Abstract:
The knowledge of quadratic functions is essential in improving learners' conceptual understanding of algebraic and geometric concepts. Hence, such knowledge is attained when learners understand quadratic functions' multiple representations. Therefore, the focus of the study was to explore the role of the Activities, Classroom discussions, and Exercises [ACE] teaching cycle in improving Grade 12 learners‟ conceptual understanding of quadratic functions. I adopted the APOS theory as a lens to improve learners' conceptual understanding of quadratic functions. Additionally, I used Merriam‟s case study design which incorporated the ACE teaching cycle as an instructional style for data collection with 30 criterion sampled learners. Subsequently, learners posit various conceptual obstacles after implementing the ACE cycle. Firstly, they seem to grapple at the action level relating to the knowledge of the properties of quadratic functions. Secondly, they posed conceptual obstacles to quadratics while interacting with quadratic functions. Thirdly, learners posed difficulties transitioning from one form to another, posing pitfalls to conceptual understanding quadratic functions. Lastly, they faced difficulty making connections between the forms of quadratic functions due to a deficiency in solving techniques. However, through the intervention of the exercise, learners' conceptual obstacles seem to be remedied. Yet, some conceptual obstacles appeared to be persistent: failure to correctly translate quadratics, confusion about the -intercept of the function and the -coordinate of the vertex, and difficulty linking the connection between the range and vertex of a function. Therefore, I recommend that future studies be broadened on learners understanding of the vertex and the -intercept of quadratic functions.
