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• Math homework: What to expect and why it is important
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Math Homework: What to Expect and Why IT Is Important

Parents across the country are starting to question the impact that math homework has on their children. This article discusses why math homework is important and what parents should expect to see in their children's assignments.

School boards around the country are beginning to place homework restrictions on K-12 grade public school teachers. These restrictions are being created in response to increasing instances of homework anxiety in students across the nation. However, before you approach your school board about creating similar restrictions, it is important to learn and understand the value of homework.

Math Homework

Math homework is any task assigned to students to complete outside of their math class, and is created to help students prepare to learn new mathematical concepts, practice ones that have already been introduced, and explore other math skills. These out-of-class assignments are help to reinforce the lessons a child is introduced during the school day.

Studies are finding a relationship between homework and student achievement in school. There has not been established a cause and effect relationship, but there is a strong correlation between the two traits. However, it is also acknowledged that these assignments are only effective when the math teacher takes time to prepare quality assignments that relate to the specific skills that students should be learning or practicing.

Too Much Math Homework?

Statements released by the National PTA and the National Education Association, kindergarten to third grade students should be assigned no more than 20 minutes total homework per day. Fourth to sixth graders should be assigned 20 to 40 minutes while seventh to twelfth grade teens have a varying recommended amount of homework per day depending on the difficulty of their courses. These figures are for all subjects combined, not just the mathematics course.

If your child is taking much longer than these recommended amounts of time on their homework, it could be for two reasons. Either your student's teachers are assigning too much homework or your child does not fully understand their assignments. If you are concerned that a teacher is overloading your child with homework then you should schedule an appointment to discuss this problem. If your child is struggling with their work due to a math skills gap then the answer may be outside tutoring. Busy families can help a child catch up with their peers through online tutoring. Tutoring centers that are located on the World Wide Web are professional and use the same proven methods as their conventional counterparts.

Other Articles You May Be Interested In

Before you can advance to more complex levels of math (like algebra) you have to master the order of operations. Read on to learn the simple steps involved in completing ordered operations math problems. This article provides tips for working your way through math problems with several steps.

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Demystifying Math 55

By anastasia yefremova.

Few undergraduate level classes have the distinction of nation-wide recognition that Harvard University’s Math 55 has. Officially comprised of Mathematics 55A “Studies in Algebra and Group Theory” and Mathematics 55B “Studies in Real and Complex Analysis,” it is technically an introductory level course. It is also a veritable legend among high schoolers and college students alike, renowned as — allegedly — the hardest undergraduate math class in the country. It has been mentioned in books and articles, has its own Wikipedia page, and has been the subject of countless social media posts and videos.

Most recently, Harvard junior Mahad Khan created a TikTok video dedicated to Math 55 that has received over 360,000 views to date. His is only one of many — his older brother created one, too — but it has the distinction of an insider’s perspective. “I thought it would be interesting if I cleared up the misconceptions about Math 55,” Khan said. While he hadn’t taken the course himself, he wanted to go beyond its reputation. “I wanted to get a real perspective by interviewing a former student and current course assistant.”

Over the years, perception of Math 55 has become based less on the reality of the course itself and more on a cumulative collection of lore and somewhat sensationalist rumors. It’s tempting to get swept up in the thrill of hearsay but while there might be kernels of truth to some of the stories, many of them are outdated and taken out of context. At the end of the day, however, Math 55 is a class like any other. Below, we take a stab at busting some of the more well known and persistent myths about the class. Or, at the very least, offering an extra layer of clarity. 

Myth #1: Math 55 is only for high school math geniuses

Most articles or mentions of Math 55 refer to it as filled with math competition champions and genius-level wunderkinds. The class is supposedly legendary among high school math prodigies, who hear terrifying stories about it in their computer camps and at the International Math Olympiad. There are even rumors of a special test students have to take before they are even allowed into Math 55. But while familiarity with proof-based mathematics is considered a plus for those interested in the course, there is no prerequisite for competition or research experience. 

