what is a homework plug

Click to choose an image or drag it here

• AI Math Solver

A Simple, Fast, and Intelligent AI Homework Helper

HomeworkAI Is The Ultimate AI Homework Helper You Need

Struggling with piles of homework and tricky assignments? Let HomeworkAI help you out! Our smart AI homework helper delivers detailed, step-by-step solutions, transforming study sessions into smooth sailing.

Covering all subjects, from complex calculus to intricate biology, our homework AI is here to ease the stress and boost your grades. Say hello to effortless learning and wave goodbye to study blues with HomeworkAI!

Get Instant Answers From Our Homework AI

Description: This is how to unlock comprehensive answers and master your studies with our homework AI, in a fast, accurate, and educational fashion.

Upload Your Assignment - Simply upload images, text files, or type your question to get started.

AI Processing - Our advanced AI homework helper will process your assignment and provide detailed, accurate solutions.

Learn & Understand - Review the step-by-step guidance to improve your knowledge and complete your homework with confidence.

Gain Academic Advantages From HomeworkAI's Top Features

Instant Solutions

Quick, clear-cut answers are just a click away with an instant AI homework helper—skip the headache and let our homework AI do the heavy lifting for you.

Maximum Accuracy

Count on Homework AI for spot-on answers. Our advanced AI algorithm digs deep into a vast knowledge base to ensure you get the most accurate solutions every time.

Around-the-Clock Help

Day or night, our homework AI is at your beck and call, ready to dismantle any academic obstacle you encounter, so learning never has to pause for a break.

Comprehensive Support

Whatever the subject, our intelligent AI homework helper has you covered. Get expert help from algebra equations to zoological classifications with ease.

Easy to Use

Enjoy a super user-friendly platform with our homework AI, tailored to empower students and academic professionals at every level to navigate through assignments with confidence.

Our Homework AI Can Help You With All Subjects !

Turn to HomeworkAI for tailored homework and assignment assistance in every subject of your choice.

Mathematics

Solve complex equations and tackle calculus challenges with our AI-powered homework helper that turns numbers into knowledge.

From cellular structures to ecosystem dynamics, easily manage your biology assignments with clear, detailed explanations.

Balance chemical equations and understand reaction mechanisms with a quick online problem solver that simplifies the periodic table.

Analyze literary themes and decipher figurative language with insights that breathe new life into classic texts.

Connect historical dots with ease, as HomeworkAI helps you interpret events and understand their lasting impacts.

Discover Success Stories with Our Homework AI

Ever since using HomeworkAI for my math homework, studying has been way less stressful, and I can say that I'm enjoying math now. My grades are up and I actually get the hang of algebra now!

- Priya K., University Sophomore

I was dreading chemistry all semester, but HomeworkAI totally turned that around. I'm now breaking down reactions and acing quizzes with confidence. The step-by-step solutions it provides are a lifesaver for someone like me! Totally recommended. 

- Marcus D., High School Junior

HomeworkAI made sense of all those crazy bio terms I could never remember. HomeworkAI’s explanations have made it manageable. My test scores are also much better, and I'm not a bundle of nerves anymore!

- Lina J., College Freshman

No more panicking over biology assignments with this AI homework helper!! Nailed my biology midterm, all thanks to HomeworkAI! It's like having a tutor in my pocket, ready to help with homework anytime, day or night.

- Carlos M., High School Senior

Why HomeworkAI Is Your Go-To AI Homework Helper ?

What types of files can I upload to HomeworkAI?

HomeworkAI supports a variety of file formats, including text files such as PDF, DOC, DOCX, and image files like JPEG and PNG. This allows you to easily upload assignments, worksheets, and questions in the format that best suits your needs.

Is HomeworkAI suitable for all educational levels?

Yes, HomeworkAI is tailored for students and educational professionals of all levels—from middle schoolers to university undergrads—providing support and solutions customized to each educational stage.

Can HoweworkAI process practice questions from textbook material?

Yes. Simply upload the textbook material with practice questions, and our homework AI will analyze them to provide detailed solutions and explanations, just as it would with any other homework assignment or study query.

Does getting help from HomeworkAI considered cheating?

HomeworkAI is an AI question answerer designed to aid your learning process, much like a traditional tutor. Thus, utilizing HomeworkAI may not be considered cheating, as long as it aligns with your institution's guidelines for using external help.

Can I use HomeworkAI to prepare for my exam?

Absolutely, HomeworkAI can be an effective tool for exam preparation. It offers practice questions, solutions, and thorough explanations to help reinforce your understanding of the subject matter, giving you an extra edge in your study routine.

How does HomeworkAI handle problems with multiple solution methods?

HomeworkAI does have the ability to handle problems with multiple solution methods. It can provide a primary solution and, where applicable, may offer alternative approaches or explanations to give you a well-rounded understanding of the problem at hand.

Get Your Hands on The Best AI Homework Helper Right Now !

HomeworkAI doesn't just deliver answers—it teaches problem-solving, becoming your ultimate homework companion.

10 Chrome Homework Extensions That Really Work for Students

Your changes have been saved

Email is sent

Email has already been sent

Please verify your email address.

You’ve reached your account maximum for followed topics.

This USB-C Dock Turned My Laptop Into a Workstation

Vpns don't do these 5 things: vpn myths busted, i use this browser to save power on my laptop.

If you mainly use Chrome to do research academic papers, projects, or assignments, why not use handy browser extensions to manage that homework for you?

These learning tools in your browser let you plan your tasks, help you research, and assist with your studies. And best of all, you don't have to worry about opening a separate application.

Lists for Assignments

Quick lists can help you stay on track. These cool tools let you add and mark off items as you go.

Synchro is a task tracker extension built for students. A clean, intuitive tool, it lets you add tasks, specify the deadlines, and choose the current status.

Synchro lists all the tasks under three columns- to-do, in progress, and completed. As you work on your tasks, you can drag and drop them into the relevant columns.

Once you're done, you can completely delete the task. Synchro also color codes the tasks, depending on the due dates, and sends task reminders. It integrates with Canvas LMS and automatically adds assignments from Canvas as tasks.

Download: Synchro (Free)

2. Tasks for Canvas

If you use Canvas LMS, then Tasks for Canvas is a must-have Chrome extension. The extension integrates with your Canvas account and adds a sidebar, showing all the tasks you need to do.

Since it is linked with the Canvas LMS, tasks will be automatically added and categorized according to the course. You can create custom tasks and mark them as complete. By default, it shows a weekly view, but you can adjust it to daily or monthly.

What's best about the\is extension is its beautiful layout. The extension adds colored rings for each course to show the progress.

Download: Tasks for Canvas (Free)

3. Homework Tracker

Sometimes simple is sensational. Maybe you just have a basic list of assignments or projects that you want to track. Homework Tracker is ideal for this. Click the toolbar button to add or view your items and see a count of uncompleted tasks with the icon badge.

Enter your class, assignment, and due date (if you have one) and click Add . Then, as you complete your work, hit the Done button. You can sort by due date, so the closest items are right at the top. Homework Tracker is basic yet effective.

Download: Homework Tracker (Free)

4. My Homework Reminder

My Homework Reminder is another good assignment list extension for Chrome. Click the toolbar button , add your assignment and due date, and hit Save .

You can sort by assignment or due date, mark the boxes for items you finish, and review your completed assignments easily. If you need to delete an item, just click the trash can and away it goes. Just like Homework Tracker, My Homework Reminder is simple but gets the job done.

Download: My Homework Reminder (Free)

Homework Helpers

Instead of random Googling, try these extensions to get the homework help you need quickly.

In case you don't know, Quizlet is a popular education website with learning tools and study guides. Thanks to the textbook solutions available on the site, you can easily find homework help. But this extension called Quizlit makes the process even easier.

The add-on lets you search Quizlet from any webpage, so you don't have to open the Quizlet site every time. Just click the Quizlit button , enter your question in the search bar, and press enter to see the relevant answers from Quizlet. Even better, you can select any question and choose Search for from the right-click context menu.

The extension shows multiple answers for each question and lets you copy the suggested answers with a single click. If you don't find the answers on Quizlet, you can try searching for them on the other tutoring sites for homework help .

Download: Quizlit (Free)

2. AIR MATH

If you need homework help specifically for mathematics, AIR MATH is a great extension. Just use the extension to take a screenshot of the question, and the tool solves the problem along with a step-by-step solution.

Although it does offer free credits, you'll likely need to purchase extra credits or upgrade to a paid subscription. If you're not keen to pay for this extension, there are other online tools for solving math problems . AIR MATH is also available as a mobile app.

Download: AIR MATH (Free, Paid)

Buttons for Searches

When you need to do a fast search, a basic button can be the answer. These Chrome extensions let you search with a click.

1. Google Scholar Button

Google offers a ton of search tools and some are specific to patents, images, and of course, education. The Google Scholar Button lets you search for a topic easily. Click the button in your toolbar, pop in your search term, and then get your results.

You will receive a short number of results within the search window and can select a title to go right to the page. Or to view all results, click the full-screen button at the bottom of the pop-up window and a new tab will open for you. This is one of the must-have online tools if you're doing academic research .

Download: Google Scholar Button (Free)

2. Course Hero

Course Hero is similar to Google Scholar in that you click the button to search for a topic and then head to the site for the results. What's a bit different is that you need to create an account to obtain the resource. But, you can create one for free in just a few minutes.

Then, you will have access to documents and flashcards relating to your topic. Plus, you can get help from educators. You can also bookmark sources, keep track of your recently viewed items, and download the mobile app to study on-the-go.

Download: Course Hero (Free, Paid)

Helpers for Focus

Don't get distracted by social media when you are doing homework. Use one of these awesome tools to help you focus and finish.

1. ReCall Study Time

Set up your study session, mark the pages you want to monitor, and get to work with ReCall Study Time. You can choose from two hours for those quick homework sessions or 24 hours for the all-nighters. Then, select the social media sites to block like Facebook, Twitter, and Instagram.

If you feel yourself weaken and head to one of the monitored sights, you will instead be greeted with a nasty-gram like the one above. If you have trouble staying away from social media to get your homework done, check out ReCall Study Time.

Download: ReCall Study Time (Free)

2. Focus Mode

Focus Mode is another site-blocking tool to use while you are doing your homework. The extension monitors four sites by default, including Facebook, Twitter, and YouTube. You can choose which to unblock and add a custom blocked site if there is an additional temptation not on that list.

When you start your study or research session, just hit the extension button in the toolbar and turn on the toggle button . Then, when you try to access one of the monitored pages, you will view a blurred screen with a message that focus mode is on.

When you finish, turn off the toggle button and check out your distraction attempts if you're curious. You can also take a five-minute break when you're tempted to check your feed.

Download: Focus Mode (Free)

Get Your Homework Done

We get it. Managing all the deadlines for assignments, projects, and quizzes can be challenging. But with the right tools and a bit of planning, you can get your homework done without sacrificing fun.

