The role of mathematical context in evaluating conditional statements

Recently there has been increasing interest in the mathematics education research community about the role of logic in the teaching, learning and production of mathematics. In this paper we investigate how conditional statements are evaluated by successful mathematics students, and argue that the role of context is vital to determine the manner in which this evaluation proceeds. We use two versions of the so-called Labyrinth Task, one in it’s original context and one in an overtly mathematical context. We report results that indicates that the manner in which conditional statements are evaluated on these tasks differs depending on the context. These results are supplemented by data from a qualitative task-based interview study

Classification and concept consistency

This article investigates the extent to which undergraduates consistently use a single mechanism as a basis for classifying mathematical objects. We argue that the concept image/concept definition distinction focuses on whether students use an accepted definition but does not necessarily capture the more basic notion that there should be a fixed basis for classification. We examine students’ classifications of real sequences before and after exposure to definitions of increasing and decreasing; we develop an abductive plausible explanations method to estimate the consistency within the participants’ responses and suggest that this provides evidence that many students may lack what we call concept consistency

Conditional inference and advanced mathematical study

Many mathematicians and curriculum bodies have argued in favour of the theory of formal discipline: that studying advanced mathematics develops one’s ability to reason logically. In this paper we explore this view by directly comparing the inferences drawn from abstract conditional statements by advanced mathematics students and well-educated arts students. The mathematics students in the study were found to endorse fewer invalid conditional inferences than the arts students, but they did not endorse significantly more valid inferences. We establish that both groups tended to endorse more inferences which led to negated conclusions than inferences which led to affirmative conclusions (a phenomenon known as the negative conclusion effect). In contrast, however, we demonstrate that, unlike the arts students, the mathematics students did not exhibit the affirmative premise effect: the tendency to endorse more inferences with affirmative premises than with negated premises.We speculate that this latter result may be due to an increased ability for successful mathematics students to be able to ‘see through’ opaque representations. Overall, our data are consistent with a version of the formal discipline view. However, there are important caveats; in particular, we demonstrate that there is no simplistic relationship between the study of advanced mathematics and conditional inference behaviour

How we assess mathematics degrees: the summative assessment diet a decade on

Two previous studies mapping university mathematics students’ summative assessment diet in the UK revealed a clear picture. In general there was a dominance of closed book examinations with a strong relationship to departmental league table position. The decade since then has seen many changes in higher education in the UK, particularly in the strength of the student voice. The study we report here replicated the earlier work to see if there has been an impact on the assessment diet. While the analysis shows a very small decrease in the use of closed book examinations, this may be accounted for by the addition of adjunct modules, rather than a broadening of the assessment diet across mainstream mathematics topics