Building Student’s Mathematical Connection Ability in Abstract Algebra: The Combination of Analogy-Contruction-Abstraction Stages

Abstract

The objective of the study was to describe the effect of six types of mathematical connections (representation connections, structural connections, procedural connections, implication connections, generalization connections, and hierarchy connections) on abstract algebraic materials through four stages, i.e., abstraction, analogy-abstraction, construction-analogy, and construction. The study employed qualitative descriptive approaches, including tests, questionnaires, and interviews. The subjects of the study were chosen based on the responses to a questionnaire regarding the employed stages. Then, two subjects who could converse and were willing to be interviewed were chosen from each stage. Data collection techniques were conducted through four stages, i.e., 1) identifying the stages used; 2) identifying the ability of six types of student mathematical connections through predictive indicators; 3) describing the capabilities of the six types of connections through interviews; and 4) conducting source triangulation and method triangulation. The results indicated that the subjects who utilized the construction stage tended to be able to construct six types of mathematical connection links in a set, as well as standard and non-standard binary operations. The subjects who utilized the construction-analogy stage likely to be able to build three forms of representation connections, structural connections, and procedural connections in a set of standard binary operations. In characterizing the symbol of a set element and the binary operation of the standard form inside the closed property of the standard form, the subjects who used the analogy-abstraction stage have the same tendency as subjects who use the abstraction-construction stage.