A Case for Using Reading and Writing in a Mathematics Classroom
Picture in your mind the "traditional" mathematics classroom. The teacher
is standing at the blackboard demonstrating examples from the lesson of the day.
The students are sitting in desks in rows, furiously copying, with little understanding
of what they are writing. Both teacher and students view these notes and the student
textbook as the only way to "learn" the material.
In English class the students are reading excerpts from a Shakespearean play and
writing reactions in their journals. In social studies the students are having a
debate regarding the historical document that they have just read. In science class
the students are working in groups to write lab reports detailing the experiments
that they have been conducting in class. With all the excitement in their other
classes, students still expect to take notes and do worksheets when they are in
Unfortunately, these old ways of teaching and learning mathematics are robbing students
of the opportunities for engagement that they are experiencing in other classes.
These opportunities include reflecting, becoming familiar and practicing with sources
of information other than the "official" textbook, and explaining problem-solving
processes and results in writing. As mathematics educators, we need to provide these
authentic learning opportunities for our students.
Communication Makes for a Deeper Understanding
The National Council of Teachers of Mathematics (2000) states that "students
who have opportunities, encouragement, and support for writing, reading, and listening
in mathematics classes reap dual benefits: they communicate to learn mathematics,
and they learn to communicate mathematically" (p. 60). The obvious advantage
of this outcome is a deeper understanding of a subject that, in the past, has been
viewed by many as something to memorize instead of something to understand.
Throughout my undergraduate experience, the importance of communication in mathematics
was impressed upon me. I discovered on my own the need for being able to read textbooks
and also to find other sources when I did not understand the text. For me, reading
and writing went hand in hand with understanding mathematics. These were both skills
that I wanted to develop in my students when I began teaching. During my first year
I had no real plan for how to do this, and I found that my desire to use reading
and writing did not automatically translate into it happening in my classroom. Going
into my second year I realized that I needed a strategy for incorporating reading
I decided to focus on reading during my second year of teaching. I observed early
on that many students entering their first high school mathematics class have an
instant aversion to their mathematics textbooks. Some students are not even aware
that their textbook has actual text that they could read, and not just pages and
pages of problems to do. Because I encountered this distaste for the textbook in
almost every student, I never used the textbook in introducing reading into my lessons.
It is key to create an atmosphere that invites discussion and questioning. Once
that atmosphere has been developed in a classroom, students often feel free to ask
why or what-if questions. These are perfect opportunities to introduce reading to
mathematics students. I would often send a group of students to the computer lab
with a list of websites that I considered accurate, understandable, and safe to use to
find the answers to their own questions. This first attempt often required some
acting on my part, with statements such as "I am not really sure the best way
to describe that―why don't you go and see if you can find a good explanation?"
It is imperative in these situations to seize the opportunity, and not to wait several
weeks or even days, as the students will lose interest and not be motivated to find
the answers to their questions. Many times students would come back empty-handed,
because they had no previous experience in finding mathematical information for
themselves. In these cases I would sometimes return with the students later or find
the answer and print out copies for the entire class to look at the next day.
The object was to show students that the teacher was not the only source of knowledge
and that they were capable of digging through information to find answers for themselves.
These fact-finding expeditions would slowly lead them to their textbook, where the
students would often be mystified by the notion that in its pages they could find
information that would be useful in helping to clarify a difficult concept. Students
became comfortable with the idea that mathematical answers were all around them,
and not only inside their teacher's mind.
At the end of the second year, all students filled out a course evaluation. One
of the questions asked the students what was the most difficult concept that they
had mastered during the year. One young lady responded that learning how to read
about mathematics had been the most challenging thing for her throughout the year.
She went on to say that she knew that she would not pursue mathematics as her career,
but she was proud that she could learn things from her textbook (and other sources)
and was sure that she could use this process in the future.
At the beginning of my third year of teaching, a class set of the novel
The Number Devil, by Hans Magnus Enzensberger, was delivered to my room.
During this year the ninth grade teachers were focusing on reading, and teachers
were expected to devote 20 minutes each week to reading in their classroom. After
I explained this to my bewildered crop of new ninth grade students, I handed each
of them a copy of the red book that featured on its cover a silly picture of a devilish-looking
creature holding a huge pencil. I instructed the students to read for 20 minutes.