In fact students whose only exposure to advanced math has been through olympiads and summer research programs can have a harder time adjusting. Their approach to the material tends to be understandably more solitary and that can be a disadvantage for the level of collaboration higher level mathematics require. “It has become a lot more open to people with different backgrounds,” said Professor Denis Auroux , who teaches Math 55,. “Our slogan is, if you’re reasonably good at math, you love it, and you have lots of time to devote to it, then Math 55 is completely fine for you.” 

Also, there is no extra test to get into the class.

Myth #2: Just take a graduate class, instead

Math 55 is hard. Whether you’re just 55-curious, or a past or present student in the class, this is something everyone agrees on. The course condenses four years of math into two semesters, after all. “For the first semester, you work on linear and abstract algebra with a bit of representation theory,” said sophomore math concentrator Dora Woodruff. “The second semester is real and complex analysis, and a little bit of algebraic topology. That’s almost the whole undergraduate curriculum.” Woodruff — incidentally, the student Khan interviewed — took Math 55 as a freshman and returned her second year as a course assistant. She is intimately familiar with the course’s difficulty level.

So why not just take an upper level undergraduate course to begin with or even one at a graduate level, if you’re really looking for a challenge? What justifies the existence of a class with the difficulty level of Math 55? One argument is that the course helps structure and systemize the knowledge with which many students come to Harvard. It gives them a firm background in preparation for the rest of their math education. Math 55 is difficult and it is purposefully structured that way as it’s meant to help students mature as mathematicians rather than as simple course takers.

But more importantly, “it’s just not true that Math 55 is at the level of a graduate class,” Auroux said. “It goes through several upper division undergraduate math classes with maybe a bit more advanced digressions into material here and there, but it sticks very close to what is taught in 100-level classes. The difference is we go through it at a faster pace, maybe with more challenging homework, and ideally as a community of people bringing our heads together.” 

A core goal of Math 55, according to Auroux, is to build a sense of community. Other schools might encourage advanced first-year students to take upper level undergraduate or even graduate classes, but Math 55 helps build a cohort of like-minded people who really like math, are good at it, and want to do a lot of it during their time at Harvard. That’s the experience Woodruff had, as well. “The community can be very strong,” she said. “You meet a lot of other people very interested in math and stay friends with them for the rest of college.”

Myth #3: Homework takes between 24 and 60 hours

Horror stories of endless homework are synonymous with the class. You’ll read or hear about “24 to 60 hours per week on homework” in almost every reference to Math 55. But one, there is a world of difference between 24 and 60 hours that is never explained, and two, this timeframe is quite misaligned with reality.

Auroux frequently sends out surveys to his students asking how long homework takes them and the average for most is closer to 15 hours a week. Those with more extensive prior math backgrounds can take as little as five to ten hours. The key factor is collaboration. “This class doesn’t lend itself to self-study,” Auroux stressed. Once they have thought about each problem set on their own, students are welcome and encouraged to talk to their friends and collaborate. “As soon as I see that something took over 30 hours I ask the student, do you know you’re supposed to be working with people and come ask me questions when you’re stuck?”

It is true that between reviewing lectures, digesting the material, and solving the problem sets, students usually end up devoting between 20 and 30 hours a week to the class. However, that includes the time dedicated to homework. So while students are discouraged from taking too many difficult classes and extracurriculars in the same semester as Math 55, they are also not expected to spend the time equivalent to a full-time job on their problem sets every week.

Myth #4: less than half of the class makes it to the second semester

Math 55 is just as infamous for its attrition rate as it is for its difficulty. Most sources like to cite the 1970 class, which began with 75 students and — between the advanced nature of the material and the time-constraints under which students had to work — ended with barely 20. Since then, the rumor has been that the Math 55 class shrinks by half its original size or more before the first semester is over. The reality is much less shocking and a bit more complicated.

Enrollment in this past fall semester’s Math 55A peaked at (ironically) 55 students. Well into the spring semester’s Math 55B, 47 students were still enrolled in the course. “On average, a drop of about 10-15 percent is much closer to what I would expect,” Auroux said. And those numbers become even more flexible if one takes into consideration the weeks math students have at the beginning of each semester to try out different classes and “shop” around before they have to commit to anything. This means students find their way in and out of Math 55 in a variety of ways over the course of the academic year.

