homework problem

Homework Struggles May Not Be a Behavior Problem

Exploring some options to understand and help..

Posted August 2, 2022 | Reviewed by Abigail Fagan

• Mental health challenges and neurodevelopmental differences directly affect children's ability to do homework.
• Understanding what difficulties are getting in the way—beyond the usual explanation of a behavior problem—is key.
• Sleep and mental health needs can take priority over homework completion.

Chelsea was in 10th grade the first time I told her directly to stop doing her homework and get some sleep. I had been working with her since she was in middle school, treating her anxiety disorder. She deeply feared disappointing anyone—especially her teachers—and spent hours trying to finish homework perfectly. The more tired and anxious she got, the harder it got for her to finish the assignments.

One night Chelsea called me in despair, feeling hopeless. She was exhausted and couldn’t think straight. She felt like a failure and that she was a burden to everyone because she couldn’t finish her homework.

She was shocked when I told her that my prescription for her was to go to sleep now—not to figure out how to finish her work. I told her to leave her homework incomplete and go to sleep. We briefly discussed how we would figure it out the next day, with her mom and her teachers. At that moment, it clicked for her that it was futile to keep working—because nothing was getting done.

This was an inflection point for her awareness of when she was emotionally over-cooked and when she needed to stop and take a break or get some sleep. We repeated versions of this phone call several times over the course of her high school and college years, but she got much better at being able to do this for herself most of the time.

When Mental Health Symptoms Interfere with Homework

Kids with mental health or neurodevelopmental challenges often struggle mightily with homework. Challenges can come up in every step of the homework process, including, but not limited to:

• Remembering and tracking assignments and materials
• Getting the mental energy/organization to start homework
• Filtering distractions enough to persist with assignments
• Understanding unspoken or implied parts of the homework
• Remembering to bring finished homework to class
• Being in class long enough to know the material
• Tolerating the fear of not knowing or failing
• Not giving up the assignment because of a panic attack
• Tolerating frustration—such as not understanding—without emotional dysregulation
• Being able to ask for help—from a peer or a teacher and not being afraid to reach out

This list is hardly comprehensive. ADHD , autism spectrum disorder, social anxiety , generalized anxiety, panic disorder, depression , dysregulation, and a range of other neurodevelopmental and mental health challenges cause numerous learning differences and symptoms that can specifically and frequently interfere with getting homework done.

The Usual Diagnosis for Homework Problems is "Not Trying Hard Enough"

Unfortunately, when kids frequently struggle to meet homework demands, teachers and parents typically default to one explanation of the problem: The child is making a choice not to do their homework. That is the default “diagnosis” in classrooms and living rooms. And once this framework is drawn, the student is often seen as not trying hard enough, disrespectful, manipulative, or just plain lazy.

The fundamental disconnect here is that the diagnosis of homework struggles as a behavioral choice is, in fact, only one explanation, while there are so many other diagnoses and differences that impair children's ability to consistently do their homework. If we are trying to create solutions based on only one understanding of the problem, the solutions will not work. More devastatingly, the wrong solutions can worsen the child’s mental health and their long-term engagement with school and learning.

To be clear, we aren’t talking about children who sometimes struggle with or skip homework—kids who can change and adapt their behaviors and patterns in response to the outcomes of that struggle. For this discussion, we are talking about children with mental health and/or neurodevelopmental symptoms and challenges that create chronic difficulties with meeting homework demands.

How Can You Help a Child Who Struggles with Homework?

How can you help your child who is struggling to meet homework demands because of their ADHD, depression, anxiety, OCD , school avoidance, or any other neurodevelopmental or mental health differences? Let’s break this down into two broad areas—things you can do at home, and things you can do in communication with the school.

Helping at Home

The following suggestions for managing school demands at home can feel counterintuitive to parents—because we usually focus on helping our kids to complete their tasks. But mental health needs jump the line ahead of task completion. And starting at home will be key to developing an idea of what needs to change at school.

• Set an end time in the evening after which no more homework will be attempted. Kids need time to decompress and they need sleep—and pushing homework too close to or past bedtime doesn’t serve their educational needs. Even if your child hasn’t been able to approach the homework at all, even if they have avoided and argued the whole evening, it is still important for everyone to have a predictable time to shut down the whole process.
• If there are arguments almost every night about homework, if your child isn’t starting homework or finishing it, reframe it from failure into information. It’s data to put into problem-solving. We need to consider other possible explanations besides “behavioral choice” when trying to understand the problem and create effective solutions. What problems are getting in the way of our child’s meeting homework demands that their peers are meeting most of the time?
• Try not to argue about homework. If you can check your own anxiety and frustration, it can be more productive to ally with your child and be curious with them. Kids usually can’t tell you a clear “why” but maybe they can tell you how they are feeling and what they are thinking. And if your child can’t talk about it or just keeps saying “I don't know,” try not to push. Come back another time. Rushing, forcing, yelling, and threatening will predictably not help kids do homework.

Helping at School

The second area to explore when your neurodiverse child struggles frequently with homework is building communication and connections with school and teachers. Some places to focus on include the following.

• Label your child’s diagnoses and break down specific symptoms for the teachers and school team. Nonjudgmental, but specific language is essential for teachers to understand your child’s struggles. Breaking their challenges down into the problems specific to homework can help with building solutions. As your child gets older, help them identify their difficulties and communicate them to teachers.
• Let teachers and the school team know that your child’s mental health needs—including sleep—take priority over finishing homework. If your child is always struggling to complete homework and get enough sleep, or if completing homework is leading to emotional meltdowns every night, adjusting their homework demands will be more successful than continuing to push them into sleep deprivation or meltdowns.
• Request a child study team evaluation to determine if your child qualifies for services under special education law such as an IEP, or accommodations through section 504—and be sure that homework adjustments are included in any plan. Or if such a plan is already in place, be clear that modification of homework expectations needs to be part of it.

The Long-Term Story

I still work with Chelsea and she recently mentioned how those conversations so many years ago are still part of how she approaches work tasks or other demands that are spiking her anxiety when she finds herself in a vortex of distress. She stops what she is doing and prioritizes reducing her anxiety—whether it’s a break during her day or an ending to the task for the evening. She sees that this is crucial to managing her anxiety in her life and still succeeding at what she is doing.

Task completion at all costs is not a solution for kids with emotional needs. Her story (and the story of many of my patients) make this crystal clear.

Candida Fink, M.D. , is board certified in child/adolescent and general psychiatry. She practices in New York and has co-authored two books— The Ups and Downs of Raising a Bipolar Child and Bipolar Disorder for Dummies.

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Sat / act prep online guides and tips, the 5 best homework help websites (free and paid).

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Listen: we know homework isn’t fun, but it is a good way to reinforce the ideas and concepts you’ve learned in class. But what if you’re really struggling with your homework assignments?

If you’ve looked online for a little extra help with your take-home assignments, you’ve probably stumbled across websites claiming to provide the homework help and answers students need to succeed . But can homework help sites really make a difference? And if so, which are the best homework help websites you can use? 

Below, we answer these questions and more about homework help websites–free and paid. We’ll go over: 

• The basics of homework help websites
• The cost of homework help websites 
• The five best homework websites out there 
• The pros and cons of using these websites for homework help 
• The line between “learning” and “cheating” when using online homework help 
• Tips for getting the most out of a homework help website

So let’s get started! 

The Basics About Homework Help Websites–Free and Paid

Homework help websites are designed to help you complete your homework assignments, plain and simple. 

What Makes a Homework Help Site Worth Using

Most of the best sites allow users to ask questions and then provide an answer (or multiple possible answers) and explanation in seconds. In some instances, you can even send a photo of a particular assignment or problem instead of typing the whole thing out! 

