Task Development to Measure Functional Thinking: Focusing on Third Graders’ Understanding

Abstract

The purpose of this study was to develop the tasks to measure functional thinking and to verify their suitability by applying them to third-grade students. For this purpose, various tasks related to functional thinking were analyzed and developed according to the different modes of functional thinking and functional relationships. To verify the tasks, the Cronbach's α value for each task type was calculated with the results of how the third graders solved the tasks. Exploratory factor analysis (EFA) was performed as needed. As a result, tasks were developed to measure four types of thinking: recursive, covariation, correspondence-particular, and correspondence-general. In particular, recursive patterning tasks were divided into repeated geometric patterns, growing geometric patterns, repeated numeric patterns, and growing numeric patterns through EFA. Only growing geometric patterning and growing numeric patterning tasks were found to be suitable for measuring third-grade students' recursive thinking. Growing numeric patterning tasks were divided by arithmetic sequences and other sequences through EFA. The covariation, correspondence-particular, and correspondence-general tasks developed in this study were also verified. Contrary to the consistently high performance regarding the additive relationships, students' functional thinking varied depending on the different types of functional relationships. This study is expected to inspire researchers to pay more attention to task development and verification to measure students' functional thinking.