Using Math Pen-Pal Letters to Promote Mathematical Communication
Crespo, Sandra M., Teaching Children Mathematics
Although letter writing is not typically associated with mathematics, I have used this activity in my teacher-education classrooms and in my collaborating teachers' elementary school classrooms to help our students learn to explain their mathematical thinking and listen to other people's mathematical ideas. I am drawn to and intrigued by this form of communication because unlike most written assignments for students, pen-pal writing offers an authentic audience and reason to communicate. Furthermore, students of all ages seem to enjoy this personalized activity. This article describes how a pen-pal letter exchange can offer students a rich and genuine mathematical writing experience. Although the examples highlighted here are from interactions between an adult and a young student, similar opportunities for learning to communicate mathematically can occur during other interactions, whether they are between older and younger students or between same-grade students.
Communication is at the heart of the NCTM (2000) visions for school mathematics. Helping students communicate their mathematical ideas orally or in writing, however, has proven to be a challenge. The nature of the writing tasks that teachers propose to students, the intended audience, and the reason for communicating greatly affect students' written communication. In most mathematics classrooms, writing tasks are contrived and the teacher is the sole audience. Some researchers suggest that writing activities that target audiences other than the teacher are more generative and appealing to students (Miller and England 1989; Pearce and Davison 1988). This article investigates this claim and discusses the opportunities for learning mathematics that genuine writing tasks with an authentic audience and reason to communicate might offer students.
Fennell (1991) inspired my strategy of writing math pen-pal letters. I have used this activity over the past few years in my preservice elementary mathematics education courses as a way to encourage my students and their young counterparts to make explicit their mathematical thinking, deepen their own understanding of the subject, and become more comfortable doing and talking about mathematics (see Crespo 2000 and Phillips and Crespo 1996). The adult students usually write to one or two youngsters once a week for the duration of the course, which is approximately twelve weeks. The letters then are photocopied and stored in each of the classrooms so that students have a record of their own letters and can easily access and share them. Depending on the distance, the letters are either hand-delivered or mailed to the respective classroom teachers.
After the pen-pal pairs (or trios) are matched, the younger students usually initiate the exchange with a "Dear Pen Pal" letter like the one in figure 1. This first letter tends to be a personal introduction in which the younger students describe what they like and dislike about mathematics, ask their adult pen pals questions, list all the topics that they have been studying, and pose a mathematical problem for the adult pen pals to solve. Figure 1 shows an introductory letter that a fourth-grade student wrote. The student poses a mathematical problem for the preservice teacher to solve but does not make it clear what should be solved. For example, she could have written, "Find two numbers whose ..." or directed the reader to explain how she figured the problem out. Receiving a response letter that highlights the strengths and shortcomings of their written communication helps students learn how to communicate their mathematical ideas.
Occasions for Mathematical Communication
Writing letters to someone outside the classroom who is not the teacher or a classmate creates opportunities for students to practice and improve their mathematical communication. The fact that the communication is not immediate tends to encourage students to write more than they would otherwise. …