Analysis of difficulties for pre-service mathematics teacher in problem solving of division and divisibility based on theory of action, process, object, and schemes

Abstract

Action, process, object, and schemes is an acronym of APOS. The difficulty in the perspective of APOS theory is the inability of students to access specific schemes in all situations, thereby inhibit the construction of other concept. Knowing student's difficulties in using the concept of division and divisibility is necessary to design genetic decomposition of that concept. This article is a report from qualitative research that discusses conceptual issues about the idea of division and divisibility given by prospective mathematics teacher students who use the APOS theory. The data for the study were collected from an interview. The researcher took three interview subjects from 30 pre-service mathematics teachers who have attended and completed a test on the division and divisibility in an elementary number theory course. These participants were selected based on their performance in the test. However, the interview conducted showed that there are five difficulties involved and they include solving the divisibility problem on integers, algebraic manipulation and recognize structures in algebraic expressions that correspond to the division algorithm or the definition of divisibility., distinguishing between variables and parameters on division problem presented in algebraic expression, associating between division algorithm and definition, and application of divisibility properties and theorems.