Students' Thinking Processes Connecting Quantities in Solving Covariation Mathematical Problems in High School Students of Indonesia

Abstract

The purpose of this study was to describe students' thinking processes in relating quantities to the problem of covariation in the process of solving mathematical problems. This study used a descriptive exploratory approach within the scope of qualitative research involving 87 students as prospective subjects from three different high schools. The schools were chosen from three different areas; where two schools were on Sumbawa island namely in Bima district and Bima town. The subject described was chosen by giving assignments related to the covariation problem. Data obtained from the answer sheets from the subjects while doing think aloud, the results of task-based interviews, and field notes. Supporting equipment for video and audio recording was used to take data of think aloud and interview. Data analysis was conducted retrospectively by combining answer sheets, think aloud, interview results and field notes with reference to APOS theory. The results obtained from students' thinking processes in connecting the quantities of covariation were two, namely Connecting Quantity by direct analytic and equation analytic. In general, it was found that students connected quantities in covariation problem solving by linking changing-quantity along with the changes in other quantities internally or externally through mathematical analysis to form new quantities based on quantitative operations.

Creative Mathematical Reasoning Process of Climber Students in Solving Higher Order Thinking Skills Geometry Problems

“…During the reasoning process, climber students can master concepts and develop different problem solving to have novelty. This is in line with the opinion [17], [46], [47], [48] that students who can relate information and mathematical concepts can provide solutions with different solutions to the same concept.…”

An exploratory study of spontaneous representations of covariational reasoning in middle school students

“…Concerning the spontaneous representations of the students, no algebraic description of variables or any representation of situations with equations was identified. Unlike studies, where it is possible to find the student's level of reasoning with the help of their graphs, a link is even described between the analysis and the development of equations, or using equations to obtain quantities that describe the problem (Gantt et al, 2022;Syarifuddin et al, 2020;Thompson & Carlson, 2017), the results obtained show such reasoning with the help of the student's diagrams, beyond an algebraic representation, an implicit arithmetic explanation is achieved in the drawings made, that is, despite the few values provided in the situations, they recognize the existence of two implicit variables whose values change.…”

“…Thinking is considered as that mental discourse, a mental reflection of the person that allows him/her to create ideas and concepts (Copi, 1978;Polya, 1984;Vygotsky et al, 1995). On the other hand, reasoning is a special process of thinking that arises from premises and conclusions of an absolute truth are reached (Copi, 1978;Peirce, 1903cited in Campos, 2010Syarifuddin et al, 2020).…”

“…Other works analyze covariation with theories that delve into the type of problems or methodological frameworks that address covariational situations. Textbook exercises are analyzed, student mental processes when modeling situations, even connections between covariation and emotions of achievement when successfully understanding an activity are addressed (Bagossi et al, 2022;Carlson et al, 2002;Chen, 2023;Confrey & Smith, 1995;Nava-Guzmán et al, 2023;Syarifuddin et al, 2020;Tasova et al, 2020). Much research is qualitative in the analysis of covariational reasoning since each student conceives and represents dynamic events at different levels.…”

Analysis of Middle School Students' Covariational Reasoning Skills in Modeling Function Charts Based on Self-Efficacy

“…In this case it can be seen the subject linking quantities based on a discrete perspective (Clement, 1989; Johnson, 2012), and there are two thought processes that can be concluded, namely linking quantity processes with direct analytics and with equation analytics (Syarifuddin et al, 2020). In distinguishing the level of covariasioinal reasoning ability, students with higher reasoning abilities were able to demonstrate an understanding of variations in quantity values.…”