Mathematical Problem-Solving Processes and Performance: Translation among Symbolic Representations.

A study of 29 students enrolled in Algebra II in an 8-week summer instructional program for minority students was conducted to reveal the skills that students have in translating among representational forms in mathematics problems where the representational form is varied in the given problem and in the required form of the answer. All students were Black or Hispanic and most were about to enter grade 11. The relationship between the kinds of translation used in instruction and students' problem solving processes and performance is also investigated. Students were presented with problems from two topics: solving simultaneous equations in two unknowns and distance-rate-time relationships. Problem sets were developed that varied the symbolic form of the problem as given (words in a story problem, graph, diagram, algebra) and of the response required (words, graph, diagram, algebra). Results of the study led to four implications. First, presenting students with only conventional symbolic representations of problems allows students to memorize algorithms for identified problem types, and is likely to give a limited picture of students' mathematical problem solving abilities. Second, it is possible to understand students' difficulties in translating among symbolic representations by systematically varying the symbolic form of problem and response required. Third, using alternative symbolic forms of the required response may be an effective way to measure students' conceptual understanding of mathematics. Fourth, the kinds of translation between symbolic forms covered during instruction did not seem to play a major role. (MDH)