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.
<hr>
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