PROOFS AND REFUTATIONS IN LOWER SECONDARY SCHOOL GEOMETRY

In this paper, we report on a teaching experiment in which we focused on students tackling 3D geometry problems in which, in general, they initially tended to produce 'primitive' conjectures by relying on visual images rather than geometrical reasoning. Following the work of Larsen and Zandieh (2008), we utilise the ideas of Lakatos (1976) on managing the refutation process and how the use of counter-examples can be important in promoting the growth of students' capability with geometrical reasoning and proof We found that students' primitive conjectures can cause an unexpected result and that this can trigger further reviewing ('Monster-barring') and modifications of the conjecture ('Exception-barring') amongst students. Whole classroom discussion followed by small group discussion allowed students to exchange various ideas and opinions and this process was important for their construction of a proof of their new conjecture ('Proof-analysis').