Developing algebraic thinking through group discussion

Abstract

This paper explores the potential of group discussion in generating algebraic thinking among learners. Algebraic thinking, particularly the recognition and articulation of generality, is vital and ought to be within reach of all learners if they are to participate fully in society. Furthermore, generalisation, being fundamental to mathematics, is a part of every mathematical topic. Indeed, a lesson without learners having the opportunity to express a generality is not a mathematics lesson. Therefore the importance of providing opportunities for learners to develop algebraic thinking in mathematics lessons cannot be overemphasised. Hence, it is vital for teachers of mathematics to move away from 'transmission‘ approaches to teaching towards more 'collaborative‘ approaches as the latter provide learners with opportunities to develop their thinking in algebra. In the transmission culture of teaching and learning, mathematics is seen as a body of knowledge and procedures to be 'covered‘. Learning is seen as an individual activity based on listening and imitating, and teaching is seen as structuring a linear curriculum for the learner, giving explanations and checking whether or not these have been understood through practice questions. Sometimes teachers 'correct‘ misunderstandings when students fail to 'grasp‘ what has been 'taught‘. This can be contrasted with the collaborative culture of teaching and learning where mathematics is seen as a network of ideas which teacher and students construct together. Here, learning is seen as a social activity in which students are challenged through discussion to arrive at the appropriate understandings, and teaching is seen as non-linear dialogue in which meanings and connections are explored, recognising misunderstandings, making them explicit and learning from them. Outcomes of research on algebra suggest that when discussion activities are used, teacher beliefs about teaching and learning change, learning increases, student-centred implementations are more effective than teacher-centred implementations, and there is significant improvement in self-efficacy. On the other hand, when discussion activities are not used, there is significant regression in confidence, lower motivation, algebra anxiety, and passive learning behaviours.

Keyword: algebraic thinking, discussion in mathematics classroom, teaching approaches