Homework help sites also offer more than just help answering homework questions. Common services provided are Q&A with experts, educational videos, lectures, practice tests and quizzes, learning modules, math solving tools, and proofreading help. Homework help sites can also provide textbook solutions (i.e. answers to problems in tons of different textbooks your school might be using), one-on-one tutoring, and peer-to-peer platforms that allow you to discuss subjects you’re learning about with your fellow students. 

And best of all, nearly all of them offer their services 24/7, including tutoring! 

What You Should Should Look Out For

When it comes to homework help, there are lots–and we mean lots –of scam sites out there willing to prey on desperate students. Before you sign up for any service, make sure you read reviews to ensure you’re working with a legitimate company. 

A word to the wise: the more a company advertises help that veers into the territory of cheating, the more likely it is to be a scam. The best homework help websites are going to help you learn the concepts you’ll need to successfully complete your homework on your own. (We’ll go over the difference between “homework help” and “cheating” a little later!) 

You don't need a golden piggy bank to use homework help websites. Some provide low or no cost help for students like you!

How Expensive Are the Best Homework Help Websites?

First of all, just because a homework help site costs money doesn’t mean it’s a good service. Likewise, just because a homework help website is free doesn’t mean the help isn’t high quality. To find the best websites, you have to take a close look at the quality and types of information they provide! 

When it comes to paid homework help services, the prices vary pretty widely depending on the amount of services you want to subscribe to. Subscriptions can cost anywhere from $2 to $150 dollars per month, with the most expensive services offering several hours of one-on-one tutoring with a subject expert per month.

The 5 Best Homework Help Websites 

So, what is the best homework help website you can use? The answer is that it depends on what you need help with. 

The best homework help websites are the ones that are reliable and help you learn the material. They don’t just provide answers to homework questions–they actually help you learn the material. 

That’s why we’ve broken down our favorite websites into categories based on who they’re best for . For instance, the best website for people struggling with math might not work for someone who needs a little extra help with science, and vice versa. 

Keep reading to find the best homework help website for you! 

Best Free Homework Help Site: Khan Academy

• Price: Free!
• Best for: Practicing tough material 

Not only is Khan Academy free, but it’s full of information and can be personalized to suit your needs. When you set up your account , you choose which courses you need to study, and Khan Academy sets up a personal dashboard of instructional videos, practice exercises, and quizzes –with both correct and incorrect answer explanations–so you can learn at your own pace. 

As an added bonus, it covers more course topics than many other homework help sites, including several AP classes.

Runner Up: Brainly.com offers a free service that allows you to type in questions and get answers and explanations from experts. The downside is that you’re limited to two answers per question and have to watch ads. 

Best Paid Homework Help Site: Chegg

• Price: $14.95 to $19.95 per month
• Best for: 24/7 homework assistance  

This service has three main parts . The first is Chegg Study, which includes textbook solutions, Q&A with subject experts, flashcards, video explanations, a math solver, and writing help. The resources are thorough, and reviewers state that Chegg answers homework questions quickly and accurately no matter when you submit them.  

Chegg also offers textbook rentals for students who need access to textbooks outside of their classroom. Finally, Chegg offers Internship and Career Advice for students who are preparing to graduate and may need a little extra help with the transition out of high school. 

Another great feature Chegg provides is a selection of free articles geared towards helping with general life skills, like coping with stress and saving money. Chegg’s learning modules are comprehensive, and they feature solutions to the problems in tons of different textbooks in a wide variety of subjects. 

Runner Up: Bartleby offers basically the same services as Chegg for $14.99 per month. The reason it didn’t rank as the best is based on customer reviews that say user questions aren’t answered quite as quickly on this site as on Chegg. Otherwise, this is also a solid choice!

Best Site for Math Homework Help: Photomath

• Price: Free (or $59.99 per year for premium services) 
• Best for: Explaining solutions to math problems

This site allows you to t ake a picture of a math problem, and instantly pulls up a step-by-step solution, as well as a detailed explanation of the concept. Photomath also includes animated videos that break down mathematical concepts to help you better understand and remember them. 

The basic service is free, but for an additional fee you can get extra study tools and learn additional strategies for solving common math problems.

Runner Up: KhanAcademy offers in-depth tutorials that cover complex math topics for free, but you won’t get the same tailored help (and answers!) that Photomath offers. 

Best Site for English Homework Help: Princeton Review Academic Tutoring

• Price: $40 to $153 per month, depending on how many hours of tutoring you want 
• Best for: Comprehensive and personalized reading and writing help 

While sites like Grammarly and Sparknotes help you by either proofreading what you write via an algorithm or providing book summaries, Princeton Review’s tutors provide in-depth help with vocabulary, literature, essay writing and development, proofreading, and reading comprehension. And unlike other services, you’ll have the chance to work with a real person to get help. 

The best part is that you can get on-demand English (and ESL) tutoring from experts 24/7. That means you can get help whenever you need it, even if you’re pulling an all-nighter! 

This is by far the most expensive homework site on this list, so you’ll need to really think about what you need out of a homework help website before you commit. One added benefit is that the subscription covers over 80 other subjects, including AP classes, which can make it a good value if you need lots of help!  

Best Site for STEM Homework Help: Studypool

• Best for: Science homework help
• Price: Varies; you’ll pay for each question you submit

When it comes to science homework help, there aren’t a ton of great resources out there. The best of the bunch is Studypool, and while it has great reviews, there are some downsides as well. 

Let’s start with the good stuff. Studypool offers an interesting twist on the homework help formula. After you create a free account, you can submit your homework help questions, and tutors will submit bids to answer your questions. You’ll be able to select the tutor–and price point–that works for you, then you’ll pay to have your homework question answered. You can also pay a small fee to access notes, lectures, and other documents that top tutors have uploaded. 

The downside to Studypool is that the pricing is not transparent . There’s no way to plan for how much your homework help will cost, especially if you have lots of questions! Additionally, it’s not clear how tutors are selected, so you’ll need to be cautious when you choose who you’d like to answer your homework questions.  

What Are the Pros and Cons of Using Homework Help Sites?

Homework help websites can be a great resource if you’re struggling in a subject, or even if you just want to make sure that you’re really learning and understanding topics and ideas that you’re interested in. But, there are some possible drawbacks if you don’t use these sites responsibly. 

We’ll go over the good–and the not-so-good–aspects of getting online homework help below. 

3 Pros of Using Homework Help Websites 

First, let’s take a look at the benefits. 

#1: Better Grades Beyond Homework

This is a big one! Getting outside help with your studies can improve your understanding of concepts that you’re learning, which translates into better grades when you take tests or write essays. 

Remember: homework is designed to help reinforce the concepts you learned in class. If you just get easy answers without learning the material behind the problems, you may not have the tools you need to be successful on your class exams…or even standardized tests you’ll need to take for college. 

#2: Convenience

One of the main reasons that online homework help is appealing is because it’s flexible and convenient. You don’t have to go to a specific tutoring center while they’re open or stay after school to speak with your teacher. Instead, you can access helpful resources wherever you can access the internet, whenever you need them.

This is especially true if you tend to study at off hours because of your extracurriculars, work schedule, or family obligations. Sites that offer 24/7 tutoring can give you the extra help you need if you can’t access the free resources that are available at your school. 

#3: Variety

Not everyone learns the same way. Maybe you’re more of a visual learner, but your teacher mostly does lectures. Or maybe you learn best by listening and taking notes, but you’re expected to learn something just from reading the textbook . 

