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Teaching Math: Homework Review

March 20, 2007 pm31 11:47 pm

Over at dy/Dan there has been an interesting discussion of why Dan doesn’t assign homework. At some other point I may blog about my differentiated assignments. But not today. I’d like to briefly touch on another aspect of homework: how it is reviewed.

If homework is assigned, then it should have value. And if it has value it should be reviewed and acknowledged.

Students put up homework problems when they enter my classroom. There are four circumstances:

  • to show off great work.
  • to get feedback on hard work that they attempted, but are unsure about as to form or one or more details
  • to learn how to do a problem that they were unable to complete (or even attempt)
  • to complete an unanswered question that another student has put up

So at the beginning of class several students go to the side board. Who? Whoever wants to. They get credit. They get credit if they are correct. They get credit if they are incorrect. And they get credit for putting up a problem that they were unable to complete (or even start). And we review those problems on the board; rarely more than they put up; rarely fewer.

(more discussion, beneath the fold —->)

Why should they get credit if they are not correct? The main idea is to get the problems that have caught the kids’ attention up on the board. If they are stuck, credit for putting up the question. If they mastered a harder problem, credit for putting up model work. And when they are unsure, question for generating a class discussion of what looks good and what is incorrect. The tie in with credit ensures their participation (I ask them to put up a problem every two weeks or so, though some go up more often. There is the occasional class when I have to set some sort of max.)

How is homework review handled in other places?

  1. In some places, homework is reviewed at the end of class. I see two problems with that. a) I count on kids having got the homework before moving on to the next topic. Why go on to the next topic, then go back and check homework? and b) The end of class? How often does the homework review just get skipped??
  2. I knew a teacher who assigned three kids each day to put up problems. But they knew who they were in advance, so kids did their homework on the day they were assigned (and some of them, on no other).
  3. Some teachers routinely review all the problems. But insofar as some are routine practice, that makes for some fairly tedious review. Some teachers don’t review unless there is a question, and collect and correct or correct and spotcheck. But unless there is 1 day turnaround, the immediacy is lost. Will a kid remember what math bothered him 3 nights ago? And 1 day turnaround is an awful lot of fast work, if homework is being collected every day.

None of these ideas please me. What I do, while not perfect, does have several virtues.

I think that I get better involvement in homework this way than I otherwise would. There are often good quick discussions about details of work. Students check each other’s work, and have chances to correct their own homework. The physical activity of moving around helps the kids, who sit too long in one place in school. And there are major issues of classroom ownership, that this technique fosters. 

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30 Comments leave one →
  1. March 22, 2007 am31 5:27 am 5:27 am

    I count on kids having got the homework before moving on to the next topic.

    But if one or more kids didn’t get to the homework, how can you factor it into your instructional planning?

    There’s a weird aspect to this for me where I’m more willing to let the student eat the consequence of not doing homework in the more advanced classes.

    In lower classes — first-year and remedial Algebra, for example, the classes my post concerned principally — it’s irresponsible for me to give the students that much stewardship over their learning experience.

  2. March 22, 2007 am31 5:45 am 5:45 am

    I was listening to some teachers’ conversation. It would be an understatement to say that they had low opinion of their students. I won’t even discuss how I feel about that, but I will say this. Students should be and are responsible for their learning. As is their teacher. And if you don’t ask them to take responsibility then why should they and how will they know that they need to?

  3. March 22, 2007 pm31 5:51 pm 5:51 pm

    One thing at a time. First, responsibility and commitment to learning in class, and then the extension outside.

  4. March 24, 2007 pm31 9:48 pm 9:48 pm

    Here here! I simply hate when homework is assigned and then nothing!

    But what do you do when your district assigns what the homework will be and of course it is crap… and anything mass assigned would be?!?!

  5. March 27, 2007 am31 8:35 am 8:35 am

    Homework should be simple enough and short enough that it is reasonable for me to expect 90% or so completion. It is my job to choose appropriate quantities, and at the right level of difficulty. Of course the level is less of a problem for me since I assign two overlapping homework sets, one of which is shorter and more difficult, the other longer and more routine.

    And then, having set a reasonable expectation, I work on my homework non-doers.

  6. March 29, 2007 am31 7:37 am 7:37 am

    Hmmmm. I like Dan’s scheme. I especially like how it would apply to kids doing history problems.

    Now, how to execute it? How to execute it?

