Nascent deductive proof schemes and proof readiness in adolescence

Abstract

Using Proof-Schemes Combined, our extension of Harel and Sowder’s Proof-Schemes taxonomy, we introduce the nascent deductive proof schemes construct (proof-scheme combinations that contain elements of deductive mathematical reasoning) and present evidence of these in written responses to ten items of 85 Year 9 (age 14–15) secondary students. We capture these students’ first encounters with proof in an educational context (mixed-ability, state schools in Greece) where proof is present in lessons and key national examinations. In previous analyses, we identified evidence in the students’ responses of Harel and Sowder’s seven proof schemes and of the eight proof-scheme combinations from our Proof-Schemes Combined taxonomy. Here, we present evidence – found in 383 out of 850 student responses – of five of the fifteen proof schemes that were nascent deductive proof schemes. Our findings contribute to non-deficit discourses about students’ mathematical reasoning potential and provide evidence in favour of proof readiness in early adolescence.