Homework Part 1

This is the first of a two-part series on homework.  Ultimately, the goal is to help you convince students of the value and benefit of homework so that they will be better math students.  But, before we can really drive home the expectation of homework, we need our ducks in a row, so to speak. 

Homework does provide students with great opportunity to learn.   In fact, homework provides a unique dynamic where students can benefit from their efforts more than in class or while studying.   In this episode we talk about how to design homework that takes full advantage of the dynamic homework offers to students.  

In episode two, after we have our end of the deal water-tight, we talk about selling the benefits of homework to students so that they really get on board.  Ultimately, we want students to be excited about the opportunities of learning, not just doing homework out of compliance.  This two part series puts the pieces together to make that happen.

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As promised, here is the video where I first heard the problem shared at the beginning of this week’s episode.  It’s a YouTube video on the channel Veritasium, and it is about thinking.  It’s an interesting video, well worth watching!


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So you can’t get kids to do their homework?

Your current batch of young minds is underachieving.  They have massive conceptual and procedural baggage in tote. They’re reluctant to engage in basic student skills required to even have the opportunity to learn.  We are talking about politeness, distraction, phones, not taking notes, not trying problems, not paying attention for more than 45 seconds in a stretch.  Once you finally get them all together, focused on the lesson, a teacher’s aide walks in with a pass for a student to go the office and BOOM, they’re all lost again. And homework, forget about it.

At a family get together someone asks, “How’s school going this year?  Like this group of kids?” 

When you unload and let it all out, Uncle Bob says, “Well, what you need to do is teach those kids respect and responsibility …” 

Let’s talk about homework, but we need to keep in mind that homework is just a symptom.  However, it can help us access the deeper issues.  We will tackle this issue with the goal of arming you, the teacher, with a fully vetted approach of how to better get students to do their homework well.  First, we’ll talk about the role homework should play in learning.  Then we will talk about some ways to motivate students to do their homework as a part of learning to promote their own success.  That is, we will discuss ways to get kids to willingly do their homework without coercion, threat, or artificial reward.



When we learn something new it goes, roughly, along these lines.  There’s a motivation to acquire knowledge.  The information is identified and integration of that information into knowledge begins.  That is, we receive the information and try to make sense of it.  Upon testing our understanding, we discover gaps and misconceptions which we then correct.  Putting this into five, grossly over-simplified steps, we see:

  1. Interest/motivation
  2. Acquisition of information
  3. Application of information
  4. Discovery of misconception/gaps
  5. Correction of misconception/gaps

That’s a blunt, broad stroke treatment of learning, but it suits our needs for now.  Consider this article as a great example.  (1) There is an interest or motivation that has caused you to (2) read this article.  There is some information you desire.    (3) Once you have gathered that information you’ll take action. (4) Upon reflection you’ll find something did not go as expected.  (5) That’s when you’ll re-examine your thinking to improve future outcomes.

Homework serves steps 3 and 4 perfectly, and provide opportunity for step 5.   Homework should give students a chance to practice what they’re learned, to smooth the paths of application, but it should also offer students opportunity to uncover common misconceptions. 

If you’ve been teaching for a while you know the common misconceptions.    You can spend all day telling the students about the misconceptions, but the majority will not recognize that what you’re telling them is different than what they already believe to be true.  They have to realize, on their own, their misconception.  A key component of effective homework is the exposing of misconception.

Think of it this way:  Unless you possess a perfect lesson that makes it impossible for students to misunderstand, they’re going to develop misconceptions and gaps in understanding.  The students that will eventually be successful will have to identify and correct those gaps and misconceptions.  That will only happen when they recognize what the error in their thinking is, and are willing to address it.

That can happen in a few ways.  It can happen during practice problems during class, on homework, during study time, on an assessment, or during review of the assessment (the de-briefing). 

It would be wonderful if the bulk of misconceptions could happen when students are doing small-group or independent short-term practice during class.  But what happens is that students hesitate at the moment they’re about to uncover a misconception.  They either buy time, waiting for the class to review the problem, or they ask for help.  In both cases they have failed to expose their own misconception.  When they see the solution they will fail to recognize their own misunderstanding (provided they had access to the information).

