Getting students to read mathematics
by Laura Taalman, James Madison University
Students have trouble reading mathematics, and worse, they often
to. When working from a textbook, many students will attempt the
exercises before reading the section, and then only refer to the
to look up examples that mimic the homework problems they are working
"Problem Zero" is a simple way to encourage students to read the
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
your own summary of the material.
In my calculus classes I now include "Problem Zero" in each of my
assignments. I collect Problem Zero (or not) according to the
of a die, and my general rules are:
students can't just copy down all the "boxed" definitions and
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
their summary makes sense to them personally;
they should do Problem Zero (and therefore the reading) before they
any of the homework exercises; and
they should try hard to fit this information on the front of one
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
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
of the first semester I did this that I almost dropped it midway
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
but even these students seemed to appreciate the "easy points" they got
for doing it. In my classes, each Problem Zero is worth five
for comparison purposes, homework assignments are worth ten
Each class day there is a 1/6 chance that Problem Zero will be
(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
thing is how different they are from each other. I smile every
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
*before* the lecture and then have an easier time following the class
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
to do Problem Zero."
"Sometimes in class we don't get to learn the entire section.
Zero motivates us to understand the whole thing."
"I started concentrating on Problem Zero and it made the
"By doing Problem Zero I see where the information is in the
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
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:
of Solids of Revolution I
of Solids of Revolution II (by another student, to illustrate that
students really do "personalize" Problem Zero)
Samples of Problem Zero made by actual students:
Laura Taalman (firstname.lastname@example.org)
is an Assistant Professor at James Madison University. Her
degree is from the University of Chicago, and her graduate work was
at Duke University. She recently wrote a textbook that combines
precalculus, and algebra -- and this textbook has "Problem Zero" at the
beginning of every homework assignment! Her research interests
singular algebraic topology and knot theory. When not teaching or
doing research, Laura reads way too many science fiction novels and
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.
Teaching Exchange is edited by Bonnie
©2005 The Mathematical Association of America
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