Category Archives: Homework

More Reflective Homework

This year, I have tried to engage my students in a more thoughtful homework process. I don’t think any math teacher, ever, has been satisfied with the way homework works in their class, and I would certainly put myself in that boat. My frustrations in the past have been that students sometimes would do something wrong and then continue to cement that wrong thing by repetition, I would get 30 homework assignments that look basically the same and spend tons of time giving useless feedback that they didn’t really even look at, and students were focused on completion over learning. I attribute this to the structure of the homework over students being their nutter butter selves. Here are the changes I made this year:

1. Every homework assignment comes with a full solution (not just answer) guide. It’s more work for me, but also makes me assign a reasonable amount of homework.

2. Students go through the assignment and do whatever they can without the solution guide.

3. Then they check the solution guide to check what they did and finish what they couldn’t. Anything they write after this point (or using the solution guide) is in a different color – which is a crucial point. They check their answers, fill in the rest of incomplete solutions and give themselves feedback on what they did well and what they did poorly.

It takes a little longer for the students, so I try to assign a little less. And some students haven’t bought totally into it yet (slash never will). But as a teacher grading it, I can see so much more. Like…

  • Where students struggled and what they still don’t understand well, which is so obvious with the colored pen. What they did in pencil is their work and what they did in pen is their work with the solution guide.
  • Evidence of learning – instead of doing something wrong over and over, they correct it and do it better the second time around, or at least know that what they did is wrong and need to get help from me.
  • Where to give them feedback on the specific things that they are struggling on.
  • Who is engaging with the homework and trying to learn from it, vs. who is just tryna get-r-done.

I also spend less time grading homework while still giving better quality feedback. I think they spend about the same amount of time doing homework but get more out of it.

The training process for this has been an investment, but worth it. I share with the class examples of things they can do to do this better, like this:




Feedback from students has been that they almost either really like it, or are fine doing it. They almost all indicate that it’s better for learning, which is what I care about.

How do you feel about the method of doing homework where you check your own answers?

It is very helpful XXXXXXXXXX

  • It allows you to learn the right way of doing it while it’s still fresh in your mind.
  • I like understanding what I did wrong right after I did it so that I can grasp what I did wrong.
  • Being able to look at the answer and find what I did wrong at my own pace helps me understand the problem and how I should do it next time.
  • Writing my own feedback is more helpful than skimming any you would give on homework.
  • Self check is a way to see what you did wrong right after you did the work instead of a couple of days later,

It’s fine XXXXXXX

  • I feel as though that making corrections and not totally understanding my mistakes is perhaps the biggest downfall.
  • maybe if i came back after a longer period of time it would be more helpful to me in particular.
  • I understand that it’s good to correct ourselves but I think I get more out of simply going up to you to clarify he things I’m struggling with.
  • I only feel like feedback is necessary for some problems if I really don’t get it
  • Well it is helpful some of the time but it does take a really long time to do this.
  • I think that it’s helpful like 85% of the time, and then other times it confuses me

Negatively X

Meh, I don’t really do it. XX

Still experimenting! Would love some thoughts.

Practicing Like an Expert (instead of a math student)

(here are some excerpts from a paper I wrote for grad school about structuring math homework for better learning – the full paper is below)

mathshampooThe traditional structure of math homework (e.g. 1-67 odd) forces students to work hard, but not effectively, as all students blindly do the same assignment consisting of a similar number of each type of problem regardless of each student’s personal weaknesses. In “Practice Perfect,” Doug Lemov’s book on how to practice more effectively, the authors compare this type of practice to shampooing your hair, something we repeat daily but probably never improve on.

Math students ought to practice math the way that experts in other fields practice. When a musician learns a piece of music, they do not just play whole piece over and over. Instead, they workshop specific parts that they need to work on. When I was learning to play piano, my teacher would have me play difficult parts repeatedly – first each hand separately, then both hands together slowly, and finally at full speed. Students do the exact opposite on math homework – they do the problems with which they are comfortable and then leave blank those they do not know how to do. Thus, they are only practicing the very material that they do not need to.

