APOS Framework Didactize Equivalence Linear Simultaneous Equations in Senior High School Mathematics

Many students followed rote-learned procedural rules without thinking about the meaning of quadratic equations, and the Chief examiners’ reports attributed the trend to poor teaching methods. In certain instances, candidates cannot use even the conventional methods to factorize quadratics equations due to a lack of understanding of the zero-product property in graphing, factorizing, and completing the squares or quadratic formula. In the worst circumstances, the candidates failed to scaffold higher-order quadratic equations using the Conjugale and Equivalence Linear Simultaneous Equation methods. However, the action, process, object, and schema theory which came out of the constructivist learning theory and created by Dubinsky can be applied to teach mathematics. With the aid of the APOS framework, this study sought to digitize the Equivalence Linear Simultaneous Equations in senior high schools. In this mixed-method embedded design, there were 286 first-year students selected from one school. All the students received four phases of the APOS framework. The four phases were collected based on the Actions for Factorization, Processes for Quadratic Formula, Object for Conjugale, and Schema for ELSE method. The data, which was both qualitatively and quantitatively, was analyzed using IBM SPSS Statistics (Version 26) deterministic analytics software. The data collection covered four contact periods of a total duration of four hours. The results showed that students in the Actions and Processes were not statistically significant. However, the results were statistically significant at the Object and Schema phases. It was concluded that students’ learning through the APOS framework improved their academic performance. The positive effect was the triumphant mental constructions involving encapsulation and interiorization in the conjugale and ELSE methods. It was, therefore, recommended that the framework be promoted to find solutions to many other complex mathematics problems.