic field, turning challenges into opportunities, and ideas into reality.

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Why Should Need Problem Solving Skills In Science?

Problem-solving is a critical skill essential for success in science and many other areas of life. In science, it is necessary to identify and solve problems to make progress and develop new solutions.

This enables scientists to identify and resolve complex issues, develop new solutions, and make progress in their research. These skills require critical thinking, analytical abilities, effective communication, and a structured problem-solving process.

Whether you are a student, researcher, or professional, having strong problem-solving skills can help you tackle complex challenges and develop innovative solutions.

In this guide, we will explore the importance of problem solving skills in science, strategies for developing these skills, and their applications in various careers.

Table of Contents

How Problem-Solving Is An Integral Part Of The Scientific Method?

Problem-solving is an integral part of the scientific method because, through this process, scientists identify and address problems or questions related to their research.

In the scientific method, problem-solving involves a structured process that includes defining the problem, gathering relevant data, formulating a hypothesis, testing the hypothesis through experiments or observations, analyzing the results, and drawing conclusions.

This process requires critical thinking, analytical skills, and effective communication and helps scientists develop effective solutions to complex problems. With problem-solving, scientific research would be improved, and progress in various fields of science would be expanded.

Problem-solving skills are essential in many areas of life, but they are particularly important in science. Scientists must be able to identify and resolve complex problems to make progress and develop new solutions:

Advancements in Science Require Problem-Solving Skills

Scientific progress is dependent on identifying and resolving problems through problem-solving skills . It is necessary for scientific research to be improved, and improvement in various fields of science would be limited.

Problem-Solving Skills are Essential for Scientific Research

Problem-solving skills are crucial in conducting experiments, analyzing data, and developing hypotheses. It helps scientists make sense of complex information and identify patterns in the data.

Helps Scientists Develop Innovative Solutions

Identifying problems and developing innovative solutions is crucial in science, where new solutions and technologies are constantly needed to address complex issues.

Skills Enhance Critical Thinking and Analytical Abilities

Problem-solving requires critical thinking and analytical abilities, which are important not only in science but in many other fields as well. Thinking critically and analyzing information is essential in developing effective solutions to complex problems.

Key to Effective Communication

Problem-solving skills facilitate clear communication of complex scientific concepts and findings. Effective communication is crucial in science, where results must be accurately conveyed to colleagues and the public.

Skills Benefit Students in Science Education

Problem-solving skills are important for students in science education. They can help students become better scientists by allowing them to approach problems and assignments systematically and analytically.

Read Also: What Are The 7 Critical Thinking Skills And How To Develop?

How Problem-Solving Skills Can Help Achieve Career Goals?

Problem-solving skills are highly valued in many careers and can play a crucial role in achieving career goals . Here are some ways in which problem-solving skills can help:

Identifying and Resolving Workplace Issues

Problem-solving skills enable individuals to identify and resolve issues that may arise in the workplace. This can range from minor issues, such as miscommunications, to more complex problems, such as logistical challenges.

Developing Innovative Solutions

Problem-solving skills are crucial in developing innovative solutions to problems businesses and organizations face. By identifying the root causes of problems and developing creative solutions, individuals can demonstrate their value to their employer and enhance their reputation within the organization.

Adapting to Change

Problem-solving skills enable individuals to adapt to changes in their work environment, such as changes in technology, processes, or organizational structure. Effectively addressing and adapting to these changes, individuals can demonstrate their flexibility and resilience, which are highly valued in the workplace.

Building Trust and Credibility

Compelling problem-solving can help individuals build trust and credibility with their colleagues and superiors. With their ability to identify and resolve issues promptly and effectively, individuals can establish themselves as valuable team members and enhance their professional reputations.

Enhancing Leadership Abilities

Effective problem-solving is a key component of leadership. By demonstrating their ability to identify and resolve complex issues, individuals can enhance their leadership abilities and position themselves for career advancement.

How to Cultivate Problem Solving Skills in Science?

Cultivating problem-solving skills in science can be challenging, but there are several strategies individuals can use to develop and improve their abilities. Here are some ways to boost problem-solving skills in science:

1. Practice Critical Thinking

Critical thinking is a key component of problem-solving skills. Individuals can practice critical thinking by asking questions , examining evidence, and considering alternative perspectives.

2. Take on Challenging Problems

Challenging problems provide an opportunity to practice problem-solving skills. Individuals can seek out challenging problems in their work or personal life and work to develop solutions.

3. Learn from Mistakes

Mistakes can be a valuable learning opportunity. They should reflect on their mistakes and consider how they could have approached the problem differently.

4. Collaborate with Others

Collaboration with others can provide new perspectives and approaches to problem-solving. Working with others can also help develop communication and teamwork skills.

5. Use the Scientific Method

A scientific method is a structured approach to problem-solving used in science. Individuals can use this approach to identify and solve problems logically and systematically.

6. Seek Out Training and Education

Training and education can provide individuals with new tools and techniques for problem-solving. Science courses, workshops, and professional development opportunities can help individuals develop problem-solving skills .

Common Challenges Problem Solving Skills In Science

While problem-solving skills are crucial in science, individuals may encounter common challenges when applying these skills. Here are some common obstacles to problem-solving skills in science:

• Lack of Information: In science, individuals can only sometimes access all the information they need to solve a problem. This can make it challenging to identify the root cause of a problem and develop effective solutions.
• Complexity of Problems: Science problems can be complex and multifaceted, requiring individuals to consider multiple variables and potential solutions.
• Limited Resources: Limited resources, such as time, money, or equipment, can make it challenging to implement solutions to scientific problems. Require individuals to be creative and resourceful in developing solutions.
• Unforeseen Obstacles: Unforeseen obstacles, such as unexpected results or complications, can arise during problem-solving. It can be flexible and adapt its approach as necessary.
• Emotional Factors: Emotions can play a role in problem-solving, as individuals may become frustrated, anxious, or overwhelmed when faced with a challenging problem. This can hinder their ability to think critically and develop effective solutions.

