Using APOS theory in learning basic mathematics to promote students’ mathematical critical thinking skills

Using Action, Process, Object, and Schema (APOS) theory in learning basic mathematics is an alternative to promote the students’ Mathematical Critical Thinking Skills (MCTS). This experimental study aims to compare the improvement of students’ MCTS in learning Basic Mathematics using a pretest-posttest control class design. Ninety students enrolled in a Basic Mathematics course became the sample of this study. It consists of three classes: two experimental and one control class. Before conducting the study, sample subjects were classified as having high, medium, or low basic mathematics abilities. Tests, questionnaires, observations, and interviews were used as research instruments. The results indicated that: (1) The MCTS of low-ability students who received Modified-APOS (M-APOS) instruction was better than students who received conventional instruction; The MCTS of medium-ability students who received APOS instruction was better than students who received conventional instruction; and (2) medium-ability students who received M-APOS instruction have more favourable attitudes toward calculus than students who received conventional instruction. Additionally, the findings indicated that (a) scaffolding was related to students’ level of material difficulty and initial ability, and (b) scaffolding was required not only by students with low initial ability but also by students with high initial ability.