Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
AN EXTERNAL CONTROL STUDY OF DIAGRAM DRAWING SKILLS FOR THE SOLUTION OF ALGEBRA WORD PROBLEMS BY NOVICE PROBLEM-SOLVERS (FIGURES, HEURISTICS, SPATIAL REPRESENTATIONS, METACOGNITION)
Abstract
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; (5) Motivation to solve the problem correctly. The interviews also generated a set of diagram drawing subskills. The main study focused on factor two. It attempted to experimentally verify the importance of the subskills identified in the exploratory study. The list of subskills was translated into a series of external control suggestions for guiding the subjects' work during individual interviews. Subjects were precalculus students at the University of Massachusetts. These suggestions were provided by the experimenter as appropriate. Subjects who received these suggestions drew significantly higher quality diagrams than did subjects in the control group. The enhanced quality was particularly apparent in the area of completeness of the diagram. In addition, the study indicated several important metacognitive skills necessary for successful diagram drawing as well as a number of specific difficulties encountered by the subjects.
Subject Area
Mathematics education
Recommended Citation
SIMON, MARTIN A, "AN EXTERNAL CONTROL STUDY OF DIAGRAM DRAWING SKILLS FOR THE SOLUTION OF ALGEBRA WORD PROBLEMS BY NOVICE PROBLEM-SOLVERS (FIGURES, HEURISTICS, SPATIAL REPRESENTATIONS, METACOGNITION)" (1986). Doctoral Dissertations Available from Proquest. AAI8701220.
https://scholarworks.umass.edu/dissertations/AAI8701220