Generated worthwhile problem promoting algebraic thinking: From pattern exploration to generalization

Abstract

Algebraic thinking has been central to the mathematics curriculum. Its development is regarded as critical for solving mathematical problems. Considering that algebraic thinking among Indonesian students and prospective mathematics teachers has been found less satisfying, this research aims to depict a mathematical lesson using a problem-posing approach, resulting in generated problems that potentially promote algebraic thinking. By involving three Indonesian prospective teachers, this study leads to answering the question: What does instruction using a problem-posing approach look like, and how does the self-proposed problem promote algebraic thinking? The data came from a single episode of an active learning workshop intended to introduce active learning strategies. One of the strategies is to use problem posing as a pedagogical tool. In the lesson, the participants were asked to pose problems based on the given picture, choose one of the posed problems, and discuss the solution. The lesson was analysed qualitatively in nature, which revealed that in addition to prospective teachers who could compose mathematical tasks, mathematical problem posing promotes the emergence of manifestation stimulating algebraic thinking. The implications of these findings are discussed in detail.