One of the best things about online homework help is that it comes in a variety of forms. The best homework help sites offer resources for all types of learners, including videos, practice activities, and even one-on-one discussions with real-life experts. 

This variety can also be a good thing if you just don’t really resonate with the way a concept is being explained (looking at you, math textbooks!).

Not so fast. There are cons to homework help websites, too. Get to know them below!

3 Cons of Using Homework Help Websites 

Now, let’s take a look at the drawbacks of online homework help. 

#1: Unreliable Info

This can be a real problem. In addition to all the really good homework help sites, there are a whole lot of disreputable or unreliable sites out there. The fact of the matter is that some homework help sites don’t necessarily hire people who are experts in the subjects they’re talking about. In those cases, you may not be getting the accurate, up-to-date, and thorough information you need.

Additionally, even the great sites may not be able to answer all of your homework questions. This is especially true if the site uses an algorithm or chatbot to help students…or if you’re enrolled in an advanced or college-level course. In these cases, working with your teacher or school-provided tutors are probably your best option. 

#2: No Clarification

This depends on the service you use, of course. But the majority of them provide free or low-cost help through pre-recorded videos. Watching videos or reading info online can definitely help you with your homework… but you can’t ask questions or get immediate feedback if you need it .

#3: Potential For Scamming 

Like we mentioned earlier, there are a lot of homework help websites out there, and lots of them are scams. The review comments we read covered everything from outdated or wrong information, to misleading claims about the help provided, to not allowing people to cancel their service after signing up. 

No matter which site you choose to use, make sure you research and read reviews before you sign up–especially if it’s a paid service! 

When Does “Help” Become “Cheating”?

Admittedly, whether using homework help websites constitutes cheating is a bit of a grey area. For instance, is it “help” when a friend reads your essay for history class and corrects your grammar, or is it “cheating”? The truth is, not everyone agrees on when “help” crosses the line into “cheating .” When in doubt, it can be a good idea to check with your teacher to see what they think about a particular type of help you want to get. 

That said, a general rule of thumb to keep in mind is to make sure that the assignment you turn in for credit is authentically yours . It needs to demonstrate your own thoughts and your own current abilities. Remember: the point of every homework assignment is to 1) help you learn something, and 2) show what you’ve learned. 

So if a service answers questions or writes essays for you, there’s a good chance using it constitutes cheating. 

Here’s an example that might help clarify the difference for you. Brainstorming essay ideas with others or looking online for inspiration is “help” as long as you write the essay yourself. Having someone read it and give you feedback about what you need to change is also help, provided you’re the one that makes the changes later. 

But copying all or part of an essay you find online or having someone write (or rewrite) the whole thing for you would be “cheating.” The same is true for other subjects. Ultimately, if you’re not generating your own work or your own answers, it’s probably cheating.

5 Tips for Finding the Best Homework Help Websites for You

Now that you know some of our favorite homework help websites, free and paid, you can start doing some additional research on your own to decide which services might work best for you! Here are some top tips for choosing a homework help website. 

Tip 1: Decide How You Learn Best 

Before you decide which site or sites you’re going to use for homework help, y ou should figure out what kind of learning style works for you the most. Are you a visual learner? Then choose a site that uses lots of videos to help explain concepts. If you know you learn best by actually doing tasks, choose a site that provides lots of practice exercises.

Tip 2: Determine Which Subjects You Need Help With

Just because a homework help site is good overall doesn’t mean that it’s equally good for every subject. If you only need help in math, choose a site that specializes in that area. But if history is where you’re struggling, a site that specializes in math won’t be much help. So make sure to choose a site that you know provides high-quality help in the areas you need it most. 

Tip 3: Decide How Much One-On-One Help You Need 

This is really about cost-effectiveness. If you learn well on your own by reading and watching videos, a free site like Khan Academy is a good choice. But if you need actual tutoring, or to be able to ask questions and get personalized answers from experts, a paid site that provides that kind of service may be a better option.

Tip 4: Set a Budget

If you decide you want to go with a paid homework help website, set a budget first . The prices for sites vary wildly, and the cost to use them can add up quick. 

Tip 5: Read the Reviews

Finally, it’s always a good idea to read actual reviews written by the people using these homework sites. You’ll learn the good, the bad, and the ugly of what the users’ experiences have been. This is especially true if you intend to subscribe to a paid service. You’ll want to make sure that users think it’s worth the price overall!

What’s Next?

If you want to get good grades on your homework, it’s a good idea to learn how to tackle it strategically. Our expert tips will help you get the most out of each assignment…and boost your grades in the process.

Doing well on homework assignments is just one part of getting good grades. We’ll teach you everything you need to know about getting great grades in high school in this article.

Of course, test grades can make or break your GPA, too. Here are 17 expert tips that’ll help you get the most out of your study prep before you take an exam.

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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Is Homework Necessary? Education Inequity and Its Impact on Students

The Problem with Homework: It Highlights Inequalities

How much homework is too much homework, when does homework actually help, negative effects of homework for students, how teachers can help.

Schools are getting rid of homework from Essex, Mass., to Los Angeles, Calif. Although the no-homework trend may sound alarming, especially to parents dreaming of their child’s acceptance to Harvard, Stanford or Yale, there is mounting evidence that eliminating homework in grade school may actually have great benefits , especially with regard to educational equity.

In fact, while the push to eliminate homework may come as a surprise to many adults, the debate is not new . Parents and educators have been talking about this subject for the last century, so that the educational pendulum continues to swing back and forth between the need for homework and the need to eliminate homework.

One of the most pressing talking points around homework is how it disproportionately affects students from less affluent families. The American Psychological Association (APA) explained:

“Kids from wealthier homes are more likely to have resources such as computers, internet connections, dedicated areas to do schoolwork and parents who tend to be more educated and more available to help them with tricky assignments. Kids from disadvantaged homes are more likely to work at afterschool jobs, or to be home without supervision in the evenings while their parents work multiple jobs.”

[RELATED] How to Advance Your Career: A Guide for Educators >> 

While students growing up in more affluent areas are likely playing sports, participating in other recreational activities after school, or receiving additional tutoring, children in disadvantaged areas are more likely headed to work after school, taking care of siblings while their parents work or dealing with an unstable home life. Adding homework into the mix is one more thing to deal with — and if the student is struggling, the task of completing homework can be too much to consider at the end of an already long school day.

While all students may groan at the mention of homework, it may be more than just a nuisance for poor and disadvantaged children, instead becoming another burden to carry and contend with.

Beyond the logistical issues, homework can negatively impact physical health and stress — and once again this may be a more significant problem among economically disadvantaged youth who typically already have a higher stress level than peers from more financially stable families .

Yet, today, it is not just the disadvantaged who suffer from the stressors that homework inflicts. A 2014 CNN article, “Is Homework Making Your Child Sick?” , covered the issue of extreme pressure placed on children of the affluent. The article looked at the results of a study surveying more than 4,300 students from 10 high-performing public and private high schools in upper-middle-class California communities.

“Their findings were troubling: Research showed that excessive homework is associated with high stress levels, physical health problems and lack of balance in children’s lives; 56% of the students in the study cited homework as a primary stressor in their lives,” according to the CNN story. “That children growing up in poverty are at-risk for a number of ailments is both intuitive and well-supported by research. More difficult to believe is the growing consensus that children on the other end of the spectrum, children raised in affluence, may also be at risk.”

When it comes to health and stress it is clear that excessive homework, for children at both ends of the spectrum, can be damaging. Which begs the question, how much homework is too much?

