The Focusing on Compression to Thinkable Concept as Shift from Procedures to Concept: Evidence from Thai Classroom

Abstract

The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and important thinking tool in developing concepts (Gray & Tall, 2002). The major act of compression to thinkable concept shifts attention from the sharing procedure as a sequence of steps to the effect of that procedure (Gray & Tall, 2007). So, the compression to thinkable concept is one important way in order to understand in development from procedures to concept. This article presented example the compression procedures in problem solving to thinkable concept under context using Lesson Study and Open Approach, with the four of first graders a project school supported by CRME. In this study based on the framework that purposed by Tall and Isoda (2007) and Poynter (2004). Under context using Lesson Study and Open Approach provide to students manipulated with designed materials for supporting and checking their various symbolic thinking before into same effect through parallel compression 5 steps into thinkable concept in blending embodiment and symbolism. In embodiment from step-by-step action, to the possible choice of several different action, to seen the overall effect as same effect that can be carried out in various ways, to compressing it as effect as prototype, to awareness and appreciation of effect used later. In symbolism from step-by-step procedure, to the possible choice of several different procedures, to seen the overall effect as a general process that can be carried out in various ways, to compressing it as thinkable concept, to awareness and appreciation of thinkable concept in extending mathematical structure. Consequently, the students used considering the way of thinking and refined the ideas in order to develop a major idea from different procedures in problem solving.