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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] .

Because differences are our greatest strength

Homework challenges and strategies

By Amanda Morin

Expert reviewed by Jim Rein, MA

At a glance

Kids can struggle with homework for lots of reasons.

A common challenge is rushing through assignments.

Once you understand a homework challenge, it’s easier to find solutions.

Most kids struggle with homework from time to time. But kids who learn and think differently may struggle more than others. Understanding the homework challenges your child faces can help you reduce stress and avoid battles.

Here are some common homework challenges and tips to help.

The challenge: Rushing through homework

Kids with learning difficulties may rush because they’re trying to get through what’s hard for them as fast as possible. For kids with ADHD, trouble with focus and working memory may be the cause.

Rushing through homework can lead to messy or incorrect homework. It can also lead to kids missing key parts of the assignment. One thing to try is having your child do the easiest assignments first and then move to harder ones.

Get more tips for helping grade-schoolers and middle-schoolers slow down on homework.

The challenge: Taking notes

Note-taking isn’t an easy skill for some kids. They may struggle with the mechanical parts of writing or with organizing ideas on a page. Kids may also find it hard to read text and take notes at the same time.

Using the outline method may help. It divides notes into main ideas, subtopics, and details. 

Explore different note-taking strategies .

The challenge: Managing time and staying organized

Some kids struggle with keeping track of time and making a plan for getting all of their work done. That’s especially true of kids who have trouble with executive function.

Try creating a homework schedule and set a specific time and place for your child to get homework done. Use a timer to help your child stay on track and get a better sense of time.

Learn about trouble with planning .

The challenge: Studying effectively

Many kids need to be taught how to study effectively. But some may need concrete strategies.

One thing to try is creating a checklist of all the steps that go into studying. Have your child mark off each one. Lists can help kids monitor their work.

Explore more study strategies for grade-schoolers and teens .

The challenge: Recalling information

Some kids have trouble holding on to information so they can use it later. (This skill is called working memory. ) They may study for hours but remember nothing the next day. But there are different types of memory.

If your child has trouble with verbal memory, try using visual study aids like graphs, maps, or drawings.

Practice “muscle memory” exercises to help kids with working memory.

The challenge: Learning independently

It’s important for kids to learn how to do homework without help. Using a homework contract can help your child set realistic goals. Encourage “thinking out loud.”

Get tips for helping grade-schoolers do schoolwork on their own.

Sometimes, homework challenges don’t go away despite your best efforts. Look for signs that kids may have too much homework . And learn how to talk with teachers about concerns .

Key takeaways

Some kids have a hard time doing schoolwork on their own.

It can help to tailor homework strategies to a child’s specific challenges and strengths.

Sometimes, there’s too much homework for a child to handle. Talk to the teacher.

Explore related topics

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By submitting my email address. i certify that i am 13 years of age or older, agree to recieve marketing email messages from the princeton review, and agree to terms of use., 8 easy ways to finish your homework faster.

How many times have you found yourself still staring at your textbook around midnight (or later!) even when you started your homework hours earlier? Those lost hours could be explained by Parkinson’s Law, which states, “Work expands to fill the time available for its completion.” In other words, if you give yourself all night to memorize those geometry formulas for your quiz tomorrow, you’ll inevitably find that a 30 minute task has somehow filled your entire evening.

We know that you have more homework than ever. But even with lots and lots to do, a few tweaks to your study routine could help you spend less time getting more accomplished. Here are 8 steps to make Parkinson’s Law work to your advantage:

1. Make a list

This should be a list of everything that has to be done that evening. And we mean, everything—from re-reading notes from this morning’s history class to quizzing yourself on Spanish vocabulary.

2. Estimate the time needed for each item on your list

You can be a little ruthless here. However long you think a task will take, try shaving off 5 or 10 minutes. But, be realistic. You won’t magically become a speed reader.

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3. Gather all your gear

Collect EVERYTHING you will need for the homework you are working on (like your laptop for writing assignments and pencils for problem sets). Getting up for supplies takes you off course and makes it that much harder to get back to your homework.

The constant blings and beeps from your devices can make it impossible to focus on what you are working on. Switch off or silence your phones and tablets, or leave them in another room until it’s time to take a tech break.

Read More: How to Calculate Your GPA

5. Time yourself

Noting how much time something actually takes will help you estimate better and plan your next study session.

