A Learning Trajectory Study on How the Concept of Variable Is Constructed by Students

Abstract

The aim of this study was to examine 6th-grade students’ mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations, interviews, and the Diagnostic Algebra Test were used as data collection instruments to reveal the students’ abstraction processes and determine their learning trajectories. Qualitative data were analyzed through content analysis, and qualitative data were analyzed through paired-samples t-test. The learning trajectories showed that only the students with good performance exhibited the “construction” action when using “variables as changing quantities,” but the “building-with” action when using the other types of variables. Mediocre students, however, needed teacher support to perform the building-with action in the process of abstraction of variables. The students’ written tips such as drawing arrows or deleting the variable show that it helps to learn how to replace a variable with a known value. This study shows that the development of thought on variables is embedded in the progression of the concept of variable as a changing quantity. Similar studies can be conducted for the use of variables in equations and for the understanding and interpretation of variables when solving equations.