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.

The Process of Conceptualization in Solving Geometric-Function Problems

“…Then, at the time of the practice, students are involved in active cognitive processes as well as building meaning (Mumu et al, 2017;Radmehr & Drake, 2017. Thus, there is an important meaning of the construction of student knowledge that involves the function of a problem (Alghadari et al, 2019).…”

“…We believe that the existence of these steps to help anyone who is confused starts the settlement step. However, what is conceptualized is to complete, and any processes occur for each problem so that a solution appears, it is not a simple sequence (Alghadari et al, 2019;Clancey, 2001;Glaser, 2002).…”

Completion for a Geometric-Function Problem: Process and Resources in Efficiency Consideration

“…Each student has a cognitive capacity on a different level (Sudirman et al, 2020;Widodo, Cahyani, & Istiqomah, 2020), so there are students who have difficult to solve a problem (Faradillah, 2018;Jelatu & Kurnila, 2019;Philpot et al, 2017). Specifically, the most error frequently from students was in conceptualizing a completion (Alghadari, Yuni, & Wulandari, 2019;Veloo & Krishnasamy, 2015). Hence, there is a needed way of conceptualization in solving a problem through an efficient conceptual process for students who have difficulties (Alghadari et al, 2019;Yuni et al, 2021).…”

Student Thinking Levels in Solving Open-Ended Geometric-Function Problem by Algebraic Representation Approach

“…Schoenfeld [10] stated that a problem was needed for thinking to solve. By the geometric-function problem, an occurred activity when solving process is thinking about the shape of geometric-function [11]. In Herbst et al [12] was stated that the geometry thinking process involves cognitive abstract reasoning, mathematical figure, and manipulation.…”