This is exactly what these Chrome extensions let you do—tracking your tasks, improving your productivity, and helping you complete your homework. If you find these homework add-ons helpful, you should try mobile apps for students.

• Productivity
• Education Technology

Please ensure that your password is at least 8 characters and contains each of the following:

• a special character: @$#!%*?&

Instant, Expert Homework Help

Reach academic excellence with our AI homework solver

• 100K+ active users
• 10M+ questions solved

It directly integrates into your assigments.

Get instant answers.

With just a click of a button, our homework solver will provide you with the answers to any question. It can provide you guidance on any website, even those without specialized support.

Additionally, it is fully integrated with Learning Management Systems (LMS) such as Blackboard, D2L, Classmarker, Khan Academy, Schoology, Canvas, Moodle, and many others.

Include graphs and image based questions

With a simple screenshot, you can capture any visual challenge — be it a detailed graph or a complex image.

Our advanced AI automatically detects the type of visual content, analyzing it to provide you with the most accurate answer.

Get step by step answer explanations

Get detailed, step-by-step guidance for each question, boosting your understanding and academic results. Whenever you're stuck, our AI steps in to clarify concepts and expand your expertise.

The most advanced tool ever

Selects the correct answer in your LMS automatically

Prevents websites from detecting our AI quiz solver

Camouflage Mode

Invisible, discreet exam chrome extension that goes unnoticed.

100% encrypted

Start Boosting Your GPA Now

What students say.

Zebby Baker University of Miami

Was kinda doubtful at first, but no joke, college tools is the real deal—no plagiarism worries at all. It's ace for nailing assignments without sweating about cheating. Feels good to keep it honest

Jessica Mutepa Harvard University

explanation feature is very useful to break down complex questions into simpler terms

Sebastian Breynart Yale University

Downloaded it right before my midterm and it works great...

Gabriel Mitchell University of California, Los Angeles

the screenshot feature is making passing chem 1411h possible

Hunter Munson University of Michigan

As someone who's back to studying as an adult, college tools is a godsend. Fits right into my crazy schedule and lets me study smart—not hard. Quality of my learning hasn't dropped a bit

Kimmy Jeremy New York University

helps with more than just homework, legit

Emiliano Cook University of Pennsylvania

This chrome extension is a time saver for Khan Academy assignments

Satisfied customers.

93% students increase grades

Chrome Reviews 300+

Try for free

• Solve unlimited questions
• Universal Compatibility
• Works on graph & image based questions
• Step by step answer explanations
• 100K+ satisfied users
• Cancel anytime
• 100k+ satisfied users
• Renews at a $9.99/month

3 simple steps to get started

Follow these simple steps and you'll find the correct answers to your homework in no time.

Get our Chrome Extension

Open any assignment

Run the extension

Works with your learning systems

Protect your identity while using our accurate quiz solutions with AI.

College Tools prevents websites from detecting our extension.

Still have questions?

Does it work on any learning platform or website, can my school detect i'm using the extension, is it more accurate than chatgpt, can i promote college tools, how do we ensure your data's safety, ready to fast-track your homework.

Please enter a valid email address

Emails do not match

Please enter a valid password

This code is expired

Already have an account? Log in

By proceeding, you agree to the Terms of Service and Privacy Policy.

Please enter a valid email address.

This field cannot be empty.

Don’t have an account? Sign up now and start having time on your quizzes, homework and exams!

Forgot your password?

Enter your address below and we’ll send you a link to reset your password.

Special offer for you

$ 9.99 /month.

• Solve equations and inequalities
• Simplify expressions
• Factor polynomials
• Graph equations and inequalities
• Advanced solvers
• All solvers
• Arithmetics
• Determinant
• Percentages
• Scientific Notation
• Inequalities

What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
• The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
• The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
• The calculus section will carry out differentiation as well as definite and indefinite integration.
• The matrices section contains commands for the arithmetic manipulation of matrices.
• The graphs section contains commands for plotting equations and inequalities.
• The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

Math Topics

More solvers.

• Add Fractions
• Simplify Fractions

Checking Answers Using Algebra Calculator

Example problem, check answer, how to check your answer with algebra calculator.

• First type the equation 2x+3=15 .
• Then type the @ symbol.
• Then type x=6 .

Clickable Demo

More Examples

• For x+6=2x+3, check (correct) solution x=3: x+6=2x+3 @ x=3
• For x+6=2x+3, check (wrong) solution x=2: x+6=2x+3 @ x=2
• For system of equations x+y=8 and y=x+2, check (correct) solution x=3, y=5: x+y=8 and y=x+2 @ x=3, y=5
• For 3xy=18, check (correct) solution x=2, y=3: 3xy=18 @ x=2, y=3

Related Articles

• Algebra Calculator Tutorial

Our websites may use cookies to personalize and enhance your experience. By continuing without changing your cookie settings, you agree to this collection. For more information, please see our University Websites Privacy Notice .

Neag School of Education

How to use homework to support student success.

• by: Sandra Chafouleas
• January 13, 2022
• Community Engagement

Editor’s Note: Board of Trustees Distinguished Professor Sandra Chafouleas shares insights on supporting students’ homework during the pandemic in the following piece, which originally appeared  in Psychology Today , where she publishes a blog.

COVID has brought many changes in education. What does it mean for homework?

School assignments that a student is expected to do outside of the regular school day—that’s homework. The general guideline is 10 minutes of nightly homework per grade level beginning after kindergarten. This amounts to just a few minutes for younger elementary students to up to 2 hours for high school students.

The guidance seems straightforward enough, so why is homework such a controversial topic? School disruptions, including extended periods of remote learning during the COVID-19 pandemic, have magnified the controversies yet also have provided an opportunity to rethink the purpose and value of homework.

Debates about the value of homework center around two primary issues: amount and inequity.

First, the amount of assigned homework may be much more than the recommended guidelines. Families report their children are stressed out over the time spent doing homework. Too much homework can challenge well-being given the restricted time available for sleep, exercise, and social connection. In a 2015 study , for example, parents reported their early elementary children received almost three times the recommended guidelines. In high school, researchers found an average of three hours of homework per night for students living in economically privileged communities.

“ Debates about the value of homework center around two primary issues: amount and inequity.”

Second, homework can perpetuate inequities. Students attending school in less economically privileged communities may receive little to no homework, or have difficulty completing it due to limited access to needed technology. This can translate into fewer opportunities to learn and may contribute to gaps in achievement.

There isn’t a ton of research on the effects of homework, and available studies certainly do not provide a simple answer. For example, a 2006 synthesis of studies suggested a positive influence between homework completion and academic achievement for middle and high school students. Supporters also point out that homework offers additional opportunities to engage in learning and that it can foster independent learning habits such as planning and a sense of responsibility. A more recent study involving 13-year-old students in Spain found higher test scores for those who were regularly assigned homework in math and science, with an optimal time around one hour—which is roughly aligned with recommendations. However, the researchers noted that ability to independently do the work, student effort, and prior achievement were more important contributors than time spent.

Opponents of homework maintain that the academic benefit does not outweigh the toll on well-being. Researchers have observed student stress, physical health problems, and lack of life balance, especially when the time spent goes over the recommended guidelines. In a survey of adolescents , over half reported the amount and type of homework they received to be a primary source of stress in their lives. In addition, vast differences exist in access and availability of supports, such as internet connection, adult assistance, or even a place to call home, as 1.5 million children experience homelessness in the United States

The COVID-19 pandemic has re-energized discussion about homework practices, with the goal to advance recommendations about how, when, and with whom it can be best used. Here’s a summary of key strategies:

Strategies for Educators

Make sure the tasks are meaningful and matched..

First, the motto “ quality over quantity ” can guide decisions about homework. Homework is not busy-work, and instead should get students excited about learning. Emphasize activities that facilitate choice and interest to extend learning, like choose your own reading adventure or math games. Second, each student should be able to complete homework independently with success. Think about Goldilocks: To be effective, assignments should be just right for each learner. One example of how do this efficiently is through online learning platforms that can efficiently adjust to skill level and can be completed in a reasonable amount of time.

Ensure access to resources for task completion.

One step toward equity is to ensure access to necessary resources such as time, space, and materials. Teach students about preparing for homework success, allocating classroom time to model and practice good study habits such as setting up their physical environment, time management, and chunking tasks. Engage in conversations with students and families to problem-solve challenges When needed, connect students with homework supports available through after-school clubs, other community supports, or even within a dedicated block during the school day.

Be open to revisiting homework policies and practices.

The days of penalizing students for not completing homework should be long gone. Homework is a tool for practicing content and learning self-management. With that in mind, provide opportunities for students to communicate needs, and respond by revising assignments or allowing them to turn in on alternative dates. Engage in adult professional learning about high-quality homework , from value (Should I assign this task?) to evaluation (How should this be graded? Did that homework assignment result in expected outcomes?). Monitor how things are going by looking at completion rates and by asking students for their feedback. Be willing to adapt the homework schedule or expectations based on what is learned.

Strategies for Families

Understand how to be a good helper..

When designed appropriately, students should be able to complete homework with independence. Limit homework wars by working to be a good helper. Hovering, micromanaging, or doing homework for them may be easiest in the moment but does not help build their independence. Be a good helper by asking guiding questions, providing hints, or checking for understanding. Focus your assistance on setting up structures for homework success, like space and time.

Use homework as a tool for communication.

Use homework as a vehicle to foster family-school communication. Families can use homework as an opportunity to open conversations about specific assignments or classes, peer relationships, or even sleep quality that may be impacting student success. For younger students, using a daily or weekly home-school notebook or planner can be one way to share information. For older students, help them practice communicating their needs and provide support as needed.

Make sure to balance wellness.

Like adults, children need a healthy work-life balance. Positive social connection and engagement in pleasurable activities are important core principles to foster well-being . Monitor the load of homework and other structured activities to make sure there is time in the daily routine for play. Play can mean different things to different children: getting outside, reading for pleasure, and yes, even gaming. Just try to ensure that activities include a mix of health-focused activities such as physical movement or mindfulness downtime.

The Council for the Accreditation of Educator Preparation (CAEP) accredits the Neag School of Education at the University of Connecticut. Read more about CAEP Accreditation, including the programs covered and the accountability measures .

Some content on this website may require the use of a plug-in, such as  Adobe Acrobat Viewer .

• Support the Neag School

Neag School of Education 249 Glenbrook Road, Unit 3064 Charles B. Gentry Building Storrs, CT 06269-3064

860-486-3815 [email protected]

Personalized homework help

*closed due to covid as of dec 2020.

Submit your assignment 

Get a detailed guide to help you understand

Learn the material and ace your class

About  Homework     lug

Online homework help.