6. Stay on task

If you’re fact checking online, it can be so easy to surf on over to a completely unrelated site. A better strategy is to note what information you need to find online, and do it all at once at the end of the study session.

7. Take plenty of breaks

Most of us need a break between subjects or to break up long stretches of studying. Active breaks are a great way to keep your energy up. Tech breaks can be an awesome way to combat the fear of missing out that might strike while you are buried in your work, but they also tend to stretch much longer than originally intended. Stick to a break schedule of 10 minutes or so.

8. Reward yourself! 

Finish early? If you had allocated 30 minutes for reading a biology chapter and it only took 20, you can apply those extra 10 minutes to a short break—or just move on to your next task. If you stay on track, you might breeze through your work quickly enough to catch up on some Netflix.

Our best piece of advice? Keep at it. The more you use this system, the easier it will become. You’ll be surprised by how much time you can shave off homework just by focusing and committing to a distraction-free study plan.

Stuck on homework?

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The 5 Best Homework Help Websites (Free and Paid!)

Other High School , General Education

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.

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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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9 Best Homework Help Websites

July 22, 2023

When I was in high school, resources for extra homework help weren’t exactly abundant. If you were struggling with a Shakespeare sonnet, you could always run to the bookstore and pick up a CliffNotes guide. SparkNotes was also gaining in popularity. But these early homework help resources had limited catalogs and were focused primarily on literature. Today, I imagine students suffer from the opposite problem—having too many choices when it comes to homework help websites. When the options are seemingly endless, knowing what to look out for takes on an added importance. Below, I’ll go through a list of 9 stand-out homework help websites and briefly discuss what makes them worth a visit.

Homework Help Websites – The Basics

The best homework help websites do more than just spit out an answer to that tricky math problem. They actually help students learn the material. Common features of homework help websites are educational videos and lectures, practice tests and quizzes, study tools like flashcards, and Q&As with experts. Many sites offer features that allow students to ask specific questions and get real-time feedback. There are also a number of services that offer one-on-one tutoring. Some homework help sites are free, while others require a paid subscription.

1) Khan Academy

Khan Academy is an amazing resource for students of all ages. It’s free, and it really is an academy—it offers full courses in a wide array of subjects, from pre-K math to high school physics. The courses consist of readings, video lectures, practice exercises, and quizzes. The breadth of material is impressive. In math alone, I see course listings for Algebra 1 and 2, Geometry, Trigonometry, Precalculus, Statistics, Multivariable calculus—you get the idea. Khan Academy also offers a wide variety of AP courses, state-specific curricula, test-prep programs, and life skill courses, like personal finance.

It’s important to note that Khan Academy isn’t a one-on-one tutoring platform. But because of their extensive library of material, the search function is especially powerful. Try it out. I did a search for argumentative essay help, and found a comprehensive guide to writing argumentative essays that was a part of a larger writing course.

Chegg is a paid homework help service. Unlike Khan Academy, Chegg isn’t built around specific courses. Rather, it offers a variety of homework-support resources. Among those resources are plagiarism and grammar checkers, a proofreading service, and a “math solver”, which allows students to enter a problem and get back both a solution and a detailed step-by-step explanation of how the problem was solved. Perhaps the most powerful tool Chegg offers is its “Expert Q&A” feature. This service allows students to take a picture of their homework problem, upload it to the site, and get a detailed response in return. Chegg’s emphasis on process and explanation make it a valuable educational resource for students—not just a way to get a quick answer.

Best Homework Help Websites (Continued)

Quizlet is a well-known and worthwhile study resource. It offers a variety of courses, and it also has an expert-response feature. But Quizlet’s best feature, in my option, is the flashcards tool. Students can create their own digital decks of cards and practice them on Quizlet—just like an old fashion set of index cards. I had a ton of success using Quizlet’s flash card feature to help me memorize words for my foreign language requirement in college. It’s a simple but powerful tool. Although often maligned as a learning method, rote rehearsal and spaced repetition are effective ways to encode information . Quizlet’s flashcard feature is a great way to put those techniques into practice.