It is a great practice and fantastic use of time to coach kids on how to properly respond when confused.   Confusion is how the best learning opportunities feel! 

When students do homework, and have an impetus driving them to learn from homework, their options of avoiding confusion are limited.  They cannot as easily ask for help, even when among peers (because not everybody will be doing the same activity outside of class).   They can avoid, but the dynamic is different.  If they avoid a problem in class, they know it is only a matter of minutes before relief comes.  They can always cheat, or get too much tutoring help, but we’ll talk about that later.

The setting homework provides has some advantages for helping students recognize their own misconceptions and gaps not offered during in-class work.  Even when students are forbidden from collaborating and required to practice independently for a short time period, they can easily buy time.  The ceiling offers interesting patterns, pencils can be a little too dull and require sharpening, or the call to be a good citizen of the planet and collect up bits of trash found on the floor can provide them opportunity for escape.   Those things typically will not happen on their own time.

Does your homework provide those opportunities?


Here’s the rub.  Homework problems must be nuanced in order to create opportunities for students to think.  If we want students to possess a solid conceptual understanding and the mathematical literacy to apply what they know, we cannot provide them with a road-map of the solutions.  We have to provide them opportunities to develop their intellect and make some connections through real discovery.

If the homework students must complete is a worksheet printed from Kuta-Soft, it is unlikely going to provide the opportunities for students to uncover misconceptions and gaps.  The only thing it will uncover is lack of procedural proficiency.  The focus on procedure in instruction is well understood to be ineffective.  There are just too many variations and applications of concept to know, retain and recall all of the procedures.  Beyond that, kids are smart.  They know that if it is just procedure and they don’t get it right away, a teacher will eventually sit down with them, one on one, and walk them through every step of each problem on the quiz they’ll retake, for a grade.  No need to do the hard work of thinking and learning when the teacher will eventually do it for them!

Now, teachers and education advocates LOVE to talk about developing conceptual understanding.  The reality is, students are rarely given the chance to develop, and even more rarely given the chance to demonstrate the development of conceptual understanding.  It just isn’t in our educational culture today.  We consider advanced classes as having more work and a faster rate of covering material.   Remediation is skill and drill.   The long-term results are truly undeniable.  Between 40% and 60% of college freshmen enroll in a remedial math class, a class substantially lower than classes they “successfully completed,” in high school.  Does your homework really help students to develop or demonstrate the development of conceptual understanding?  

The Requirement of Homework


If you want your students to develop conceptual understanding and mathematical literacy, homework needs to be on point.   The good news is, a large portion of homework can be procedural, the Kuta-Soft style assignment.  But there must be non-negotiable opportunities in the homework that provide students opportunity to either discover a connection or uncover a misconception or gap.  (Here non-negotiable means that credit for the assignment is not awarded if these problems are skipped.)

Homework must frequently contain opportunities for students to challenge their conceptual understanding.  It would be easy to labor this point to exhaustion, so I’ll settle on this on statement. 

It is our job to provide students with the opportunities to develop intelligence.  The two components of intelligence we can promote in math class are the ability to integrate complex information into a practical body of knowledge, and problem solving.

If the homework assigned in your class is not fulfilling that responsibility we have to our students, then it is unrealistic to expect buy-in from students and a good rate of homework completion.  Those do-gooder kids who never question authority will do all the homework, those afraid of consequences will do their homework.  The grade-chasers will eventually do their work.  Many will simply do some of it, some of the time.  But, none of them will be developing their mathematical thinking if the homework is low-quality.

From grades K through 5, procedural homework is 100% appropriate.  Through middle school the transition should be made where gradually students are being expected to be problem solvers.  Once in high school, the role of homework changes because the content is no longer about reciting information, but instead is about synthesis of ideas and application of ideas. 

Where to source these types of problems, and how to author them yourself is beyond the scope of this article.  But I will offer this advice.  You may already have problems that can serve the purpose here.  The difference will be in how you expect students to approach the problems, and how you support their efforts.  You can read more about that in the article about mathematical literacy.


My Homework is Spot-On … Now What?


