10/18/2004 Entry: "Math homework"

Math teachers tend to assign large sets of very similar problems as homework. The usual explanation for this is that students need lots of practice and repetition in order to learn math successfully. This explanation does not actually make sense, because induction does not exist. Students do not learn things by repeating an experience until they draw the appropriate conclusion from it.

The reason repetitive math assignments are useful is because math is nuanced, and diverse experience helps one to gain a broad understanding. The problems are slightly different from each other, and the value lies in working out how to solve slightly different problems. The assignment reveals nuances that a student is unaware of, and allows him or her to come to understand them.

Little, if anything, is gained from solving problems when the method of finding the solution is completely obvious to the student. If a student understands the principle behind a problem set, it's likely that many of its problems will be essentially educational useless to that student. Teachers are right to assign large problem sets not because it is necessary to do large numbers of problems, but because a teacher is better placed to assign a large problem set that is likely to contain some useful problems and some useless problems than to create an appropriate problem set for each student.

However, students are well placed to figure out which portions of an assignment are applicable to their educational needs. They can figure out which questions are obvious and which are challenging, and work only the educationally useful problems. Students should be allowed and encouraged to do this, and helped to develop the skills they need to do this well. For this reason, requiring students to complete all homework assignments in order to pass math classes is not only unnecessary, it is actually counter-productive.