Overcoming Common Problem Solving Skills In Science

To overcome the common challenges faced in problem-solving skills in science, individuals can adopt the following strategies:

• Research: Conducting thorough research and gathering all the necessary information is crucial to problem-solving in science. This can involve reviewing the literature, consulting with experts, and conducting experiments.
• Break Down the Problem: Breaking down a complex problem into smaller, more manageable components can make it easier to identify the root cause and develop effective solutions.
• Brainstorming: Brainstorming with colleagues or experts can help generate a wide range of potential solutions and ideas. Also, allow individuals to consider alternative perspectives and approaches.
• Use Critical Thinking: Critical thinking involves questioning assumptions, analyzing evidence, and evaluating potential solutions. By using critical thinking, individuals can develop effective solutions and identify potential obstacles.
• Utilize Resources: Utilizing available resources, such as time, equipment, or funding, can help individuals implement solutions to scientific problems. This may involve being creative and resourceful in finding solutions.
• Effective Communication: Clear and effective communication is critical in problem-solving, especially when working in a team. This involves active listening, open-mindedness, and respectful communication.
• Manage Emotions: Managing emotions, such as frustration or anxiety, is important to maintain a clear and objective perspective during the problem-solving.

Final Words

Problem solving skills in science are crucial as they enable individuals to identify and address complex issues, develop effective solutions, and achieve their career goals. These skills can be developed and improved through various strategies like research, critical thinking, effective communication, and managing emotions.

While there may be common challenges in the problem-solving process, individuals can overcome them by utilizing these strategies and being persistent in their efforts.

By cultivating problem-solving skills in science, individuals can contribute to scientific advancements, improve their career prospects, and ultimately positively impact society.

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What is problem solving and why is it important

By Wayne Stottler , Kepner-Tregoe

• Problem Solving & Decision Making Over time, developing and refining problem solving skills provides the ability to solve increasingly complex problems Learn More

For over 60 years, Kepner-Tregoe has been helping companies across industries and geographies to develop and mature their problem-solving capabilities through KT’s industry leading approach to training and the implementation of best practice processes. Considering that problem solving is a part of almost every person’s daily life (both at home and in the workplace), it is surprising how often we are asked to explain what problem solving is and why it is important.

Problem solving is at the core of human evolution. It is the methods we use to understand what is happening in our environment, identify things we want to change and then figure out the things that need to be done to create the desired outcome. Problem solving is the source of all new inventions, social and cultural evolution, and the basis for market based economies. It is the basis for continuous improvement, communication and learning.

If this problem-solving thing is so important to daily life, what is it?

Problem-solving is the process of observing what is going on in your environment; identifying things that could be changed or improved; diagnosing why the current state is the way it is and the factors and forces that influence it; developing approaches and alternatives to influence change; making decisions about which alternative to select; taking action to implement the changes; and observing impact of those actions in the environment.

Each step in the problem-solving process employs skills and methods that contribute to the overall effectiveness of influencing change and determine the level of problem complexity that can be addressed. Humans learn how to solve simple problems from a very early age (learning to eat, make coordinated movements and communicate) – and as a person goes through life problem-solving skills are refined, matured and become more sophisticated (enabling them to solve more difficult problems).

Problem-solving is important both to individuals and organizations because it enables us to exert control over our environment.

Fixing things that are broken

Some things wear out and break over time, others are flawed from day-1. Personal and business environments are full of things, activities, interactions and processes that are broken or not operating in the way they are desired to work. Problem-solving gives us a mechanism for identifying these things, figuring out why they are broken and determining a course of action to fix them.

Addressing risk

Humans have learned to identify trends and developed an awareness of cause-and-effect relationships in their environment. These skills not only enable us to fix things when they break but also anticipate what may happen in the future (based on past-experience and current events). Problem-solving can be applied to the anticipated future events and used to enable action in the present to influence the likelihood of the event occurring and/or alter the impact if the event does occur.

Improving performance

Individuals and organizations do not exist in isolation in the environment. There is a complex and ever-changing web of relationships that exist and as a result, the actions of one person will often have either a direct impact on others or an indirect impact by changing the environment dynamics. These interdependencies enable humans to work together to solve more complex problems but they also create a force that requires everyone to continuously improve performance to adapt to improvements by others. Problem-solving helps us understand relationships and implement the changes and improvements needed to compete and survive in a continually changing environment.

Seizing opportunity

Problem solving isn’t just about responding to (and fixing) the environment that exists today. It is also about innovating, creating new things and changing the environment to be more desirable. Problem-solving enables us to identify and exploit opportunities in the environment and exert (some level of) control over the future.

Problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations. Developing and refining these skills through training, practice and learning can provide the ability to solve problems more effectively and over time address problems with a greater degree of complexity and difficulty. View KT’s Problem Solving workshop known to be the gold standard for over 60 years.

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What Are Critical Thinking Skills and Why Are They Important?

Learn what critical thinking skills are, why they’re important, and how to develop and apply them in your workplace and everyday life.

We often use critical thinking skills without even realizing it. When you make a decision, such as which cereal to eat for breakfast, you're using critical thinking to determine the best option for you that day.

Critical thinking is like a muscle that can be exercised and built over time. It is a skill that can help propel your career to new heights. You'll be able to solve workplace issues, use trial and error to troubleshoot ideas, and more.

We'll take you through what it is and some examples so you can begin your journey in mastering this skill.

What is critical thinking?

Critical thinking is the ability to interpret, evaluate, and analyze facts and information that are available, to form a judgment or decide if something is right or wrong.

More than just being curious about the world around you, critical thinkers make connections between logical ideas to see the bigger picture. Building your critical thinking skills means being able to advocate your ideas and opinions, present them in a logical fashion, and make decisions for improvement.

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Why is critical thinking important?

Critical thinking is useful in many areas of your life, including your career. It makes you a well-rounded individual, one who has looked at all of their options and possible solutions before making a choice.

