Tuesday, August 16, 2011

My Thoughts On Homework

Lately I have been thinking about how I assign, collect, and give points (or not) for homework. (For the record, when I say ‘homework’ I really mean ‘practice’. I want my students to practice every day. Sometimes they practice at home.)

I know a lot of bloggers have had success with not giving points for homework, but I am not ready to go there yet. I tried not giving points once during my first year of teaching and it was a disaster. Then again, lots of things during my first year of teaching were a disaster. But if giving students a score on a paper helps them to reflect on the quality of their efforts as they practice math, then I’m okay with using points.

So this is what I do . . . In bold is the thing I am trying to accomplish, and after that is how I attempt to make it happen.

1.     The perfect system emphasizes quality practice. Students need to reflect and make corrections as they are working:  I spend a lot of time teaching students how to practice. I want them to work out a problem, and then check the answer and find any mistakes and revise their work as needed. I hate to say just “show your work”. I do emphasize the importance of justifying your solution so that you can communicate to others how you found it, and prove it is correct. I make up a page of problems where some are perfect, others are missing work/justification, others have a wrong answer, and some have a right answer but the work/justification is incorrect or incomplete. Then students work with a partner to critique and discuss the quality of the practice. This takes time, but it is worth it.

2.     A good system gives students feedback while they are working, whether at home or at school. Ideally, they can find out if their answer is right or wrong without being told the actual correct answer: I put the answers to the problems in random order in the margin of the assignment. When students finish a problem, they find the answer in the margin and cross it out.  The only drawback here is that they can use the process of elimination to know the answer to the problems at the bottom of the page. Still, it works pretty well. I am thinking of tweaking this a little this year using the sum of a couple answers (sort of like Kate’s Add ‘em up). Instead of writing all the answers in the margin, I think I will try something like “the sum of #1 and #2 is _____”.  Then they will know if they need to fix their work without giving away any answers.

3.     If points are given, the points should reflect the quality of the practice vs. the number of answers that are correct on the first try:  A problem counts for points if it has correct work (or justification of some kind) leading to the correct answer, regardless of how many tries it takes you to get there. I don’t really even think of it as a “homework” grade. I want the point value to help students think about how well they are practicing. Hmm, maybe I will start calling it the “quality of practice” grade. Or something like that . . . I will have to think of something more catchy.

4.    If points are given, the system minimizes teacher time spent grading and recording:  My students spend so much time learning what good practice looks like that they know whether a problem they have finished qualifies. It has correct work leading to the correct answer and it counts, or it doesn’t. So students take the number of problems that qualify as good practice divided by the total number of problems times 5 (because I want a practice assignment with 20 short problems to have the same value as a practice assignment with 4 or 5 lengthy ones). I will even put that formula at the top of the paper to make it simple. Round the number to the nearest tenth and hand it in. Teacher records that number.

I am pretty happy with this system, but I still have a few problems. Sometimes students put a score on their paper that isn’t accurate (pretty easy to catch). Sometimes students rely too heavily on clues from the answers in the margin (maybe my little tweak will help that). Sometimes students copy their friend’s homework in the hallway before school (but at least they have to copy the work, too).

What's your homework system?


  1. Would you mind sharing some of your handouts with missing/incorrect justification? I'm curious to see how you set that up.

    Thanks for sharing your homework plan! I like that they are doing "quality practice" :)

  2. here's my HW plan, although I am trying to stir away from saying HW.

    Practice Problems: Practice problems are an essential part of learning. It is expected that you complete the practice problems assigned with each lesson. You are expected to use class time wisely to work on these problems and complete any assignment not finished during class on your own time (study hall, home, bus from a sporting event, etc.). Most assignments will between 15-25(+/–) problems depending on the type of problem. These are “self-assessment” assignments; you are expected to check your answers as you complete each problem; this is NOT cheating. If you are struggling with a problem and do not get the correct answer please make sure you ask about it during question time in class.

    Challenge problems will be offered for those wanting more of a “challenge”. Any problem from the basic problem set can be replaced with a Challenge problem. Challenge problems must be highlighted by the student. We will NOT discuss Challenge problems during class, but I am always available outside of class to help with these problems.

    Assignment Check: At the end of each chapter, after the chapter test, you will be given an Assignment Check. Two to three problems per section (typically 5 sections per chapter) will be chosen randomly, and students will be assessed on those problems only. All work must be shown to receive full credit. If you have completed Challenge problems, it is your responsibility to communicate CLEARLY that you did a challenge problem rather than the problem being asked on the Assignment Check. If you choose to do the basic Practice set AND the Challenge Problems you will be given extra credit points for each Challenge Problem completed correctly. All original assignments must be stapled, in order behind the Assignment Check. All must be completed in PENCIL, and must be labeled with the Lesson, page # and problems assigned. Failure to do so will result in loss of points.

  3. Thank you for taking the time to share! I agree with your dislike of the word 'homework' . . . I've been trying to avoid that, too. Funny how we have to convince students that checking their answers is NOT cheating. When mine find out that I am giving them access to all the answers they are happy like Christmas morning! It takes time to communicate that we are teaching them how to self-assess and how to practice well. I also like that your students can swap regular problems for challenge problems. Do many take advantage of that? Thanks again for your thoughts, I really appreciate it!

  4. We don't have an "honors" track for math (the only subject area where we don't). So I have to do something to differentiate to the ~20 freshman taking Geometry and the ~10 Sophomores that double up with Algebra 2 and Geo. It was something I started doing at the end of the year last year, and then I was just giving them extra points if they did them. But they ended up doing extra problems. If they are advanced students they don't really have to do the basic problem set, and I don't want to make them do extra. So the "replacing" is new this year. It is definitely a work in process and will keep you posted on how it works out and tweeks that I make.

  5. Amy,
    Could #2 also be solved by giving more answers than questions so that they can't eliminate so easily?

    Also, I just read a great article about differentiated assessment that mentions how to differentiate homework that you might be interested in:


  6. Misscalcul8, I was just re-reading some old comments and saw your suggestion about providing extra answers. I don't know how I missed that the first time, but I really like it. Students can still self-check without the answer being so obvious. I will try that. Thanks for the idea.

  7. I love your idea about making a sample page of worked-out practice problems for students to dissect in order to have a class discussion on justification and math reasoning. I may use this idea for one of the first day of school activities!! Thanks!