A Case for Using Reading and Writing in a Mathematics Classroom

by Sarah E. Kasten

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 In social studies the students are having a debate regarding the historical document that they have just read.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 mathematics class.

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 and writing.

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 understand.

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.

Writing

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.

The Benefits

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.

Sarah E. Kasten is working on a doctoral degree in mathematics education at The Ohio State University. Before that, she taught ninth grade mathematics in a high school in Columbus, Ohio, for three years.

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References

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.