How Do Students' Problem Solving Strategies and Preferences in Learning Environments Relate to Their Mathematical Performance? A Comparative Study between South Korea and the United States
Author: Yang, Christine K.
Date: 2011-00-00
Type: Reports - Evaluative
Subjects: Foreign Students,Mathematics Education,Problem Solving,Metacognition,Foreign Countries,Comparative Analysis,High School Students,Preferences,Learning Strategies,Cognitive Style,Comparative Education,Performance Factors,Mathematics Achievement,Educational Environment,Performance Based Assessment,Comparative Testing,Predictor Variables,Aptitude Treatment Interaction

Mathematics education has emerged to be of prime importance in the United States, as American students' performance has shown to be consistently and significantly lower than many other nations in the world (Rampey, Dion, &amp; Donahue, 2009; National Center for Education Statistics, n.d.; OECD Programme for International Student Assessment, n.d.). Sparked by an interest to understand factors that are associated with such differential performance, mathematics education researchers have been drawn to international comparative research. In order to understand the differences and similarities between the U.S. and other countries across multiple dimensions of the learning and teaching of mathematics, curricula, and educational systems, international comparative studies in mathematics education have resulted in both in-depth, qualitative studies as well as hard, quantitative data analyses. Most prominent studies include those that compare the U.S. and other high-performing East Asian countries such as China, Korea, Singapore, and Japan, across elementary and middle school levels (Cai, 2000, 2002; Kaiser, Leung, Romberg, &amp; Yaschenko, 2002; Leung, 2001; Paik, 2004; Stevenson, 1993; Stevenson &amp; Stigler, 1992; Stigler, Lee &amp; Stevenson, 1987; Tsao, 2004). However, there is a dearth of studies that focus on high school students, especially in comparing those of South Korea with the United States. The purpose of this study is to fill this gap in research, and to identify the extent to which different cultural and institutional factors influence student mathematical learning. Specifically, this will be a comparative analysis between high school students in South Korea and the United States, across three context levels: national level, school organizational level (e.g., mathematics curricula), and modes of mathematical problem solving and preference (e.g., metacognition). By using available data from the PISA 2003 study, which had a focus on mathematical learning, the author employed hierarchical linear modeling (HLM) to analyze how much variation in student performance can be accounted for by various levels of contexts, and specifically examine the relationship between student modes of mathematical problem solving and preference for learning environments and their actual learning outcomes. The preliminary results indicate that the cognitive strategies and preference for learning environments share some similarities and differences across Korea and the United States. In addition, these factors are differentially associated with mathematical performance. As mentioned before, these results are based on a simple model and are amenable to change after the inclusion of country-level and other factors which have not yet been examined. However, based on these results, one could argue that significant differences exist on the use of elaboration techniques and its relationship to students' mathematical performance, as well as on the relationships between preference for cooperative or competitive learning environments and students' actual performance. This study points to the importance of more in-depth qualitative studies that will illuminate the processes in which students engage in these problem strategies, and investigate whether there could be any universal deliverables that can be ported to other learning contexts. This study also points to the importance of understanding the overarching context in which learning occurs, as societal, institutional, cultural values can influence the relationship between cognition and performance in different ways. (Contains 2 tables.