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I teach algebra at a community college. I assign homework which counts for 2 points. After going over the HW, I give the students a quiz (worth 20 points) with problems similar to the HW.

I spend about 30 minutes at the start of class going over the homework. I have tried a few different things and I don't really think either of the methods really works great.

Method A--I ask students to work in pairs and talk to one another about the homework. Meanwhile, I circulate and answer individual questions.

Method B--I ask students which problems they would like to go over. I write the problem numbers on the board and then ask for volunteers to write the problem on the board. I then go one by one talking through the problems, while directing my comments to the person who asked about the problem.

Any thoughts on how to make this "going over homework" time better?

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    $\begingroup$ Can you expand on why you feel these methods are ineffective? $\endgroup$ – Ross Sweet Oct 21 '14 at 19:38
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    $\begingroup$ How long are your classes? Do you lecture on the material or provide a review? Is working together a critical part of what you want them to do? $\endgroup$ – Chris C Oct 21 '14 at 20:26
  • $\begingroup$ My class is 5 hours long, meets once a week on Fridays. $\endgroup$ – Kara Oct 22 '14 at 1:59
  • $\begingroup$ My students work in groups almost always. $\endgroup$ – Kara Oct 22 '14 at 1:59
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    $\begingroup$ What i like to do, if i have the time, is work out full solutions to each problem, scan them, and project the key. Let students look over it for five or ten minutes. Chances are, a lot of mistakes that are "stupid" (dropping negatives, missing a term when writing a step, etc.) will be uncovered and the only questions left will be about the processes which are probably good to go over anyways. $\endgroup$ – celeriko Oct 25 '14 at 16:54
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Method B is great, but I'd suggest that you require students put away their pens, pencils, and own homework assignments away while other students present the problems on the board. If you don't, the students will just either: copy down exactly what is on the board, or check to see if there solution matches, without actually listening to the presentation. Several times, I've seen a non-presenting student say something like "that's not what i did, but it looks like it could be right,". I'd suggest further signing a volunteer "referee": a person designated to evaluate the solution of the presenter (of course others can make remarks as well). Require that the referee do more than just say "yeah it's right" or "that's what I did" but comment on the presentation and the reasoning.

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    $\begingroup$ I tried Method B with a little modification and it went great. I asked the class which problems they wanted to go over and then made a list on the board with problem numbers with names of who asked about them. Then, I used the overhead projector. I asked the student what was their specific question about the problem. One student didn't know how to get started. So I asked the rest of the students if someone would be willing to show their HW on the overhead to help him get started. $\endgroup$ – Kara Jan 16 '15 at 16:37
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    $\begingroup$ Another student didn't get the correct answer to her problem. I asked her if she would be willing to show her HW on the overhead. We then played "can we find the mistake?" $\endgroup$ – Kara Jan 16 '15 at 16:37
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For method A, you should not wait for people to ask questions. Glance at what they have done, and if there is a mistake or unclear parts, ask about them. If everything looks okay, you can still ask how does the student know that this or that manipulation is legal, for example. Then ask them to write down their reasoning, not only the calculations.

You can also combine the methods - have people discuss in pairs or groups first, and then have someone do it on blackboard (with enhanced confidence or understanding from the group work). Or use method A, but when there is a common issue or problem, have someone do the exercise on board or do it by yourself. Students might be more interested when they have first discussed the issue and noticed a problem.

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When reviewing homework, if you gather a list of problems from students and then do them by popularity (simple raise of hands vote). This should help with getting to the problems that the most students have issue with and keep the majority's attention. Additionally, if you get down with a few problems with only one or two votes, then that might be an indication that you can move on with the lecture. I like to present the problems myself instead of having them come to the board as that seems like grade-school type of attitude. I also tend to go quickly through the jist of the problem or ask the class which part of the problem they are having issue with. For all you know, they can get everything up to the end where they are just messing up punching in numbers to a calculator. They are adults and should be responsible enough to keep up with this type of presentation.

You can then swing the lecture a bit by kind-of flipping the classroom. Perhaps instead of having them present the homework, work on review handouts in class and have them present the solutions to those. This de-emphasizes the "I must have the correct answer for a solution to get a good grade" drive that the homework has and encourages a bit more of a creative and build a more intuitive approach to the problems for them. In the long run, this might help mitigate the homework review in the beginning.

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  • $\begingroup$ How is having them coming to the board "grade-school type of attitude"? Do you just mean that is something that is frequently done in grade school? If so, then what is wrong with it? $\endgroup$ – MathTeacher Dec 30 '14 at 0:48
  • $\begingroup$ I don't just mean something that is done in grade school, but a maturity level. At a university, I expect students to start to seek out help for what they don't know and be responsible for their own knowledge, while in grade school, that responsibility is more limited or guided. That's just my experience. $\endgroup$ – Chris C Dec 30 '14 at 1:53
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I like method B, but go ahead and call people to the blackboard versus taking volunteers. Of course if they say "not prepared", just go to the next person. But they should at least feel some mild social pressure from being put on the spot. Sometimes you will have kids like me that try to brave it out and figure it out on the fly and make a hash out of it...but not enough to derail the class. And it can be fun to watch them flail.

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