According to the University of the People in California, having critical thinking skills is important because they are [ 1 ]:

Crucial for the economy

Essential for improving language and presentation skills

Very helpful in promoting creativity

Important for self-reflection

The basis of science and democracy 

Critical thinking skills are used every day in a myriad of ways and can be applied to situations such as a CEO approaching a group project or a nurse deciding in which order to treat their patients.

Examples of common critical thinking skills

Critical thinking skills differ from individual to individual and are utilized in various ways. Examples of common critical thinking skills include:

Identification of biases: Identifying biases means knowing there are certain people or things that may have an unfair prejudice or influence on the situation at hand. Pointing out these biases helps to remove them from contention when it comes to solving the problem and allows you to see things from a different perspective.

Research: Researching details and facts allows you to be prepared when presenting your information to people. You’ll know exactly what you’re talking about due to the time you’ve spent with the subject material, and you’ll be well-spoken and know what questions to ask to gain more knowledge. When researching, always use credible sources and factual information.

Open-mindedness: Being open-minded when having a conversation or participating in a group activity is crucial to success. Dismissing someone else’s ideas before you’ve heard them will inhibit you from progressing to a solution, and will often create animosity. If you truly want to solve a problem, you need to be willing to hear everyone’s opinions and ideas if you want them to hear yours.

Analysis: Analyzing your research will lead to you having a better understanding of the things you’ve heard and read. As a true critical thinker, you’ll want to seek out the truth and get to the source of issues. It’s important to avoid taking things at face value and always dig deeper.

Problem-solving: Problem-solving is perhaps the most important skill that critical thinkers can possess. The ability to solve issues and bounce back from conflict is what helps you succeed, be a leader, and effect change. One way to properly solve problems is to first recognize there’s a problem that needs solving. By determining the issue at hand, you can then analyze it and come up with several potential solutions.

How to develop critical thinking skills

You can develop critical thinking skills every day if you approach problems in a logical manner. Here are a few ways you can start your path to improvement:

1. Ask questions.

Be inquisitive about everything. Maintain a neutral perspective and develop a natural curiosity, so you can ask questions that develop your understanding of the situation or task at hand. The more details, facts, and information you have, the better informed you are to make decisions.

2. Practice active listening.

Utilize active listening techniques, which are founded in empathy, to really listen to what the other person is saying. Critical thinking, in part, is the cognitive process of reading the situation: the words coming out of their mouth, their body language, their reactions to your own words. Then, you might paraphrase to clarify what they're saying, so both of you agree you're on the same page.

3. Develop your logic and reasoning.

This is perhaps a more abstract task that requires practice and long-term development. However, think of a schoolteacher assessing the classroom to determine how to energize the lesson. There's options such as playing a game, watching a video, or challenging the students with a reward system. Using logic, you might decide that the reward system will take up too much time and is not an immediate fix. A video is not exactly relevant at this time. So, the teacher decides to play a simple word association game.

Scenarios like this happen every day, so next time, you can be more aware of what will work and what won't. Over time, developing your logic and reasoning will strengthen your critical thinking skills.

Learn tips and tricks on how to become a better critical thinker and problem solver through online courses from notable educational institutions on Coursera. Start with Introduction to Logic and Critical Thinking from Duke University or Mindware: Critical Thinking for the Information Age from the University of Michigan.

Article sources

University of the People, “ Why is Critical Thinking Important?: A Survival Guide , https://www.uopeople.edu/blog/why-is-critical-thinking-important/.” Accessed May 18, 2023.

Keep reading

Coursera staff.

Editorial Team

Coursera’s editorial team is comprised of highly experienced professional editors, writers, and fact...

This content has been made available for informational purposes only. Learners are advised to conduct additional research to ensure that courses and other credentials pursued meet their personal, professional, and financial goals.

Encyclopedia of Science Education pp 786–790 Cite as

Problem Solving in Science Learning

• Edit Yerushalmi 2 &
• Bat-Sheva Eylon 3  
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Introduction: Problem Solving in the Science Classroom

Problem solving plays a central role in school science, serving both as a learning goal and as an instructional tool. As a learning goal, problem-solving expertise is considered as a means of promoting both proficiency in solving practice problems and competency in tackling novel problems, a hallmark of successful scientists and engineers. As an instructional tool, problem solving attempts to situate the learning of scientific ideas and practices in an applicative context, thus providing an opportunity to transform science learning into an active, relevant, and motivating experience. Problem solving is also frequently a central strategy in the assessment of students’ performance on various measures (e.g., mastery of procedural skills, conceptual understanding, as well as scientific and learning practices).

A problem is often defined as an unfamiliar task that requires one to make judicious decisions when searching through a problem...

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Yerushalmi, E., Eylon, BS. (2015). Problem Solving in Science Learning. In: Gunstone, R. (eds) Encyclopedia of Science Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2150-0_129

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Facebook ate and then ignored the news industry. It's hard, but we should leave it be

Analysis Science Facebook ate and then ignored the news industry. It's hard, but we should leave it be

Facebook owner Meta's decision to stop paying Australian publishers for news marks a bitter end to a long and often toxic relationship with digital news publishers.

It was a hot-and-cold affair that defined over a decade of online publishing and the work experience of a generation of reporters, and has ultimately left the industry a shadow of its former self.

Although it may be tempting for lots of reasons, the Australian government should avoid putting the boot into Meta by enforcing the News Media Bargaining Code as it's threatened to do.

Doing so will only make a bad situation worse and won't solve the underlying problem of who will pay for the news.

Meta isn't stealing news content. It's ignoring it

Last week, the US social media giant announced it would not renew the commercial deals it ( reluctantl y) signed with some Australian digital news publishers in 2021.

The response since has generally been one of outrage and anger, plus calls to force Meta back to the bargaining table.

The government said Meta was "appropriating" the work done by Australian companies. By this argument, the tech giant is effectively stealing the content of struggling Australian publishers.

But that doesn't properly describe the problem facing the news industry.

The reality of the situation is far worse.

Having spent years getting news outlets to publish their content on its platforms, and then years making this content less visible, Meta has gone one step further.