If teachers would like them to engage with it differently, they need to make intentional changes in the structure. To make math homework more like expert practice, teachers should:

Force students to differentiate their homework experience.

Though the other suggestions below would be a helpful addition to traditional homework assignments, this first one would require a more radical shift. Instead of a linear assignment that encourages students to spend an equal amount of time on each part of the course, a math assignment should consist of minimal core problems for each learning objective that each student must complete, and a bank of other problems that the student could use to remedy any misconceptions. The set of core problems should be small enough that students can complete all and still have time to tackle their weak areas. Students should be instructed that a wrong answer should be a sign to reflect for a moment about what went wrong, perhaps even formally, and then immediately try more problems until they understand. To give space for this thoughtful type of work, a teacher might have to assign less work, but the quality of the work that is completed has the potential to be much higher.
(some thoughts on grading and accountability in the full paper)

Make homework objectives transparent.

With a differentiated homework assignment that required metacognition about weaknesses, students would need the tools to pick out their own weaknesses. When picking out problems from a math textbook to assign, I have an objective in mind for each group of problems. In retrospect, it seems obvious that I should simply share these objectives with students, paralleling Standards Based Grading for the wider structure of the class. Simply grouping math problems into learning objectives would help students focus their effort more effectively by allowing them to isolate skills and measure their success.

Ensure students can get immediate and actionable feedback

But even with clear learning objectives, students can’t make progress without feedback. Too often, students will power through their entire homework doing something wrong the entire time, encoding something in their brains the wrong way. Worried that students will copy answers out of the back of the book, teachers will assign problems that do not have attached solutions. We have to get over this fear – if students cannot check their work, or are not in the habit of doing so even when they are confident they got a problem correct, they risk not knowing that they are doing something wrong. Doing one problem wrong, fixing a misunderstanding and then doing a few more correctly will lead to far better results than doing five wrong and having to unlearn something incorrect a week later. For complex problems that only have a simple answer in the back of the book, teachers could post a solution guide that details not only the answer but the process that it takes.

No idea if this will work! I’m interested to try it out when I get back to the classroom. Here is the full paper:

Teach them HOW to do homework

One of my grad school professors taught me how to read.

Okay, so I knew HOW to read (hold your snarky math teacher comments, English folk), but I didn’t realize I had no idea how to read for an academic context. For one of our very first assignments, our professor set up a very sneaky experiment that taught me I wasn’t reading very well. He told the whole class that for one of our more dense and academic readings for the next week*, one person would be randomly selected to lead a class-wide discussion. This was early on in a program with a group of 22 all-star, experienced educators. Very scary.

I was terrified into competency.

Instead of just reading it straight through and perhaps highlighting, I wrote questions in the margins, connected various parts of the text, made a list of the main ideas, pulled out quotes that could generate discussion, and generally actively thought about the content of the article.

It turned out he was bluffing, which he revealed in class the next week. Phew, *changes underwear*.  But with this exercise, he made the point to us that the way we read that article was totally different from the way we probably read most of the other stuff. And more effective. I was thankful for this because for the rest of grad school, I read much more effectively. Even if I didn’t have time to read an entire article, I would spend a bit of time diagramming, writing questions in the margins, and actively engaging with the content. Instead of expending more effort, I used my effort more effectively.

How did I make it through so many years of education without knowing how to read? How much more could I have gained from both my high school and college education? How does this apply to our math students? How many of them are trying to do better by working MORE instead of by working MORE EFFECTIVELY? What can we do to show the how to do homework?

What’s a good meta-assignment that can show students how to do math homework effectively (without making them sh*t some bricks to learn the lesson)?

*Alfred North Whitehead, The Aims of Education. NB: I don’t really remember what it was all about 9 months later, but hey, I guess good teaching techniques have their limits?