There is no magic bullet to get kids to perform.  Ultimately, they perform when they want to.  At the high school level, that’s our trick … to get them to want to.  Of course, that desire is itself fickle and inconsistent.  In order to achieve great things a quality work ethic must be developed.  Just because the homework now will serve the needs of our students doesn’t mean they’ll suddenly do well with homework.  But, once your end of the deal is fulfilled it is a lot easier to get kids to follow through with their end of the bargain.  Let’s talk about how.

The first way to help get students to do their homework is through social obligation, protocol and procedure.  Students need immediate feedback on their homework, however frequently assigned.  That’s feedback for the academic performance (how well they did, what they learned, what they need to learn), as well as the fulfillment of expectation.  In some ways, this is a non-negotiable best practice of teaching.  If you’re teaching students, not just covering curriculum, you need a way to be in touch with their progress.  If you’re waiting three days to see where they are, and in the mean-time driving forward uniformed, you’re likely off-target!

Here’s how you can combine protocol, expectation and social obligation to gently coerce students (initially), into completing homework.

I no longer physically collect homework.  (I’ll explain how you can apply a similar approach if you do collect it.)  I have students perform the vast majority of homework in their notes and they always keep their notes.  At the beginning of class, I survey the room and make note of those that failed to try all problems.  It gives me opportunity to connect in a more personal fashion with students as I go around inspecting the work.  It also allows students to ask me a question or two with great anonymity.  This allows me to thank and reward students whose efforts are improving, or just random students who typically perform well.  But, it also allows me the opportunity to ask students why they failed to do their work.  I can hold them accountable right there and then.  It might not seem like much, but it is powerful!

When we review the homework, after I’ve tallied up who didn’t complete it, I can highlight how much those that did the homework would’ve learned by doing the work.  For example, if students commonly messed up a particular problem because of a specific misconception, those that fell into the trap really will have learned from the experience.  Those that are just observing will not benefit any more than when I warned them of the common mistake the first time.  Experience is also very powerful!

Suppose students in Algebra 1 were trying to solve the equation for x:

x(a + b) = 2ax – 3

This is sneaky because it is difficult to combine the xs.  Typically, the best approach is to avoid any operation that will create “more” xs.  But here, the easiest method is to distribute the x

x(a + b) = 2ax – 3

ax + bx = 2ax – 3

When the 2ax is moved to the left side students might notice that 2ax and ax are in fact like terms. 

-ax + bx = – 3

From here a little factoring and division, and boom, done.  Students that really try this problem and get stuck will latch onto the efficacy of a tool or procedure.  They’ll understand why it is a good application in this situation.  Students that do not attempt the problems, with fidelity, on their own, will be behind those that have.  By drawing this relationship between attempt, confusion and resolution, and improved understanding which will lead to improved assessment scores, students will start to understand how the experience contextualizes the information you provide them.

Quality relationships must be in place to follow this next piece of advice, which is the social obligation.  I call out, publicly, the students who failed to do their homework. I don’t always do this, and I don’t push it far.  It is always with a gentle touch and a way out.  It could go something like this.  As I’m conducting a full class discussion about the previous day’s homework I’ll intentionally call on someone who didn’t do it to participate. 

Johnny, what did you get for number 3? … Oh, wait, I’m sorry, I forgot, you didn’t do your homework.  Forgive me, almost everybody else did, and I am a bit surprised you didn’t.  That’s okay though, I know you’ll try these problems and not miss today’s assignment.

Regardless of how this is handled, and it will greatly vary by individual teacher and student, students need to be publicly accountable for not doing homework.  It is not public shaming, just a simple question asked by you, to the student.  If you’re uncomfortable with the public question, you can ask individually, more quietly.  But, students MUST account for why they failed to fulfill the expectation, every time. 

Keep in mind, the moment you start accepting excuses and quit being interested in asking the student is the very moment you’ve given up on that student.  That is the moment you have lowered your expectations.  That sends a message to all other students about what is expected.  I’ll not chase this too far, but will conclude with this thought.  Sometimes, that is what happens.  In public education there are students that have zero interest in working and will refuse, at all costs, to comply.

That extreme situation aside, hold them accountable, immediately.  But, the idea is not to punish to persuade, and allow resolution to the conflict you’ve instigated through the student doing work.