4) Socratic

is an AI-powered homework support app that allows students to type or take pictures of questions and receive solutions right away. Since it works with AI, it relies on the web’s vast stores of accumulated knowledge—you’re not interacting with a human tutor. Nonetheless, I found it to be an extremely helpful tool. I tried it out first using a specific math problem. In just a few seconds I was provided with the solution and an explainer with relevant formulas, plus a graphic to help visualize the underlying logic. There were also suggested links to additional resources. For example, when I asked Socratic to explain how the German genitive case works, it suggested a YouTube video and a number of articles from blogs and other language-learning sites.

Since Socratic doesn’t feature courses or one-on-one tutoring support, I wouldn’t lean on it if I were really struggling in a particular class. But as a tool to check your work, make sure you’re on the right track, and become aware of additional resources, it’s worth a download.

5) Photomath

Photomath is, as you might have guessed, a site for math homework help. Like other homework help websites, Photomath allows students to take a picture of a problem and receive an instant, step-by-step solution. Included along with the solution is an explanation of relevant concepts and formulas, plus videos covering mathematical concepts. Photomath does offer a few basic courses, too. So if in addition to homework-specific help you want to brush up on the basics, they’ve got you covered in arithmetic, algebra, and calculus crash courses.

6) Studypool

Studypool is a paid homework support service that provides solutions to specific questions. Studypool offers support in all the major subjects, with a particular emphasis on science. Students can ask questions on everything from anatomy to physics. Like other services, students upload their exact questions or problems directly to the site. But Studypool’s payment model is a bit different: instead of paying for tutoring time or a monthly subscription, students pay for solutions to each question they submit. When a student submits a question, tutors submit bids to answer them. The student then can select which tutor/price option works best. After students select the price and tutor they want, they’re connected with the tutor and given the solution and explanation via messenger.

The draw of Studypool is that it gives students access to real (i.e., human) tutors who are experts in their field. The downside is that pricing isn’t transparent, and students pay per question.

7) College Info Geek

College Info Geek is the study-support website that I wish I knew about when I was in high school and college (they didn’t pay me to write that, I swear). The site focuses not on specific courses or questions, but on how to become a more effective learner. Here it’s all about “learning how to learn”—study tips, memorization and note-taking techniques, and much more. The articles are well-researched, clearly-communicated, practical, and comprehensive. For example, the article on how to improve your memory includes a breakdown of the different types of memory processes, memorization techniques, and even a discussion of how nutrition affects memory. College Info Geek is a great resource for everyone, not just high school and college students.

8) SparkNotes

Yes, Sparknotes made the list! The site offers lessons in a whole bunch of subjects—biology, chemistry, computer science, history, philosophy, math—but its specialty is literature. SparkNotes provides summaries and analyses of novels, short stories, poetry, and non-fiction, from The Canterbury Tales to Toni Morrison, Saul Bellow, and Junot Diaz. SparkNotes breaks down books into sub-sections and provides synopses and analyses for each section. There are also separate pages for character breakdowns, discussions of themes and motifs, and explanations of important quotes. I’d caution against using SparkNotes if you’re trying to “hack” a novel or poem and get simple answers about what it “means.” But as a way to supplement your own understanding and interpretation, it’s a great resource. Shmoop is also worth checking out for extra support in literature, poetry, mythology, and the history of literary movements.

9) Grammarly

I’m not sure if Grammarly is an obvious or unexpected choice to round out the list. Either way, it deserves a mention here. Grammarly is a writing tool. It checks and suggests corrections for incorrectly spelled words and misused punctuation. But Grammarly also scans and corrects for things like clarity and vocab usage. It flags sentences that are vague, or overly wordy, and alerts you if you’re using that flashy vocab word incorrectly. It even gives suggestions if it thinks your writing is a bit bland. I don’t see Grammarly as a crutch, but rather as a tool. It can help you master those pesky recurring grammar and usage issues. Always mix up effect and affect? Grammarly will continue to course correct until you’ve got it down yourself.

Homework Help Websites – Final Thoughts

None of the above homework help websites should be seen as a panacea. Each has benefits and drawbacks, strengths and weak points. The list is far from exhaustive. And the sites don’t have to be used in isolation. Try a few out, mix and match. College Info Geek is an excellent supplement to any study regimen. Socratic can be used as a tool to check answers for math homework, and at the same time you can use Grammarly to describe your problem to a tutor on Chegg. At their best, these sites are more than quick fixes to stubborn homework problems—they’re aids to genuine learning.

