Problem Solving in Geometry: Comparing the effects of non-goal specific instruction and conventional worked examples

Abstract

This study examines the extended effects of an instructional program designed to enhance schema development by using non-goal specific problems, in the teaching of geometry to high school students in need of remedial tuition. A multiple baseline across-subjects experimental design was used to compare the effects of this program with another method of teaching this subject--that is, using worked examples. This methodology provides detailed information on the shifts and changes associated with learning processes for particular individuals during the actual process of schema acquisition. Dependent measures included test performance, error analysis, time analysis, directionality and generalisation. Results indicate that participants in the non-goal specific group showed greater improvements, solving problems faster, more efficiently, more accurately and with fewer errors and greater consistency. These findings are discussed in terms of their implications for the design of mathematics instructional material.