Conceptualization in solving a geometric-function problem: An effective and efficient process

Abstract

There has been more than one the solving process of the problem sometimes. It has been named an open-ended context when related to an approach, and in this study, purposed to use a geometric-function problem for analyzing each process that was experienced a student when they were conceptualizing the completion. Three students purposively who was a sample is registered by the senior high school in a science program at the region of West Jakarta, Indonesia. Student solved the problem in this explorative study, there were two choices of completion ways, technical or conceptual, but they used the procedural technique operational. Two conceptualizing process in solving the problem, it was constructing the algebraic representation of the function and organizing concepts. But, there is only one between the other where was effective and efficient of the process based on the perspective of the management theory. The first process was efficient by recognizing the function in algebraic and graphic representation. But, the second process affected the solution ineffective because all three students have been miss controlling the domain function concept even though it is a resource. So, an effective and efficient for learning is when students involving more conceptual knowledge.