  7. April 1, 2007 am30 2:40 am 2:40 am

    You collect homework after the in-class review, then? How many students simply copy the homework as you go over it? Is the idea that it does not matter as long as they do it?

  8. April 1, 2007 am30 4:18 am 4:18 am

    I prefer to check rather than collect homework, but I do some of each. I expect them to check and correct their work based on what’s on the board.

    They are responsible for being able to do everything we have done in the homework, so a good number of students make it their business to put up anything that stumped them. (Plus they get credit, double incentive). Either me or other students will complete the problems.

    On average a quarter to a third of the problems go up, and we review them. Nothing else gets reviewed.

    I check their assignments for completeness, and only spot check for accuracy, since they have had a chance to make corrections. I want them to come in with good homework, and then to correct as necessary. I strongly believe that this combination of individual work with group review is a good one.

  9. April 1, 2007 am30 5:00 am 5:00 am

    Thank you for the details. I’m writing new homework policies this weekend.

  10. April 1, 2007 am30 5:25 am 5:25 am

    No kidding? What did you do up to this point?

    A word of advice (since you seem quite open to it), proceed cautiously. Be prepared for parts of a new system not to work, and to need adjustment and tinkering. It can take a while. Give it a chance before deciding whether it is working for you or not.

    Good luck!

  11. April 1, 2007 pm30 8:49 pm 8:49 pm

    Hey, I’m curious: how many minutes do you guys have per period and how much of that goes to homework checking / collecting / reviewing ? On average.

  12. April 1, 2007 pm30 9:07 pm 9:07 pm

    We meet 4x per week, 55, 55, 55, and 48 minutes. Homework goes up early in the period (without the class focusing on the activity, there is always something else to do). Blank questions get answered. Kids check work. All of this within the flow of class. Now, I stop what we are doing to review the assignment at some point. If we need the previous day’s work to move on, this will be early, but it can be at the end.

    I will scan the work for mistakes first. The actual review can be anything from 1 minute (simple assignment, all the work looks good, no one struggled) to 10 minutes, or even more for a tricky assignment, or one where my teaching the previous day had been off. I usually use a lot of questioning and kid-comments to drive the review. Usually I will let them ask for explanations, but sometimes I will select a problem that I think needs extra emphasis.

    I contend that I can teach any one of our topics in a few minutes (lecture, my board work, a couple of well-chosen examples). Thursday, I did exactly that. In doing so I get to allocate the bulk of class time where I choose:
    One day might be a rich development,
    another a more intense homework review,
    Thursday was a related but unnecessary topic,
    some days there might be an activity leading to the next piece of learning (discovery or somesuch),
    some days I squeeze the lesson to let them play a game,
    and some days I squeeze the lesson to do some off-topic problem solving.

    To get away with this, I need very good control of the homework. Better than review are the two questions: “How did you find last night’s assignment?” and “How long did it take you?” (I require them to time it if they suspect it is going long. My rule is that my target is 20 – 40 minutes. If it is too short the practice is insufficient, and they must tell me; after sitting doing math for an hour they are unlikely to derive much benefit. Therefore they must stop, done or not, if they go on for an hour, and must alert me if assignments are taking that long, or almost that long.)

    You probably can guess, I revise the assignments each year. Some classes handle more, some less. I also retarget the challenge vs practice sections. An unreasonable goal of mine is to have exactly half of each class doing each.

  13. mr. paul permalink
    September 17, 2007 pm30 8:28 pm 8:28 pm

    why give homework if it is not reviewed in class?

  14. September 18, 2007 am30 9:30 am 9:30 am

    1. We review much, but usually not all.
    2. Practice is useful for kids, especially for identifying what seemed clear in class, but then wasn’t.

  15. Gen permalink
    September 25, 2007 pm30 10:13 pm 10:13 pm

    I don’t understand one thing how anybody can question the need of homework review. Yes, there could be many ways how to go about it and to make improvement but reviewing homework is the only way to monitor students progress on a daily basis, make sure that he/she continuously has previous material grasped correctly so no new knowledge is based on old wrong assumptions (tests could reveal these problems but they too rare to do this timely). I am not a teacher but I am very disappointed the way homework is handled in my daughter’s school and I feel like I cannot do anything about it. Yesterday I found that on a half page homework my daughter made 6 mistakes and the teacher had already checked it (it is signed). She says that the teacher checks individual homework during a class mainly scanning for ‘done/not done’. No QA (quality assurance). Frustration… We immigrated to the USA from Russia and here is one of the ways that my homework was handled at school in Russia (sure, their could be some variations of this process, but that’s how I remember it now):
    – specific tasks will be given at the end of a class and a student completes his/her homework at home;