Additional Resources

You should also check out College Transitions’ “ High School Success ” blogs for help with a number of common high school assignments, including:

• Lord of the Flies Summary & Analysis 
• The Great Gatsby and The American Dream
• Analysis of Hamlet’s “To be or not to be” Speech
• Robert Frost’s Road Not Taken Analysis 
• High School Success

Dane Gebauer

Dane Gebauer is a writer and teacher living in Miami, FL. He received his MFA in fiction from Columbia University, and his writing has appeared in Complex Magazine and Sinking City Review .

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For more information about the Homework tab on your course homepage, please see this page .

If you're having trouble with the homework, we're here to help! Check out the When You Get Stuck guide for suggestions and to learn more all the resources available to you.

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What is the homework, description of homework types, the aops honor code, homework faqs.

Find the name of your class below for more information about the types of homework and other practice. You can find brief descriptions of each type below .

Textbook Readings

The textbook readings provide a brief introduction to the week's class topics. The assigned chapters or sections are listed on both the Overview and Homework tabs of your Course Homepage . Readings should be completed before that week's live class session, to help you get the most out of the class.

Handouts provide a brief introduction to the week's class topics. Handouts can be found on the Handouts tab of your Course Homepage and should be read before that week's live class session, to help you get the most out of the class.

Alcumus is our online learning system, and it is the main source of practice you'll have in this course. Alcumus monitors your progress and carefully selects problems, just for you, based on your performance on earlier problems. The course homepage will tell you what subjects are assigned each week. Alcumus feeds you problems, checks your answers, provides solutions, and then picks more problems.

If your course has Alcumus assignments, these are the problems we recommend starting with, before the Challenge or Writing Problems.

For more about Alcumus assignments, please see this page .

Short-Answer Challenge Problems

Short-answer problems are those for which you'll enter a "short" answer of some sort, such as a number, letter, or expression. These problems are graded instantly by the computer; you'll immediately know if your answer was correct. As their name suggests, these problems are meant to be challenging !

For more details on Short-Answer Challenge Problems, please see this page .

Writing Problems

Writing Problems will ask you to write complete solutions to the problems, not just a sentence or final answer. You will get feedback on both the style and content of your solutions to these writing problems. Writing problems are those that give you true practice as a mathematician, communicating all of your ideas.

For more about Writing Problems, please see this page .

For more information on what to do if you need a little more time for a writing problem, please see our Extensions page .

Python Writing Problems: What good is a programming course without some actual programming practice? For more information on the unique homework in our Python courses, please see this page .

Practice Tests

Contest-preparation courses for the AMC 10, AMC 12, and AIME each provide one practice test in the style of that exam. We strongly encourage students to take the exam under test conditions. If the test is available, students will find a link to the test problems as well as a space to enter their answers. If the test is not yet available, its release date will be indicated. Once answers are submitted, the students will immediately be shown their score. Answers to these practice tests may not be re-submitted.

There is a due date for the test answers to be entered on this page—students are asked not to discuss the content of the test until after that date, but answers can be submitted after that date.

Discussion Problems

Discussion Problems invite you to engage directly with your peers. Collaborating and communicating are vital skills for any mathematician. Discussion Problems are a place to bounce ideas off of other students and explore new mathematical concepts together. You may be asked to dive deeper into class concepts, experiment with mathematical constructions, trade proofs of a theorem, or challenge your peers by writing your own math problems.

A student must agree to the AoPS Honor Code before accessing the course homepage. This honor code outlines our major expectations of students throughout the course.

The Art of Problem Solving Honor Code is as follows:

• I will be respectful of all other AoPS users while in this class and on this site as stated in the AoPS Terms of Service .
• I will not misrepresent another person's words or ideas as my own.

More details about the Honor Code can be found here .

When and in what order should I work?

In general, our most successful students start by reading the textbook or handouts (when available) before class, then attending class or reviewing the transcript, and then finally attempting the homework. Within the homework, we recommend Alcumus first, then the Challenge Problems on the Homework tab, then the Writing Problems. You can find more details on the Working Through Class Material page.

Many classes also have a My Goals tab on the course homepage to help you keep track of and pace yourself with the the weekly assignments.

When is the homework due?