The National Education Association and the National Parent Teacher Association recommend that students spend 10 minutes per grade level per night on homework . That means that first graders should spend 10 minutes on homework, second graders 20 minutes and so on. But a study published by The American Journal of Family Therapy found that students are getting much more than that.

While 10 minutes per day doesn’t sound like much, that quickly adds up to an hour per night by sixth grade. The National Center for Education Statistics found that high school students get an average of 6.8 hours of homework per week, a figure that is much too high according to the Organization for Economic Cooperation and Development (OECD). It is also to be noted that this figure does not take into consideration the needs of underprivileged student populations.

In a study conducted by the OECD it was found that “after around four hours of homework per week, the additional time invested in homework has a negligible impact on performance .” That means that by asking our children to put in an hour or more per day of dedicated homework time, we are not only not helping them, but — according to the aforementioned studies — we are hurting them, both physically and emotionally.

What’s more is that homework is, as the name implies, to be completed at home, after a full day of learning that is typically six to seven hours long with breaks and lunch included. However, a study by the APA on how people develop expertise found that elite musicians, scientists and athletes do their most productive work for about only four hours per day. Similarly, companies like Tower Paddle Boards are experimenting with a five-hour workday, under the assumption that people are not able to be truly productive for much longer than that. CEO Stephan Aarstol told CNBC that he believes most Americans only get about two to three hours of work done in an eight-hour day.

In the scope of world history, homework is a fairly new construct in the U.S. Students of all ages have been receiving work to complete at home for centuries, but it was educational reformer Horace Mann who first brought the concept to America from Prussia. 

Since then, homework’s popularity has ebbed and flowed in the court of public opinion. In the 1930s, it was considered child labor (as, ironically, it compromised children’s ability to do chores at home). Then, in the 1950s, implementing mandatory homework was hailed as a way to ensure America’s youth were always one step ahead of Soviet children during the Cold War. Homework was formally mandated as a tool for boosting educational quality in 1986 by the U.S. Department of Education, and has remained in common practice ever since.  

School work assigned and completed outside of school hours is not without its benefits. Numerous studies have shown that regular homework has a hand in improving student performance and connecting students to their learning. When reviewing these studies, take them with a grain of salt; there are strong arguments for both sides, and only you will know which solution is best for your students or school. 

Homework improves student achievement.

• Source: The High School Journal, “ When is Homework Worth the Time?: Evaluating the Association between Homework and Achievement in High School Science and Math ,” 2012. 
• Source: IZA.org, “ Does High School Homework Increase Academic Achievement? ,” 2014. **Note: Study sample comprised only high school boys. 

Homework helps reinforce classroom learning.

• Source: “ Debunk This: People Remember 10 Percent of What They Read ,” 2015.

Homework helps students develop good study habits and life skills.

• Sources: The Repository @ St. Cloud State, “ Types of Homework and Their Effect on Student Achievement ,” 2017; Journal of Advanced Academics, “ Developing Self-Regulation Skills: The Important Role of Homework ,” 2011.
• Source: Journal of Advanced Academics, “ Developing Self-Regulation Skills: The Important Role of Homework ,” 2011.

Homework allows parents to be involved with their children’s learning.

• Parents can see what their children are learning and working on in school every day. 
• Parents can participate in their children’s learning by guiding them through homework assignments and reinforcing positive study and research habits.
• Homework observation and participation can help parents understand their children’s academic strengths and weaknesses, and even identify possible learning difficulties.
• Source: Phys.org, “ Sociologist Upends Notions about Parental Help with Homework ,” 2018.

While some amount of homework may help students connect to their learning and enhance their in-class performance, too much homework can have damaging effects. 

Students with too much homework have elevated stress levels. 

• Source: USA Today, “ Is It Time to Get Rid of Homework? Mental Health Experts Weigh In ,” 2021.
• Source: Stanford University, “ Stanford Research Shows Pitfalls of Homework ,” 2014.

Students with too much homework may be tempted to cheat. 

• Source: The Chronicle of Higher Education, “ High-Tech Cheating Abounds, and Professors Bear Some Blame ,” 2010.
• Source: The American Journal of Family Therapy, “ Homework and Family Stress: With Consideration of Parents’ Self Confidence, Educational Level, and Cultural Background ,” 2015.

Homework highlights digital inequity. 

• Sources: NEAToday.org, “ The Homework Gap: The ‘Cruelest Part of the Digital Divide’ ,” 2016; CNET.com, “ The Digital Divide Has Left Millions of School Kids Behind ,” 2021.
• Source: Investopedia, “ Digital Divide ,” 2022; International Journal of Education and Social Science, “ Getting the Homework Done: Social Class and Parents’ Relationship to Homework ,” 2015.
• Source: World Economic Forum, “ COVID-19 exposed the digital divide. Here’s how we can close it ,” 2021.

Homework does not help younger students.

• Source: Review of Educational Research, “ Does Homework Improve Academic Achievement? A Synthesis of Researcher, 1987-2003 ,” 2006.

To help students find the right balance and succeed, teachers and educators must start the homework conversation, both internally at their school and with parents. But in order to successfully advocate on behalf of students, teachers must be well educated on the subject, fully understanding the research and the outcomes that can be achieved by eliminating or reducing the homework burden. There is a plethora of research and writing on the subject for those interested in self-study.

For teachers looking for a more in-depth approach or for educators with a keen interest in educational equity, formal education may be the best route. If this latter option sounds appealing, there are now many reputable schools offering online master of education degree programs to help educators balance the demands of work and family life while furthering their education in the quest to help others.

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Stanford research shows pitfalls of homework

A Stanford researcher found that students in high-achieving communities who spend too much time on homework experience more stress, physical health problems, a lack of balance and even alienation from society. More than two hours of homework a night may be counterproductive, according to the study.

Education scholar Denise Pope has found that too much homework has negative effects on student well-being and behavioral engagement. (Image credit: L.A. Cicero)

A Stanford researcher found that too much homework can negatively affect kids, especially their lives away from school, where family, friends and activities matter.

“Our findings on the effects of homework challenge the traditional assumption that homework is inherently good,” wrote Denise Pope , a senior lecturer at the Stanford Graduate School of Education and a co-author of a study published in the Journal of Experimental Education .

The researchers used survey data to examine perceptions about homework, student well-being and behavioral engagement in a sample of 4,317 students from 10 high-performing high schools in upper-middle-class California communities. Along with the survey data, Pope and her colleagues used open-ended answers to explore the students’ views on homework.

Median household income exceeded $90,000 in these communities, and 93 percent of the students went on to college, either two-year or four-year.

Students in these schools average about 3.1 hours of homework each night.

“The findings address how current homework practices in privileged, high-performing schools sustain students’ advantage in competitive climates yet hinder learning, full engagement and well-being,” Pope wrote.

Pope and her colleagues found that too much homework can diminish its effectiveness and even be counterproductive. They cite prior research indicating that homework benefits plateau at about two hours per night, and that 90 minutes to two and a half hours is optimal for high school.

Their study found that too much homework is associated with:

• Greater stress: 56 percent of the students considered homework a primary source of stress, according to the survey data. Forty-three percent viewed tests as a primary stressor, while 33 percent put the pressure to get good grades in that category. Less than 1 percent of the students said homework was not a stressor.

• Reductions in health: In their open-ended answers, many students said their homework load led to sleep deprivation and other health problems. The researchers asked students whether they experienced health issues such as headaches, exhaustion, sleep deprivation, weight loss and stomach problems.

• Less time for friends, family and extracurricular pursuits: Both the survey data and student responses indicate that spending too much time on homework meant that students were “not meeting their developmental needs or cultivating other critical life skills,” according to the researchers. Students were more likely to drop activities, not see friends or family, and not pursue hobbies they enjoy.