    – a student brings his/her homework to school and students’ notebooks with completed homework are gathered by the teacher for homework to be checked (you need to have 2 notebooks for each subject so you can write in one of them while the other is checked by the teacher);

    – the teacher would review/summarize the previous topic at the beginning of a class and answer any questions that students might have, this would include questions about any difficulties anybody faced doing their homework. Often only the most tricky tasks would be covered;

    – the teacher does NOT check individual students’ homework during class. It’s done either between classes or after in a place where nobody could bother him/her. It’s I would call one-on-one virtual work with a student.The teacher would focus on individual homework evaluating the QUALITY of student’s work and would leave corresponding comments (you are not allowed to use red ink at school as this is the color that only the teacher uses so it stands out). As you see individual reviews address individual needs of a student, the teacher looks not only for ‘done/not done’, ‘right/wrong’ but encourages students to make their work as more interesting as they can (even in Math, you can come up with alternative ‘nice’ solutions to a problem). No teacher wants to spend a lot of their time reviewing dull work (naturally, this kind of review takes a lot of teachers’ time). And what is important students know that the QUALITY of their work is going to be assessed on a daily basis;

    – next time students get notebooks with their checked homework back and give the current homework to the teacher for checking. Usually, the same subject has at least one day gap. Depending on a subject you may be required to redo a task correcting mistakes before doing your next home. This is done by a student at home. Also you may get general comments that would direct you in your future work (highlights of your strong and weak points). Yes, you would address teacher’s comments only after another class when you come home, but you would not get too much new material during this class so even if you got some concepts wrong it is still manageable to catch up.

    – my parents coming home would get all my notebooks and scan for teacher’s comments (in red) and would know immediately whether they need to address any issues in a timely manner, dedicate more time to something their children need now or just praise them for good work. I have to do thorough check of my daughter’s work myself as I don’t see any comments from her teachers (I cannot say anything about the quality of their comments as they just don’t exist at all). Sure, I don’t have enough time for this working from 8am till 7pm, so I do this irregularly. Also my parents would check for grades. We don’t get our student’s work graded on a daily basis, self esteem thing…sure…this is another great topic for discussion, we are scared to grade them on a daily basis but then let’s do this grading on a test, let’s make a nice surprise for them, once in a few months; especially that there would be no time to correct this, this test result grade will be final and will affect their lives (what eventual grade you would get, what school you can get into, so on)…but grades on a daily bases that students know that there’s nothing scary about them as they have plenty of TIME to work on to correct their final grade (which is an average of all kind of grades you may get during a study quarter in Russia) is something scary. Life is tough but you do toughening slowly on a daily basis and without such words as ‘final’.

    Looks like I have written too much, no time to edit… I don’t know why teachers in USA are not doing individual student’s work check to ensure the quality of their education… May be the reason for this is that teachers are paid only for class hours and not for checking hours when they work on their own. If it is like this then teaching multi-stage process (present info/practice/feedback/correction) will stay broken as it’s only partially implemented in the current system.
    Correct me if I am wrong (I would prefer to be wrong)…

    There are also many good things that I like about my daughter’s school but this is not the subject of this thread…

  16. September 26, 2007 am30 6:49 am 6:49 am

    There should be a mechanism that ensures that students’ homework is corrected. What you describe would work. What I describe (comment #12, above) also works.

    There is a natural human tendency to overvalue our individual experience. In the case of education, most people think that the way in which they were taught was the best. But if one person is right, all others are wrong…

    No, it is best not to insist that the exact same methods be used. (even there people have survived several waves of education reform).

    Rather, it would be good to pick up where you started, with a few basic ideas. “Homework should be corrected.” This is basic. Let the school and teacher have some flexibility in how they make certain that this is done. But there should not be flexibility about whether it is done.

  17. October 7, 2007 am31 9:02 am 9:02 am

    Whats the bloody point of homework when literally everything can be bought off the internet. I used to think the large number of english and philosophy majors out there are the only cause of essay mills. But apparnently you can get anything done online, from math homework (sites like [spam deleted]) to physics (several online shops).

    There has got to be a better educational system that doesnt rely heavily on homework!

