Proving in the Elementary Mathematics Classroom

Andreas J. Stylianides is a Reader in Mathematics Education at the University of Cambridge. Previously he held an academic fellowship at the University of Oxford and, before that, a postdoctoral fellowship at the University of California-Berkeley. A Fulbright scholar, he received MSc degrees in mathematics and mathematics education, and then his PhD in mathematics education, at the University of Michigan. He was the Deputy Editor of the International Journal of Educational Research, and he has served on the editorial boards of Research in Mathematics Education and Science and Education. He received an American Educational Research Association publication award for his 2007 article "Proof and Proving in School Mathematics."

... a coherent approach to proof and proving in the elementary mathematics classroom, including a framework for conceptualising mathematical proof and proving activities, a categorisation of tasks that may be linked with qualitative different opportunities for the students to be engaged in proof and proving, and a discussion about the role of the teacher. Importantly, [the author] orchestrates the theoretical discussion of these topics with a well-structured analysis of illustrative examples... "Proving in the Elementary Mathematics Classroom", at the very least, opens a fascinating discussion about explicitly communicating and practising that proof is taught and learned within the elementary mathematics classroom.

• 1: Introduction 2: The importance and meaning of proving, and the role of mathematics tasks 3: The set-up of the investigation 4: Proving tasks with ambiguous conditions 5: Proving tasks involving a single case 6: Proving tasks involving multiple but finitely many cases 7: Proving tasks involving infinitely many cases 8: Conclusion