It says it shouldn't pay for news content because it doesn't actually want news on Facebook .

And the worst part? It's telling the truth.

Facebook's hot-and-cold relationship with news publishers

How times have changed.

Ten years ago, in 2014, the Facebook news feed was prime real estate for digital news publishing.

Reporters were drilled to "post on social". Shared articles went "viral". Armies of moderators blocked trolls in the comments. 

Facebook itself (the company changed its name to Meta in 2021) encouraged this by making news content more visible, and producing tools to make it easier for publishers to share their content with its users.

Digital-only media outfits such as BuzzFeed and Vice rode a wave of growth, generating huge numbers of clicks that translated into ad revenue.

In 2023, BuzzFeed folded.

Its founding editor, Ben Smith, described this as "the end of the marriage between social media and news".

In 2024, just last month, Vice laid off reporters and closed its flagship website.

A few years earlier, it had been valued at $US5.7 billion.

What went wrong?

It can be argued that, from the 2016 US election onwards, Facebook tired of the responsibilities that came with hosting news content and weeding out misinformation.

Readers also grew weary of what news had become in the 2010s era of social media. Endless hot-takes. Clickbait headlines. A fast-spin news cycle. Content designed to polarise and inflame. 

Whatever the reason, Facebook tweaked its algorithm so readers saw less news.

By 2021, when the Australian Parliament passed the News Media Bargaining Code legislation to make Facebook pay for news, Facebook had been incrementally quitting news for years.

It said at the time news made up less than 4 per cent of people's feeds.

Meta now says that figure is down to 3 per cent.

"Facebook encouraged news providers onto the platform in the ways it promoted content," Dan Angus, a professor of digital communications at QUT, said.

"Now it has the eyes of the world and doesn't need news any more."

Axel Bruns, also a professor of digital communications at QUT, agreed that Facebook seems done with news content.

"They're saying, 'Why should we be the ones paying for it?'

"I hate to admit it, but there is a certain amount of logic to Facebook's argument."

Why the code doesn't solve the underlying problem facing news

And so we come to the News Media Bargaining Code, which is designed to address (to varying degrees) three related problems:

• 1. Google and Facebook hold a monopoly over online advertising in Australia
• 2. Big tech in general pays very little tax in Australia, including tax on all the revenue generated by that ad spending
• 3. Australian news outlets don't make enough money to pay for quality journalism, partly as a result of a long-term loss of advertising revenue.

Instead of breaking up that monopoly, or closing tax loopholes, the Code effectively takes money from a profitable industry (big tech) and distributes it to an unprofitable one (news).

It's estimated the confidential two-to-three-year deals negotiated by Meta and Google with news media businesses in 2021 amounted to around $200 million.

That's great for the news outlets, but is it fair?

Arguably not.

First, why should a general purpose communications service like Facebook have to prop up the news industry?

"It's a bit like taking mining royalties to fund kindergartens," Professor Bruns said.

"There is a good argument for using one to fund the other, but it doesn't usually involve making BHP pay money directly to childcare companies."

Second, it's impossible to accurately calculate the advertising revenue Facebook and others generate from news content.

Without going into too much detail, what advertisers pay to appear beside the content is determined by an automated bidding war as a user scrolls their feed or visits a site. 

This price is determined as much by the user's profile as the content itself.

But even if you could accurately calculate revenue, and even if you gave digital news publishers every cent , it still wouldn't solve the problem of how to pay for quality journalism.

The reason for this was news organisations were never in the news business, Amanda Lotz, a professor of media studies at QUT, said.

"They were in the attention-attraction business.

"In another era, if you were an advertiser, a newspaper was a great place to be.

"But now there are just much better places to be."

The business model that sustained news for over a century is dead

The moment news moved online, and was "unbundled" from classifieds, sports results, movie listings, weather reports, celebrity gossip, and all the other reasons people bought newspapers or watched evening TV bulletins, the news business model was dead.

News by itself was never profitable, Professor Bruns said.

"Then advertising moved somewhere else. 

"This was always going to happen via Facebook or other platforms."

This technological change has been generally costly for news outlets and very profitable for Facebook, but that's not Facebook's problem.

The News Media Bargaining Code is trying to restore a model for financing journalism that has gone the way of the fax machine, the fountain pen, and the pocket address book.

The real question is how to pay for a public good that's no longer being adequately privately funded, Professor Angus said.

"How do we pay for this thing that we know is pretty important in a functioning democracy?

"The thing that's annoyed me through the News Media Bargaining Code discussion is that it fundamentally misrepresents that challenge.

"This is not the regulatory solution that many think it is."

One widely proposed solution was more public funding of quality journalism, Professor Lotz said.

"We need to look at journalism the way we look at streets and hospitals. 

"It's a thing that's good for all of us to have."

The value of journalism shouldn't be solely defined by readership figures and advertising revenue, she said.

"The idea that you have entities keeping an eye on things, that you have governments that are aware that if they're not following the rules, there's somebody paying attention to them ... that's the thing we've been losing.

"And so there is enormous public value in simply having journalism doing its role, whether or not it's being consumed by hundreds of thousands of people every day."

What happens next probably won't be good

With Meta's announcement last week, Australia is heading towards another Facebook news ban similar to 2021. This will be bad for everyone.

Here's a likely scenario for what will happen next. 

The government will designate Meta under the Code, which means it will force it to negotiate with media companies to pay for content. 

Assistant treasurer Stephen Jones recently told reporters, "we'll be taking all of the actions that are available to us under the code".

Meta will then ban news on its platforms in Australia.

It did this in Canada in July last year, in response to similar government regulation. Canada's news ban is still going.

As a result of this ban in Australia, fewer Australians will read the news.

A third of Australians use Facebook for "finding, reading, watching, sharing or discussing news" — more than any other social media platform.

Much of this news consumption on Facebook was "incidental and unwilling", Professor Bruns said.

That is, Facebook users didn't seek out news, but it popped up in their feeds. That won't happen any more.

