Assessing Zimbabwean Children's Mathematics Problem Solving for Cognitively Guided Instruction
Fast, Gerald R., Focus on Learning Problems in Mathematics
Cognitively Guided Instruction (CGI) has been highly effective in helping elementary school children in America develop number sense and mathematics problem solving ability. This study attempted to determine if children in Zimbabwe, a developing country with cultures and educational experiences very different from those in the United States, could also potentially benefit from CGI. Thirty-five grade 2 Zimbabwean students' mathematics problem solving attempts were assessed using the 14 CGI problem types. Their solution strategies were consistent with findings in previous research. Most of the children were at the direct modeling stage in their development and they had difficulty solving the more complex problems where modeling is not as effective. Cognitively Guided Instruction appears to offer considerable benefits for elementary school children in Zimbabwe.
Keywords: mathematics problem solving, Cognitively Guided Instruction, Zimbabwe
The National Council of Teachers of Mathematics (2000) in their visionary document on the curriculum and instruction of mathematics, Principles and Standards for School Mathematics, has made a strong case for the necessity of teachers helping students develop a deep understanding of mathematics. Contributions to this deep understanding come in part from developing good number sense and problem solving ability. The importance of problem solving is emphasized by its prominence as one of the ten standards at all levels from PK--12 in the NCTM document.
Mathematics performance by students in the United States, as indicated by recent national and international mathematics assessment data (NAEP, 1992; TIMSS, 1996), has not always been to the entire satisfaction of American educators and has supported the need for change in mathematics curriculum and pedagogy. Although scores by American fourth graders have been satisfactory compared to other countries participating in the TIMSS study, results of seventh and eighth graders leave something to be desired. One should however not conclude that the middle school must bear the total burden of responsibility. In order for middle school students to have the number sense and problem solving proficiency required at this level, a solid foundation must be laid in the elementary grades.
Considerable research in the area of elementary school children developing a deep understanding of the mathematics they are learning has resulted in a number of promising findings. Cognitively Guided Instruction (CGI), developed by Carpenter, Fennema, and others (1999) at the University of Wisconsin, Madison, is a well-proven, successful approach based on such findings. Children in CGI classrooms have shown remarkable development in mathematical understanding particularly regarding number, operations, and authentic problem solving.
To further investigate the appropriateness of CGI, particularly in a setting considerably different from previous investigations, the author focused on a mixed-ability grade 2 classroom in Zimbabwe. Furthermore, the author's extensive experience with education in Zimbabwe (Fast, 2000) suggested a need for a different approach to teaching mathematics in the elementary school.
The author's observation in Zimbabwean classrooms over an eight-year period indicated that direct instruction was the preferred approach at all levels. Students' procedural knowledge in mathematics was admirable but their conceptual understanding was often limited. Problem solving on O Level and A Level mathematics exams was therefore rather challenging for many students. Developing a better conceptual understanding of the mathematics, beginning in the (Fast, 2000) elementary school, is as much a necessity in Zimbabwe as it is in America.
Cognitively Guided Instruction (CGI) developed from an extensive mathematics research project at the University of Wisconsin Madison. …