Homework Plug is a West Coast based business dedicated to the satisfaction of our customers. We do however cater to people across the states and have tutors from both West and East coasts to match your schedule. We cater to a large variety of subjects all the way through college level courses, and have experiences with all kinds of projects. A commitment to our clients is a commitment to excellence.

Because you would rather be doing  more of this

TESTIMONIALS

“I have used this service for a very long time now. They work quick and on time. Have great originality. Most importantly, their quality of work is outstanding. Extremely satisfied with the results.”

Our online homework  Tutors

Homework Plug tutors go through rigorous screening and verification processes to ensure they are the best of the best and dedicated to producing stellar work. Our tutors are most often college grads and will always be matched with you based on your need and their area of study. They are hand selected from many applicants as the experts in their fields, and have a reputation for being timely and dedicated to the job. We have intense admin review and oversight to ensure their work is timely and of the highest quality.

My Top 5 (Free-ish) Cool Tools that Integrate into Canvas

• Author By Lindsey Van Gieson
• Publication date January 31, 2018
• Categories: Canvas , Interesting Technologies , Tools for Teaching
• Categories: Canvas , How-to , LMS , Resources

Canvas has this great wealth of tools that are just waiting to be deployed into your course.  These tools are located in Canvas’  EduAppCenter .  There are hundreds of apps in the  EduAppCenter , so I thought I’d summarize just a few of the interesting ones available there, and some others that are available on the web.  Many of these tools are free, others cost money or are subscription based for added features.  Faculty and students alike are always asking for more collaborative tools, so I’ve mostly selected tools that have a collaborative slant.

How do I find the apps?

From the Settings area of your course site click on Settings, and then Apps, to find the EduAppCenter!

On to the apps!

Trello is a visual list tool that can be used for project management, collaboration, and much more! When Trello launched in 2011, the developers described it as “a web page where you make a bunch of lists. Each list contains cards. Each card is a thing that someone might want to work on” ( Trello Launch blog post ). On the back of each card, there’s room for including a description, conversations, file attachments, links, checklists, labels, and more.  So why use this instead of just covering your whiteboard in post it notes? You can invite others to collaborate with you on your Trello board.  So this tool ends up being useful for group projects, collaborations with your colleagues, etc.

One of its strong suits is providing templates that can help get you started (see links below).  And the best part? It integrates into Canvas.  Just go to your Canvas course, click on Settings > Apps and search the app center for Trello.  Trello can be added into Assignments and Modules as an External Tool.   Tip: You must first create a Public board in your Trello account (and grab the board ID) in order to add it to your Canvas site via the LTI.

TL;DR Trello is a list-making, task-delegating, collaboration tool. Cost: Free. Integrates into Canvas from App Center.

More About Trello Board of Templates More Templates Use Trello Like a Pro How to find your Trello Board ID

Padlet is a similar tool to Trello, but simplified.  It presents more like a Pinterest board, but without all the clutter and ads.   Padlet’s website describes the tool as, “Somewhere between a doc and a full-fledged website builder, Padlet empowers everyone to make the content they want, whether it’s a quick bulletin board, a blog, or a portfolio” ( What is Padlet? ) The “free” version of Padlet is generously-featured enough to be used in a classroom or for group projects. You can collaborate with classmates or colleagues in Padlet simply by knowing their email address.

Compared to Trello, which is project-oriented, Padlet is set up more like social media- a user posts text, a link, or a file- and other users may comment on, favorite, rank, or even grade the posting (based on settings you select). A benefit of Padlet over Trello is that Padlet can be set up to be private.  Trello can also be private, but not if you want to use the Canvas integration.   Padlet offers mobile apps, and the option to share or embed a full board into Canvas.  There is currently no LTI integration for Canvas, but Padlet provides simple  instructions on how to embed  into Canvas.  There are also mobile apps and browser plug-ins available to make adding to your Padlet wall easier!

TL;DR Padlet is a media-rich bulletin-board, Pinterest-y, collaboration tool Cost: Free, decent feature set (with ability to upgrade) No direct integration, needs to be embedded into Canvas content page.

More about Padlet Educational Resources & Reviews Make your own Padlet

3. Flipgrid

From edshelf.com , “Flipgrid is an active, social learning platform that engages learners through video-based discussion. The app extends the web-based environment and creates new possibilities for reflection, discussion, demonstration and collaboration.” Instructors create a “grid” with a topic, and create a short (2.5 min or less) video prompt to share with the class.  Then the students respond with their own videos!  Students may reply to other videos with their own videos (90 seconds or less).

Use cases for Flipgrid include Introduction or Ice Breaker videos for online classes, or weekly discussions around readings or current events.  The downside of Flipgrid is that it is free to use, but you may only create 1 grid in a class (with unlimited Topics and responses) with a Free account- so if you teach more than one class at a time that you’d like to use Flipgrid in, you can purchase an upgrade if desired.  Flipgrid integrates seamlessly into Canvas and has mobile apps as well.  To try it in your Canvas course, just go to Settings > Apps in your course site, and search for Flipgrid.

TL;DR Flipgrid is a quick, fun, video recording collaboration tool Cost: Free, limited functionality (with ability to upgrade) Integrates into Canvas seamlessly

More about Flipgrid Info about Flipgrid (official site) Flipgrid teaching tips and reviews

Piazza is a free, easy to use Q&A discussion platform that can be used as an alternative to the native Canvas Discussions tool.  Some of the differences between Piazza and Canvas’ Discussion board is that the discussions are more like a traditional online forum, and as a bonus- are filterable and searchable!  Comments occur in real time, so students can leave their browser open and see answers appear on the screen.  Students also have the option to remain anonymous to their peers, which relieves some of the intimidation of ‘speaking in front of the class.’ Instructors have the ability to endorse correct answers to help steer the class in the right direction.

Piazza integrates directly into Canvas and at WPI is already added to your course (it’s just hidden by default)!  For WPI faculty, all you need to do is go to your course Settings area, then click on the Navigation tab at the top of the page.  Locate the Piazza link under “Drag items here to hide them from students” and click and drag it to the top of the page to show it in your left-hand navigation. Don’t forget to click Save.

TL;DR Piazza is a Q&A style discussion board that allows anonymous posting Cost: Free Integrates into Canvas (WPI faculty, check your Settings > Navigation area to enable it)

More about Piazza About Piazza Piazza Support

5.  Feed the Me

Feed the Me is an open source, free, news feed aggregator that you can integrate into your Canvas course.

From Feed the Me’s description in the EduAppCenter: “Feed The Me lets teachers aggregate a number of news feeds (Atom or RSS), filtered by tags, within the course environment. For example, this might be relevant blogs or news feeds from external sources, or perhaps a collection of student-produced blogs.  Teachers can allow Students to add their own news feeds to the course feeds list, and can even submit a feed to fulfill an assignment requirement.”

To add this app, you’ll need a Twitter account in order to generate a key and secret.  Make sure you save that information, because you’ll enter it to configure the app in Canvas.  To configure, go to Settings > Apps and enter the key and secret when prompted.  Don’t worry- you can enter a custom name for the app, you don’t need to see a confusing “Feed the Me” link in your class.  I called mine something boring like “NewsFeeds.”

TL;DR Feed the Me is a newsfeed aggregator for your class. It’s open source, free to use, and integrates directly into Canvas. You can allow students to contribute their own feeds!

More about Feed the Me About Feed the Me Feed the Me LTI Page

Honorable mentions worth a closer look:

Perusall – a social, collaborative annotation tool integrated into Canvas Prulu – a Q & A discussion board integrated into Canvas Inoreader – another RSS feed widget with multiple viewing options

Got any cool free apps that you are using in your course from the EduAppCenter that you want to let us know about? Feel free to comment below or email us. Want to learn more about these? Reach out to the ATC-TTL team at [email protected] .

• Whole Home Solutions
• Color, Style, & Fabrics
• Residential Applications
• Right Environment
• Human Centric Lighting
• Tunable White & Color Control
• Smart Buildings
• Color, Style & Fabrics
• Service Overview
• Market Segments Market Segments
• Case Studies
• Dimmers & Switches
• Fan Controls
• In-wall Sensors
• LED+ Dimmers
• Wallplates & Accessories
• Commercial Lighting Overview
• Code Smart Guestroom System
• Contract Roller
• Hyperion Solar-adaptive Shading
• Ketra Lighting
• Finiré Downlights
• Lumaris Tape Light
• LED Upgrades
• Vive Fixture Control
• Service Offerings
• Technology Support Plan
• Replacement & Upgrade
• Service FAQs
• Technical Documentation & Support Overview
• Specification Guides
• Product Specification Submittals
• Performance Specifications
• Installation Instructions
• Wiring Diagrams

CAD Downloads

• Revit Downloads
• Engraving Sheets
• Product Customization Forms
• UL Conditions of Acceptability
• Technical Papers

Application Notes

Technical Reference Guides

• Design & Configuration Software
• Product Selection Tools
• User Guides & Videos
• Technical FAQs
• Legacy Products
• Customer Support
• Serena Shades
• Not Sure Who to Contact?
• Dimming Basics
• How to install a dimmer
• Quick & Easy Troubleshooting
• What is Light Control?
• Energy Efficiency
• LED Center of Excellence
• Technologies
• Glossary of Terms
• Codes & Standards, US & Canada
• Commercial Application Guides
• Energy Saving Strategies
• Energy Benchmarking
• Continuing Education (CEU)
• North America Locations
• Lutron Worldwide
• The Lutron Experience Center
• Media & Press Center
• International Contact Information
• Provide Site Feedback
• Register or Login to myLutron
• United States | English (US)
• Where to Buy

How can we help you today?

Product Selection

FAQs Documents

Troubleshooting

Popular Topics

• Cleaning Recommendations for Lutron Products
• Help wiring your dimmer
• All your 0-10V questions answered
• Find the correct LED bulb or LED Dimmer

For the most uncompromising home integration projects. Equip yourself and your team of technology craftspeople with the ultimate in design freedom, innovative technology, and reliable quality. Push against the limits of what’s possible with the Lutron HomeWorks home automation system.

Design Freedom

Every project is different. Equip your team with the freedom to design, customize, and integrate a solution tailored to the unique demands of each project.

Reliable Quality

What’s the opposite of planned obsolescence? That’s what HomeWorks is. Build each system to be a durable part of the home with components that Lutron end-of-line tests and backs with an extensive warranty.

Innovative Technology

Innovation is more than new for new’s sake—it has to deliver real value. HomeWorks lets your team enrich and simplify your clients’ lives with Lutron’s most advanced and customizable technology.

Download the Luxury Experience App

The Lutron Luxury Experience App brings the showroom to your iPad. Guide clients on an immersive, virtual journey where they can interact with Lutron products—and visualize designs in their homes. Available now for iPadOS 16.4 or later.

Only with HomeWorks. We designed and engineered the Lutron Intelligent Light Portfolio from the ground up, authoring dozens of patents and industry firsts to redefine how light in the home should feel.