Misinformation will flourish, as has happened in Canada.

Digital publishers will see even less ad revenue, due to Facebook referring fewer readers to their sites.

"If I'm going to take a punt, I think the government will designate Meta," Professor Angus said.

"They will want to be seen to be tough on platforms and Facebook."

In trying to force a platform that doesn't want news to pay for news content, Australia may end up doing itself more harm.

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Can you solve NASA's Pi Day 2024 riddle?

Hungry for Pi? Check out NASA's Pi Day challenge and put your wits to the test solving problems just like NASA scientists and engineers.

Happy Pi Day 2024!

Have you ever wondered what it would be like to solve problems for NASA to help with the exploration of other planets in the  solar system ?

In celebration of  Pi Day 2024 , you can do just that and take the annual  NASA Pi Day Challenge . This is a fun way to put on your scientist and engineer thinking cap and try your best at a series of questions all surrounding the mathematical constant, pi. 

What is pi? If you recall from mathematics class back in grade school, it's approximately 3.14159 and can be used to figure out the circumference of a circle of the volume of a square.

While there are many uses for it in different STEM jobs and fields, it's also very important for  engineers and scientists at NASA  to help study not just our planet but others across the solar system and even other galaxies.

Related: Pi Day 2024: Why NASA uses only 16 of the 62 trillion digits of pi we know

This challenge is a tradition that has been on-going for the last decade put on by NASA's Jet Propulsion Laboratory 's Education Office and features numerous math problems you have to solve using pi.

Sign up for the Live Science daily newsletter now

Get the world’s most fascinating discoveries delivered straight to your inbox.

Some of the questions you can answer this year pertain to missions including the Deep Space Optical Communications technology on NASA's Psyche spacecraft, the Double Asteroid Redirection Test (DART) spacecraft, Earth-orbiting satellites, rovers on the Moon, and even the  Hubble Space Telescope  and  James Webb Space Telescope .

— 8 ways you can see Einstein's theory of relativity in real life

— 12 surprising facts about pi to chew on this Pi Day

— Pi Day 2024: Why NASA uses only 16 of the 62 trillion digits of pi we know

So, let's get solving! You can find  each of the problems  with an accompanying worksheet you can do all your work online and the answers will be posted by NASA so you can check your work!

There are nearly four dozen different questions you can figure out, so try a few or do them all to "cook up" a unique way to get space-y and celebrate Pi Day 2024!

Originally posted on Space.com .

Meredith is a regional Murrow award-winning Certified Broadcast Meteorologist and science/space correspondent. She most recently was a Freelance Meteorologist for NY 1 in New York City & the 19 First Alert Weather Team in Cleveland.  A self-described "Rocket Girl," Meredith's personal and professional work has also been recognized over the last decade. This includes the inaugural Valparaiso University Alumni Association First Decade Achievement Award, two special reports in News 12's Climate Special "Saving Our Shores" that won a Regional Edward R. Murrow Award, multiple Fair Media Council Folio & Press Club of Long Island awards for meteorology & reporting, and a Long Island Business News & NYC TV Week "40 Under 40" Award.  Meredith's 15 year career includes a wide variety of experience across the US stemming from her internship at WGN-TV in Chicago. Meredith worked at local television stations in New York, Ohio, South Dakota, Florida, and California and nationally with WeatherNation. Meredith is also an accomplished reporter, producing weather and science stories.  This includes rocket launches at Vandenberg Space Force Base and Cape Canaveral, in depth special reports and features on NOAA's GOES-R and JPSS satellite series, and coverage on some of NASA's biggest accomplishments. She's interviewed some of the top scientists and leaders of the space & science community, being selected as the only meteorologist to travel with the GOES-West satellite from Colorado to Florida in 2017 on the C-5M Super Galaxy.  Meredith frequents as a panel moderator at the Space Symposium & Satellite Conference, has been a judge for the Space Foundation's Space Technology Hall of Fame & reoccurring moderator for Foundation for the Future. Meredith spends countless hours doing school, career, & motivational talks and podcasts to help encourage women pursuing STEM careers and inspire our future generations. She moderates panels, serves as emcee for events, & conducts interviews to further storytelling on space & science topics.

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Aliens attack science in '3 Body Problem,' a new adaptation of a Chinese sci-fi novel

Eric Deggans

The new Netflix series brings to life a sprawling, successful Chinese novel outlining a new kind of alien invasion. Above, Zine Tseng in 3 Body Problem. Maria Heras/Netflix hide caption

The new Netflix series brings to life a sprawling, successful Chinese novel outlining a new kind of alien invasion. Above, Zine Tseng in 3 Body Problem.

My favorite kind of science fiction involves stories rooted in real science — much as I love a good lightsaber or phaser fight, there is something special about seeing characters wrestle with concepts closer to our current understanding of how the universe works.

That's why I enjoy so much of what happens in Netflix's 3 Body Problem , the TV series which brings to life a sprawling, successful Chinese novel rooted in science, outlining a new kind of alien invasion.

Book Reviews

'three-body problem' asks a classic sci-fi question, in chinese.

3 Body Problem actually starts with two problems. First, we meet investigators tackling a string of unexplained suicides by scientists, including one who had a bizarre countdown written on the walls of his home in blood with his eyes gouged out. (Fortunately, viewers only see the horrific aftermath.) Benedict Wong plays one of those investigators, continually lightening the show's ominous vibe with his spot-on portrayal of a world-weary gumshoe tracking the world's biggest mystery with a healthy dose of gallows humor.

Benedict Wong plays Da Shi in 3 Body Problem. Ed Miller/Netflix hide caption

Benedict Wong plays Da Shi in 3 Body Problem.

"One of the betting sites had him picked as a favorite for the next Nobel Prize in physics," Wong's assistant tells him of the scientist who died.

"You can bet on that?" Wong's character replies, looking over the gruesome scene.

