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Quantitative Reasoning Process in Mathematics Problem Solving: A Case on Covariation Problems Reviewed from APOS Theory

The focus of this study was to describe the students' quantitative reasoning process in solving covariate problems using APOS theory. This research was a case study conducted on 9th grade students of junior high schools in five different schools in Bima Regency, Indonesia. The data collection in this study was initially done by providing Covariation Problem Task (CPT) for students in a 60-minute task. Afterwards, it was followed up by holding task-based interviews with students who performed different processes. These interviews were intended to confirm the existing mental process. The data obtained were analyzed by combining retrospective and continuous analysis, namely by analyzing work results and student interviews simultaneously, then thinking structures were described based on APOS theory. The results of this study showed two different students' quantitative reasoning processes for covariation problems. First, the inductive quantitative reasoning process (IQRP) was conducted by linking the quantity involved in covariation problems and substituting it into the formula directly, without making any modeling. Second, the deductive quantitative reasoning process (DQRP) was conducted by connecting quantity through the process of mathematical modeling by producing formula equations. This study indicated that the students comprehended the situation caused by covariate quantity relationships and the process (reasoning) of how quantity values change together.