Precise, whisper-quiet, natural-light control. Lutron Shading solutions bring low-voltage and battery-powered glare reduction, UV protection, and privacy control to new and existing homes.

Powerful simplicity. Elevate the home’s design and simplify system interactions with a line of custom-engraved, HomeWorks-exclusive switches, remotes, and keypads.

Integrations

Security, climate control, A/V, home automation, voice—with Lutron’s LEAP API, third-party integrations have never been more responsive, reliable, or secure.

Lutron Connect

Unified teams equals extraordinary results. Accelerate your business and deliver industry-defining client experiences with a breakthrough platform of cloud-connected hardware and software. Lutron Connect streamlines, synchronizes, and simplifies work, establishing the new foundation for future Lutron innovations. 

Streamlined Workflow

Simplify the design, commissioning, and maintenance of a project with cloud-connected tools. 

Quick Integration

Save time with responsive, reliable, and secure 3rd-party integrations via the LEAP API.

Cloud-Synced Collaboration

Work with confidence and keep the whole team in sync with real-time project updates, tracked file versions, and automatic backups.

Over-The-Air Updates

Eliminate downtime for your clients and future-proof connected systems by delivering pain-free system enhancements.

HomeWorks System Options

Keypad, Dimmer, Switch, Fan Control and Companion

Dimmer, Switch, Fan Control, and Companion

Dynamic spectrum illumination

High performance downlight supporting both warm dimming and white tuning.

Static white lighting with warm-dimming option

High performance tape lighting supporting both warm dimming and white tuning.

HomeWorks Resources

Specification Documents

Installation Guides

Need a Rep?

Find a sales rep to help create, design, and deliver a complete solution for your workplace.

Have a question?

Let us help you choose the right solution for your job.

Advertisement

Beyond Plug and Chug: an Analysis of Calculus I Homework

• Published: 11 July 2015
• Volume 1 , pages 268–287, ( 2015 )

Cite this article

• Jessica Ellis 1 ,
• Kady Hanson 2 ,
• Gina Nuñez 2 &
• Chris Rasmussen 2  

3284 Accesses

19 Citations

2 Altmetric

Explore all metrics

We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that arose as important: structure, content, and feedback. Selected universities employed more varied homework structure, included more content emphasizing skills as well as solving novel problems, and provided higher amounts of and frequency of feedback to students. Students felt positively towards conceptually driven homework, but their feelings were mixed or negative regarding the logistical aspects of online and group homework assignments. We draw on Herbst and Chazan’s ( ZDM – The International Journal on Mathematics Education, 44 (5), 601–612, 2012 ) adaptation of the instructional triangle and Brousseau’s ( 1997 ) notion of the didactical contract to make sense of how homework is understood as an instructional resource by instructors and by students.

Similar content being viewed by others

Mathematics Homework

Designing for Learning: Key Decisions for an Open Online Math Tutor for Elementary Students

Examining the Pedagogical Approaches in Five Curriculum Programs

Avoid common mistakes on your manuscript.

Homework is an important part of how students develop fluency with the ideas and techniques in mathematics in general, and in calculus in particular. This is especially true at the undergraduate level, where the expectation is that students spend considerable time outside of class working on homework and studying course material. For example, Rasmussen and Ellis ( 2013 ) found that post-secondary science, technology, engineering, and mathematics (STEM) intending students in the United States (US) reported spending approximately six h a week preparing (studying, reading, and doing homework or lab work) for Calculus I, a course with typically four contact hours per week. The time undergraduate students spend outside of class is an important venue to grapple with the material and interact with the content. In this study, we investigate the relationship between the nature of Calculus I homework at five PhD-granting universities identified as having a more successful Calculus I program than comparable universities.

The Calculus I programs at the five universities were selected as part of a large, US national study at over 500 institutions, including Associates-granting 2-year colleges, Bachelors-granting 4-year colleges, Masters-granting universities, and PhD-granting universities (as determined by the highest degree offered in mathematics). These five sites were selected because students at these universities were more successful in Calculus I when compared to students at comparable universities when controlling for student background and other factors. Student success variables included increased confidence, interest, and enjoyment of mathematics, grade in Calculus I, and persistence to Calculus II. This project enabled us to ask the following questions that shed light on how homework is related to student success in Calculus I:

What characterizes the nature of homework at the selected PhD-granting universities with demonstrated successful Calculus I programs?

What differentiates the nature of Calculus I homework at selected and non-selected PhD-granting universities?

As detailed in the methods section, we answer the first research question by analyzing student focus group interviews that were conducted as part of the case studies at the five selected universities. These universities were selected for case studies because the survey results indicated that their students retained confidence, enjoyment, and interest in mathematics more than comparable universities involved in the survey. To answer our second research question, we draw on the large-scale survey data to compare the nature of homework at selected universities to non-selected PhD-granting universities. We complement the quantitative analysis with illustrative findings from the student focus group interviews at the selected universities. These interviews shed light on students’ accounts of the role of homework on their success. This study contributes to the literature examining the role of mathematics homework in students’ learning and success, further extends a theoretical lens in which to view the role of homework, and offers pragmatic insights for other institutions into the nature of homework systems of successful calculus programs.

Theoretical Background

We draw on Herbst and Chazan’s ( 2012 ) elaboration of the instructional triangle (Cohen et al. 2003 ) to understand the nature of homework within the broader context of instruction. This theoretical tool employs the concepts of didactical contract and milieu (Brousseau 1997 ) to describe the interactions between teachers, students, and knowledge at stake through instruction (see Fig.  1 ). The knowledge at stake is used by Herbst and Chazan synonymously with content, and refers to the potential mathematical knowledge one might learn through instruction. In this context, the milieu is “a counterpart environment that provides feedback on the actions of the students” (Herbst and Chazan 2012 , p. 607). Included within the milieu are the goals for students and the resources available to students while working on tasks. The teacher is responsible for maintaining harmony between the milieu and the students by ensuring proper functioning of the milieu, shown in Fig.  1 by the arrow from the teacher’s component to the milieu within the student subsystem.

Instructional Triangle adapted by Herbst and Chazan ( 2012 ) describing the interactions between the teacher, knowledge at stake (content), students, and milieu around the completion of tasks

Herbst and Chazan ( 2012 ) argue that successful instruction occurs when all aspects of this system work together. They employ the notion of didactical contract (Brousseau 1997 ) to understand the ways in which teachers, students, and the knowledge at stake (content) are bound to each other and the environment through predominantly implicit responsibilities. To satisfy the didactical contract teachers are responsible for students’ development of the knowledge and students are responsible for partaking in the tasks needed to construct the knowledge.

Differences in the didactical contract exist between education at the K-12 level and education at the undergraduate level. At the K-12 level teachers tend to guide students through the development of knowledge with tasks largely completed in class. At the undergraduate level, however, there is a shift in the didactical contract and students are expected to construct knowledge outside of the classroom after being presented the material during lecture. This shift in the didactical contract at the undergraduate level places a heightened importance on resources, such as homework, that can support the construction of knowledge. At this level, homework becomes a vehicle used by instructors to provide students with the practice needed for developing understanding, but leaves much of the responsibility of the construction of knowledge to the student. Therefore, studying the nature of homework at the undergraduate level can aid in the understanding of student success and the interactions that come into play between the instructor, the student, and the content.

Herbst and Chazan’s ( 2012 ) elaboration on the instructional triangle and the didactical contract (Brousseau 1997 ) allow us to view homework assignments as an important part of the milieu for the Calculus I course. This particular perspective provides a lens in which homework is examined as part of a system that directly interacts with teachers, students, and content to support instruction and student success.

Literature Review

Studies of the role of homework span several decades and have demonstrated the potential positive influence homework can have on student learning as well as on student confidence (Black and Wiliam 1998 ; Cartledge and Sasser 1981 ; Halcrow and Dunnigan 2012 ; Kitsantas et al. 2011 ; Lenz 2010 ; Morrel 2007 ; White and Mesa 2014 ; Young et al. 2011 ). Our review of these studies suggests that these positive influences are often implicitly dependent on aspects of the instructional environment and the interactions that take place between the teacher, student, and content within the instructional environment.

Research relating student learning to homework indicates that the mode of delivery of the homework is less important than the content of the homework itself and how it may serve as a form of formative assessment for the student. For instance, Lenz ( 2010 ) found no significant difference in student learning whether students were assigned online based homework or traditional paper-based homework with similar content. From our perspective, this indicates that variation in the milieu and homework structure may exist if the teacher interacts accordingly with the knowledge at stake and creates tasks that students may successfully interact with when constructing knowledge. In other research, Young et al. ( 2011 ) studied how modifying content to include an application rich treatment of Calculus I and Calculus II related to students’ success in these courses by assessing the mathematical knowledge developed through pre and post exams on six different calculus topics. Students in the experimental group took a one-credit course in tandem with their Calculus I and Calculus II courses that was solely dedicated to the applications of the content from each course in an attempt to create deeper understanding and increase student success. Young and colleagues found that students eventually benefited from the introduction of applications, but the benefit was not realized until the students were in Calculus II, as reflected by the scores on the pre and post exams. This study highlights the connections between the knowledge at stake and student success both within the immediate classroom environment, as well as in subsequent courses.

A number of researchers have connected specific aspects of either written homework or online homework to students’ affect toward mathematics. For example, Morrel ( 2007 ) investigated the effects of written homework on her Calculus I students’ confidence. The content of these assignments focused on arguments and explanations, and involved many multi-step and/or context-free problems. She asserted that these assignments encouraged students to interact with the content at a deeper level by gaining skills in communicating and writing about mathematics. She argued that the written homework specifically contributed to students’ confidence by encouraging them to tackle cognitively difficult problems. Further, she noted that including cognitively demanding written homework allowed students who had seen calculus before to remain interested. This is an especially applicable benefit for Calculus I, as approximately two-thirds of US students enrolled in post-secondary mainstream Calculus I have previously taken a calculus class at the secondary level (Bressoud et al. 2013 ).

Halcrow and Dunnigan ( 2012 ) also reported an increase in students’ confidence when they looked at the benefits of online homework, and argued that online homework provided additional opportunities for students to think about and practice mathematics outside of the immediate classroom environment. The authors attributed the gain in students’ confidence to students’ ability to attempt problems multiple times and to receive immediate feedback. This finding illustrates how online homework can contribute to a milieu in which more practice and resources, such as immediate feedback or hints, are available to students while completing assignments that ultimately can increase students’ construction of knowledge and success in the course. These resources position online homework as an assessment with both formative and summative purposes. In many instructional environments, summative assessments are unavoidable, especially in high enrollment undergraduate courses with multiple sections. However, incorporating feedback (both immediate feedback for online homework and written feedback) turns these assessments into tools to improve learning in the short term while retaining the purpose of measuring the students’ current understanding (Black and Wiliam 1998 ).