When I did collect homework I spent the time checking who did, and who did not, turn it in.  I did so right then and there.  Here’s how.  The procedure I used was to have them pass the work forward by rows.  I’d pick up a row’s homework and count how many papers were in the stack.  If one was missing, I’d ask who didn’t turn it in.  I do not prefer this method as it is difficult for the students to get the immediate academic feedback on their performance, but it is effective for holding the students socially accountable.

One last issue to mention about this.  By holding them socially accountable you feed into the idea that a rising tide floats all ships.  When Johnny starts turning in his homework it makes it increasingly difficult for Robert and Diana to continue to NOT complete their homework.  Eventually, a culture develops where students expect themselves and each other to perform well on homework.

Another thing you can do, regardless of how credit is awarded for homework, is to sell students on the purpose of homework.  But, make it real.  With careful planning, sprinkle a few quiz questions in the homework throughout the week.  Treat them like any other question, they exist to help students learn.  Also, place some questions similar to homework questions on the quiz.  (This is not something I’d do on a permanent basis, but just to show students the benefit of homework.)  In addition to this, make sure you can articulate which homework questions would help students on particular quiz questions.

When students have completed the week’s homework and the quiz, it is time to debrief them.  You can do so like this.  Suppose you know that #3 from Tuesday corresponds directly to #4 on the quiz.  Have the students compare the two questions and draw out similarities.  Depending on time and how accurate your data is, you can share with the class how many students completed the homework on Tuesday and also got #4 on the quiz right. 

This is a two-fold relationship here.  If students got #3 on Tuesday right, and #4 on the quiz wrong there’s a conversation that needs to take place.  What happened?  Did they get too much help on the homework, did they get lucky on the homework, did they get unlucky on the quiz?  Was time an issue, nerves?  Most likely you will find that students didn’t use the homework as a learning experience to the level required.  They will have to learn that homework is not for compliance, it is for learning.  If they do not understand and do not act to gain deeper understanding, that lack of understanding will be exposed on the quiz.  Simply getting an answer is not the same thing as gaining deeper understanding.

Once your homework is serving the learning needs of students, and they begin to see the design, can you imagine how easy it will be to respond to the student that claims, “I have a bad grade because of the quizzes.  I get the homework.”

There are more aggressive methods of coercion, manipulation and fear.  However, students will only be doing homework out of compliance.  If you’re expecting students to attempt complicated thinking (at their level), and to do so out of compliance, well, you’ll be disappointed.  You’ll not get the effort from them that is required.  However, in the short-term, sometimes that is what is required to get the ball rolling.  Once they begin, even half-heartedly, you can start to draw out those connections between homework performance and learning.  Many students, at that point, will start doing homework out of self-interest!  That’s a glorious day.

There has been a lot of information in this article.  Let’s compress it into a few compact statements.

  1. Homework should serve the learning of students, not just be rote practice (for high school and higher levels of mathematics).
  2. Once students experience the value of learning from quality homework, they’ll become increasingly interested in doing their homework.
  3. To help students realize the value of homework, you need to engineer, and highlight the outcomes of, experiences where the learning that occurs on homework directly impacts future performance.
  4. Have a protocol of immediate reward and punishment in place for students that do their homework.
  5. The purpose of education is to develop the minds of young people. Homework should serve that purpose, regardless of how you go about it.  

One last thought, to address a common defense of assigning homework.  It is my opinion that when homework is assigned with the intention of teaching students how to do homework, or to teach kids the value of hard work, they do learn something.  They learn that homework is a waste of time.  Homework should be an integral part of learning the content at hand, not some far-fetched objective lesson. 

I hope you found this article helpful and that you go away with some new ideas to try, and maybe a new philosophy about the role and importance of homework.  Leave me a comment to let me know how you received this article.  I’d love to hear from you whether you agree or disagree. 

Feel free to look around the website.  There is an ever-growing collection of topics being treated with lessons, homework assignments, quizzes, videos and the like.  I try to publish four new pages a week on different math topics.  If there is one you’re particularly interested in and you can’t find anything here on that topic, let me know!  Leave me a comment or send me an email at mailto:[email protected].