According to Auroux, some students shop Math 55 in the fall and switch to the less intense Math 25 for the remainder of the semester. Others start out in Math 25 and, if not sufficiently challenged, switch to Math 55. Even people who end up in academia are not exempt from this. During his time as a student, our own Department of Mathematics’ Professor Emeritus Benedict Gross switched to the lower level Math 21 after two weeks in Math 55. In fact, those two weeks almost made him reconsider his desire to pursue mathematics. “By the beginning of sophomore year, I had decided to major in physics,” he recalled. “But during shopping period that fall, I walked past a math class taught by Andrew Gleason and stopped in to listen. It turned out to be Math 55.” He enrolled and by the end of the semester had found his vocation in mathematics.

All this means that Auroux sees student numbers vacillate up and down throughout the academic year. “There are about four or five students in this spring semester’s Math 55 that took Math 25 or even Math 22 in the fall, and they’re doing mostly fine,” he said. “It’s a lot of work, but I think they’re having a great time.”

Myth #5: 55-er culture is cult-y and exclusionary

Even though her experience with Math 55 was a positive one, Woodruff is very aware of the unhealthy culture the class has been rumored to cultivate. It’s easy for students to form exclusionary cliques that consist only of other Math 55 students, and some look down on anyone taking lower level math classes. But Woodruff also stressed that the instructors are very aware of this and actively take steps to curb that kind of toxic behavior. She said Auroux frequently brings up the importance of keeping the Math 55 community inclusive through Slack messages and lecture references.

Some students come to Harvard just for the opportunity to take Math 55. Some view enrolling in the class as proof of their mathematical gumption and competence. A Harvard Independent article called Math 55 the “premiere mathematical challenge for overachieving and…ridiculously mathy freshmen” and a piece in The Harvard Crimson referred to it as “a bit of a status thing as far as math majors here are concerned.” Over the years, the Harvard Department of Mathematics has taken steps to correct these assumptions. 

For one thing, neither the Math 55A nor the Math 55B official course descriptions boast the dubious honor of referring to it as “probably the most difficult undergraduate math class in the country” (don’t trust everything you read on Wikipedia). For another, “we’re trying to emphasize that there’s no magic to Math 55,” Auroux said. “It contains the same material as some of the other classes we have. People who take it are not intrinsically better or smarter than the ones who don’t.” 

Myth #6: You have to take Math 55 if you’re serious about going into academia

One reason math concentrators could feel pressured to enroll in Math 55 is because they view it as a prerequisite for a career in academia. It’s a sort of badge of honor and proof of their commitment to the field of mathematics. It is true that quite a few graduates of the course have gone on to pursue a career in mathematics. Woodruff herself believes that will be the most likely path for her, and several faculty members in our own Department of Mathematics took Math 55 during their days as Harvard freshmen.

“Several times in my research career when I understood something fundamental, I would realize that this was what Math 55 was trying to teach us,” Gross said. “It was an amazing introduction to the whole of mathematics and it was transformative for me.” In fact, Gross met Higgins Professor of Mathematics Joe Harris when they took the class together, forging a lifelong friendship. When they returned to Harvard as faculty, they took turns teaching Math 25 and Math 55. 

However, Auroux is quick to point out that while many graduates of the course do end up in academia, most professional mathematicians have likely never even heard of Math 55. “I would like to think that it’s a success story if people end up doing math, because the goal of Math 55 is to show students how beautiful math can be,” he said. “If they love it enough to go to grad school and become mathematicians, that’s wonderful. And if they want to take that math knowledge and do something else with their life, that’s just as wonderful.”

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Assigning More Meaningful Math Homework

A small set of problems or even one substantial problem can be enough to supplement classroom instruction.