Homework is typically due 8 days after the class. The due date for a week's assignment will be displayed in the top-left gray box on the Homework tab of the course homepage . Writing Problems due dates are most strictly tied to those deadlines. You'll need to request an extension if you need more time to work on those problems. Short-Answer Challenge Problems can be solved at any point after they are available, and Alcumus assignments may be completed after the due date. However, we encourage you to keep up with the due dates as much as possible so that you do not fall behind the class!

How can I get help?

We're glad you've asked! The course message board is the best place to get help with any class material, whether you need some clarification about a topic, you have a question about a homework problem, or you'd like some help understanding a particular solution. Course staff, other AoPS administrators, and even your classmates are able to help answer you questions, make suggestions, or provide any other assistance you might need!

Check out our guide for When You Get Stuck , which outlines the other resources available as part of the course and recommendations for how to use them!

How do I keep track of my homework?

The information displayed at the top of Homework tab will help you keep track of all the assignments due each week and their due dates. We've also created a few other ways to help you keep track of how it's going, including the Report tab, the My Goals tab , and weekly class reminder emails with a summary of your progress. Check out the Tracking Your Progress page for more information.

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What is my grade?

The data we put on the class homepage is there to communicate with you about what work is assigned and to help you complete that work. This page provides more information about the different ways you can track your progress in the class. At the end of any subject or computer science course, we should be able to provide a letter grade upon request. Visit our Grades and Documentation page for instructions on how to submit a request, as well as more details on our grading philosophy.

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7 Apps That Can Do Your Homework Much Faster Than You

In the field of educational technology, some apps might be getting too smart.

More and more apps are delivering on-demand homework help to students, who can easily re-purpose the learning tools to obtain not just assistance, but also answers. Whether or not that’s cheating—and how to stop it—is one of the concerns surrounding a new app that can solve math equations with the snap of a camera . While the software has inspired teachers to create real-world homework problems that can’t be automatically solved , that strategy doesn’t hold up to other apps that tap into real-life brains for solutions.

Here’s a look at 7 apps that can do your homework for you, and what they have to say about cheating:

Price : Free Availability : iOS, Android app coming in early 2015

The new, seemingly magic app allows users to take pictures of typed equations, and then outputs a step-by-step solution. As of Wednesday, the app is the number one free app on the App Store. But the biggest issue, one teacher argues , isn’t if students will use the app to cheat, because many will. Rather, it’s about how teachers will adapt. A PhotoMath spokeswoman said educators have welcomed the app with positive reviews, but the software remains “quite controversial.”

“We didn’t develop PhotoMath as a cheating tool. We really wanted kids to learn,” said Tijana Zganec, a sales and marketing associate at tech company MicroBlink, which created PhotoMath. “If you want to cheat, you will find a way to cheat. But if you want to learn, you can use PhotoMath for that.”

Whether you’re a high schooler with eight periods of classes or a college student tackling dozens of credits, there’s one thing you’ve got for sure: a mess of assignments. iHomework can help you keep track of all your work, slicing and dicing it in a variety of ways. Sorting it by due date, week, month, or by course, the app is more organized than a Trapper Keeper. And in integrating data from Questia, you can link your reading material to your assignments so you don’t have to dig through a pile of papers to find the right information.

A scheduling feature can help you keep track of those random bi-weekly Thursday labs, and you can even mark the location of your courses on a map so you don’t end up on the wrong side of campus. And finally, with iCloud syncing, you can access all this information on whatever Apple-compatible device you’re using at the moment — no need to dig for your iPad.

Google Apps for Education

Taking the search giant’s suite of free browser-based apps and sandboxing them so they are safe for school use, Google Apps for Education is an excellent alternative to the mainstream installable productivity software, but this one has a perk that almost school board will love—it’s free. Packaging together favorites like Gmail, Hangouts, Google Docs, Google Sheets, and Google Drive with Classroom, a digital hub for organizing assignments and sending feedback, the goal of this collection is to make learning a more collaborative process.

Though Google Apps for Education is cloud-hosted, the programs can be used offline, ideal for when your student needs to escape the internet and work distraction-free. And since it works on any device, it also helps students avoid buying overly expensive hardware. That means more money for extracurricular activities.

