### By H. Smith Risser

Many new mathematics professors encounter the dilemma of how much time to spend in each class going over homework problems. In my first semester, I was teaching a service course that was so large that collecting and grading the homework was impractical. This meant that my students often did not get feedback on what they were doing incorrectly before the test. I also would answer all of their homework questions in class. This meant that I was often bogged down working homework problems and had to rush through the new material. Even the questions students asked gave me no way to determine what students knew and understood. Students would ask questions like "Could you work number 23?" that gave me no real idea what mistakes students were making. After grading the first test, I discovered that although I was going over homework problems in class, I wasn't addressing student misunderstandings by doing so.

Going over homework can be one of the most time consuming and frustrating activities in any mathematics class. There are several difficulties to the standard approach of going over homework in class. While there are some problems that the majority of the students need the instructor to discuss, most of the problems on each assignment are missed by very few students. Also, since there is no way to know how many students had difficulty with each particular question, the instructor may spend precious class time answering a question for only one or two students rather than focusing on concepts that the majority of students in the class are struggling with.

In service courses especially, the classes may be large and collecting or grading homework impractical. If homework isn't collected, it can also be difficult for the instructor to ascertain why students were having difficulty working those particular problems. Did they have difficulty setting up the problem or did they make an algebra mistake while they were working it? Did they get the correct answer and have trouble simplifying it? If students don¹t know where they are making their mistakes, they cannot correct them. Finally, many college students are procrastinators. This means that not all of the students in the class have attempted the homework from the previous class. So, these students miss the chance to ask questions on that homework assignment.

This semester I decided to take a different approach to homework. I no longer spend class time answering homework questions. Instead, I ask students to post their questions on the class discussion board. Many academic institutions have invested a lot of time and money in making online course delivery software available to their faculty. The ways in which faculty use this software varies widely both between and within departments. Traditionally, mathematics departments have had a difficult time using features like the discussion board because of the lack of mathematical symbols. However, in the current software, equations can be inserted into discussion threads. This makes it much easier to use the discussion software in mathematics courses. As an added benefit, you can assign grades for the posts using the built in gradebook.

At the end of each class period, I post a new thread for that night's assignment. Students post their questions on the thread and answer questions from other students. I moderate the discussion and sometimes post answers.

The discussion helps me gauge how many students are struggling with a particular problem. I often see posts like the following:

mathstudent1: i dont get how to set up #67

mathstudent 2: me neither

mathstudent 3: me too

If several students have posted that they don't understand a problem, I discuss that problem in class. Many times, however, a single student will post their question and the accompanying incorrect work. Either another student or myself then will answer the post and correct the work:

mathstudent 1: How come the book got on #55?

mathstudent 2: you can't work it that way. You have to get zero on one side and use the quadratic formula to get the answer

once you get it you can simplify to get what the book got.

This has the benefit of telling me both where the student was making their mistake and how serious the mistake was. In this case, mathstudent 1 did not understand how to correctly solve a quadratic equation. If the mistake is fairly serious, I send the student a message directly and ask them to make an appointment to come in during office hours. I also go back and read the new posts on previous nights' assignments. That way, even students who procrastinate still get feedback before the tests.

During the semester, I did discover the need for some ground rules. First, you have to give students an incentive to post. I required students to post to the discussion board in order to have an opportunity to drop their two lowest quiz grades. However, this approach had some drawbacks. Students that did well on their quizzes didn't need to drop grades. That meant that many of the students doing well in the class weren¹t participating in the discussion. Dropping the two lowest quiz grades also did not have much of an effect upon the overall average. So, even students that were not doing well on their quizzes did not have much of an incentive to post. In the future, I will count participation in the discussion boards as a much more significant part of the overall grade in the course.

Second, students have to know what content and how often they are required post. For my course, I asked students to post once per homework assignment. However, I didn't include any requirements on what they were supposed to post. When I first started having them post, they were posting questions like "Can someone work #25?" Answering this type of question on the discussion board was no more effective than answering the question in class. After the first few assignments, I required students to post a detailed question about a problem, with the relevant work. If they didn't have a question, I asked them to respond to another student's question.

Third, you have to consider what types of homework problems to assign. At first, I assigned problems with answers in the appendices of the book. Students knew whether or not their answer was correct before they posted. Students with correct answers had no reason to post or to participate in the discussion. The more valuable discussions occurred on homework problems not answered in the appendix. On these questions, every student had a reason to participate in the discussion.

Finally, you have to tell students how quickly they can expect answers. At first, I was getting twenty posts on each thread the night before the test. Students were waiting until the night before the test to do their homework and ask questions. By the end, I required students to post within four days after the homework was assigned in order to receive credit for participating. I also instructed students to expect their question to be answered no less than 36 hours after their post. By waiting to post myself, I gave the other students in the class a chance to post answers before I stepped in and answered the question. I also tell students that they should have finished posting at least two days before the test. This gives me time to respond to any last minute questions.

I have found this technique to be particularly effective in my college algebra course. I am spending the majority of each class on the new material rather than answering homework problems. As an added benefit, this strategy has helped me to learn how my students think, which has helped me to be a more responsive and proactive teacher.

**Time Spent:** 1040 minutes per week outside of class reading and responding to student posts.

**Time Saved:** Up to 20 minutes of class time per class

*H. Smith Risser is Assistant Professor of Mathematics at Texas Woman¹s University. She can be reached at* hrisser@twu.edu