Investigating How the Activity, Classroom Discussion, and Exercise (ACE) Teaching Cycle Influences Learners’ Problem-Solving and Achievement in Circle Geometry

This chapter reports on how the ACE teaching cycle influenced participants’ problem-solving competence and achievements when learning the circle geometry concept. The ACE teaching cycle was primarily used as the medium for teaching participants the concept of circle geometry. Circle geometry lessons were conducted in four stages in accordance with APOS theory mental conceptions – action, process, object, and schema – with a control and an experimental group. For each group, four lessons were given – GD 1 lesson, GD 2 lesson, GD 3 lesson, and GD 4 lesson. A standardized test was administered at the end of each of the four lessons. The constructivists’ theory was implemented as the theoretical framework for this study, and it followed a mixed method design – both qualitative and quantitative data collection, data analysis, and interpretation procedures were used. Data was obtained through classroom observations – group discussions, group presentations, and analysis of the standardized tests conducted. The quantitative data was analyzed using descriptive and inferential statistics, while content analysis was carried out on the qualitative component of the collected data. It was established from this study that (1) there was a statistically significant improvement in the circle geometry test scores of learners who were taught using the ACE teaching cycle as an instructional approach; (2) the ACE teaching instructional approach significantly guided and enhanced participants’ cognitive engagements and development, which, ultimately, optimized their problem-solving competence.