The Holistic and Partial Quantitative Reasoning Process of Students in Linking Covariation Quantities

Abstrak

Quantitative reasoning becomes the basis for students in solving mathematical problems, especially problems related to quantities on a graph and functions. The problem is closely related to covariation. Therefore, the purpose of this research was to categorize and describe the students' quantitative reasoning processes in solving covariation mathematical problems. The process of quantitative reasoning was reviewed from APOS Theory. Research subjects were 38 high school students from three schools. The research was conducted in three stages. The first stage, students completed the Covariation Problem Solving Task while they were doing think aloud. In the second stage, the researcher evaluated the answer sheet and played back the think aloud record, then noted several important things that needed to be reconfirmed to the subject. On the third stage, task-based interview was conducted to clarify and explore data that had not been obtained through think aloud. Data were analyzed by the stages of transcribing data, reducing and categorizing data, drawing the structure of reasoning, and drawing conclusions. This study found and described that there were two categories of the covariation quantitative reasoning processes, namely holistic and partial covariation quantitative reasoning. The holistic covariation quantitative reasoning process was carried out by students through linking quantities, by coordinating the value of quantities from the whole part. On the other hand, the partial covariation quantitative reasoning process was applied by partitioning the whole part to determine the quantity value, then coordinating the quantities based on the quantities of the part.