As a math teacher of more than 23 years, I have had the habit, almost like a muscle memory repetition, of assigning daily math homework for my middle school students. It wasn’t until recently that I paused to reflect, “Why am I assigning this?” The easy answer is, “My students need to practice to develop their skills.”

If I dig a bit deeper into the “why,” I wonder, “Are all of my students benefiting from this assignment? Did I assign an appropriate amount and level of problems? What resources do my students have or not have to be successful with this assignment? Is the assignment meaningful or busywork?”

Consider the following suggestions for making math homework more meaningful.

3 Ways to Create More Meaningful Math Homework

1. Think quality over quantity. The National Council for Teachers of Mathematics Homework page of tips for teachers suggests, “Only assign what’s necessary to augment instruction. If you can get sufficient information by assigning only five problems, then don’t assign fifty.”

Worksheets and problem sets from textbook publishers might contain dozens of problems that repeat the same concepts. It is OK to assign part of a page, such as “p. 34 #s 3, 5, and 17.” I tell my middle school students, “I handpicked these particular problems because they capture the objective of today’s lesson.” When students know that their teacher carefully “handpicked” a problem set, they might pay more attention to the condensed assignment because it was tailored for them.

Even one problem can be sufficient. Robert Kaplinsky, cofounder of Open Middle , routinely shares on X (formerly Twitter) single problems that are really engaging and give students a good chance to practice skills.

The depth and exploration that can come from one single problem can be richer than 20 routine problems. You might be surprised by how much depth can be inspired by a single problem.

2. Consider choice and variety. It’s unrealistic to create a personalized daily homework assignment for each student in your class. Student voice and choice can be applied to your preexisting assignments without your having to re-create the homework wheel.

Traditional assignments can be modified by offering students choice. This might look like “ Choose any five of these problems ,” or take this tip from educator Peter Liljedahl and designate problems as “mild, medium, or spicy” and let students pick their level for that assignment.

Offering homework level choice also promotes a culture of growth mindset through messaging like “You might choose mild problems for this lesson; however, tomorrow you might feel you’re ready for a medium level.” Level choice can vary day to day—your math level is not fixed.

Daily homework can also be spiced up by offering a variety of types of assignments. Consider assigning problems that go beyond providing a single number answer. Here are a few examples to get students thinking beyond just getting a particular problem right:

• When simplifying (4 + 5) x 5 - 3, what is the first step?
• When simplifying (4 + 5) x 5 - 3, Ali got the answer 18. What advice do you have for her?
• Write your own order of operations problem with a solution of 42.

Check out these websites for even more creative ways to vary homework:

• Three-Acts Math Tasks
• Open Middle
• Would You Rather Math

3. Remember, accountability doesn’t have to result in a grade. There is a major difference between assigning homework for a grade and assigning homework purely for practice. When a grade is the result of an assignment, the stakes get higher for the student.

In the February 2023 Washington Post article “ A deep dive into whether—and how—homework should be graded ,“ former teacher Rick Wormeli wrote, “When early attempts at mastery are not used against them, and accountability comes in the form of actually learning content, adolescents flourish.” If homework is truly for practice, this is an opportunity for students to make mistakes and take risks without the fear of a penalty.

Even if homework is graded as a completion grade, there are considerations of equity and meaningfulness of the practice.

Consider the following questions when deciding to give a completion grade for a homework assignment: Do all students have a home environment that is supportive of homework? Do some students have additional support, such as tutors or parents, to help them get the homework completed? Would students copy homework assignments from each other just to earn the completion grade?

If not grades, then how do we hold students accountable for practicing outside of class?

Student presentations and discussions are a way to check for understanding of an assignment and to let students know you expect them to attempt the problems. This might look like a debate in which students take sides on how to approach a problem . Alternatively, students could post their work on the board to share their strategies with the class or discuss their solutions in small groups. Communicating their mathematical thinking deepens their understanding .

Education consultants Ashley Marlow and Katie Novak write in their Edutopia article “ Making Math Accessible for All Students ” (July 2022), “When students have opportunities to think, reason, explain, and model their thinking, they are more readily able to develop a deep understanding of mathematics beyond rote memorization. The goal is for all students to experience success in higher learning of mathematics—requiring those reasoning and sense-making skills and increasing engagement.”