Tracking why science is broken

The other problem which surfaces immediately is that science seems to have stopped working. Researchers are reporting results from experiments in supercolliders that make no sense, putting the lie to all our accepted theories of physics. Saul Durand — played by Jovan Adepo, Durand is one among a group of brilliant, young scientist friends at the center of the story — notes simply, "science is broken."

Jovan Adepo and Jin Cheng in 3 Body Problem. Ed Miller/Netflix hide caption

Jovan Adepo and Jin Cheng in 3 Body Problem.

This all adds up to a unique attack on humanity's scientific progress. But who – or what – is behind these bizarre occurrences, involving events which don't seem possible in the modern world?

Netflix's show takes its time unveiling the full scope of the story and answering these questions, which leads to the third problem here. It takes a while for the series' narrative to really gain momentum – my advice is to hang on through the first three episodes (yes, I also hate streaming shows which ask this of beleaguered viewers; but in this case, it's worth it).

The pacing may not be a surprise, given that two of the series' three creators are David Benioff and D.B. Weiss, former showrunners of HBO's Game of Thrones , which had its own problems with narrative flow at times (the third creator is former True Blood writer/executive producer Alexander Woo). Once the show does find its groove, the series builds into an epic science fiction tale with eye-popping special effects – the tragic destruction of a huge ship packed with people is one that stuck with me long after viewing — and a timeline stretching from China's 1960s-era cultural revolution to the present day.

Bringing a Chinese sci fi-literary triumph to TV

Netflix's 3 Body Problem is based on a 2008 novel from Chinese engineer and science fiction writer Liu Cixin; the original novel became a book series touted by big names like Barack Obama. It managed the neat trick of popularizing Chinese science fiction internationally while delivering compelling observations on the nature of humanity's societal and technological progress, some of which actually find their way into the TV show.

Cultural Revolution-Meets-Aliens: Chinese Writer Takes On Sci-Fi

It makes sense that a story like this — which crosses between Western and Chinese culture to tell the story of a planet under threat – would be cracked by Netflix. The streaming service has educated a generation of American customers to appreciate smart, entertaining TV from South Korea, Latin America, Europe and elsewhere across the globe.

So kicking off 3 Body Problem with a scene showing a young Chinese scientist watching an angry mob murder her father – who is also a scientist – during the purges of China's cultural revolution feels daring and entirely on brand. Later on, that younger scientist, fueled by hate and loss, will make a decision that puts the entire planet at risk, showing how disappointment in humanity's missteps can lead to desperate, misguided solutions.

Fans of the books will find some tweaks here to make for better television, amping up the thriller elements of the story to ask a compelling question: How to fight an alien enemy targeting the world's scientific progress?

As the characters in 3 Body Problem lurch toward answers, we all get to bask in an ambitious narrative fueling an ultimately impressive tale. Just remember to be patient as the series sets the stage early on.

Universities Have a Computer-Science Problem

The case for teaching coders to speak French

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Produced by ElevenLabs and News Over Audio (NOA) using AI narration.

Updated at 5:37 p.m. ET on March 22, 2024

Last year, 18 percent of Stanford University seniors graduated with a degree in computer science, more than double the proportion of just a decade earlier. Over the same period at MIT, that rate went up from 23 percent to 42 percent . These increases are common everywhere: The average number of undergraduate CS majors at universities in the U.S. and Canada tripled in the decade after 2005, and it keeps growing . Students’ interest in CS is intellectual—culture moves through computation these days—but it is also professional. Young people hope to access the wealth, power, and influence of the technology sector.

That ambition has created both enormous administrative strain and a competition for prestige. At Washington University in St. Louis, where I serve on the faculty of the Computer Science & Engineering department, each semester brings another set of waitlists for enrollment in CS classes. On many campuses, students may choose to study computer science at any of several different academic outposts, strewn throughout various departments. At MIT, for example, they might get a degree in “Urban Studies and Planning With Computer Science” from the School of Architecture, or one in “Mathematics With Computer Science” from the School of Science, or they might choose from among four CS-related fields within the School of Engineering. This seepage of computing throughout the university has helped address students’ booming interest, but it also serves to bolster their demand.

Another approach has gained in popularity. Universities are consolidating the formal study of CS into a new administrative structure: the college of computing. MIT opened one in 2019. Cornell set one up in 2020. And just last year, UC Berkeley announced that its own would be that university’s first new college in more than half a century. The importance of this trend—its significance for the practice of education, and also of technology—must not be overlooked. Universities are conservative institutions, steeped in tradition. When they elevate computing to the status of a college, with departments and a budget, they are declaring it a higher-order domain of knowledge and practice, akin to law or engineering. That decision will inform a fundamental question: whether computing ought to be seen as a superfield that lords over all others, or just a servant of other domains, subordinated to their interests and control. This is, by no happenstance, also the basic question about computing in our society writ large.

When I was an undergraduate at the University of Southern California in the 1990s, students interested in computer science could choose between two different majors: one offered by the College of Letters, Arts and Sciences, and one from the School of Engineering. The two degrees were similar, but many students picked the latter because it didn’t require three semesters’ worth of study of a (human) language, such as French. I chose the former, because I like French.

An American university is organized like this, into divisions that are sometimes called colleges , and sometimes schools . These typically enjoy a good deal of independence to define their courses of study and requirements as well as research practices for their constituent disciplines. Included in this purview: whether a CS student really needs to learn French.

The positioning of computer science at USC was not uncommon at the time. The first academic departments of CS had arisen in the early 1960s, and they typically evolved in one of two ways: as an offshoot of electrical engineering (where transistors got their start), housed in a college of engineering; or as an offshoot of mathematics (where formal logic lived), housed in a college of the arts and sciences. At some universities, including USC, CS found its way into both places at once.

The contexts in which CS matured had an impact on its nature, values, and aspirations. Engineering schools are traditionally the venue for a family of professional disciplines, regulated with licensure requirements for practice. Civil engineers, mechanical engineers, nuclear engineers, and others are tasked to build infrastructure that humankind relies on, and they are expected to solve problems. The liberal-arts field of mathematics, by contrast, is concerned with theory and abstraction. The relationship between the theoretical computer scientists in mathematics and the applied ones in engineers is a little like the relationship between biologists and doctors, or physicists and bridge builders. Keeping applied and pure versions of a discipline separate allows each to focus on its expertise, but limits the degree to which one can learn from the other.

