It is important to give homework, because then they have to review the material. One should try to give the assignment in time before the bell rings, time enough for them to easily copy down the assignment. Otherwise, some students may rush out and not copy down the homework, and, as a result, not do any. Occasionally it is okay not to give homework, possibly as a reward or bonus for doing certain things right, or if the material was not covered in class fully.

 

Homework is practice in applying the math concepts and learning how to think clearly about the math. It must also be exercises in how to do math, namely, to write neatly, to clearly state the assumptions and reasoning, and to check the work. 

 

Illegible work should be so noted. One student realized that his homework problem was wrong. I asked him where he made his mistake. He could not read his work to find his error. He did not understand his flow of thinking in doing the problem. If he had the attitude that another student may read the work, he may have acted differently.

 

Homework can be viewed as public work. We like to keep tests private, out of respect for the students, but this is not the case for homework. The goal is the effort, the correct understanding of the mathematics, and the proper approach. The activities of one student, successes and failures, can be shown as examples to enhance the learning of all.

 

It is good if students collaborate (as long as they simply do not copy from each other) doing homework. It is good if they teach each other. This should be encouraged. Collaboration is not acceptable on tests, of course, most of the time, although there may be exceptions.

 

Students need to learn how to study together, for teamwork is the norm for adult behavior. In the real world of mathematics, it is almost never the case where a mathematician works alone. Instead, there are teams, with both close intense collaboration, and teams who collaborate occasionally.

 

What I say to them is that the best way to learn is to teach. Two students can get together to teach each other, so that the student teacher can benefit much more than studying alone. With problems, they can review each other’s work for correctness, neatness, and validity of checking.  The homework review in the class can be utilized as encouragement for working together, by discussing aloud with the students nearby work that was very good or contained errors.