Twenty-six sixth grade low achievers in the rural south experienced a problem centered mathematics curriculum for nine weeks. Potentially meaningful tasks were utilized in the class, which was divided into small collaborative groups of two or three like-ability students. The groups then presented and defended their solutions and strategies before their peers. The students showed marked increases in achievement and positive attitude towards mathematics when compared to a control group at the same school that was experiencing a traditional approach.
The Effect of a Problem Centered Approach to Mathematics on Low-Achieving Sixth Graders
The results from the Third International Mathematics and Science Study (TIMSS) and TIMSS-R (TIMSS-Repeat) have become a source of concern for mathematics educators in the United States (USDE, 1996). Our nation is consistently out-ranked by the other industrialized countries that participated in these tests. Considering the money spent on education in this country and the economic and technological advantages we enjoy, educators are not satisfied with such low performance in a globally competitive market.
Japanese students consistently scored among the top three in these tests. Prior investigations by Stigler (1991) and Stigler and Perry (1988) at UCLA infer possible reasons for this superiority. In Japan, students spend a great deal of classroom time analyzing meaningful situations and working for long periods to solve non-routine problems. In contrast, U.S. students spend the majority of their time independently practicing a specific procedure demonstrated by the teacher. This educational strategy is contrary to research that shows that knowledge of rote procedures often interferes with students' attempt to build on their informal knowledge (Mack, 1990). In fact, traditional drill-and-practice teaching can even inhibit understanding, reify the divide between school and the "real world," and suppress the transfer of knowledge (Boaler, 1996).
Low achievers present special difficulties when considering any type of teaching approach. Apparently, the act of grouping students by ability level can of and by itself have an influence on motivations, perceptions, and eventual achievement of students (Boaler, 1997). A child who is labeled as a low achiever may experience detrimental consequences that last throughout their entire school career. In support of this effect, research has indicated that low achieving students tend to score lower and lower each subsequent year in comparison to others on standardized tests (Denvir, Stoltz, & Brown, 1984). Given the current level of their performance, it is unlikely that remedial work will be sufficient to close the gap between these children and their higher achieving peers, especially when that remediation is focused on skill deficits (Hankes, 1996).
Recent publications have suggested that a problem-centered approach might improve the mathematics competency of low achieving students (Hankes, 1996, Nicholls et al., 1991). Silver and Lane (1995) were able to demonstrate that middle school students from low-income disadvantaged backgrounds were able to outperform their peers in a demographically similar school when they participated in the Quasar Project, a program that emphasized reasoning, problem solving, and understanding. Research by Ginsburg-Block and Fantuzzo (1998) also showed that instruction that emphasized problem solving and peer collaboration enhanced the mathematics achievement, motivation and self-concept of low-achieving third and fourth graders. In fact, problem centered learning has been shown to foster high mathematics achievement and meaningful communication for all students in the second grade (Cobb, Wood, & Yackel, 1991a; Cobb et al., 1991; Thompson, 1985; Wood & Sellars, 1996).
Sfard (2000) asserts, "thinking is subordinate to, …