Didactical conceptual structures in extending the triad to the tetrahedron exemplified in the teaching and learning of equations of the circle

Abstract

The study explored didactical conceptual structures in extending the didactical triad to the tetrahedron in equations of the circle. Studies have shown that there are still inadequate interactions in the didactic triad and lack of knowledge of mathematics classrooms as indelible cultural forces. However, the didactic tetrahedron has helped students interact better in such situations. Therefore, the sequential explanatory mixed methods design was used in this study. This design adequately illuminated the interactions in the intersubjective didactic instructional models because meaning is based on one’s experiences and socially situated. The research population was 1,500 senior high school Elective Mathematics students. Out of this number, 500 students were randomly sampled through the use of table of random number procedures. This was subsequently followed up by a purposive sample of 12 students whose responses were so interesting for the qualitative data. Having satisfied statistical assumptions, controlled internal and external threats to validity, established reasonable reliability of instruments and confounded possible covariates, the researcher analysed the quantitative results with probability values, estimated marginal means, effect sizes and statistical powers. The results and findings showed that there were steady improvements in interactions in the didactic tetrahedron. This was evident in students’ scores in the tasks and equations of the circle. The interview transcripts confirmed and explained the reasons for these improvements. The researcher therefore, recommended among other things, that policy makers should adopt the didactic tetrahedron to enable students to fully interact during classroom discourse in order to enhance performance in elective mathematics.