The book tells the story of a young man named Robert who is visited in his dreams
each night by the number devil. The mathematics presented in the book has varying
degrees of difficulty, but all of it is explained on a level that the students could
When we discussed the book as a class after the first day, the students had various
reactions. Some were surprised to be reading at all because they knew that you could
not learn math if you were reading. Others said the book was fun and they would
like to read it every day, instead of learning mathematics. The goal of reading
this book was to present mathematics to the students in a new light. I was not addressing
any specific content standard in my curriculum, but I hoped that the students gained
a new way of looking at mathematics through the experience.
During my third year, I continued to use many of the reading activities that I had
used the previous year, and in addition I decided to build in some writing activities.
While many different types of writing occurred in my classroom that year, I will
outline just three of them here.
- Do Impromptu Writing. As with the reading,
I allowed students to engage in impromptu writing when I thought that they were
ready to reflect or that they had questions they were not asking. In both instances,
I asked students to take 5 minutes to explain their understanding of the concept
that we had been discussing or to ask questions about the parts that they still
did not understand. These spur-of-the-moment activities helped me know where to
direct my efforts in the coming days.
- Explain the Process. In addition to this
informal writing, I began asking students to explain their problem-solving processes.
This was difficult for many students because they did not understand how to put
their thoughts into words. It was often necessary to have students work in pairs
and explain their process orally to each other and then write what they were saying.
As this type of assignment became more familiar to the students, I began asking
them to include in their explanations what part of the problem was most difficult
for them and how they would improve the problem.
- Explain the Concept; Create and Solve the Problem.
Another type of writing assignment that I used asked students to explain in their
own words a concept that we had been discussing in class. Then they had to come
up with an example problem, solve it, and explain their technique. This was the
most difficult writing assignment for the students―as well as for me. It seemed
that never before had the students been asked to explain a concept. The idea of
explaining how to solve a single problem was not totally unfamiliar to them, but
to think of what they had been learning in terms of concepts was overwhelming. The
first assignment of this type took 4 days.
Despite the amount of time needed for these assignments, the benefits were worth
it. Students began to connect skills to concepts and sought out the appropriate
words to explain themselves. Students were encouraged to work together and read
each other's work. This resulted in comments like "this makes no sense"
or "I didn't really understand what you meant here." In addition to helping
students develop an understanding of mathematics, I was able to understand what
they were thinking and why they were thinking it in a way that I could not before.
When students were asked to comment on the experience of writing in a mathematics
class, a majority of their responses were very positive. Some students noted that
writing about mathematics helped them write better in other classes, while others
said, "You get it better when you write it." Almost all the students agreed
that their overall understanding of mathematics had increased.
With both the reading and writing assignments, students were surprised in the beginning
by how different these activities were from what they were used to. The students
exhibited an overwhelming excitement. They felt that these alternative activities
showed that I was interested in helping them learn. Even if the students did not
enjoy reading and writing in my classroom, they recognized my attempt to make their
learning more meaningful and authentic, and they were willing to make a greater
effort in response. Also, the students expressed in their writing activities a sense
of amazement that I wanted to hear how they understood the concepts, instead of
a summary of how I had explained it. They were empowered by the idea that their
understanding could be as important and as correct as mine.
Using reading and writing in my classroom resulted in many wonderful changes in
both my own and my students' perceptions of the learning of mathematics. My students
enjoyed looking at mathematics in a different way, and many of them acquired a greater
understanding of the material than they would have through more traditional methods.
I was able to learn things about my students' understanding and use that knowledge
to guide my instruction, instead of working only on my own schedule and with my
own notions of how the concepts should be understood. It will be important in the
future for methods and materials to be developed so that all teachers and students
of mathematics can benefit from reading and writing in their classrooms.
Return to top
Enzensberger, Hans Magnus. (2000). The number devil.
New York: Henry Holt.
National Council of Teachers of Mathematics. (2000). Principles
and standards for school mathematics. Reston, VA: Author.