The next time you’re planning your lessons and assignments, pause and reflect on the meaningfulness of the homework assignment. Could it be shorter but more in-depth? Can students have a choice in their work? Will students find value in doing the work even if it is not for a grade? You might find that students take more ownership and care in their homework if it’s more meaningful to them.

IM 6–12 Math: Grading and Homework Policies and Practices

By Jennifer Willson,  Director, 6–12 Professional Learning Design

In my role at IM, working with teachers and administrators, I am asked to help with the challenges of implementing an IM curriculum. One of the most common challenges is: how can we best align these materials to our homework and grading practices? This question is a bit different from “How should we assess student learning?” or “How should we use assessment to inform instruction?” 

When we created the curriculum, we chose not to prescribe homework assignments or decide which student work should count as a graded event. This was deliberate—homework policies and grading practices are highly variable, localized, and values-driven shared understandings that evolve over time. For example, the curriculum needed to work for schools where nightly, graded assignments are expected; schools where no work done outside of class is graded; and schools who take a feedback-only approach for any formative work.

IM 6–8 Math was released in 2017, and IM Algebra 1, Geometry, and Algebra 2 in 2019. In that time, I’ve been able to observe some patterns in the ways schools and teachers align the materials to their local practices. So, while we’re still not going to tell you what to do, we’re now in a position to describe some trends and common ways in which schools and districts make use of the materials to meet their local constraints. Over the past four years, I have heard ideas from teachers, administrators, and IM certified facilitators. In December, I invited our IM community to respond to a survey to share grading and homework policies and practices. In this post I am sharing a compilation of results from the 31 teachers who responded to the survey, as well as ideas from conversations with teachers and IMCFs. We hope that you find some ideas here to inform and inspire your classroom.

How do teachers collect student responses?

Most teachers who responded to the survey collect student work for assessments in a digital platform such as LearnZillion, McGraw-Hill, ASSISTments, Edulastic, Desmos, etc. Others have students upload their work (photo, PDF, etc.) to a learning management system such as Canvas or Google classroom. Even fewer ask students to respond digitally to questions in their learning management system.

How do teachers tend to score each type of assessment, and how is feedback given?

The table shows a summary of how teachers who responded to the survey most often provide feedback for the types of assessments included in the curriculum.

How are practice problems used?

Every lesson in the curriculum (with a very small number of exceptions) includes a short set of cumulative practice problems. Each set could be used as an assignment done in class after the lesson or worked on outside of class, but teachers make use of these items in a variety of ways to meet their students’ learning needs.

While some teachers use the practice problems that are attached to each lesson as homework, others do not assign work outside of class. Here are some other purposes for which teachers use the practice problems:

• extra practice
• student reflection
• as examples to discuss in class or use for a mini-lesson
• as a warm-up question to begin class
• as group work during class

How do teachers structure time and communication to “go over” practice problems?

It’s common practice to assemble practice problems into assignments that are worked on outside of class meeting time. Figuring out what works best for students to get feedback on practice problems while continuing to move students forward in their learning and work through the next lesson can be challenging. 

Here are some ways teachers describe how they approach this need:

• We don’t have time to go over homework every day, but I do build in one class period per section to pause and look at some common errors in cool-downs and invite students to do some revisions where necessary, then I also invite students to look at select practice problems. I collect some practice problems along with cool-downs and use that data to inform what, if anything, I address with the whole class or with a small group.
• Students vote for one practice problem that they thought was challenging, and we spend less than five minutes to get them started. We don’t necessarily work through the whole problem.
• I post solutions to practice problems, sometimes with a video of my solution strategy, so that students can check their work.
• I assign practice problems, post answers, invite students to ask questions (they email me or let me know during the warm-up), and then give section quizzes that are closely aligned to the practice problems, which is teaching my students that asking questions is important.
• I invite students to vote on the most challenging problem and then rather than go over the practice problem I weave it into the current day’s lesson so that students recognize “that’s just like that practice problem!” What I find important is moving students to take responsibility to evaluate their own understanding of the practice problems and not depend on me (the teacher) or someone else to check them. Because my district requires evidence of a quiz and grade each week and I preferred to use my cool-downs formatively, I placed the four most highly requested class practice problems from the previous week on the quiz which I substituted for that day’s cool-down. That saved me quiz design time, there were no surprises for the students, and after about four weeks of consistency with this norm, the students quickly learned that they should not pass up their opportunity to study for the quiz by not only completing the 4–5 practice problems nightly during the week, but again, by reflecting on their own depth of understanding and being ready to give me focused feedback about their greatest struggle on a daily basis.
• I see the practice problems as an opportunity to allow students to go at different paces. It’s more work, but I include extension problems and answers to each practice problem with different strategies and misconceptions underneath. When students are in-person for class, they work independently or in pairs moving to the printed answer keys posted around the room for each problem. They initial under different prompts on the answer key (tried more than one strategy, used a DNL, used a table, made a mistake, used accurate units, used a strategy that’s not on here…) It gives the students and I more feedback when I collect the responses later and allows me to be more present with smaller groups while students take responsibility for checking their work. It also gets students up and moving around the room and normalizes multiple approaches as well as making mistakes as part of the problem solving process.

Quizzes—How often, and how are they made?

Most of the teachers give quizzes—a short graded assessment completed individually under more controlled conditions than other assignments. How often is as varied as the number of teachers who responded: one per unit, twice per unit, once a week, two times per week, 2–3 times per quarter.

If teachers don’t write quiz items themselves or with their team, the quiz items come from practice problems, activities, and adapted cool-downs.

When and how do students revise their work?

Policies for revising work are also as varied as the number of teachers who responded. 

Here are some examples:

• Students are given feedback as they complete activities and revise based on their feedback.
• Students revise cool-downs and practice problems.
• Students can revise end-of-unit assessments and cool-downs.
• Students can meet with me at any time to increase a score on previous work.
• Students revise cool-downs if incorrect, and they are encouraged to ask for help if they can’t figure out their own error.
• Students can revise graded assignments during office hours to ensure successful completion of learning goals.
• Students are given a chance to redo assignments after I work with them individually.
• Students can review and revise their Desmos activities until they are graded.
• We make our own retake versions of the assessments.
• Students can do error logs and retakes on summative assessments.
• We complete the student facing tasks together as a whole class on Zoom in ASSISTments. If a student needs to revise the answers they notify me during the session.

Other advice and words of wisdom

I also asked survey participants for any other strategies that both have and haven’t worked in their classrooms. Here are some responses.

What have you tried that has not worked?

• Going over practice problems with the whole class every day. The ones who need it most often don’t benefit from the whole-class instruction, and the ones who don’t need it distract those who do. 
• Grading work on the tasks within the lessons for accuracy
• Leaving assignments open for the length of the semester so that students can always see unfinished work
• Going through problems on the board with the whole class does not correct student errors
• Most students don’t check feedback comments unless you look at them together
• Grading images of student work on the classroom activity tasks uploaded by students in our learning management systems
• Providing individual feedback on google classroom assignments was time consuming and inefficient
• Allowing students to submit late and missing work with no penalty
• Trying to grade everything
• Below grade 9, homework really does not work.
• Going over every practice problem communicates that students do not really think about the practice problems on their own. 

What else have you tried that has worked well?

