Integrating algebraic thinking in problem-based learning among secondary school students

Abstract

Algebraic thinking is a very important skill that should be mastered by students at an early stage before learning algebra. However, algebraic thinking is not emphasized in learning algebra. Therefore, this study aims to develop a framework that integrates students’ algebraic thinking into the problem-based learning (PBL) process. Three different learning approaches; the conventional approach (CA), the integration of algebraic thinking (AT) and the PBL approach with the integration of algebraic thinking (ATPBL); were implemented in three different boarding schools (SBP) involving 85 participants in a quasi-experimental study. Results showed that the algebraic thinking process of students in ATPBL sessions was enhanced. A parametric test using MANCOVA revealed that the students from the ATPBL group performed better in exploring relationships, generalizing and formalizing, reasoning about and with representations, and using algebra as a tool compared to the students from the AT group. The ATPBL group performed significantly better in the manipulation of symbols and procedures, exploring relationships, generalizing and formalizing, reasoning about and with representations, and using algebra as a tool compared to the students from the CA group. Next, there was significant difference in students’ algebraic thinking in the AT group compared to the CA group. Qualitative data from a learning task, namely, PBMAThinking (which consisted of teaching notes, self-readings, reflections, selfevaluations, evaluation of scenario problems, task-based interview transcripts, and task-based interview notes) were used to explore the acquisition of algebraic thinking into the ATPBL group. In summary, this study suggests that the PBL approach with the integration of algebraic thinking is able to enhance algebraic thinking among SBP students at lower secondary level. Accordingly, the framework that integrates students’ algebraic thinking with the PBL process is expected to assist teachers in enhancing the effectiveness of teaching and learning of algebra and can potentially serve as a basis for developing algebraic thinking among SBP students, particularly at lower secondary level. Therefore, a conclusion was reached that algebraic thinking should be emphasized in the teaching process when learning algebra.