Justifying and proving in secondary school mathematics

grantor: University of TorontoOne of the central features of mathematics that distinguishes it from other academic disciplines is the manner in which it develops and accepts new knowledge. Mathematical proof is one of the defining features of mathematics and as such it should be a major part of the secondary mathematics curriculum. This study examined the beliefs that students have about proof. These beliefs underpin what students believe constitutes acceptable proof. This study also explored their abilities in proof construction and how their beliefs impact on this ability. Two survey instruments were used to collect data and information. One instrument provided data about beliefs whilst the other provided students with opportunities to evaluate sample proofs and to construct their own. This study confirms that senior secondary school students have a generally positive view of the role of proof in the curriculum. Although students have difficulty constructing proofs, they do appreciate the value of general arguments and of proofs that offer explanation. However, students also have many misconceptions about proof, its nature and its role. The results of this study suggest that more curricular emphasis on proof's different functions and on the process of proving would improve the proving capabilities of our students. It is also evident that there is a great need for rich mathematical tasks that create, in students' minds, a reason for proof. There is also a need for more study about how proofs that explain can assist our students' mathematical understanding.Ph.D