• My students do best when I consistently assign practice problems. I have tried giving them an assignment once a week but most students lose track. It is better to give 2–3 problems or reflective prompts after every class, which also helps me get ahead of misconceptions.
• I don’t grade homework since I am unsure who completes it with or for the students.
• A minimum score of 50% on assignments, which allows students the opportunity to recover, in terms of their grade in the class
• Time constraints imposed during remote learning impact the amount and type of homework I give as well as what I grade
• Give fewer problems than normal on second chance assignments
• I have used platforms such as Kahoot to engage students in IM material. I also build Google Forms to administer the Check Your Readiness pre-assessment and End-of-Unit assessments, but I may start using ASSISTments for this in the future.
• The value of homework in high school is okay, but personally I skip good for great.
• Students are able to go back and revise their independent practice work upon recognizing their mistakes and learning further about how to solve the problems.
• Sometimes I select only one or two slides to grade instead of the whole set when I use Desmos activities.
• Allow for flexibility in timing. Give students opportunities for revision.
• Frequent short assessments are better than longer tests, and they allow students to focus on specific skills and get feedback more frequently.
• Especially during the pandemic, many of my students are overwhelmed and underachieving. I am focusing on the core content.
• Homework assignments consist of completing Desmos activities students began in class. Additional slides contain IM practice problems.
• I am only grading the summative assessment for accuracy and all else for completion. I want the students to know that they have the room to learn, try new strategies and be wrong while working on formative assessments.

What grading and homework policies have worked for you and your students that aren’t listed? Share your ideas in the comments so that we can all learn from your experience.

What would you like to learn more about? Let us know in the comments, and it will help us design future efforts like this one so that we can all learn more in a future blog post.

We are grateful to the teachers and facilitators who took the time to share their learning with us.

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Sat / act prep online guides and tips, 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.

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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For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start – to approach the subject with playfulness and curiosity, not anxiety or dread.

“Most people have only ever experienced what I call narrow mathematics – a set of procedures they need to follow, at speed,” Boaler says. “Mathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.”

Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced How to Learn Math , the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users.

In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls “ishing” a math problem can help students make better sense of the answer.

What do you mean by “math-ish” thinking?

It’s a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport – these are generally answered with what I call “ish” numbers, and that’s very different from the way we use and learn numbers in school.

In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. They’re given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 – but the most common answer 13-year-olds gave was 19. The second most common was 21.

I’m not surprised, because when students learn fractions, they often don’t learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.

But don’t you also risk sending the message that mathematical precision isn’t important?

I’m not saying precision isn’t important. What I’m suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, they’ll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.

Some people ask me, “Isn’t ‘ishing’ just estimating?” It is, but when we ask students to estimate, they often groan, thinking it’s yet another mathematical method. But when we ask them to “ish” a number, they're more willing to offer their thinking.

Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mindset. I think we all need a little more ish in our lives.

You also argue that mathematics should be taught in more visual ways. What do you mean by that?

For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things – all of that contributes to our understanding of how it works.

There’s an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubik’s Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking.

Some years back we were interviewing students a year after they’d done that activity in our summer camp and asked what had stayed with them. One student said, “I’m in geometry class now, and I still remember that sugar cube, what it looked like and felt like.” His class had been asked to estimate the volume of their shoes, and he said he’d imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.

When we learn about cubes, most of us don’t get to see and manipulate them. When we learn about square roots, we don’t take squares and look at their diagonals. We just manipulate numbers.

I wonder if people consider the physical representations more appropriate for younger kids.

That’s the thing – elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school it’s all symbolic. There’s a myth that there’s a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.

There’s an example in the book where you’ve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldn’t it be easier to teach students one standard method?

A depiction of various ways to calculate 38 x 5, numerically and visually. | Courtesy Jo Boaler

That narrow, rigid version of mathematics where there’s only one right approach is what most students experience, and it’s a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, they’re not developing number sense. They don’t learn how to use numbers flexibly in different situations. It also makes students who think differently believe there’s something wrong with them.

When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, it’s powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.

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The Algebra Problem: How Middle School Math Became a National Flashpoint

Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it.

By Troy Closson

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system. Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly four in five poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12 percent of Black and Latino eighth graders do, compared with roughly 24 percent of white pupils, a federal report found .

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research . A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Mass., the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside of school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, Mr. de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80 percent from 60 percent. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s current schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won both support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Mr. Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Mr. Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100 percent, yes,” he added. “That was not something that I could live with.”

Troy Closson reports on K-12 schools in New York City for The Times. More about Troy Closson