A balancing act

The results offer empirical evidence that many students struggle to find balance between homework, extracurricular activities and social time, the researchers said. Many students felt forced or obligated to choose homework over developing other talents or skills.

Also, there was no relationship between the time spent on homework and how much the student enjoyed it. The research quoted students as saying they often do homework they see as “pointless” or “mindless” in order to keep their grades up.

“This kind of busy work, by its very nature, discourages learning and instead promotes doing homework simply to get points,” Pope said.

She said the research calls into question the value of assigning large amounts of homework in high-performing schools. Homework should not be simply assigned as a routine practice, she said.

“Rather, any homework assigned should have a purpose and benefit, and it should be designed to cultivate learning and development,” wrote Pope.

High-performing paradox

In places where students attend high-performing schools, too much homework can reduce their time to foster skills in the area of personal responsibility, the researchers concluded. “Young people are spending more time alone,” they wrote, “which means less time for family and fewer opportunities to engage in their communities.”

Student perspectives

The researchers say that while their open-ended or “self-reporting” methodology to gauge student concerns about homework may have limitations – some might regard it as an opportunity for “typical adolescent complaining” – it was important to learn firsthand what the students believe.

The paper was co-authored by Mollie Galloway from Lewis and Clark College and Jerusha Conner from Villanova University.

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Solutions to Homework Problems

Getting Students to Practice Expert Thinking

Nobel-winner Carl Wieman will be speaking at FSU next week ; we want to fit in one last message citing his practical advice on teaching, which is applicable across disciplines. We’ve condensed a bit, but the original is available here (and includes both references and strategies for minimizing the burden of grading).

Creating good homework problems

by Carl Wieman Homework is a vital part of learning in university courses, arguably it is where most of the learning takes place. Doing homework is typically where the student will put in the most hours of intense thought about the subject, and such intense thought has been shown to be essential for developing mastery.  However, the sheer amount of effort expended is not sufficient to ensure mastery. Students have completed thousands of practice physics problems and still do poorly on problems involving the use of simple physics concepts.

The essential features for making homework support learning are:

• there is challenging and prolonged practice of the components of expert thinking the student is to learn
• the student is motivated to invest the necessary time and effort
• the student gets feedback on their practice that gives them guidance as to how they can improve

We have shown large learning gains by analyzing the thinking a physicist uses, and then having students practice and get feedback on this type of thinking in class. The same approach can be applied to the design of homework problems in science and engineering. We start by considering the components of expert thinking that one wants the students to develop and the shortcomings of typical “back of the textbook chapter” problems.

Generic components of expertise in all fields of science and engineering. Be able to:

• Identify what concepts are useful for solving the problem and have criteria to use to decide which concepts are relevant and which are not;
• separate surface features from the underlying structural elements that determine what concepts apply;
• identify what information is needed to solve the problem and what is irrelevant;
• look up and, as appropriate, estimate values and/or deduce information that is needed but not given;
• make appropriate simplifying assumptions;
• break down a complex problem into appropriate pieces;
• plan a solution;
• carry out routine frequently-needed solution procedures quickly and correctly, and have criteria for choosing when a specific procedure should be used;
• articulate and suitably apply a set of criteria for evaluating if a solution or intermediate result makes sense.

If one considers a typical back-of-the-chapter homework problem, it is clear that few of these components are practiced….The typical problem will result in the student primarily practicing and getting feedback on carrying out routine procedures that are given in textbook. In addition, most standard problems…will strip away the context, to avoid complicating the routine practice. Such idealized artificial problems provide no motivation for students put in effort or see any value in mastering the subject.

A criteria for any homework problem should be that it can pass the “Why should anyone care about the solution to the problem?” test. (Anyone other than the instructor.) The best problems are ones that the students can see provide solutions that are obviously relevant and useful to their immediate surroundings or intended future careers, but admittedly that can be a high bar. However, it is not so difficult to find some meaningful task a person in some occupation would need to carry out that utilizes the knowledge and skills involved in the problem. If you find yourself unable to find any such context, you should ask yourself why you are bothering to teach this material. I have dropped more than one topic from my courses after confronting such a realization.

As you incorporate the design features a)-j) in your homework problems, make them an explicit part the solution that students are required to produce (or stand-alone problems for specific features). For example, a part calling for a list of the concepts that apply and what features of the problem determine that choice, a part asking for what quantities/information are needed and estimates for values of any quantities not given, what procedures or techniques will be employed (Fourier transformation, use of multiple equations with multiple unknowns, …), approximations to be used, justification for why the answer makes sense and the criteria used to support that justification. This means a solution will involve far more than something like a simple number or fact. It provides them with far more explicit practice and feedback on how to develop and improve expert skills than does producing a single number which they find out is correct or not.

Having students attend to feedback on homework

Students attending to feedback and using it to improve is vital for learning. We have found three simple ways to encourage students to do this.

• For any question on which a student loses points, give them the option of getting some fraction (1/4-1/2) back by turning in an explanation of what was incorrect about their thinking that resulted in the error.
• Have each homework set contain a “reflection” problem such as, “Review your previous homework and the solution set, and then list all the problems you did incorrectly, what you did that was incorrect on each of those problems, and what you need to do differently on future problems of this type. If you did all the problems correctly, identify how you could improve a solution or which problem was most difficult and explain why.”
• Have the exam problems be very similar to homework problems and advertise to the class that this will be the case. It is easier to do this if you have good explicit learning goals for the course where it is clear that both homework and exam problems are testing the achievement of the learning goals.

UPCOMING EVENTS

Tuesday, february 14, 11:00, college of medicine auditorium.

Lecture by Carl Wieman : “Taking a scientific approach to science education.” Guided by experimental tests of theory and practice, science has advanced rapidly in the past 500 years.  Guided primarily by tradition and dogma, science and engineering education has remained largely medieval.  Research on how people learn combined with classroom experiments is now revealing much more effective ways to teach and evaluate learning at the university level than what is in use in most science and engineering classes.  This research is setting the stage for a new approach to teaching that can provide the relevant and effective science education for all students that is needed for the 21st century.

NEW SERVICE

Student consultants.

If you’d like feedback on how your class is going, and you’d like a student’s perspective, you can now invite our trained student consultants to visit your class and gather data. There are multiple options:

– Informal evaluation : The student consultants can come to one of your classes to interview students about how well they are learning and how they perceive the class. The interview usually takes around 20 minutes. The student consultant then compiles the student responses into a report and meets with you to discuss the results.

– Observer/Note-taker : The student consultant records in writing what happened in your class (e.g., chronology of classroom activities; time spent in questioning, board work, small group discussion; and so on). If you wish, they can use the COPUS . The student consultant describes rather than evaluates, and meets with you to present and discuss the report.

– Primed student : Prior to class, you inform the student consultant what he or she should watch for. Examples: How often do certain students respond? Are the students discussing course material among themselves? What seems difficult for the students? What are the students in the back rows of the class doing? The student consultant writes his or her observations in a report to share with you.

To schedule a visit by a student consultant, contact Fabrizio Fornara at [email protected] .

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Executive Functions

Signs of attention problems, attention or other learning issues, attention strategies.

