Semantic Analysis of the Concrete Pictorial Abstract Approach in Understanding Mathematical Concepts

Abstract

Mathematics is not only procedural, but also conceptual. When students are able to interpret mathematical concepts, then students have freedom and are not just stuck to standard procedures from rote memorization. Therefore, a concrete pictorial abstract approach is needed as a bridge to understanding mathematical concepts. In this study, we investigated prospective teachers in making sense of concrete, pictorial, and abstract processes in understanding mathematical concepts. The subjects of this research were 4th semester students taking school mathematics courses I. Data collection was carried out by means of task-based interviews which were carried out after the learning process ended. The data analysis and interpretation technique uses a semantic framework. The results of the data analysis found two categories in the semantic CPA process, namely full and partial use of CPA. In the full semantic CPA process, students are able to use concrete, pictorial and abstract approaches in solving problems and interpreting mathematical concepts. In the partial semantic CPA process, students use concrete and pictorial stages to help illustrate the problem. Apart from that, students only use an abstract approach in solving problems. When students are able to fully understand the use of CPA, it can be concluded that the concept of mathematics has been internalized