Mathematical Problem-Solving Processes and Performance: Translation Among Symbolic Representations

Abstract

This study involving 29 students enrolled in an 8-week summer Algebra II class for minority students was undertaken to determine the relationship between the kinds of symbolic forms used in problem-solving instruction and students' problem-solving processes and performance. All subjects were Black or Hispanic and were about to enter grade 11. For problems involving solving simultaneous equations in two unknowns and distance-rate-time relationships, sets of problems were developed that varied in the symbolic form of the problem presented and of the response required. Approximately half of the problem. were open-ended; the other half were multiple-choice. Data on teacher instructiorn1 methods came from the printed materials used by teachers, student notes, and interviews with teachers. Results indicate that: (1) sole use of conventional symbolic representations provides a limited picture of students' problem-solving abilities; (2) students' difficulties in translating symbolic representations can be understood by systematically varying the symbolic form of problem and response required; (3) using alternative symbolic forms of the required rest,onse may be a good means of measuring students' conceptual understanding of mathematics; and (4) types of translation between symbolic forms during instruction did not seem to play a major role. Two data tables and 11 sample test items are included. (TJH) * Reproductions supplied by EDRS are the best that can be made * * from the original document. * **************w******************************************************** U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDSJGtATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as received from the person or organization originahno O Minor CilVIS have been made to improve reproduction dustily. Pornts of view or opnions stated in thodccu. ment do not necessary represent official 0 ERI position or poky. Center for Research on Evaluation, Standards, and Student Testing Final Deliverable February 1990 Research on Instructional Assessment Validity of Alternative Measurement Procedures for Assessing Mathematical Problem-Solving Processes and Performance Project Director: Noreen Webb Grant Number CERI -G -86 -0003 Center for the Study of Evaluation Graduate School of Education University of California, Los Angeles 2 BEST COPY AVAILABLE c.