By second grade, you can reasonably expect students to maintain attention for 20-30 minute stretches of time, even for topics they don’t like. The most common signs that students age 8+ might have attention problems:

Often fidgety, calls out, or disruptive

Frequently stares off into space or struggles to follow along in conversations or group discussions

Seems forgetful or often doesn’t remember

Attentive for long periods of time for activities they enjoy (video games, sports, a good book) but struggles to focus for short periods on topics they find less interesting

Inconsistent performance or scattered errors on assignments despite good understanding

Be cautious! Do not assume attention difficulties when you see a struggling student. Attention difficulties are commonly confused with other learning or emotional challenges, including:

Anxiety or Depression

Self-confidence

Other academic difficulties

Given that many of the observable signs overlap, an objective screener or evaluation is always the best way to avoid misidentification and ensure you’re supporting your student in the way they will benefit most.

In short, students who are not paying attention are not learning. Unaddressed attention difficulties often lead to gaps in knowledge and declining performance, even among the brightest students. These strategies are a great starting point to help students who struggle with attention.

Sit students away from   distractions  like the window or door. Ideally sit near the front of the room where a teacher can support them

Incorporate stretch  breaks  breaks every 20 minutes

Provide an organized desk space so they have everything they need readily accessible

Develop self-awareness of when they lose focus so they learn to get themselves back on track

Help them develop an achievable homework routines  that enable them to be successful

Show empathy ! Understand that these kiddos are likely trying hard to sit still and stay focused but it’s not easy for them.

Keep in mind, if your student does have an attention problem they are likely to need more structured, individualized supports over time. Early identification and support is always best.

Signs of Homework Struggles

Reasons for homework struggles, homework strategies.

While every student resists doing homework on occasion, getting a kid to finish homework really shouldn’t be a daily struggle. Here are the signs that a student might need some additional support to address homework problems:

Often hands in sloppy or unfinished homework 

Resists sitting down to start homework

Has difficulty getting started on assignments/Asks for help immediately

Falls asleep during homework

Gets up frequently to take bathroom breaks, sharpen a pencil, find a pen

Takes significantly longer than the recommended time for homework

Cries or complains often about homework

Often says they never learned the information in class or the teacher never told them

The reasons for homework struggles can vary widely, so it might take multiple conversations among teachers, parents and the student to fully understand homework problems, particularly if a student does not seem to be struggling while at school. Here are some of the most common reasons for homework challenges:

Too tired at the end of a long day of activities

Lack of structured routine

Weaker executive functions

Poor organization & time management skills

Weaker memory

Slower processing speed

Subject-specific learning difficulties

Parents and teachers can work together to provide homework support. Teachers can help students leave school with the books they need and clarity on their assignments. Parents can ensure students follow-through when they get home. Getting students on the right track can (and might need to) be a team effort.

Create a daily  checklist  or  planner  students check off as they pack up their backpack at the end of the day.

Have a homework schedule with the  estimated amount of time to be spent by assignment .

Provide an  organized desk space  and ensure students turn off all distractions like television or cell phones.

Using proven-effective study strategies such as  retrieval practice , rather than re-reading their notes.

Ensure students get a good night sleep

Poor homework habits can be hard to break. Helping students learn to manage the demands of homework while at home will be important for them to be successful in college and in life.

Listening & Following Directions Concerns

Is it a listening issue, strategies for listening & following directions.

By second grade, students should be able to listen and follow directions without constant reminders. These are the most common signs that students might be struggling to follow directions.

Follows single step instructions but struggles with two or more steps without help

Consistently misses steps in written or verbal instructions

Usually needs help getting started after instructions are given

Gets frustrated when asked to follow instructions independently

Struggles to follow along or understand class discussions 

Has difficulty understanding during read alouds or circle time

It’s important to pinpoint why your student is struggling, as listening & following directions are multi-faceted skills. Listening difficulties can have their roots in one or several areas.  The most common reasons students struggle to listen or follow directions:

Hearing problems. Check-in with your pediatrician or school nurse

Attention or executive functions struggles

Processing challenges

Reading or comprehension challenges

Too tired to listen/ insufficient sleep

Bored or uninterested

Since most teaching is done via lecture, and directions are usually given verbally, children with trouble listening and following directions often struggle. They may also underperform on tests because they do not follow the instructions correctly.

These strategies won’t solve the listening challenges, they can help students succeed while you are addressing the underlying cause:

Provide  verbal and written instructions  to make sure they can follow along and reference as needed. 

Give information in chunks , rather than giving information all at once.

Have students sit closer to the front of the room so you can spot check regularly for understanding.

Organization & Time Management Challenges

Organization strategies, organization & time management strategies.

By middle school, students should be capable of basic time management and organizational skills. Even the brightest students will struggle in school without good organizational skills. Here are signs that your student might be struggling more than most teens.

Understands the material but hands in incomplete or late assignments

Often the last to finish in-class assignments

Often asks for extensions or says homework takes too long

Very messy locker or desk

Often can’t find things when he needs them

Often late or unprepared for class

Struggles more than most to complete long-term projects

Doesn’t do “fair share” in group assignments

The reasons for poor organization can vary widely, so it might take multiple conversations among teachers, parents and the student to fully understand how to help. Here are some of the most common reasons for organization and time management struggles:

Feels anxious or overwhelmed and then gets “paralyzed”

An objective screener or consultation is always the best way to be certain to understand why the student is struggling and how to best help.

Even the brightest students who struggle with organization skills might not live up to their full potential. These strategies can result in spending less time on homework, less stress, and better grades.

Provide clear  expectations  on assignments and check in to be sure they are understood

Teach basic time management

Help them  organize their lockers  or homework space 

Show them how to  plan for longer projects .

Be patient. Provide gentle reminders  and encouragement, especially if you know they are trying their best.

• Focus & Attention Problems
• Homework Struggles
• Listening & Following Directions
• Organization & Time Management

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This Mindprint blog explains why study groups can be very effective for some students, provided students adhere to certain guidelines for participation. View Article

This Mindprint blog suggests the best flashcard apps along with the strategies to use them so students memorize quicker. View Article

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• Derivatives of multivariable functions
• Applications of multivariable derivatives
• Integrating multivariable functions
• Green’s, Stokes’, and the divergence theorems
• First order differential equations
• Second order linear equations
• Laplace transform
• Vectors and spaces
• Matrix transformations
• Alternate coordinate systems (bases)

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3.4: Homework Problems

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• Kathryn Haas
• Duke University

Each practice problem below requires that you correctly apply propagation of errors to report the correct value and its precision (including the error). You should attempt all seven problems prior to our schedule lab meeting on this topic (and submit prior to the meeting on Canvas). This pre-lab assignment will prepare you to participate in the lab meeting by presenting problems on the board, answering questions from your peers, and asking your own questions.

You will submit your work and final answers after the in-lab problem session. Your answers to these problems may be hand-written or typed. However, any submissions that are deemed illegible, unclear, or poorly organized will not be accepted.

(1) We will give you a MatLab template to get you help you in using MatLab for this problem set. However, you may use whatever technology (calculators, software, etc.) you like to aid in working these problems.

(2) It is important to show how your calculations are set-up and, where appropriate, give a sample calculation. Simply giving the final answer is not acceptable.

(3) In reporting all results, you should always round your reported answer to be consistent with your estimated uncertainty. For example: a calculated result of 56.2189 ± 0.0386 would be reported as 56.20 ± 0.04 where 0.04 is the standard deviation, 95% confidence level, or propagated uncertainty.

The seven problems are below. Note that there are Hints that you can click on for each problem. 

PROBLEM 1: Statistics

A student makes five independent measurements of each of the linear dimensions of a box. The results are tabulated as follows:

A. Calculate the average values of length, width, and height, and calculate the standard deviation in each of these three quantities. Report the values appropriately, considering the calcuated precision.

B. Calculate the variance of the length, width, and height. 

C. Calculate the 95% confidence limits to the measurements of length, width, and height.

D. Calculate the 95% confidence limits to the average volume obtained from the independent measurements of length, width, and height.

