Problem Zero:

Getting students to read mathematics

by Laura Taalman, James Madison University

Students have trouble reading mathematics, and worse, they often refuse to. When working from a textbook, many students will attempt the exercises before reading the section, and then only refer to the reading to look up examples that mimic the homework problems they are working on. "Problem Zero" is a simple way to encourage students to read the material and organize it into information that makes sense to them. A tiny idea, but one that works, and is easy to grade!

"Problem Zero" is the following question: Read the section and make your own summary of the material.

In my calculus classes I now include "Problem Zero" in each of my homework assignments. I collect Problem Zero (or not) according to the roll of a die, and my general rules are:

students can't just copy down all the "boxed" definitions and theorems in the section;

what they write should prove to me that they read the section;

they should think hard about what to include and how to include it so that their summary makes sense to them personally;

they should do Problem Zero (and therefore the reading) before they do any of the homework exercises; and

they should try hard to fit this information on the front of one page (this forces them to pick and choose from the material).

Grading Problem Zero is easy and fast; most of the time I just check to make sure that they didn't blindly copy down the boxed definitions and theorems, and that they didn't try to substitute their class notes for Problem Zero (this happens more often than you would think!). If they pass those requirements, and have written down a sufficient amount of information, I usually give them full credit.

At the beginning of the semester, students really don't like Problem Zero very much. In fact, they disliked it so much at the beginning of the first semester I did this that I almost dropped it midway through the semester. But then students started coming around; by the end of the semester, more than half of the students in the class said they liked Problem Zero, and that it helped them a lot. Some students never grew to like Problem Zero, mostly because it was more work for them, but even these students seemed to appreciate the "easy points" they got for doing it. In my classes, each Problem Zero is worth five points; for comparison purposes, homework assignments are worth ten points. Each class day there is a 1/6 chance that Problem Zero will be collected (according to the roll of a die).

I have photocopies of some of my students' Problem Zero assignments, and they are really interesting to look at. Maybe the most interesting thing is how different they are from each other. I smile every time I grade Problem Zero, because I can see my students taking "ownership" of the material. Some of my students even decided on their own to do their Problem Zeros a day in advance, so that they would read the section *before* the lecture and then have an easier time following the class discussion.

Here are some quotes from my students about Problem Zero:

"I don't know if I would actually read the section if I didn't have to do Problem Zero."

"Sometimes in class we don't get to learn the entire section. Problem Zero motivates us to understand the whole thing."

"I started concentrating on Problem Zero and it made the homework so much easier!"

"By doing Problem Zero I see where the information is in the chapter. Then when I am doing the homework and I have a question I know exactly where to look back in the chapter."

"I didn't like Problem Zero at first, but when I went to take the first test they really helped me review!"

"Getting credit for doing something easy is always a plus!"

Samples of Problem Zero that I made to give to my students:

Numbers and Sets

Algebraic Functions

Samples of Problem Zero made by actual students:

Rational Functions

Inverse Trigonometric Functions

Volumes of Solids of Revolution I

Volumes of Solids of Revolution II (by another student, to illustrate that students really do "personalize" Problem Zero)

Laura Taalman (taal@math.jmu.edu) is an Assistant Professor at James Madison University. Her undergraduate degree is from the University of Chicago, and her graduate work was done at Duke University. She recently wrote a textbook that combines calculus, precalculus, and algebra -- and this textbook has "Problem Zero" at the beginning of every homework assignment! Her research interests include singular algebraic topology and knot theory. When not teaching or doing research, Laura reads way too many science fiction novels and spends time with her husband and her new son Calvin.

Mailing address: James Madison University, Department of Mathematics and Statistics, 127 Burruss Hall, MSC 7803, Harrisonburg, VA 22807.

The Innovative Teaching Exchange is edited by Bonnie Gold.