White and Mesa ( 2014 ) further investigated the specific content of homework problems (in addition to in-class problems and exam problems) at a community college Footnote 1 that had demonstrated a higher than expected level of student success in Calculus I. They found that instructors at this more successful institution assigned more problems that required students to learn more cognitively demanding skills, but that instructors varied on the amount of rich tasks and complex procedure problems they assigned.

The previous studies point to various ways in which homework has been related to student success and illustrates the importance of interactions between the teacher, content, and student when constructing and completing the assignments. Specifically, this body of research indicates that the content of homework is especially important, and that there are aspects of both written and online homework that have been connected to student success. Our study contributes to this literature by exploring the nature of homework assignments at selected universities that were identified as having a successful Calculus I program. We ground this exploration within the perspective of the instructional triangle as adapted by Herbst and Chazan ( 2012 ), which allows us to understand and focus on relationships between the aspects of homework as part of a system involving content, students, and the teacher.

To answer our research questions we conducted a mixed method analysis on data from a large, national study focused on successful calculus programs in the US, the Characteristics of Successful Programs in College Calculus (CSPCC) project. Footnote 2 The CSPCC project study involved over 500 institutions, including AS-granting 2-year colleges, BA-granting 4-year colleges, MA-granting universities, and PhD-granting universities (as determined by the highest degree offered in mathematics) (Bressoud et al. 2013 ). For this report we focus on the PhD-granting universities because it is these institutions that are contributing the most STEM graduates to the workforce (Blair et al. 2012 ) and hence understanding the features of these institutions is of national importance. Further, by focusing on one institution type rather than analyzing data from all institution types we are able to remove this contextual variable. Future analyses should be conducted to situate how our findings about homework at the PhD-granting universities relate to the homework systems of other institution types.

The larger CSPCC study consisted of two phases, the first of which was a survey given to Calculus I students and their instructors at the beginning and end of the fall term. The goal of this phase was to identify institutions with more successful Calculus I programs, as well as to learn more about the landscape of Calculus I in the US. The second phase of this study included explanatory case studies at five PhD-granting universities. These universities were selected because the responses to our surveys indicated that they had more successful Calculus I programs (compared to counterpart universities while controlling for student background and other factors) as measured by increased student confidence, enjoyment, and interest in mathematics, Calculus I grade, and persistence onto Calculus II (Sonnert and Sadler 2015 ).

The goal of the second phase was to identify characteristics of the different Calculus I programs identified as having a relatively more successful Calculus I program. During case study site visits we interviewed students, instructors, and administrators, observed classes and recitation sections, and collected any relevant documents, such as homework and exams. Due to the design of this study, no such data is available from the non-selected universities.

The five selected universities varied in characteristics related to institution type, enrollment, the structure and class size of Calculus I sections, and the type of faculty employed to teach Calculus I. These five universities included private, public, technical, small (less than 20,000 undergraduate population) and large (more than 20,000 undergraduate population) universities. The enrollment of undergraduate students ranged from approximately 3000 to over 25,000. Also important to note was that the structure of the Calculus I course and class size varied. Three of the universities convened small class sizes of about 30 students, while the others had large lecture sections of about 200 students accompanied by smaller recitation sections. Additionally, two of these universities used the Hughes-Hallett et al. ( 2009 ) textbook in all Calculus I classes, and the others used Stewart ( 2007 ), Rogawski ( 2011 ), and Edwards and Penney ( 1998 ). For an analysis of the content covered among these five universities see Johnson et al. ( 2014 ). The diversity of institution size and population and class size enables us to comment on what is similar and different regarding homework across the different institutions.

Data Collection and Analysis

We draw on both quantitative survey data and the qualitative case study data from the CSPCC study. Specifically, end-of-term survey data from 2000 students and 204 instructors were analyzed as well as student focus group interviews at the five case study sites. Of the 2000 students, 580 came from a selected case study universities. There were 204 instructors who completed the end of term survey, 46 of which came from a selected university. A multiphase mixed methods approach was taken to analyze the quantitative and qualitative data (Creswell 2002 ). In particular, the case study data from the selected universities were first used to understand the nature of the homework assignments implemented at each of the case study sites. Subsequently, descriptive analyses were conducted on both student and instructor responses to understand the nature of the homework at selected and non-selected universities. Homework and exam problems pertaining to related rates from the five selected universities were also examined in order to better understand the nature of the problems assigned at these institutions within a specific mathematical context. Additional case study data (including class documents, instructor interviews, and classroom observations) from the selected universities were then used to triangulate findings.

In examining the case study data we conducted inductive thematic analysis on focus group interviews. Thematic analysis is a qualitative approach that involves “identifying, analyzing and reporting patterns (themes) within data. It minimally organizes and describes the data set in rich detail. However, frequently it goes further than this, and interprets various aspects of the research topic” (Braun and Clarke 2006 , p.79). Inductive thematic analysis is a bottom-up approach where the themes are data-driven, though are not developed in an epistemological vacuum. Thus, these themes emerged from the data, but were also informed by our reading of the relevant literature and our previous experiences with the data.

We conducted a total of 12 student focus groups across the five case study universities. After coding the interview transcripts for excerpts related to homework, we distinguished between factual references to homework and personal reflections on homework. Fifty of the 68 excerpts were of the latter type. We then conducted a more fine-grained analysis on these excerpts, resulting in 10 codes that captured positive and negative statements about an aspect of homework. These 10 codes were then grouped according to three themes: structure, content, and feedback. Following this thematic analysis, we conducted descriptive quantitative analysis on the student and instructor survey data. More specifically, we conducted t-tests and Chi-squared analyses to compare responses from instructors at the five selected case study universities ( N  ~ 158) and their students ( N  ~ 1410) to instructors from all other PhD-granting universities (referred to as the non-selected universities) ( N  ~ 46) and their students ( N  ~ 590). These comparative analyses enabled us to explore the relationships between the aspects identified in answering the first research question to student success in a quantitative manner. In our presentation of these quantitative results, we provide examples of related excerpts from interviews with students regarding the various aspects of the nature of homework identified in answering the first research question. These excerpts were selected as vivid, representative, and compelling examples of each theme. As previously mentioned, due to the design of the CSPCC study, no such data is available from the non-selected universities.

While we make no causal claims, the five case study universities were selected due to higher student success compared to comparable universities, where student success was measured by increased student confidence, enjoyment, and interest in mathematics, Calculus I grade, and persistence onto Calculus II. Thus, in comparing selected universities to non-selected universities, we can begin to connect specific aspects of the nature of homework to specific aspects of student success in Calculus I. Further studies are needed to more clearly explore the relationships we identify.

To begin we present the results of our first research question by characterizing the nature of homework at the selected PhD-granting universities with demonstrated successful Calculus I programs. We then address our second research question by first quantitatively comparing the nature of homework at selected universities to non-selected universities. Lastly, we complement and triangulate these quantitative comparisons with qualitative analyses of student focus group interviews and collected classroom data, including observations and assigned homework.

The Nature of the Homework at Selected Universities

The inductive thematic analysis of the case study data resulted in the creation of 10 codes, each with possible positive and negative expressions, as shown in Table  1 . Through thematic analysis, these 10 codes were grouped into three salient features related to the nature of homework: structure, content, and feedback. Structure refers to the format and delivery mode of the homework: the frequency with which it was assigned, how much homework was assigned, the level of coordination across instructors, whether it was online or written, and whether it was group or individual. Content refers to the nature of the problems or tasks on the homework, whether they emphasize or assess procedural or conceptual knowledge. We draw on Hiebert and Lefevre’s ( 1986 ) definitions of procedural and conceptual knowledge, where procedural knowledge is understood as fluency with symbols, rules, algorithms, and procedures and conceptual knowledge is characterized as “knowledge that is rich in relationships” (p. 4). Feedback refers to dialogue between the instructor and the student (potentially via automated online homework response systems) that informs the student about the quality of his or her work. Black and Wiliam ( 1998 ) argue that to be considered feedback the goal of this dialogue must be to improve learning and thus feedback is viewed as a defining component of formative assessments. Moreover, while grades have a summative aspect, they can also be formative in so much that they function to improve learning. We refer to these three components (structure, content, and feedback) as a homework system.

After identifying the three main themes of a homework system, we then used these themes to compare the homework systems at each of the five selected universities. This comparison is shown in Fig.  2 , where the rows indicate each institution and the columns specify the extent to which particular aspects of the structure, content, and feedback are uniform across instructors. The system of coordination (or uniformity across sections) was identified as a key feature of selected successful programs in a related study (Rasmussen and Ellis 2015 ). We use a dotted circle or a completely filled in circle to indicate that a particular aspect exists, where a dotted circle indicates that only some instructors implemented this aspect, and a completely filled in circle indicates that this component is implemented uniformly across all instructors.

Homework systems at selected universities

For example, Private Technical University (PTU) had an online procedural component that every Calculus I instructor assigned, as indicated by the solid circles in the online column under structure and the procedural column under content. Along with the uniform component, we also saw that some individual instructors at PTU assigned additional written conceptual homework, as indicated by the circles with several dots in the written column under structure and the conceptual column under content. There were no instructors at PTU that assigned group homework or gave a homework quiz, represented by an empty circle in the group column under structure and the HW quiz column under feedback.

In addition to illustrating the homework systems at PhD-granting universities with successful Calculus I programs, Fig.  2 highlights the commonalities among the homework systems. All universities incorporated a combination of procedural and conceptual problem solving in their assignments, and all provided some form of feedback to the students. However, the structure of the different homework components, whether it be written, online, or how they gave feedback, varied among the five selected universities.

Using Brousseau’s ( 1997 ) language, the homework system (structure, content, and feedback) functions as an important component of the milieu in which students interact with the mathematics. The homework system allows students to complete tasks, receive feedback, and avail themselves of certain resources to complete the tasks. For example, a homework system may create an environment where students can receive instant feedback by completing online homework and have access to resources such as hints provided by the online homework provider. Viewing the homework system as an important component of the milieu allows us to focus on the interactions between the homework system, the teacher, and the knowledge at stake for the course as well as the external environment that the interactions take place within.

We next direct our attention to how the homework systems vary across the five selected universities. Understanding different homework systems provides insight into how instruction can affect student success. We draw on the instructional triangle used by Herbst and Chazan ( 2012 ) to understand how the interactions between students, the teacher, and the content relate to instruction, and further to student success. Within this environment we view the teacher as anyone in a position to alter or create the homework system. This may include the course instructor, as well as recitation leader, or Course Coordinator. We view the knowledge at stake as the mathematical content covered within the course that is specified in the syllabus, textbook, or course objectives. In Herbst and Chazan’s ( 2012 ) elaboration of the instructional triangle, they discuss the milieu as a “counterpart environment that provides feedback to the student” and includes the goals students are working towards and the resources with which the students are operating (p. 607). While homework systems may be viewed as a resource to students, they can also be viewed as something beyond a resource, especially within the undergraduate context. The homework system is an especially important component of the milieu within the undergraduate mathematical environment, necessitated by the shifted didactical contract. Students are expected to spend more time struggling with the material and constructing their own knowledge outside of class, and the structure, content, and feedback of the homework are important components of how students do these things.