This problems is one where there are five replicate measurements of length, width, and height. That's enough to use some basic statistics to determine our confidence of each measurement. Normally the standard deviation is an appropriate indicator of the data's precision in a case like this where there are multiple measurements. The problem also asks for the variance and the 95% confidence limit. Be sure to report all values in the appropriate number of digits, considering the calculated precision. The equation for variance and for 95% confidence can be found in Section 3.2 .

PROBLEM 2: A Simple Case for Propogation of Error

A student weighs a sample using an analytical balance that has an estimated precision of ±0.5 mg. From the data below, calculate the weight of the sample and the range of uncertainty in the net weight.

This is a simple propagation of error problem – any time we add, multiply, divide, or subtract multiple measurements, the final value's error is a propagation (or a combo of) the error associated with each measurement. So, you just need to recognize this fact, and then find the appropriate equation to propagate error in the case when values are subtracted. The appropriate equation is given in Section 3.2 (also on pg 57 of Shoemaker, equation 55...but in the Shoemaker text, you'd need to take the square root of both sides of the equation).

In this case, the function (F) that determines the sample weight is \(F = \text{Mass of Sample in Flask }-\text{ Mass of empty flask} = x - y\)

Apply Equation 3.2.7 where \(a, b= 1\) (and thus can be ignored), and the uncertainty in the measurements are \(\Delta x = \Delta y = 0.0005 \; g\). Specifically for this case, the uncertainty is:

\[\Delta F = \sqrt{(0.0005)^2 + (0.0005)^2}\]

PROBLEM 3: Statistics and Rejection of Discordant Data

An investigator measures the photon emission in the reaction

\( Na^{+} + O^{-} \rightarrow Na^{*} + O \overset{h\nu }{\rightarrow} Na + O \)

in which the emitted photon (at 589 nm) is counted by means of a photomultiplier. Here are some typical "run" data

Evaluate the data using statistical methods only and calculate:

A. The average signal value.

B. The variance in the average signal value.

C. The 95% confidence limits to the average signal value.

D. Using the Q test, determine whether the results from any one run can be rejected as discordant data at the 90% confidence level

This is a noisy data set where the signal is just barely detectable. The problem explicitly asks for calculation of variance (variance is just the square of standard deviation), 95% confidence limit (see problem 1), and application of the Q-test to determine whether any of the data points should be rejected. The Q-test is described in Section 3.3.1 .

PROBLEM 4: Least Squares Analysis and Rejection of Discordant Data

A. Fit a straight line:

\( y = a + bx \)

to the following set of data points by the linear least-squares method

x 26 30 44 50 62 68 74 y 92 85 78 81 54 51 40

and calculate the coefficients \(a\) and \(b\) using the Equations (3.3.5) and (3.3.6) from Section 3.3 .

B. Plot the x,y data and the least-squares line, and submit this with your report.

C. Calculate the standard deviation of the coefficients, \(a\) and \(b\) using Equations (3.3.11), (3.3.12) and (3.3.13) from from Section 3.3 (note that the lsq script does this automatically for you, and you are welcome to use it!).

D. Calculate the correlation coefficient, using equation (3.3.14) from Section 3.3 . What is the significance of the sign of r?

E. Apply the Q-test to the y-residuals (see Equation (3.3.2) from Section 3.3 ), to determine whether there is a statistical basis for rejection of any of the data points as an outlier, (I) at the 96% confidence level (II) at the 90% confidence level.

F. If a data point is rejected, repeat the regression analysis (steps A-D) using the remaining data.

G. Comment quantitatively on the effect of data removal on the regression analysis.

You will need to plot the x,y data and then perform a linear fit. You are explicitly instructed to determine the standard deviation of the slope and y-intercept of the least squares fit linear function. There are three ways I know to determine these values: (1) Excel, using the "LINEST" array function. (2) MatLab, using the lsq custom script or the Statistics and Machine Learning Toolkit (3) Logger pro does it automatically with linear fitting. The LSQ script is recomended.

Hints for individual parts:

• A,B) - just plot the data and best fit line and get the equation.
• C, D) use lsq (Matlab) 
• E) Following the linear regression analysis, perform a Q-test at two different confidence intervals - 96% and 90%. For this, you will need the critical Q-values for these two confidence limits (see Section 3.3.1 ).

PROBLEM 5: Error Propagation

In a chemistry lab, students obtain the following data and are asked to find the molecular weight (M) of methanol using PV = nRT. Determine the uncertainty in the result using a propagation of error treatment.

The volume (V) in both trials was 1.05678 liter, with no uncertainty given. You must decide on the uncertainty in V.  If necessary, perform appropriate conversions of the units for each quantity, including R, so that the final value of M is reported in the correct units.

This is a propagation of error problem, where we are multiplying and dividing individual measurements to find the value of interest. In this case, it is the determination of the molecular weight (which I'm going to represent as MW) of methanol from the mass of methanol, pressure, temperature, and volume measurements.

So, first…how would we do this? 

\[M W=\frac{\text { mass of methanol in grams }}{\text { moles methanol }}=\frac{m}{n}\]

The mass of methanol was measured in the experiment, and the number of moles can be determined from \(PV=nRT\). The calculation involves multiplication and division to determine  \(n=\dfrac{PV}{RT}\), and then involves division again to determine \(MW=\dfrac{m}/{n}.

We can substitute into the equation for \(MW\) and get everything into one combined equation:

\[MW=\frac{m}{n}={m}{\frac{PV}{RT}}={mRT}{PV}\]

Once you recognize that it is simply a propagation of errors problem in which the factors are multiplied and divided, you can determine the error in the molecular weight value using Equation 3.2.8 .

The errors in P, T, and m are explicitly given. The error in V is not explicitly given, but we can assume that the error is indicated in the number of digits given in the volume measurement. The volume given is 1.0567 8 liters or 1,056.7 8 mL - so we assume we are uncertain in the last digit (the 8) by roughly half a digit…. to +/- 0.00005 L or +/- 0.05 mL.

Note : Pay attention to units. Depending on which units you choose for R, unit conversion may be necessary. 

PROBLEM 6: Error Propagation

The rate constant for the reaction

\( 2DI \rightarrow D_{2} + I_{2} \)

is measured at two temperatures with the given estimated uncertainties:

\( k_{660}=(1.2 \pm 0.2)\times 10^{-3}\frac{liter}{mol\; sec} \) at \( 660\pm 2 K \)

\( k_{660}=(1.8 \pm 0.2)\times 10^{-3}\frac{liter}{mol\; sec} \) at \( 720\pm 2 K \)

A. Calculate the activation energy E act for the reaction using

\( \large {ln\left ( \frac{k_{2}}{k_{1}} \right )=-\frac{E_{act}}{R}\left (\frac{1}{T_{2}} -\frac{1}{T_{1}} \right )} \)

B. Assuming the above equation is a correct expression for E act , what is the uncertainty in E act ?

The calculation of  \(E_{act}\) using the given data is relatively straightforward. The error in the value of \(E_{act}\) is a propagation of the uncertainty of the two \(k\) values and two \(T\) values. The function is complicated enough that it should be addressed using partial derivatives ( Equation 3.2.6 ). There is no one simple shortcut in this case, but if the function is broken down into simpler functions, then error can be determined in a step-wise fashion using the shortcuts .