Price: Free, but some homework services require payment Availability: iOS and Android

HwPic is a tutoring service that allows students to take send pictures of their homework to tutors, who will then respond within minutes to your questions with a step-by-step solution. There’s even an option to expedite the answers if a student is in a hurry. HwPic Co-Founder Tiklat Issa said that the app was initially rejected by Apple’s App Store, which believed it would promote cheating, but he successfully argued that just because someone uses the app in a way that it’s not meant to be used doesn’t mean the app should be punished.

Issa added that HwPic prohibits cheating in its terms and conditions. Tutors don’t solve homework that has words like “Quiz” or “Exam,” and they often know if a student is sending a photo during a test if they’ve paid for expedited answers, and if the photo is dim, blurry and taken under a desk. “We’ve minimized cheating,” said Issa. “We haven’t eliminated it. That’s kind of unrealistic.”

Wolfram Alpha

Price : $2.99 Availability : iOS and Android

Wolfram Alpha is similar to PhotoMath, only that it targets older students studying high levels of math and doesn’t support photos. The service also outputs step-by-step solutions to topics as advanced as vector calculus and differential equations, making it a popular tool for college students.

“It’s cheating not doing computer-based math, because we’re cheating students out of real conceptual understanding and an ability to drive much further forward in the math they can do, to cover much more conceptual ground. And in turn, that’s cheating our economies,” said Conrad Wolfram, Wolfram Research’s Director of Strategic Development, in a TEDx Talk . “People talk about the knowledge economy. I think we’re moving forward to what we’re calling the computational knowledge economy.”

Homework Helper

Price: Free Availability: iOS and Android

Chinese Internet search company Baidu launched an app called Homework Helper this year with which students can crowdsource help or answers to homework. Users post a picture or type their homework questions onto online forums, and those who answer the questions can win e-coins that can be used to buy electronics like iPhones and laptops.

The app has logged 5 million downloads, much to the dismay of many some parents who argue that the students spend less time thinking about challenging problems. A Homework Helper staffer admitted to Quartz , “I think this is a kind of cheating.”

Price: Free, but some homework services require payment Availability: iOS

Slader is a crowdsourcing app for high school and college students to post and answer questions in math and science. While students can post original homework for help, many questions in popular textbooks have already been answered on the app, according to Fast Company . An Illinois high school said earlier this year that it suspected students were using the service to cheat on their math homework.

Slader argues that it’s “challenging traditional ideas about math and education,” and said that the ideas behind its app “aren’t a write-off to teachers,” according to its blog . Slader told San Francisco media outlet KQED that it shouldn’t be dismissed as a cheating tool, but rather considered a way for students to access real-time help.

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How We Can Solve the Homework Problem

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This week I worked with another teenager who is failing in school because he doesn’t do his homework. He sat across the desk from me in my office and told me he spends seven hours a day in school and feels he’s “put in his time.” Homework is an unfair burden to impose on top of his long day in school, he says. Or maybe he told me he has the best of intentions each day when he gets home from school but he just can’t bring himself to open his books. Or, since this is a composite picture and it’s not just boys I work with, perhaps it was a girl who told me that she’s too busy doing things with friends and doesn’t see the importance of homework. Or maybe she has a job after school, which gives her both satisfaction and spending money but leaves her little time to spend on schoolwork. Or perhaps the youngster lives in a family where education is not valued, or where it’s denigrated, or where the student is needed to help out with child care or housekeeping and, again, has no time for homework.

Failure to do homework leads students to fail classes, flunk grades, and ultimately to drop out of school. I would like to propose a simple solution to the homework problem.

Here’s how it would work. We know most high schools in the United States track students: They offer vocational tracks, college-preparatory tracks, general education tracks, and honors tracks. Some schools even track within tracks (by offering high and low college-prep classes, for example). I propose we add one more track: a no-homework track.

In this track, students would not be assigned homework. In order to pass their classes, they simply would need to attend them regularly and carry out the in-class assignments. If they needed help with those assignments, the teacher--or other students--would be there to assist them.

Presumably, classes without homework would not be able to cover the same amount of material in the same amount of time. That problem could be solved by adding more time to the no-homework track, either by adding a fifth year to high school or by having no-homework-track students attend summer school for every summer they’re in high school.

