Communicating in the Language of Mathematics
Buschman, Larry, Teaching Children Mathematics
As the classroom mathematics curriculum expands to encompass the entire range of skills included in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), the process by which a student arrives at the answer to a problem becomes as important as the answer itself. Answers alone often fail to reveal the nature of a student's thinking, the strategies used in the problem-solving process, or the level of understanding. Additionally, the standards document includes the expectation that students will be able to "relate their everyday language to mathematical language and symbols" (NCTM 1989, 26).
Using oral or written communication as a tool with which students can reflect their understanding of mathematics helps them make connections and personalize mathematical concepts. When students communicate mathematical information, they remember it, understand it, and use it to uncover and find even more information (Perkins 1992).
Teachers need to know how to help students grow into accomplished communicators of mathematics who can describe their thinking processes clearly. Teachers must help students make their thinking visible to others by encouraging them to talk and write about the process they use to solve problems.
The author's past efforts to encourage students to discuss and explain their problem-solving process have focused on (1) joumal writing, (2) student-authored story problems, (3) the mathematician's chair, (4) cooperative-learning activities, and (5) parent newsletters. However, two articles in the May 1992 issue of Educational Leadership - "Creating Tests Worth Taking" by Grant Wiggins and "Evaluating Problem Solving in Mathematics" by Walter Szetela and Cynthia Nicol - present more ideas to add to the existing student-communication activities occurring in a second-grade classroom. The goal of embedding speaking and writing into the daily mathematical activities of students is being met through the following activities.
Ask students to keep a mathematics journal, which not only can constitute a major part of the daily curriculum but, when added to a student's portfolio, can furnish an ongoing record of the student's mathematical growth.
In our classroom, students begin each day by recording statistical data related to the date, weather, and various problem-solving activities: (1) day, date, number of school days attended in the current school year, and number of school days remaining; (2) at least five number sentences that equal the date; (3) the weather report - temperature, precipitation, wind speed, wind direction, and cloud type; (4) predictions for the next day's weather and the color, size, and shape of the next day's calendar piece; (5) answers to various measurement activities, such as the time shown on a Judy clock, the amount of money in a container, the weight of an object or group of objects, or an estimation of the quantity, weight, or length of an object using a standard for comparison; and (6) the solution to an open-ended mathematics problem.
At the end of each day, students use their journals to reflect on the day's mathematics activities. Students are asked to think about how they would answer such questions as "How did you help another person?" and "What did you learn that you did not know before?"
Student-Authored Story Problems
Ask students to create original story problems for someone else - a classmate, a teacher, a student in another classroom, or a family member - to solve.
The directions to the student include the following:
* Write a story problem using your imagination or the information in a picture, newspaper advertisement, poster, or short story.
* Have other people solve your problem.
* After seeing the solutions to your problem, lead a class discussion about your problem and the solutions.
Ask students to sit in a chair that has been designated the "mathematician's chair" and to share original problems that they have authored or solutions to a problem written by someone else. …