PROBLEM 7: Error Propagation

In the method of Clement and Desormes, the heat capacity ratio of an ideal gas is determined from the manometrically determined values of P 1 , the gas pressure at temperature T 1 ; P 2 , the gas pressure immediately after a reversible adiabatic expansion when the temperature is T 2 ; and, P 3 , the gas pressure after the gas has warmed back up to temperature T 1 . The equation used to calculate the heat capacity ratio is

\( \large {\gamma=\frac{C_{P}}{C_{V}}=\frac{\frac{C_{V}}{R}+1}{\frac{C_{V}}{R}}} \)

\( \large {\frac{C_{V}}{R}=\frac{P_{2}\left [ 1-\left ( \frac{P_{3}}{P_{1}} \right ) \right ]}{P_{3}-P_{2}}} \)

Calculate the uncertainty in the heat capacity ratio γ, given the following data: P 1 = 763.1 ± 0.2 mmHg P 2 = 757.0 ± 0.1 mmHg P 3 = 758.7 ± 0.2 mmHg

This is propogation of error problem where the error in the value of \(\gamma\) is a propagation of the uncertainty of the three \(P\) measurements. The calcaution of \(\gamma\) involves a complex function for which no short cuts are available. I recomend using partial derivatives to arrive at a proper estimation of error in the heat capacity ratio.  Some students have broken the function into separate parts and used shortcuts for each, and have arrived at a reasonable estimation of error…though I find this to be more work than doing it using partial derivatives).  

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The Pros and Cons of Homework

Updated: December 7, 2023

Published: January 23, 2020

Homework is a word that most students dread hearing. After hours upon hours of sitting in class , the last thing we want is more schoolwork over our precious weekends. While it’s known to be a staple of traditional schooling, homework has also become a rather divise topic. Some feel as though homework is a necessary part of school, while others believe that the time could be better invested. Should students have homework? Have a closer look into the arguments on both sides to decide for yourself.

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Why should students have homework, 1. homework encourages practice.

Many people believe that one of the positive effects of homework is that it encourages the discipline of practice. While it may be time consuming and boring compared to other activities, repetition is needed to get better at skills. Homework helps make concepts more clear, and gives students more opportunities when starting their career .

2. Homework Gets Parents Involved

Homework can be something that gets parents involved in their children’s lives if the environment is a healthy one. A parent helping their child with homework makes them take part in their academic success, and allows for the parent to keep up with what the child is doing in school. It can also be a chance to connect together.

3. Homework Teaches Time Management

Homework is much more than just completing the assigned tasks. Homework can develop time management skills , forcing students to plan their time and make sure that all of their homework assignments are done on time. By learning to manage their time, students also practice their problem-solving skills and independent thinking. One of the positive effects of homework is that it forces decision making and compromises to be made.

4. Homework Opens A Bridge Of Communication

Homework creates a connection between the student, the teacher, the school, and the parents. It allows everyone to get to know each other better, and parents can see where their children are struggling. In the same sense, parents can also see where their children are excelling. Homework in turn can allow for a better, more targeted educational plan for the student.

5. Homework Allows For More Learning Time

Homework allows for more time to complete the learning process. School hours are not always enough time for students to really understand core concepts, and homework can counter the effects of time shortages, benefiting students in the long run, even if they can’t see it in the moment.

6. Homework Reduces Screen Time

Many students in North America spend far too many hours watching TV. If they weren’t in school, these numbers would likely increase even more. Although homework is usually undesired, it encourages better study habits and discourages spending time in front of the TV. Homework can be seen as another extracurricular activity, and many families already invest a lot of time and money in different clubs and lessons to fill up their children’s extra time. Just like extracurricular activities, homework can be fit into one’s schedule.

The Other Side: Why Homework Is Bad

1. homework encourages a sedentary lifestyle.

Should students have homework? Well, that depends on where you stand. There are arguments both for the advantages and the disadvantages of homework.

While classroom time is important, playground time is just as important. If children are given too much homework, they won’t have enough playtime, which can impact their social development and learning. Studies have found that those who get more play get better grades in school , as it can help them pay closer attention in the classroom.

Children are already sitting long hours in the classroom, and homework assignments only add to these hours. Sedentary lifestyles can be dangerous and can cause health problems such as obesity. Homework takes away from time that could be spent investing in physical activity.

2. Homework Isn’t Healthy In Every Home

While many people that think homes are a beneficial environment for children to learn, not all homes provide a healthy environment, and there may be very little investment from parents. Some parents do not provide any kind of support or homework help, and even if they would like to, due to personal barriers, they sometimes cannot. Homework can create friction between children and their parents, which is one of the reasons why homework is bad .

3. Homework Adds To An Already Full-Time Job

School is already a full-time job for students, as they generally spend over 6 hours each day in class. Students also often have extracurricular activities such as sports, music, or art that are just as important as their traditional courses. Adding on extra hours to all of these demands is a lot for children to manage, and prevents students from having extra time to themselves for a variety of creative endeavors. Homework prevents self discovery and having the time to learn new skills outside of the school system. This is one of the main disadvantages of homework.

4. Homework Has Not Been Proven To Provide Results

Endless surveys have found that homework creates a negative attitude towards school, and homework has not been found to be linked to a higher level of academic success.

The positive effects of homework have not been backed up enough. While homework may help some students improve in specific subjects, if they have outside help there is no real proof that homework makes for improvements.

It can be a challenge to really enforce the completion of homework, and students can still get decent grades without doing their homework. Extra school time does not necessarily mean better grades — quality must always come before quantity.

Accurate practice when it comes to homework simply isn’t reliable. Homework could even cause opposite effects if misunderstood, especially since the reliance is placed on the student and their parents — one of the major reasons as to why homework is bad. Many students would rather cheat in class to avoid doing their homework at home, and children often just copy off of each other or from what they read on the internet.

5. Homework Assignments Are Overdone

The general agreement is that students should not be given more than 10 minutes a day per grade level. What this means is that a first grader should be given a maximum of 10 minutes of homework, while a second grader receives 20 minutes, etc. Many students are given a lot more homework than the recommended amount, however.

On average, college students spend as much as 3 hours per night on homework . By giving too much homework, it can increase stress levels and lead to burn out. This in turn provides an opposite effect when it comes to academic success.

The pros and cons of homework are both valid, and it seems as though the question of ‘‘should students have homework?’ is not a simple, straightforward one. Parents and teachers often are found to be clashing heads, while the student is left in the middle without much say.

It’s important to understand all the advantages and disadvantages of homework, taking both perspectives into conversation to find a common ground. At the end of the day, everyone’s goal is the success of the student.

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Homework 35.a - sp 24.

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12 thoughts on “HOMEWORK 35.A - SP 24”

Just want to note that the problem statement says the cross section area is 2 ft by 4 ft which I believe is supposed to be inches. If an instructor or TA is reading this, should we change the ft to inches or just solve it in the wacky way it is?

Try solving it out as is. It works out to be pretty realistic numbers. All you have to do is convert the moment from kip-ft to kip-inches by multiplying by 12, and then do the rest of your equations as is (converting the y-max and area moment to inches before calculating!).

does our maximum normal stress need to be in psi ?

I haven't worked out the problem yet, but I think ksi or psi either works, as long as the units cancel.

I kept mine in kips/ft^2 (equal to ksi) because it never specified the specific units to use. I'm guessing any unit is fine as long as you make sure its converted correctly.

To determine where pure bending exists, is drawing a basic shear and moment graph the best way to go about it? Or are there simpler methods you would recommend?

That is what they want you to do. It is a pretty good method for finding pure bending.

The professor recommended to start by drawing the diagrams because they can very see where pure bending happens.

Is I=(b^2)(h^2)/4 the correct value?

Yes, I believe so

How exactly can we check ourselves to know we have the correct answer?

I would say just verify the equilibrium is correct and ensure correct signs.

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