Justifying and Proving in School Mathematics: Student Conceptions and School Data, 1996

In recent years there has been considerable interest in reassessing the role of mathematical proof, influenced by developments in computer technology and an increasing awareness of the role of proof in conveying and illuminating as well as verifying mathematical ideas. Research in mathematics education has shown proof to be an elusive concept for many students. This has been one influence underlying the shift away from formal methods in schools to the more process-orientated approaches now enshrined in the UK National Curriculum <i>Using and Applying Mathematics</i>.<br> In this project a nationwide survey was conducted to ascertain the current profile of conceptions amongst 15-year-old high-attaining students of the validity of a range of modes of justification in geometry and algebra. Analysis of the survey data informed the design of two teaching experiments in these mathematical domains incorporating computer use and aiming specifically to encourage links between empirical and deductive reasoning. Case studies were constructed to evaluate the influence of these innovations on students' understanding of proving the role of formal mathematical proof.<br> Both strands of the research contributed to the formulation of recommendations concerning the emphasis on and positioning of mathematical proof in the school curriculum.