The sequence of algebraic problem-solving paths: Evidence from structure sense of Indonesian student

Abstract

The algebraic structure is one of the axiomatic mathematical materials that consists of definitions and theorems. Learning algebraic structure will facilitate the development of logical reasoning, hence facilitating the study of other aspects of axiomatic mathematics. Even with this, several researchers say a lack of algebraic structure sense is a source of difficulty in acquiring algebraic structures. This study aims to examine a pattern of sequences of problem-solving paths in algebra, which is an illustration of learners' algebraic structure sense so that it can be utilized to enhance the ability to solve problems involving algebraic structure. This study employed a qualitative descriptive approach. Students who have received abstract algebra courses were chosen to serve as subjects. The instruments include tests based on algebraic structure sense, questionnaires, and interviews. This study reveals the sequence of paths used by students in the structure sense process for group materials, i.e., path of construction–analogy (constructing known mathematical properties or objects, then analogizing unknown mathematical properties or objects), path of analogy–abstraction (analogizing an unknown mathematical property or object with consideration of the initial knowledge, then abstracting a new definition), path of abstraction-construction (abstracting the definition of the extraction of a known mathematical structure or object, then constructing a new mathematical structure or object), and path of formal-construction (constructing the structure of known and unknown mathematical properties or objects through the logical deduction of a familiar definition). In general, the student's structure sense path for solving problems of group material begins with construction, followed by analogy, abstraction, and formal construction. Based on these findings, it is suggested that there is a way for lecturers to observe how students develop algebraic concepts, particularly group material, so that they can employ the appropriate strategy while teaching group concepts in the future.