Korean and American elementary school teachers' beliefs about mathematics problem solving

School Science and Mathematics, Apr 1996 by Zambo, Ron, Hong, Eunsook

Elementary school teachers in South Korea and the United States completed a beliefs and practices questionnaire pertaining to mathematical problem-solving instruction. Although both groups of teachers shared a general approach to teaching with a focus on problem-solving strategies, many differences were apparent. Korean teachers rated themselves and their students higher in problem-solving ability than American teachers. Korean teachers perceived their mathematics textbook as a more valuable source for problem-solving instruction and word problems. Korean teachers more strongly agreed that students should know the key-word approach for solving problems. American teachers reported more frequent use of calculators, manipulatives, and small group instruction. The results indicate that American teachers may more often use instructional techniques that are aligned with current recommendations for mathematics instruction.

The results of the International Assessment of Educational Progress released in February of 1992 indicated that in mathematics and science the United States ranks near the bottom, while South Korea and Taiwan rank at the top (Educational Testing Service [ETS], 1992). The gap between American and Asian students is especially wide in mathematics. For example, nine-year old American students scored an average of 58% correct while the top scorers, Korean students, scored an average of 75% correct. Korean students' superiority in mathematics in general was mirrored by their achievement in specific areas of mathematics including problem solving. Korean students averaged 70% correct and American students averaged58%correct on items categorized as problem solving. This superiority has been confirmed by other studies, as well. Stevenson (1987) found that Asian students scored higher than American students on tests involving mathematical word problems.

Attempts have been made to explain why American students are not doing well in the international mathematics competition. It was found that Asian students were not more intelligent than American students as measured by intelligence tests (Stevenson, 1987). The ETS study offered several environmentalcultural factors that may contribute to Korean children's relative success in mathematics. For example, it has been suggested that the differences in the amount of time spent at school, teaching methods, homework behavior, and/or time spent watching television might account for the differences between Korean and American students' mathematics performance.

American students attend school on an average 44 fewer days than Korean students (ETS,1992). American students might also attend fewer instructional hours per school day compared to their Asian counterparts (Kim, 1993). Textbook choices within the two cultures also differ. American school districts have a choice among textbooks produced by any of the major publishers and as a result selections vary among school districts. Aligned to the national curriculum, elementary school textbooks used in Korea are uniform. The textbooks used in Korea contain fewer review lessons than American textbooks (Kim, 1993).

Researchers have reported that Asian teachers approach mathematics instruction differently than American teachers. Stigler(1988) reported that American teachers tend to focus first on the development of mathematical skills and then on the application of those skills to solve problems. In contrast, Stigler (1988) reported that Asian teachers tend to use a problemcentered approach to teaching mathematics. In a problem-centered approach mathematical skills are developed within a primary focus on problem solving. The problem-centered approach involves students in activities that should accentuate their problem-solving performance, for example, exploring multiple solution strategies for the same problem. A problem-centered approach to mathematics instruction could have a positive effect on the problem solving performance of students.

This article compares the nature of mathematical problem solving instruction in Korean elementary schools to American elementary schools. Elementary school teachers' instructional behaviors in mathematics problem solving were measured by using their selfassessment of factors/strategies involved in mathematical problem-solving instruction. The aspects of problem-solving that were investigated included: (a) time spent on problem-solving instruction, (b) instructional strategies to promote problem-solving, (c) perceptions of the usefulness of specific problem solving strategies, (d) confidence in using those strategies, (e) sources of problems, and (f) beliefs about problem-solving instruction.

The instructional factors/strategies investigated were selected after an analysis of instructional strategies for problem solving suggested by different scholars (e.g., Kloosterman, 1992; Duren & Cherrington, 1992; Proudfit, 1992; Carey, 1991), as well as those appearing in teacher publications (e.g., Silverman, Winogard, & Strohauer, 1992; Kroll, Masingila & Mau,1992; Maher& Martino,1992). The items on the questionnaire were also intended to reflect the recommendations for instruction of the National Council of Teachers of Mathematics (NCTM). The NCTM Curriculum and Evaluation Standards for School Mathematics (1989) have been a major influence on mathematics instruction in America. The Standards have become the criteria by which curricula and textbooks are often evaluated.