Integrating Mathematics with Problem Solving Using the Mathematician's Chair
Hildebrand, Charlene, Ludeman, Clinton J., Mullin, Joan, Teaching Children Mathematics
Mathematics, like language development, is essentially a process of construction, not acquisition. The National Council for Teachers of Mathematics (NCTM) has issued a standards-and-evaluation document calling for mathematics classrooms in which students apply their own strategies and construct algorithms to solve everyday problems. Joan Mullin, a third-grade teacher, integrated mathematics problem solving and process writing in a way to bring her students' everyday social worlds and school together in a meaningful partnership. Her teaching strategies focused on process similarities between whole-language instruction and teaching that supports the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989).
This article describes how Mullin, in collaboration with two college instructors, designed and carried out an action research study to answer her own instructional questions. Action research is a process of studying some aspect of teaching through the use of disciplined inquiry (Association for Supervision and Curriculum Development 1995). Teachers engage in action research to improve their instructional practices on the basis of a deeper understanding gained through the collection and analysis of relevant data. Action research can take place on three levels: an individual teacher might examine his or her classroom, a group of teachers might collaborate to research a shared interest, or an entire school might research an issue. In this study, the teacher-researcher looked most directly at the aspect over which she had control: the nature of instruction in mathematics problem solving.
The purpose of this article is to share what this third-grade teacher-researcher learned through action research. More specifically, this article is intended to -
* guide teachers in modeling a process for students in "formulating problems from everyday and mathematical situations" and
* describe a rubric with three facets used to evaluate students' original word problems.
The results of the action research indicate that students in Mullin's third-grade class increased their ability to create mathematical word problems on the simple- and complex-translation levels. Students' attitudes toward the problem-solving process also improved.
Mullin examined the effects of students' previous experience with conference-based language arts instruction on writing and solving original mathematics word problems. Students challenged their peers in a mathematics problem-solving situation using the Mathematician's Chair, an activity in which one student shared his or her word problem with peers, who then attempted to solve it. They wrote, solved, and shared original mathematics word problems. Daily mathematics periods began with the Mathematician's Chair, which is a modification (Winograd 1992) of Author's Chair (Graves 1983) in Writers' Workshop (Calkins 1986) in which the students read their original pieces to a whole-group audience. Students attempted to solve problems and provided constructive feedback to the problem poser. The original problems were later analyzed using a Focused Holistic Scoring Point System (Charles, Lester, and O'Daffer 1987) consisting of a teacher-made, four-point rubric with three facets containing specific mathematics and writing criteria (see table 1).
According to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 23), "problem solving should be the central focus of the mathematics curriculum," that is, problem solving is a part of all mathematics reality. Schroeder and Lester (1989) delineated three approaches to problem solving: (1) teaching about problem solving, (2) teaching for problem solving, and (3) teaching by means of problem solving. Mullin's research focused on the second approach, that is, teaching for problem solving: she concentrated on applications of problem solving to students' written problems. …