We focus on the relationships that exist between the homework system (as part of the milieu), the teacher, and the knowledge at stake, which all function within the larger environment of the department and institution. For example, the teacher uses the knowledge at stake to alter and create the homework system. The teacher is responsible for choosing the method of homework whether it is online or written based. Additionally, she decides what aspects of content to emphasize through the problems assigned and what content to cover throughout the course. As the students complete the homework, both the student and the teacher receive feedback, which affects future instruction. The teacher can look at the students’ progress and accuracy of the homework and assess the students’ learning of that certain topic and respond by altering lesson plans or changing the pace of the course, therefore changing the homework system. The students are also provided feedback from the teacher when their homework is returned in the form of a grade and/or receive written comments about certain problems. Students can also be given feedback within the homework system through the online program marking the problems correct or incorrect. Depending on the institution and corresponding homework system, these relationships exist to varying degrees.

Differences Between Selected vs. Non-selected Universities

After identifying the salient features of the homework systems at selected universities through the thematic analysis of the case study data, we investigated how the homework systems at non-selected universities compared to the selected universities by drawing on the survey data. In the following sections, we compare the responses from students or instructors at the selected universities to those at the non-selected universities along each of the three components of a homework system. We complement these descriptive analyses with illustrative and representative quotations from interviews with students at the selected universities.

Through the qualitative analyses, we attended to the mode of delivery of the homework as the key component of structure (online, written, and/or group). In the quantitative analyses, we also have reports of how often homework was assigned and/or collected. As shown in Table  2 , there were significant differences between student reports of the structure of homework at selected versus non-selected universities. Compared to students at non-selected universities, (a) students at selected universities report that assignments were assigned and collected more frequently, (b) that group projects were assigned more frequently, and (c) that online homework was more likely to be used to complete homework assignments.

These findings indicate that students at selected universities are being offered more opportunities to interact with the knowledge at stake and are often being held more accountable for practicing the course material outside of the classroom. Thus, these homework systems have developed in accordance to an altered didactical contract, where the students are expected to spend more time outside of class working with the material, but also are provided supports in order to succeed when doing so. Students at selected universities also indicated a higher use of online homework, which contributes to a greater amount of instant feedback within the milieu of the homework system. As discussed by Halcrow and Dunnigan ( 2012 ), the greater the amount of time spent outside of class thinking and practicing the material as well as the ability to gain instant feedback and persist in a problem until the correct solution is found reflected an increase in students’ confidence. Therefore, the increased existence of homework and feedback provided at selected universities appears to provide the practice and guidance needed for students to gain confidence in mathematics and may have an indirect affect on their increased persistence to Calculus II.

During the focus group interviews, students at selected universities often reflected on the structure of the homework. Seventy-four percent of 50 reflective student comments were related to structure, and 62 % of these were positive statements. The most commonly discussed aspect of structure was online homework, followed closely by group homework, and then the existence of homework. The negative statements regarding online homework were almost uniformly about the logistics of entering solutions into the online system. A few students also disliked the procedural nature of online homework. For instance, one student from LPU1 disliked the online homework because “it doesn’t really have a lot of application on it. It’s just cranking out formulas.” However, many students also had positive experiences with the online component, and appreciated the ability to try a problem multiple times until they got it correct.

The negative statements regarding group homework were also logistically oriented, citing the difficulty of finding a time when all group members could meet and the high expectations relating to the presentation of the homework and the content. Students appreciated that the group homework exposed them to “how different students answer the problems in different ways…Different ways to help you learn the problems better”, and that the group homework offers “another way to do math outside of class” that is “really interactive and if you don’t understand it someone else is going to teach you how to do it.”

Students also made statements (100 % positive) regarding the existence of homework, and how it helped them stay on top of the material and gave them multiple entry points into the content.

LEPU Student: Throughout the entire week we have to at least think about calculus, at least once a day. So it’s not like a lot of workload, so it’s still really manageable, it’s just it’s always there so I feel like that helps. LPrU Student: I would say probably I learn more when I’m doing my homework when, because he’ll do a couple of examples but then there’s so many more still. Then there’s a broader range of them in the homework, so base what you learn in class and like you realize you’re going to use the same steps, but you really have to think about what, I don’t know. You have to think differently every time.

The student statements help to illustrate why some specific structures of homework systems may lead to student success. The combination of having multiple opportunities to interact with the material with supports available allows students to benefit from the extra time they are spending outside of class grappling with the content.

The content of the homework can be thought of as a source of knowledge at stake for students to develop. The balance between procedures and concepts is often an issue for instructors, both in terms of what is valued and what one has time for (Johnson et al. 2014 ). All five of the selected universities assigned both procedural and conceptual questions on their homework. Interestingly, we do not find the same balance at non-selected universities. Table  3 shows that students at selected universities reported having to explain their thinking more on homework problems and were assigned more word problems than students at non-selected universities. Table  3 also shows that instructors reported assigning more homework that focused on graphical interpretation, complex or unfamiliar word problems, and proofs or justifications than instructors at non-selected institutions.

Table  3 also shows that instructors at both selected and non-selected universities report that they assigned homework involving standard word problems. Selected universities assigned standard word problems that were complemented by complex or unfamiliar word problems more so than non-selected universities. White and Mesa ( 2014 ) also found this to be true when they studied the types of assignments at one of the selected AS-granting 2-year colleges. They saw instructors at this one selected institution overall assigning simple procedure problems 54 % of the time, having the rest of the problems either be complex procedure problems or rich tasks.

In order to understand more concretely and triangulate findings about the content of assessments at selected universities we looked in detail at all problems involving related rates that were part of assignments collected during the case study. We chose related rates over a different content area (such the chain rule) because this topic can be rich in content, often presents challenges for students, and allows for both a more conceptual or more procedural treatment (Cartledge and Sasser 1981 ; Martin 2000 ; Piccolo and Code 2013 ). Our goal in looking to the actual problems assigned at the selected universities was to understand how reported emphasis in the content was manifested in actual problems.

The ladder problem is a very common word problem involving related rates, and we saw versions of this classic problem assigned or discussed during the case study visits at multiple selected universities:

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft per second, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?

Along with the standard ladder problem, instructors at selected universities also assigned more complex related rates word problems that allowed students to apply the concepts they learned in the ladder problem to a novel, more complicated problem, such as the following:

The lookout on board a ship spots an unknown ship on the open seas and immediately alerts Chris, the ship’s captain. The unknown ship is currently 4 miles south and 3 miles east of Captain Chris’s ship, and it is at that moment sailing due west at 20 mph. Captain Chris’s ship, meanwhile, is at that moment sailing due north at 16 mph. (a) Is the distance between Captain Chris’s ship and the unknown ship increasing or decreasing? How fast? (Distance is measured along a straight line joining the two ships.) (b) How does your answer change if Captain Chris’s ship is going 14 mph instead of 16 mph?

The students at the selected universities spoke about their assignments as being challenging and more than the routine “plug-and-chug” problems they had seen in previous mathematics courses. None of the students overtly discussed the procedural nature of the content, except when in comparison to the conceptual problems. In these cases, the statements were coded as predominantly about the conceptual problems. For instance, one student from LPrU noted that his experience with mathematics in high school was about applying algorithms, while in his current Calculus I course he was expected to “think- it’s much deeper.”

LPrU student: Well because generally for me math has always been nice because it’s very like, you see this situation, ‘apply this, get this answer.’ Then all of a sudden with a proof, you have to like think all of a sudden. It’s not something I’ve been trained to do in high school, was to like actually have to think and break down and say, ‘Theorem 1, theorem 2 and theorem 3 make theorem 1 become theorem 3. And then also you can use theorem 2.’ You have to think, it’s like much more deeper.

In addition to working on more novel and/or complex problems, the content of the homework at selected universities went beyond students’ previous experiences with mathematics homework in other ways. As seen in Table  3 , many students were asked to explain their thinking on their homework, which was not something many students were accustomed to.

LPU2 student: And she asks that, with each problem we write a little explanation of what we did. So if we say we took the derivative and set it equal to zero to solve for a max or a min, she wants us to explain how and why we did it that way. So it’s more than just the plug-and-chug.

Some of the students expressed that being challenged and being able to complete the assignments successfully increased their expectations of the kinds of problems they were capable of completing and understanding in mathematics.

LPU2 student: I think it’s increased [my confidence], because like I’ll look and sometimes I’ll look at a problem and be like holy [moly], I have no idea what I’m doing here, but then once I can figure, actually figure out what I’m doing, it’s like ‘wow I was able to do that’. I just had to look at it in a different way to figure it out, so it kind of boosts your expectation of what you can do next.

Only one student mentioned that she did not like the conceptual nature of the homework, because the conceptual problems “are definitely kind of a pain on the homework” but she did appreciate working on them with her teaching assistant during recitation.

Feedback on homework emerged as a salient feature of the homework systems at selected universities. The feedback given on the homework is a critical way the teacher can interact with the student and the student can interact with the content. When giving feedback, especially at the undergraduate level, it is implicitly understood as part of the didactical contract that students will use this feedback to ask and answer questions such as “Where am I going? Where am I now?; and How can I get there from here?” (Stiggins and Chappuis 2005 , p. 4).

Students were asked to report on a number of aspects of the nature of the feedback on their homework, both written and online. As shown in Table  4 , students from selected universities report that their assignments are more frequently completed and graded online and are more frequently returned with helpful feedback/comments. These results indicate that students from selected universities receive more feedback on both online and written homework than students at non-selected universities.

During the site visits at the selected universities, we identified seven statements about feedback on homework, with six of these being negative. One thing that students liked about online homework was the ability to know right away if their response was correct. However, some students were frustrated that they were “not really getting feedback. It’s just right or wrong.” For some students, this was an indicator to seek additional help to understand what they got wrong.

PTU student: With [the online homework] you immediately know if you’re wrong, and sometimes you can look up a hint to see what you’re doing wrong. So that will help if you don’t understand a certain tool, you can definitely look it up and understand better, especially if you’re doing it wrong, you don’t want to keep doing it wrong.

One instructor at PTU saw this as a chance to take advantage of students working together in the dormitories and viewed their online homework as an extra resource for studying, as opposed to solely a venue for assessment.

PTU instructor : But yet on the other hand, with this [online homework] stuff that we do, you know that there’s a group of students in a dorm right now… all doing their homework together. And I think as faculty what we have to do is just accept that is happening, so we have to structure our course in such a way where we can actually use that in a good way. We can say, ‘Let’s view it as this is their study time.’

