(Page 1 of 7) - Strengthening Inservice Secondary Mathematics Teachers� Understanding and Strategies in Mathematical Problem Solving authored by Epperson, James.

STRENGTHENING INSERVICE SECONDARY MATHEMATICS TEACHERS’

UNDERSTANDING AND STRATEGIES IN MATHEMATICAL PROBLEM SOLVING

James A. Mendoza Epperson

The University of Texas at Arlington

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The study reported here is part of a larger yearlong study on inservice secondary mathematics
teachers’ knowledge and understanding of problem solving and the teaching of problem solving.
The report here focuses on examining the outcomes on a problem solving assessment that
indicate that the most significant gains in the abilities of the inservice teacher participants to
demonstrate mathematical understanding in problem solving and to use complex strategies in
mathematical problem solving occurred after a mathematical problem-solving (MPS) course
focusing on reading articles from research and practice in problem solving, applying and
discussing Polya’s problem solving strategies in the context of in-depth problems, and examining
rubrics for assessing students’ work in problem solving.

As a Process Standard in the Principles and Standards for School Mathematics (NCTM,

2000), problem solving plays a prominent role in reform efforts in mathematics education.
However, many teachers feel ill-prepared to teach problem solving and have had little experience
solving open-ended or open-middle problems that require more than simple applications of
algorithms and formulas. For this reason, courses for mathematics teachers at the graduate and
undergraduate levels must be refined to address mathematical problem solving in a rich manner.

Teachers need to be the first to become problem solvers in their classroom (Wilson,

Fernandez, & Hadaway, 1993).Wilson et al. (1993) also discuss different aspects of
mathematical problem solving in secondary classrooms and some of the inconsistencies in
instruction. Comparing the emphasis on problem solving in the NCTM Standards and the manner
in which it is taught in the classroom raises questions about how teachers’ beliefs about problem
solving affect their teaching behavior in the classroom. Teachers often cite various reasons for
not incorporating more problem solving in their teaching: time factors, difficulty for students,
curriculum issues, complicated to assess, not easy to find appropriate mathematical tasks.

To be competent problem-solving practitioners, teachers need knowledge that includes both

procedural (Eisenhart, Borko, Underhill, Brown, Jones & Agard, 1993) and conceptual or
content knowledge (Leinhardt, 1988; Eisenhart et al., 1993). Procedural knowledge denotes the
rules, procedures, and skills necessary for completing a task. However, procedural knowledge
may or may not be supported by conceptual knowledge (Hiebert & Lefevre, 1986). Conceptual
or content knowledge denotes the ability to understand the concept and connect or apply several
different ideas. For mathematics teachers, conceptual knowledge also includes ability to
generalize, determine multiple representations, describe relationships, and exhibit higher order
reasoning skills. In addition, developing problem-solving practitioners need to explore the role of
metacognition in mathematical thinking or problem solving (Schoenfeld, 1985).

Information about teachers’ problem solving progress in the classroom can be gathered by

discussions with teachers about the scores they assign to student problem-solving work and their
rationale in assigning the scores (Vasquez-Levy, Garofalo, Timmerman and Drier, 2001).
Though teachers expressed the same rationales they weren’t valued to the same degree. Hiebert
and Leferve (1986) claim that competency in mathematics involves knowing how concepts,