Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom

Abstract

One of the aims of teaching secondary school mathematics in Malawi is to promote learners’ logical reasoning, problem-solving and critical thinking skills (Ministry of Education, Science and Technology [MEST], 2013). Euclidean geometry is regarded as the main area of mathematics that is a key source for teaching mathematical argumentation and proof, developing learners’ deductive reasoning and critical thinking (Kunimune, Fujita, & Jones, 2010). But the Malawi National Examinations Board (MANEB) chief examiners’ reports indicate that secondary school learners fail to develop geometric proofs at national examinations (MANEB, 2013). Poor teaching practices are highlighted as a major cause of learners’ inability to understand geometric proof development (MANEB, 2013). The reports emphasise that due to lack of both content knowledge and pedagogical knowledge, the teachers are not creative in conducting effective lessons to support learners’ understanding of geometric proof development. Studies conducted in different parts of the world also indicate that despite the importance of reasoning and proving in learners’ learning, many learners face serious challenges in proof development (Kunimune et al., 2010; Otten, Males & Gibertson, 2014; Stylianides, 2014). These studies support MANEB’s by arguing that learners’ challenges in proof development should be attributed more to classroom inappropriate practices that mainly emphasise rules of verification and devalue or omit exploration. As a result, the learners memorise the rules without understanding the process of proof development; hence, they are able to reproduce similar proofs but cannot apply the principles to develop a different proof (Ding & Jones, 2009). Use of exploratory teaching strategies is suggested as one way of helping learners to understand geometric proof development (Ding & Jones, 2009; Jones et al., 2009). This implies that the solution for improving classroom practices for enhancing learners’ understanding of geometric proof development lies in teacher professional development and teacher education.