What are the advantages of this solution? Here are some:

• It would end the homework wars. Parents would no longer have to fight with their children about doing their homework. In fact, parents could request that their kids be placed in the no-homework track as a way to avoid those battles right from the start.
• Teachers would no longer have to hound students about homework. If homework problems became chronic, teachers could just suggest to students that they were placed in the wrong track and invite them to make an appointment with the guidance counselor to request a transfer. A no-homework track would also free students from the burden of dreaming up novel excuses for what happened to their homework and why they failed to hand it in.
• Teachers could more closely supervise the students’ acquisition of skills. They could also provide alternative learning or performance strategies. They could build study skills into classes before exams and teach kids different ways to study. For students who have trouble sitting down and reading a book, they could have them listen to the books on tapes or have them read parts of books and then watch movies. For students who need help with writing papers, the assistance would be there.
• A no-homework track would acknowledge up front the reality of family lifestyles today. Parents have less time to supervise homework, and students have more options for how they spend their time after school than ever before. Students who want to hold jobs, participate in sports, or get involved in a variety of extracurricular activities would no longer have to juggle these demands with homework. And those students for whom seven hours in school is thoroughly draining would not be confronted with more hours of tedium in the afternoon or evening.

What are the possible disadvantages of adding a no-homework track? These come to mind:

• Cost. But, at least in many urban schools, statistics have shown that upwards of 40 percent of 9th graders flunk their freshman year in high school--there’s the extra year right there. It’s quite possible that, given a choice, fewer than 40 percent of the student population would choose the no-homework track, so this solution might save schools money rather than cost them. And if it kept more students in school until graduation, it would certainly save communities money in the long run, as it would keep more young people away from welfare or other forms of public assistance.

• Space. Adding the extra time needed for a no-homework track could lead to overcrowding. This could be alleviated by offering the additional time during the summer. The added advantage to summer school is that it would build in two months a year when the school is actually “smaller.” This could make it easier for teachers and other caring adults to “connect” with students. A personal connection with adults in schools is a proven way to lower dropout rates. And if the no-homework track begins the summer before the students starts high school, this might ensure their getting off to a good start and would enable them to graduate in June of their senior year along with the rest of their classmates.
• Some might suggest that a no-homework track would cause scheduling nightmares. But as long as the numbers of students enrolled in the no-homework track were equivalent to those placed in other tracks, this shouldn’t be a significant problem.
• Students might resist spending the extra time in school needed to cover the curriculum without assigning homework. For those students, perhaps choosing one of the other tracks would appear more attractive, once they are given a reasonable choice.

Of course, I write this proposal with tongue planted firmly in cheek. I’m not really encouraging schools to create no-homework tracks. What I do suggest--and this would be far more difficult to achieve than a no-homework track--is that schools alter their conception of high school graduation. High school graduation should no longer be thought of as a specific date at the end of four years consisting of a ceremony in which students receive a certificate that shows they “put in their time.”

A high school diploma should be replaced by a series of certificates earned by students, each one articulating a set of skills that society values and the student has mastered. When students have acquired the certificates representing the full set of skills the community believes high school students should possess--whether mastered in two years or six--then we grant them a diploma.

The analogy that comes to mind is the “belts” used in martial arts programs such as karate or tai kwan do. Each different-colored belt represents a set of skills the martial arts student has learned, practiced, and mastered. Students proceed through the martial arts course at the pace that works for them, fast or slow, passing on the first exam or failing and trying again. The belt is a powerful symbol of achievement, because its meaning is universally under- stood by all who practice that martial art.

Is it coincidental that the student who sat in my office this week because he fails to see the value of homework is now a third-degree black belt in tai kwan do? He has been working for a year and a half to earn the next belt, and he thinks it may take him six months to a year longer to earn it. This same student has trouble completing tomorrow’s homework assignments.

Surely there’s a better way.

A version of this article appeared in the March 18, 1998 edition of Education Week as How We Can Solve the Homework Problem

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Stumped five ways to hone your problem-solving skills.

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Respect the worth of other people's insights

Problems continuously arise in organizational life, making problem-solving an essential skill for leaders. Leaders who are good at tackling conundrums are likely to be more effective at overcoming obstacles and guiding their teams to achieve their goals. So, what’s the secret to better problem-solving skills?

