A study of schema and cognitive models in teaching and learning geometry

Abstract

The aim of this paper is to investigate the role of schema and cognitive models in teaching and learning geometry. Differences in schema structure and problem solving behavior for different ability levels will be analyzed. In this study I will also introduce some instructional design strategies based on the findings. There are three parts in this paper: The pre-test, the instructional design and the post-test. In the pre-test there are two groups of higher secondary school students – high achievers group and low achievers group – participating in a test with different kinds of geometric problem about properties of circle. Questions are designed to test language ability, cognitive loads, problem solving style and generative ability in problem solving. An open-ended question is set to investigate the schema difference for high and low achievers through an analysis by solution path diagram. Results show that high achievers organize their knowledge with structured schema and demonstrate a higher generative ability. In the instructional design part I will present some strategies such as diagram- text integrated teaching to help students overcoming limits of cognitive loads. In the post-test part, low achievers show significant improvements in solving geometric problems after attending the class that is carefully designed with strategies mentioned in the previous part. The effectiveness of instructional design will be evaluated.