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

<p>Abstract copyright UK Data Service and data collection copyright owner.</p>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.<B>Main Topics</B>:<br> The study consists of two datasets:<br> the larger dataset contains the responses of the sample of Year 10 students (14 or 15 years old) to a proof questionnaire, which comprised a question to ascertain students' views on the role of proof, followed by items in two domains of mathematics - arithmetic/algebra and geometry - presented in open and multiple-choice formats. In the open format, students were asked to construct one familiar and one unfamiliar proof in each domain. In the multiple-choice format, students were required to choose from a range of arguments in support of or refuting a conjecture in accordance with two criteria: which argument would be nearest to their own approach if asked to prove the given statement, and which they believed would receive the best mark.<br> The smaller dataset contains responses of the respondent students' teachers to the school questionnaire. This questionnaire was designed to obtain data about the school and the mathematics teacher of the class selected to complete the proof questionnaire. These teachers also completed all the multiple-choice questions in the proof questionnaire, in order to obtain their choices of argument and to identify the proof they thought their students believed would receive the best mark. The responses are included in this dataset