The previous excerpt exemplifies the shift in the didactical contract between education at the K-12 level and education at the undergraduate level, and how the homework systems can be used to complement this shift. If undergraduate students are expected to spend more time constructing knowledge outside of class compared to during high school, then the nature of the homework must support them in doing so. One key component of this appears to be providing responsive feedback to students as they grapple with the material outside of the classroom, with or without their peers, complemented by providing resources to get additional support.

Taken together, the above findings point to a significant shift in the didactical contract surrounding who is responsible for grappling with difficult material and where this takes place. The homework systems at the selected universities manifest a response to this shift by (1) providing multiple opportunities for students to interact with the content outside of class, (2) providing feedback as a way for the teacher to interact with the students and the content while students work outside of class, and (3) expecting students to struggle with more complex content and explain their thinking related to this content. We posit that these features are one reason why students at the selected universities experienced an increase in their mathematical confidence, realizing that they are capable of succeeding with more difficult material.

In this report we investigated the nature of Calculus I homework at five PhD-granting universities identified as having more successful Calculus I programs compared to comparable institutions. We drew on case study site visits at these five universities in order to gain an understanding of characteristics of these programs that potentially contributed to their success. One such characteristic was the nature of homework. Based on our analysis of the case study data, we identified the content, the structure, and the feedback of the homework as salient aspects of the homework systems. In order to better understand how the nature of Calculus I homework may be related to student success, we (1) conducted comparative analyses of the reported content, structure, and feedback by students and instructors at selected versus non-selected universities, and (2) analyzed student focus group interviews from the case studies to better understand the connection between these aspects of homework and student success. By viewing these analyses through the lens of the instructional triangle (Herbst and Chazan 2012 ) and the didactical contract (Brousseau 1997 ), we situate the homework system within the broader context of the instructional environment. This allowed us to focus on how relationships between students, the instructor, and the content interact with the homework system, and how all of these interactions are governed by the didactical contract between the students and the instructor.

The quantitative analyses indicate that compared to non-selected universities, homework and group projects at selected universities were assigned more frequently, online homework systems were used more frequently, this homework was more frequently graded and returned with feedback, and the content focused on more novel, cognitively demanding tasks. Moreover, by analyzing the student focus groups, we see a much more nuanced relationship between specific aspects of Calculus I homework and increased student confidence in mathematics and persistence onto Calculus II. As we articulate next, these findings lead to a number of conjectures about the relationships between the nature of homework at selected universities and student success.

At the selected universities we saw that the online homework had two components that students felt contributed to their growth in confidence throughout the course. The students received instant feedback and were then given multiple or unlimited chances to complete the problems correctly. Halcrow and Dunnigan ( 2012 ) explain that there are high achievers who complete their homework and spend outside class time studying regardless of the rewards given by the instructor, but not all students can be classified as high achievers. They also found that both high achieving and low achieving students were more motivated to complete the homework when online homework was the main source of homework. We saw in our study that many students reported that they completed their online homework and used it as a study resource outside of class. They were able to complete many different problems multiple times, which motivated them to spend time outside of class going through the homework and receiving the feedback and using that to prepare for the next class or the next exam.

Both online and written homework contributed to students increase in confidence in mathematics and changed their perception of their ability to learn, which itself has likely affects on their persistence onto Calculus II (Ellis et al. 2014 ). Online homework, which allows students to attempt the problems multiple times, helped students gain confidence because it showed them that they could persist through a problem and eventually succeed and get the correct answer. Along with increasing their confidence in mathematics, students also changed their beliefs about their ability to learn. Dweck ( 2008 ) delineates between a fixed mind set and a growth mind set. A fixed mindset is characterized by a belief that there is not much one can do to affect their intelligence level, whereas a growth mindset is characterized by the belief that one’s intelligence can be significantly changed. Dweck found that mindsets can predict math/science achievement over time and interventions that change mindsets can boost achievement and reduce achievement discrepancies.

Students that may have entered the course with a fixed mindset were given multiple chances to correct their mistakes and see that they were capable of eventually getting the correct answer. This may have encouraged them from a fixed mindset, thinking they would never be able to solve the problems, to a growth mindset, where they believed they could practice until they succeeded.

At some of the selected universities, written homework was also implemented to provide students with more conceptual and application problems. Instructors believed that assigning written homework was important because of the types of problems the students had to work through, but because it also allowed students to practice organizing their work and explain their thinking. Morrel ( 2007 ) found that assigning written homework in his class benefited students in many ways, asserting that, “my students gain mathematical confidence by tackling these more difficult problems, and it keeps the class more interesting for those who had calculus in high school” (p. 383). We also found that at the selected universities, Calculus I students attributed their increase in confidence to their ability to work through difficult problems together and being able to explain their mathematical thinking.

These findings regarding the role that the homework system plays in student success in college calculus is embedded within a larger context. In our large national study, we identified seven features of calculus programs at PhD-granting universities as supporting student success. These seven features are: the collection (and use) of local data, support for teaching and active learning, graduate student teaching preparation, adaptive placement strategies, learning resources, coordination, and rigorous courses (Rasmussen et al. 2014 ). These seven features do not exist in isolation, but rather work together at the successful universities to create a successful calculus program. Homework systems are a component of rigorous courses, and thus cannot be thought of as the sole contributing factor to students’ success.

Our findings also provide evidence for the applicability of the instructional triangle at the undergraduate level. At the K-12 level, the majority of the interactions between student, teacher, and content occur within the classroom. However, at the undergraduate level, many of these interactions take place outside of the classroom. Thus, the homework system plays a heightened role in undergraduate mathematics because it acts as the milieu for these interactions to occur both inside and outside the classroom. Our findings also have direct implications for the classroom. As an undergraduate instructor, the homework system is an especially important resource for extending and furthering the learning that takes place during lecture. One must be purposeful about how to utilize online and/or written homework as a medium for students to practice skills and grapple with concepts, while providing feedback for the successful (and more enjoyable) development of both.

This institution was also part of the same larger national study from which this study draws.

For more information about the CSPCC project, see: www.maa.org/programs/faculty-and-departments/curriculum-development-resources/characteristics-of-successful-programs-in-college-calculus

Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment . London: King’s College.

Google Scholar  

Blair, R., Kirkman, E. E., & Maxwell, J. W. (2012). Statistical abstract of undergraduate programs in the mathematical sciences in the United States. Conference Board of the Mathematical Sciences. Providence, RI: American Mathematical Society.

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3 (2), 77–101. doi: 10.1191/1478088706qp063oa .

Article   Google Scholar  

Bressoud, D., Carlson, M., Mesa, V., & Rasmussen, C. (2013). The calculus student: insights from the Mathematical Association of America national study. International Journal of Mathematical Education in Science and Technology, 44 (5), 685–698. doi: 10.1080/0020739X.2013.798874 .

Brousseau, G. (1997). Theory of didactical situations in mathematics . Dordrecht, The Netherlands: Kluwer.

Cartledge, C. M., & Sasser, J. E. (1981). The effect of homework assignments on the mathematics achievement of college students in freshman algebra . ERIC document ED206495. Washington, DC: US Dept. of Education.

Cohen, D., Raudenbush, S., & Ball, D. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25 (2), 119–142.

Creswell, J. W. (2002). Educational research: Planning, conducting, and evaluating quantitative and qualitative approaches to research . Upper Saddle River, NJ: Merrill/Pearson Education.

Dweck, C. S. (2008). Mindsets and math/science achievement . New York, NY: Carnegie Corp. of New York–Institute for Advanced Study Commission on Mathematics and Science Education.

Edwards, C. H., & Penney, D. E. (1998). Calculus with analytic geometry: Early transcendentals . Upper Saddle River, NJ: Prentice Hall.

Ellis, J., Kelton, M., & Rasmussen, C. (2014). Student perception of pedagogy and persistence in calculus. ZDM – The International Journal on Mathematics Education, 46 (4), 661–673.

Halcrow, C., & Dunnigan, G. (2012). Online homework in calculus I: friend or foe? PRIMUS, 22 (8), 664–682.

Herbst, P., & Chazan, D. (2012). On the instructional triangle and sources of justification for actions in mathematics teaching. ZDM – The International Journal on Mathematics Education, 44 (5), 601–612.

Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1–27). Hillsdale, NJ: Lawrence Erlbaum.

Hughes-Hallett, D., Gleason, A. M., McCallum, W. G., Lomen, D. O., Lovelock, D., Tecosky-Feldman, J., Tucker, T. W., Flath, D. E., Thrash, J., Rhea, K. R., Pasquale, A., Gordon, S. P., Quinney, D., & Lock, P. F. (2009). Calculus, single and multivariable (5th ed.). Hoboken, NJ: John Wiley & Sons.

Johnson, E., Ellis, J., & Rasmussen, C. (2014). It’s about time: How instructors and students experience time constraints in Calculus I. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, 6 (pp. 119–120). Vancouver, British Columbia: PME.

Kitsantas, A., Cheema, J., & Ware, H. (2011). Mathematics achievement: the role of homework and self-efficacy beliefs. Journal of Advanced Academics, 22 (2), 310–339.

Lenz, L. (2010). The effect of a web-based homework system on student outcomes in a first- year mathematics course. Journal of Computers in Mathematics and Science Teaching, 29 (3), 233–246.

Martin, T. (2000). Calculus students’ ability to solve geometric related-rates problems. Mathematics Education Research Journal, 12 (2), 74–91.

Morrel, J. (2007). Using problem sets in calculus. PRIMUS, 16 (4), 376–384.

Piccolo, C., & Code, W. J. (2013). Assesment of students’ understanding of related rates problems. In S. Brown, G. Karakok, K. H. Roh, & M. Oehrtman (Eds.), Proceedings of the 16 th Annual Conference on Research in Undergraduate Mathematics Education (pp. 607–610). Denver, CO.

Rasmussen, C., & Ellis, J. (2013). Who is switching out of calculus and why? In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, 4 (pp. 73–80). Kiel, Germany: PME.

Rasmussen, C., & Ellis, J. (2015). Calculus coordination at PhD-granting universities: More than just using the same syllabus, textbook, and final exam. In D. Bressoud, V. Mesa, & C. Rasmussen (Eds.), Insights and recommendations from the MAA national study of college calculus . Washington, DC: Mathematical Association of America.

Rasmussen, C., Ellis, J., Zazkis, D., & Bressoud, D. (2014). Features of successful calculus programs at five doctoral degree granting institutions. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, 5 (pp. 33–40). Vancouver, British Columbia: PME.

Rogawski, J. (2011). Calculus: Early transcendentals (2nd ed.). New York, NY: Freeman, W. H. and Company.

Sonnert, G., & Sadler, P. (2015). The impact of instructor and institutional factors on students’ attitude. In D. Bressoud, V. Mesa, & C. Rasmussen (Eds.), Insights and recommendations from the MAA national study of college calculus . Washington, DC: Mathematical Association of America.

