Written by Teresa Green, Plano, TX
Writing can be a powerful vehicle for empowering learners. As students write about their math, they are encouraged to synthesize their ideas about new mathematical concepts and apply those concepts to problem-solving situations. They demonstrate their learning processes and outcomes as they formulate, organize, internalize and evaluate math concepts. For the teacher, the student's writing provides a valuable assessment tool.
Early in the school year, I give my first graders the Exemplars "Ten Feet Apartment" problem as a diagnostic instrument to determine their ability to use mathematical skills in an authentic way. They are encouraged to use pictures, numbers, and words to show their solutions. This first attempt shows limited understanding of the problem and strategies useful in solving it. The following day, I present the same problem again and model how to solve it. I model for the class how to write about their solution so that I can understand the process used to arrive at it. Thereafter, I spend time each week modeling one or two approaches to the problem before giving it to the children to complete. After the class has worked on it for a reasonable amount of time, we come back together to share solutions they have found and strategies used. Gradually, as they gain experience with problem solving, I alternate the modeling with giving them a problem "cold" to see how their ability to apply strategies independently is progressing.
Questions, such as the following, help guide them as they organize their thoughts:
- What strategies did you try when solving the problem?
- If you tried a strategy that was not helpful, what made you decide to try a different one?
- Explain the steps you used to solve the problem.
- Did you find all the answers?
- How do you know you found all the answers?
- How do you know your answers are right?
The students are expected to write about the process used in their solutions. Including this writing component in problem-solving leads students to evaluate their work more critically.