Homework exercises can often be exercises in frustration, both for the instructor and for the students. The students do not know what the instructor really wants and do not agree with the grades they get, while the instructor can not understand why students communicate so little in their work. But with a little care, homework can enrich our students and educate us. The first thing that we must do is to make the homework an important part of the course. Homework assignments should be a significant part of the total grade. If we tell our students that homework will be used only to decide borderline course grades, or that it will be counted as some type of minor extra credit at the end of grading period, many of them will not bother much with the assignments, feeling that they are not worth the effort. We should decide how much the homework will be worth (e.g., percentage of the total grade), and then let students know its worth in advance. If the students feel that not doing the homework will hurt them, they are much more likely to work consistently on the exercises. Unfortunately, most students do not realize that they will not learn the material without doing the homework. They need to be motivated by having homework be a part of their grade. Secondly, we must take care when we draw up assignments. Assigning every problem at the end of the section may not be the thing to do. Repetition is not necessarily a good learning tool, and can sour students' attitudes. If we expect students to work every single exercise in the problem set, we should grade every one. Otherwise, if we are going to grade five or six representative exercises, why assign forty? We need to choose problems which will expose the students to different aspects of the current area of discussion, or to different methods of computation. By making the assignment reasonable in terms of time, relative to what we want the students to learn and what we plan to grade, students are much more likely to complete the assignment. Thirdly, we must make the standards very clear and precise and discuss them in advance. Many instructors complain about how poorly students write mathematics, but how many students have studied any work other than their own, or have ever been told how better to write mathematics? This is, I feel, a major problem, but the cure is simple, if demanding. We, teachers, must work very precisely and completely at the chalkboard, and tell the students that we expect the same in the homework. That is, we expect them to rewrite the problem as stated in the book (except, say, in the case of word problems). We expect them to write their steps clearly, one line after an- other; not in scattered columns, but neatly across the the page so their reasoning can be followed. Their computations are to be complete; their steps are to be connected with grammatically correct English sentences. Answers are to be marked as such (by boxing, underlining, "Ans." etc). Then grade accordingly. If a student gives "#3. 42" for an answer, points should be taken off, even if the answer is actually 42; the students will not take our standards seriously if we do not. Point out to them that properly worked-out homework problems are good study helps at test time. Certainly they will complain for a while, but once they become accustomed to the new standards, the quality of their work will pick up considerably. The only requirement remaining is consistency. We must maintain these standards for the entire grading period, including quizzes and tests. When we do this, not only will we be better able to help our students, since we are getting more communication from them through the homework, but also the students will gain some measure of dis- cipline and a comprehension of mathematics that otherwise they might not have. Make the homework important. Give assignments that will teach students. Tell them what we want, and penalize if we dot not get it. Repeat for the entire grading period. These four requirtements can be time-consuming, but the reward in improving our students' depth of understanding and performance is well worth the effort. |

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