Stewart, J. (2007). Essential calculus: Early transcendentals . Belmont: Thomson Higher Education.

Stiggins, R. J., & Chappuis, J. (2005). Using student-involved classroom assessment to close achievement gaps. Theory Into Practice, 44 (1), 11–18.

White, N., & Mesa, V. (2014). Describing cognitive orientation of calculus I tasks across different types of coursework. ZDM – The International Journal on Mathematics Education, 46 (4), 675–690.

Young, C., Georgiopoulos, M., Hagen, S., Geiger, C., Dagley-Falls, M., Islas, A., Ramsey, P. J., Lancey, P. M., Straney, R. A., Forde, D. S., & Bradbury, E. (2011). Improving student learning in calculus through applications. International Journal of Mathematical Education in Science and Technology, 42 (5), 591–604.

Download references

Acknowledgments

This research was supported with funding from the National Science Foundation (DRL-0910240).

Author information

Authors and affiliations.

Department of Mathematics, Colorado State University, 1874 Campus Delivery, Fort Collins, CO, 80523-1874, USA

Jessica Ellis

Department of Mathematics and Statistics, San Diego State University, 6475 Alvarado Road, Suite 206, San Diego, CA, 92120-5013, USA

Kady Hanson, Gina Nuñez & Chris Rasmussen

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Jessica Ellis .

Rights and permissions

Reprints and permissions

About this article

Ellis, J., Hanson, K., Nuñez, G. et al. Beyond Plug and Chug: an Analysis of Calculus I Homework. Int. J. Res. Undergrad. Math. Ed. 1 , 268–287 (2015). https://doi.org/10.1007/s40753-015-0012-z

Download citation

Published : 11 July 2015

Issue Date : July 2015

DOI : https://doi.org/10.1007/s40753-015-0012-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Post-secondary
• Student reports
• Didactical contract
• Mixed methods
• Find a journal
• Publish with us
• Track your research

• +1 321-684-6093
• [email protected]

Homework Plug

For all your essay online classes thesis project proposal needs, no matter what kind of academic paper you need, it is simple and secure to hire an essay writer for a price you can afford at homework plug. save more time for yourself..

• - select service -
• From Scratch
• Proof-Reading
• - select academic level -
• High School
• Undergraduate
• - select papertype -
• PowerPoint Slides
• - select deadline -
• Less than 6 Hrs
• - select a field -
• Mathematics
• Computer Science
• Architecture
• Design Analysis
• Communications and Media
• Advertising
• Communication Strategies
• Creative Writing
• Public Relations
• Accounting & Finance
• Company Analysis
• International Affairs/Relations
• Investments
• Application Essay
• Education Theory
• Teacher's Career
• Civil Engineering
• African-American Studies
• American history
• Asian Study
• Canadian Studies
• East-European Studies
• Latin-American Studies
• Native-American Studies
• West-European Studies
• Criminology
• Legal Issues
• Linguistics
• American Literature
• Antique Literature
• Asian Literature
• English Literature
• Shakespeare Studies
• Mathematics & Statistics
• Medicine and Health
• Alternative Medicine
• Pharmacology
• Agricultural Studies
• Antropology
• Environmental Issues
• Political Science
• Religion and Theology
• Aeronautics
• Information Technology
• Architectural Design
• Mechanical & Electrical Engineering
• Unspecified
• IT management
• Power Point
• - select paper format -
• Chicago/ Turabian
• Not Applicable

ORDER SUMMARY

Full Name: {first_name}{last_name}

Phone number: {phonenumber}

Contact Email: (Order will be sent here) {email}

Twitter: {twitter}

Type of Service: {service;label}

Academic Level: {academic;label}

Paper Format: {format;label}

Course/ Field of Study: {field;label}

Type of Paper: {_paper_type}

Due in: {deadline;label}

Topic: {topic}

Instructions: {instructions}

Files: {file}

Total Cost: {total}

• - select a category -
• Programming
• Excel Project
• Proctored Exam
• Accuplacer Test

6+ years of experience in the custom writing market

Security, confidentiality, and quality guaranteed!

Satisfaction rate 9.8/10 based on 6500 customer testimonials

How It Works?

01. fill out order form.

Submit your order details on my website (subject, type of work, level, format, size, and deadline).

02. Proceed with Payment

Pick any of the safe online payment methods: Paypal, debit, or credit card to pay for my essay writer services.

03. Communicate with writer

Contact me at any time if you need any assistance, follow up the process or to handle your homework.

04. Get your order

Have your essay ready before the deadline. Revisions are done within two weeks after submission.

Why Choose Us

No hidden fees.

The pricing model of Hwplug is standard, open, and calculated for you automatically as you place your order.

Free Revision

Within two weeks after delivery clients can request for revision of submitted work which is done free of charge by Hwplug!

Plagiarism Free

Hwplug ensures zero plagiarism on all types of papers. Plagiarism penalties in your homework should never worry you!

Best Quality Papers from HW plug!

Frequently asked questions.

To learn about how our service works, please visit How It Works page where you can read a detailed explanation of our features, along with a step-by-step guide.

Yes, we are a private company and uphold a strong sense of decorum in dealing with confidentiality. We will not, under any circumstance (unless required to do so by federal law), give out any of your personal information to anyone, ever.

All of our writers are seasoned veterans of the trade. They all went to prestigious universities and graduated with high GPA’s. They know the ins and outs of how to get A’s.

We guarantee that our papers are absolutely original! Every paper is checked with several sophisticated plagiarism checking services to make absolutely sure that it is completely plagiarism — free.

Absolutely, we use PayPal — the safest and easiest way to pay online. Your transaction, along with your personal information, is 100% confidential

Every client can contact his/her writer directly VIA the personal control panel on this website. Additionally, effective cooperation between the customer and the writer is supported by our team members VIA the Phone (toll free), Live Chat or Email 24/7.

Your paper will be completed by a qualified ENL writer. We NEVER outsource work from ESL writers. Your dedicated writer will also specialize in the topic you have requested and have the necessary experience to complete your paper in the best possible and accurate way.

We have a very fair 100% money back guarantee policy that fairly resolves all the disputed and questionable cases. You will certainly get your money back if there were any violations from our side.

We will be happy to revise your order for free as long as the revision you request fits the scope of your original order. Please note that you have fourteen (14) days after the actual deadline (the moment that we have sent you your completed paper) of your order to ask for a free revision according to our Revision Policy.

Our Services

HWPlug offers academic writing services for clients across the wold. We accommodate both native speaking students and non-English speaking students overcoming the language barrier.Get professional assistance from our experts. Our writers only write English language essays and papers.

Here are the types of academic assignments you can order from us:

• Online classes
• Assignments
• Research paper
• Dissertation

Message us to learn more about what our experts can do!

Made with love in San Francisco. Send us an email to [email protected]

• How it Works
• HWPlug for businesses
• Important Articles
• HWPlug for universities
• Terms of use
• Privacy Policy
• Refund Policy
• Report Abuse
• HWPlug Scholarship

Providing custom academic papers covers any academic levels, paper formats, and subjects. By accessing this website you agree to our Terms of Use, Privacy and Cookie Policies.

Get the Reddit app

This is a place for engineering students of any discipline to discuss study methods, get homework help, get job search advice, and find a compassionate ear when you get a 40% on your midterm after studying all night.

Website to see chegg answers.

I was wondering if anyone had a link that allowed you to copy the link from a hidden chegg answer and then this website would show you the answer.

By continuing, you agree to our User Agreement and acknowledge that you understand the Privacy Policy .

Enter the 6-digit code from your authenticator app

You’ve set up two-factor authentication for this account.

Enter a 6-digit backup code

Create your username and password.

Reddit is anonymous, so your username is what you’ll go by here. Choose wisely—because once you get a name, you can’t change it.

Reset your password

Enter your email address or username and we’ll send you a link to reset your password

Check your inbox

An email with a link to reset your password was sent to the email address associated with your account

Choose a Reddit account to continue

Plug & socket types

Last updated: 22 January 2024

Plug & socket types around the world

There are currently 15 types of domestic electrical outlet plugs in use worldwide, each of which has been assigned a letter by the US Department of Commerce International Trade Administration (ITA), starting with A and moving through the alphabet. These letters are completely arbitrary: they don’t actually mandate anything.

Click here for a global map showing the spread of the different plug types used around the world.

Click here for a detailed list of the countries of the world with their respective plug and outlet types, voltage and frequency.

• mainly used in the USA, Canada, Mexico & Japan
• not grounded
• almost always 100 – 127 V
• socket compatible with plug type A
• mainly used in the USA, Canada & Mexico
• socket compatible with plug types A & B
• commonly used in Europe, South America & Asia
• 2.5 A, 10 A & 16 A
• almost always 220 – 240 V
• socket compatible with plug type C
• mainly used in India
• 220 – 240 V
• socket compatible with plug type D (partial and unsafe compatibility with C, E & F)
• primarily used in France , Belgium , Poland , Slovakia & Czechia
• socket compatible with plug types C, E & F
• used almost everywhere in Europe & Russia, except for the UK & Ireland
• mainly used in the United Kingdom , Ireland , Malta , Malaysia , Singapore & the Arabian Peninsula
• 220 – 250 V
• socket compatible with plug type G
• used exclusively in Israel , the West Bank & the Gaza Strip
• socket compatible with plug types C & H (partial and unsafe compatibility with E & F)
• mainly used in Australia, New Zealand, China & Argentina
• 2 or 3 pins
• 2 pins: not grounded / 3 pins: grounded
• socket compatible with plug type I
• used almost exclusively in Switzerland & Liechtenstein
• socket compatible with plug types C & J
• used almost exclusively in Denmark & Greenland
• socket compatible with plug types C & K (partial and unsafe compatibility with E & F)
• used almost exclusively in Italy & Chile
• 10 A & 16 A
• 10 A socket compatible with plug types C & L (10 A version)
• 16 A socket compatible with plug type L (16 A version)
• mainly used in South Africa
• socket compatible with plug type M
• used in Brazil and South Africa
• 10 A, 16 A & 20 A
• 100 – 240 V
• socket compatible with plug types C & N
• used exclusively in Thailand
• socket compatible with plug types C & O (partial and unsafe compatibility with E & F)

© 2003-2024 WorldStandards. All Rights Reserved.

• Types A & B
• Universal wall sockets
• Plug, socket & voltage by country
• World map showing the spread of plug types
• Why isn’t there a universal standard electric plug?
• Why isn’t there a standard voltage around the world?
• Useful information for travellers
• Three-phase electric power
• Why do some countries drive on the left and others on the right?
• List of left- & right-driving countries
• Trivia about driving on the left
• What if Britain gave up driving on the left?
• Oval car stickers
• The world’s scripts and alphabets
• Internet country domains list