AN EXTERNAL CONTROL STUDY OF DIAGRAM DRAWING SKILLS FOR THE SOLUTION OF ALGEBRA WORD PROBLEMS BY NOVICE PROBLEM-SOLVERS (FIGURES, HEURISTICS, SPATIAL REPRESENTATIONS, METACOGNITION)

cn. CONTROL STUDY OF DIAGRAM DRAWING SKILLS FOR THE SOLUTION OF ALGEBRA WORD PROBLEMS BY NOVICE PROBLEM SOLVERS SEPTEMBER, 1986 MARTIN A. SIMON, B.A., NEW YORK UNIVERSITY M.A.T. , ST. MARY'S COLLEGE Ed.D., UNIVERSITY OF MASSACHUSETTS Directed by: Dr. Portia Elliott Diagram drawing is generally accepted as an important heuristic strategy for solving mathematical problems. However, novice problem solvers do not frequently choose to use this strategy. Further, when asked to draw a diagram, their attempts often do not result in a useful representation of the problem. The exploratory study, which used individual interviews with remedial mathematics students at the University of Massachusetts, identified five factors that influence whether a diagram is used and whether its use is successful : 1. Understanding of the mathematics involved in the problem and of basic arithmetic concepts (i.e. fractions , ratio) 2. Diagram drawing skills and experience 3. Conceptions of mathematics 4. Self-concept in mathematics

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