Read: Programmers, stop calling yourself engineers

By the time I arrived at USC, some universities had already started down a different path. In 1988, Carnegie Mellon University created what it says was one of the first dedicated schools of computer science. Georgia Institute of Technology followed two years later. “Computing was going to be a big deal,” says Charles Isbell, a former dean of Georgia Tech’s college of computing and now the provost at the University of Wisconsin-Madison. Emancipating the field from its prior home within the college of engineering gave it room to grow, he told me. Within a decade, Georgia Tech had used this structure to establish new research and teaching efforts in computer graphics, human-computer interaction, and robotics. (I spent 17 years on the faculty there, working for Isbell and his predecessors, and teaching computational media.)

Kavita Bala, Cornell University’s dean of computing, told me that the autonomy and scale of a college allows her to avoid jockeying for influence and resources. MIT’s computing dean, Daniel Huttenlocher, says that the speed at which computing evolves justifies the new structure.

But the computing industry isn’t just fast-moving. It’s also reckless. Technology tycoons say they need space for growth, and warn that too much oversight will stifle innovation. Yet we might all be better off, in certain ways, if their ambitions were held back even just a little. Instead of operating with a deep understanding or respect for law, policy, justice, health, or cohesion, tech firms tend to do whatever they want . Facebook sought growth at all costs, even if its take on connecting people tore society apart . If colleges of computing serve to isolate young, future tech professionals from any classrooms where they might imbibe another school’s culture and values—engineering’s studied prudence, for example, or the humanities’ focus on deliberation—this tendency might only worsen.

Read: The moral failure of computer scientists

When I raised this concern with Isbell, he said that the same reasoning could apply to any influential discipline, including medicine and business. He’s probably right, but that’s cold comfort. The mere fact that universities allow some other powerful fiefdoms to exist doesn’t make computing’s centralization less concerning. Isbell admitted that setting up colleges of computing “absolutely runs the risk” of empowering a generation of professionals who may already be disengaged from consequences to train the next one in their image. Inside a computing college, there may be fewer critics around who can slow down bad ideas. Disengagement might redouble. But he said that dedicated colleges could also have the opposite effect. A traditional CS department in a school of engineering would be populated entirely by computer scientists, while the faculty for a college of computing like the one he led at Georgia Tech might also house lawyers, ethnographers, psychologists, and even philosophers like me. Huttenlocher repeatedly emphasized that the role of the computing college is to foster collaboration between CS and other disciplines across the university. Bala told me that her college was established not to teach CS on its own but to incorporate policy, law, sociology, and other fields into its practice. “I think there are no downsides,” she said.

Mark Guzdial is a former faculty member in Georgia Tech’s computing college, and he now teaches computer science in the University of Michigan’s College of Engineering. At Michigan, CS wasn’t always housed in engineering—Guzdial says it started out inside the philosophy department, as part of the College of Literature, Science and the Arts. Now that college “wants it back,” as one administrator told Guzdial. Having been asked to start a program that teaches computing to liberal-arts students, Guzdial has a new perspective on these administrative structures. He learned that Michigan’s Computer Science and Engineering program and its faculty are “despised” by their counterparts in the humanities and social sciences. “They’re seen as arrogant, narrowly focused on machines rather than people, and unwilling to meet other programs’ needs,” he told me. “I had faculty refuse to talk to me because I was from CSE.”

In other words, there may be downsides just to placing CS within an engineering school, let alone making it an independent college. Left entirely to themselves, computer scientists can forget that computers are supposed to be tools that help people. Georgia Tech’s College of Computing worked “because the culture was always outward-looking. We sought to use computing to solve others’ problems,” Guzdial said. But that may have been a momentary success. Now, at Michigan, he is trying to rebuild computing education from scratch, for students in fields such as French and sociology. He wants them to understand it as a means of self-expression or achieving justice—and not just a way of making software, or money.

Early in my undergraduate career, I decided to abandon CS as a major. Even as an undergraduate, I already had a side job in what would become the internet industry, and computer science, as an academic field, felt theoretical and unnecessary. Reasoning that I could easily get a job as a computer professional no matter what it said on my degree, I decided to study other things while I had the chance.

I have a strong memory of processing the paperwork to drop my computer-science major in college, in favor of philosophy. I walked down a quiet, blue-tiled hallway of the engineering building. All the faculty doors were closed, although the click-click of mechanical keyboards could be heard behind many of them. I knocked on my adviser’s door; she opened it, silently signed my paperwork without inviting me in, and closed the door again. The keyboard tapping resumed.

The whole experience was a product of its time, when computer science was a field composed of oddball characters, working by themselves, and largely disconnected from what was happening in the world at large. Almost 30 years later, their projects have turned into the infrastructure of our daily lives. Want to find a job? That’s LinkedIn. Keep in touch? Gmail, or Instagram. Get news? A website like this one, we hope, but perhaps TikTok. My university uses a software service sold by a tech company to run its courses. Some things have been made easier with computing. Others have been changed to serve another end, like scaling up an online business.

Read: So much for ‘learn to code’

The struggle to figure out the best organizational structure for computing education is, in a way, a microcosm of the struggle under way in the computing sector at large. For decades, computers were tools used to accomplish tasks better and more efficiently. Then computing became the way we work and live. It became our culture, and we began doing what computers made possible, rather than using computers to solve problems defined outside their purview. Tech moguls became famous, wealthy, and powerful. So did CS academics (relatively speaking). The success of the latter—in terms of rising student enrollments, research output, and fundraising dollars—both sustains and justifies their growing influence on campus.