  18. October 7, 2007 am31 9:14 am 9:14 am

    The above comment looks meaningless with the advertisement deleted.

  19. February 1, 2008 am29 9:06 am 9:06 am

    They should get credit even if they’re incorrect… especially if it’s something as silly as forgetting a sign or a bracket somewhere along the line.

    You need to reward kids for DOING their homework, because if you don’t, (or if they just always lose the marks because they did it wrong), soon they simply won’t do the homework, and that’ll hurt them more than attempting it.

  20. February 1, 2008 am29 10:06 am 10:06 am

    My students are, in a way, penalized – not for wrong answers (I just check that homework is complete) – but for not correcting their answers. I don’t grade the homework, but I often recycle problems onto tests or quizzes.

  21. ncmathteacher permalink
    May 19, 2008 am31 6:57 am 6:57 am

    To: jd2718: Can you please explain in a bit more detail how your homework review begins? You say that students put up problems. If there were 15 problems assigned, what exactly is the normal protocol?

    I currently have warm-up problems the students work on while I check each student’s homework completion. I am considering a different approach next year and am curious how your method goes exactly.

    thanks

  22. May 19, 2008 am31 7:17 am 7:17 am

    I do not require homework to go up.

    Students chose which, if any, problem to put on the board.

    They receive credit for good answers, bad answers, or just complete questions without answers (others might complete those, or I might)

    Because credit is involved, I usually get at least a few questions up. And because any homework problem can appear on the test, there is motivation to figure out things they didn’t get.

    I assign 90% odd problems (answers in the back), so we are talking about looking for explanations. And I have enough kids who want to show off that I usually get one or two harder, completed questions.

  23. ncmathteacher permalink
    June 28, 2008 am30 12:44 am 12:44 am

    Thanks for replying to my question. At what point do you look at student’s homework for credit? I have anywhere from 25-30+ students in a class and looking at each student’s takes a sufficient amout of time.

    Let’s say you assign 20 problems. Your class begins the next day. What do you say first to the class when it comes to checking the homework? If no problems are requested do you just walk around at that point and check homework completion (if so what are the students doing at this point?)

    Can you tell me what grade you teach?

    thanks.

  24. June 28, 2008 pm30 8:48 pm 8:48 pm

    I seem to have a gazillion questions about pay, and more comments about our state exams, but today, yours is the most interesting.

    I teach high school, mostly 9th grade. When the kiddies come in, some put up homework, some copy other’s work, some do other things.

    Two more things need to happen. At some point we need to stop and ask questions about the homework on the board. I will answer all questions (or have kids answer them, if I think they can be clear).

    And at another point I will collect the homework, or check it at their desks. Typically, lesson goes well, there’s 3 or 4 practice problems they are working on, and I will ask them to have their homework out while they work, so that I can check it. Goes very easily.

    You asked what I do if no problems go up. I’ll whine and complain and ask why no one wants credit, and doesn’t anyone need credit, and don’t you know that any homework problems could be on the next test, and if no one goes up I’ll have to start assigning people. Usually a few kids march up right away, but honestly, I rarely need to complain. I had one class this year, not once was it necessary. And the others, not common. Kids like being at the board, and getting extra credit, and answering each others questions. It becomes part of our class culture.

  25. lupe permalink
    September 19, 2008 am30 6:18 am 6:18 am

    9

    2

    5

  26. November 4, 2008 am30 3:46 am 3:46 am

    In college, kids genuinely want to solve the homework problems because they have the hope that the test will be much like those problems. But then, if the instructor dares to ask something slightly different they really get mad….Funny.

  27. June 5, 2009 am30 5:53 am 5:53 am

    The bad thing is that students just want to pass the class and they’re not genuinely interested in learning. That’s the heart of the problems

  28. October 19, 2013 pm31 1:59 pm 1:59 pm

    what do you mean by giving students credit for board work? is this extra credit, or are students required to come to the board a certain number of times?

    • October 23, 2013 am31 11:19 am 11:19 am

      I keep a record of how many times a kid goes up, and I use it in calculating a participation grade (in my classes, generally 10%). I also use how often they ask questions, answer questions, how well they work in groups. I occasionally deduct from someone who consistently detracts from the class.

      So board work is neither required, nor extra credit. It is one of several factors that contributes to a small part of the grade. I think it can make no more than a 2-3 point difference on a final grade – but that’s enough.

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