1. Understand the root cause of the problem

“Too often, people fail because they haven’t correctly defined what the problem is,” says David Ross, an international strategist, founder of consultancy Phoenix Strategic Management and author of Confronting the Storm: Regenerating Leadership and Hope in the Age of Uncertainty .

Ross explains that as teams grapple with “wicked” problems – those where there can be several root causes for why a problem exists – there can often be disagreement on the initial assumptions made. As a result, their chances of successfully solving the problem are low.

“Before commencing the process of solving the problem, it is worthwhile identifying who your key stakeholders are and talking to them about the issue,” Ross recommends. “Who could be affected by the issue? What is the problem – and why? How are people affected?”

He argues that if leaders treat people with dignity, respecting the worth of their insights, they are more likely to successfully solve problems.

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Best 5% interest savings accounts of 2024, 2. unfocus the mind.

“To solve problems, we need to commit to making time to face a problem in its full complexity, which also requires that we take back control of our thinking,” says Chris Griffiths, an expert on creativity and innovative thinking skills, founder and CEO of software provider OpenGenius, and co-author of The Focus Fix: Finding Clarity, Creativity and Resilience in an Overwhelming World .

To do this, it’s necessary to harness the power of the unfocused mind, according to Griffiths. “It might sound oxymoronic, but just like our devices, our brain needs time to recharge,” he says. “ A plethora of research has shown that daydreaming allows us to make creative connections and see abstract solutions that are not obvious when we’re engaged in direct work.”

To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. “At this stage, don’t worry about actually solving the problem,” says Griffiths. “You’re simply giving your subconscious mind the information it needs to get creative with when you zone out. From here, pick a monotonous or rhythmic activity that will help you to activate the daydreaming state – that might be a walk, some doodling, or even some chores.”

Do this regularly, argues Griffiths, and you’ll soon find that flashes of inspiration and novel solutions naturally present themselves while you’re ostensibly thinking of other things. He says: “By allowing you to access the fullest creative potential of your own brain, daydreaming acts as a skeleton key for a wide range of problems.”

3. Be comfortable making judgment calls

“Admitting to not knowing the future takes courage,” says Professor Stephen Wyatt, founder and lead consultant at consultancy Corporate Rebirth and author of Antidote to the Crisis of Leadership: Opportunity in Complexity . “Leaders are worried our teams won’t respect us and our boards will lose faith in us, but what doesn’t work is drawing up plans and forecasts and holding yourself or others rigidly to them.”

Wyatt advises leaders to heighten their situational awareness – to look broadly, integrate more perspectives and be able to connect the dots. “We need to be comfortable in making judgment calls as the future is unknown,” he says. “There is no data on it. But equally, very few initiatives cannot be adjusted, refined or reviewed while in motion.”

Leaders need to stay vigilant, according to Wyatt, create the capacity of the enterprise to adapt and maintain the support of stakeholders. “The concept of the infallible leader needs to be updated,” he concludes.

4. Be prepared to fail and learn

“Organisations, and arguably society more widely, are obsessed with problems and the notion of problems,” says Steve Hearsum, founder of organizational change consultancy Edge + Stretch and author of No Silver Bullet: Bursting the Bubble of the Organisational Quick Fix .

Hearsum argues that this tendency is complicated by the myth of fixability, namely the idea that all problems, however complex, have a solution. “Our need for certainty, to minimize and dampen the anxiety of ‘not knowing,’ leads us to oversimplify and ignore or filter out anything that challenges the idea that there is a solution,” he says.

Leaders need to shift their mindset to cultivate their comfort with not knowing and couple that with being OK with being wrong, sometimes, notes Hearsum. He adds: “That means developing reflexivity to understand your own beliefs and judgments, and what influences these, asking questions and experimenting.”

5. Unleash the power of empathy

Leaders must be able to communicate problems in order to find solutions to them. But they should avoid bombarding their teams with complex, technical details since these can overwhelm their people’s cognitive load, says Dr Jessica Barker MBE , author of Hacked: The Secrets Behind Cyber Attacks .

Instead, she recommends that leaders frame their messages in ways that cut through jargon and ensure that their advice is relevant, accessible and actionable. “An essential leadership skill for this is empathy,” Barker explains. “When you’re trying to build a positive culture, it is crucial to understand why people are not practicing the behaviors you want rather than trying to force that behavioral change with fear, uncertainty and doubt.”

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