If computing colleges have erred, it may be in failing to exert their power with even greater zeal. For all their talk of growth and expansion within academia, the computing deans’ ambitions seem remarkably modest. Martial Hebert, the dean of Carnegie Mellon’s computing school, almost sounded like he was talking about the liberal arts when he told me that CS is “a rich tapestry of disciplines” that “goes far beyond computers and coding.” But the seven departments in his school correspond to the traditional, core aspects of computing plus computational biology. They do not include history, for example, or finance. Bala and Isbell talked about incorporating law, policy, and psychology into their programs of study, but only in the form of hiring individual professors into more traditional CS divisions. None of the deans I spoke with aspires to launch, say, a department of art within their college of computing, or one of politics, sociology, or film. Their vision does not reflect the idea that computing can or should be a superordinate realm of scholarship, on the order of the arts or engineering. Rather, they are proceeding as though it were a technical school for producing a certain variety of very well-paid professionals. A computing college deserving of the name wouldn’t just provide deeper coursework in CS and its closely adjacent fields; it would expand and reinvent other, seemingly remote disciplines for the age of computation.

Near the end of our conversation, Isbell mentioned the engineering fallacy, which he summarized like this: Someone asks you to solve a problem, and you solve it without asking if it’s a problem worth solving. I used to think computing education might be stuck in a nesting-doll version of the engineer’s fallacy, in which CS departments have been asked to train more software engineers without considering whether more software engineers are really what the world needs. Now I worry that they have a bigger problem to address: how to make computer people care about everything else as much as they care about computers.

This article originally mischaracterized the views of MIT’s computing dean, Daniel Huttenlocher. He did not say that computer science would be held back in an arts-and-science or engineering context, or that it needs to be independent.

The world is not moving fast enough on climate change — social sciences can help explain why

Assistant Professor of urban planning, University of Minnesota

Associate professor, School of Public Policy and Global Affairs, and Institute for Critical Indigenous Studies, University of British Columbia

Associate Professor of Anthropology, Oregon State University

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In late 2023 the United States government released its Fifth National Climate Assessment (NCA). The NCA is a semi-regular summation of the impacts of climate change upon the U.S. and the fifth assessment was notable for being the first to include a chapter on social systems and justice .

Built on decades of social science research on climate change, the fifth NCA contends with two truths that are increasingly being reckoned with in U.S. popular and academic conversations .

The first is that climate change has the potential to exacerbate health, social and economic outcomes for Black, Indigenous, people of colour (BIPOC) and low-income communities. The second is that social systems and institutions — including governmental, cultural, spiritual and economic structures — are the only places where adaptation and mitigation can occur.

Read more: It is not just heat waves — climate change is also a crisis of disconnection

We only have to compare mortality rates for the COVID-19 pandemic disaggregated by race, income, and other axes of inequality to recognize that we are not all in the same boat, despite experiencing the same storm. Today, race and income similarly predict who is likely to be displaced permanently after a major hurricane — and forced relocation can have negative impacts on individuals and communities for generations.

Understanding how existing social systems influence, and are influenced by, climate change is key to not only slowing the effects of an increasingly warming Earth, but also ensuring that society’s transition to a new world is a just one .

And there is no doubt that we are indeed facing a new world.

Not moving fast enough

Decades of scientific research have shown that increasingly devastating and rapid climatic changes are ahead of us, including more intense hurricanes, droughts and floods.

Our recent levels of resource consumption — particularly in the Global North and countries with large developing economies — are untenable . To be clear, the world is responding to these risks with the U.S. alone achieving a 13 percent decrease in annual greenhouse gas emissions between 2005 and 2019 , but these responses are not good enough.

It is the purview of social scientists — the scientists tasked with studying human society and social relationships in all of their complexity — to ask why.

What is it about the ethics, cultures, economies, and symbols at play in the world that have made it so difficult to turn the tide and make change? Why do we — individuals, societies, cultures, and nations — mostly seem unable to curb emissions at the rates necessary to save ourselves and our planet?

These are questions that can only partially be answered by new information and technologies developed by physical scientists and engineers. We also need an understanding of how humans behave. Having new technology matters for little if you do not also understand how social, economic and political decisions are made — and how certain groups are able to develop habits around lower rates of emissions and consumption .

Read more: Telling stories of our climate futures is essential to thinking through the net-zero choices of today

We know that inequitable systems create unevenly distributed risk and capacities to respond. For example, a hurricane’s intensity scale is less predictive of its mortality rates than the socio-economic conditions within the nation where the storm makes landfall . Understanding these dynamics is the only way to respond to climate change in a way that does not entrench deep tendencies towards racist, sexist and classist landscapes of vulnerability.

Empowering real change

Recognizing that disasters and climate disruptions have the potential to make inequality worse also means that we have the opportunity to do better.

There are a range of outcomes that may stem from climate related disasters with a vast inventory of what is possible. There are also hopeful examples that point the way to rich collaborations and problem solving. For example, Tulsa, Okla. was the most frequently flooded city in the U.S. from the 1960s into the 1980s, but a coalition of concerned citizens came together with the city government to create a floodplain management plan that serves as a model for other cities.

In another example, Indigenous communities around the U.S. have some of the most proactive planning in place for adapting to climate change, despite histories of persecution, theft and violent exploitation.

There is an adage that says in order to go quickly, go alone; if you want to go far, go together. Make no mistake, climate change is the most urgent issue of our time. However, moving quickly and carelessly will serve only to re-entrench existing social, economic, political and environmental inequalities.

Instead, we must look at other ways of being in the world. We can repair and recreate our relationships with the Earth and the consumption that has gotten us to this point. We can pay attention and listen to global Indigenous peoples and others who have cared for this earth for millennia .

Read more: COP28: Climate change theatre and performances reveal new narratives about how we need to live

We must be more creative with our solutions and committed to ensuring that all, and not just a privileged few, are able to live in a better world than the one in which they were born into. Technological approaches alone will not achieve this goal. To build a better world we need the social sciences.

• Fossil fuels
• Climate change
• United States
• Sustainability
• Global warming
• Social sciences
• Environmental justice
• Greenhouse gas emissions (GHG)

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