Teacher Noticing for Supporting Student Proving: Gradual Articulation

Abstract

Proof has been paid much attention in school mathematics and the literature. To date, the extant literature has focused more on difficulties in teaching and learning of proof rather than support that can help teachers to teach proof and develop student’s understanding about proof. This study examined a teacher’s practice that offers an explicit instruction of proof as part of everyday lesson. The results showed that the teacher supports student proving by way of teacher noticing with a clear definition of proof in the literature and that teacher noticing instructional practice needs to be more attuned for teaching proof. In particular, the teacher’s moves for supporting student proving differ by what aspects of proof that the teacher pays attention to at a given time and by judgement on whether an argument qualifies as a valid proof. This instructional practice would provide a guidance and foundation for teachers to engage students in proving as part of everyday lesson.

Keywords

• proof
• reasoning
• teacher noticing
• teacher practice
• enacted curriculum