The Calculator as a Cognitive Tool: Upper-Primary Pupils Tackling a Realistic Number Problem

This paper examines the idea that the arithmetic calculator can act as a cognitive tool, supporting the amplification or reorganisation of systems of thought. It analyses how a structured sample of pupils in the last year of English primary education, with differing degrees of experience of a ’calculator-aware‘ number curriculum, tackled a realistic number problem, focusing on their use of calculator, written and mental modes of computation. Examples were found in which use of the calculator helped pupils to work with unusual problem representations, and to adopt solution strategies in which they focused on planning and monitoring computations executed by the machine. For most pupils, however, other issues were more salient. First, there was an important dissonance between pupils‘ conception of division and the calculator‘s operationalisation of it, although some cases showed how further experiment or computation with the machine could help to make appropriate connections. Second, while the calculator made it possible to redistribute computation from human to machine, important limitations arose from the transience of the calculator‘s record of operations and results. The observations suggest the importance of developing pupils‘ skill in making effective use of the calculator beyond single, simple computations; and the need to help pupils apprehend the relationship between mathematical concepts and their operationalisation in the machine. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mathematical literacy in undergraduates: role of gender,emotional intelligence and emotional self-efficacy

This empirical study explores the roles that Emotional Intelligence (EI) and Emotional Self-Efficacy (ESE) play in undergraduates’ mathematical literacy, and the influence of EI and ESE on students’ attitudes towards and beliefs about mathematics. A convenience sample of 93 female and 82 male first-year undergraduates completed a test of mathematical literacy, followed by an online survey designed to measure the students’ EI, ESE and factors associated with mathematical literacy. Analysis of the data revealed significant gender differences. Males attained a higher mean test score than females and out-performed the females on most of the individual questions and the associated mathematical tasks. Overall, males expressed greater confidence in their mathematical skills, although both males’ and females’ confidence outweighed their actual mathematical proficiency. Correlation analyses revealed that males and females attaining higher mathematical literacy test scores were more confident and persistent, exhibited lower levels of mathematics anxiety and possessed higher mathematics qualifications. Correlation analyses also revealed that in male students, aspects of ESE were associated with beliefs concerning the learning of mathematics (i.e. that intelligence is malleable and that persistence can facilitate success), but not with confidence or actual performance. Both EI and ESE play a greater role with regard to test performance and attitudes/beliefs regarding mathematics amongst female undergraduates; higher EI and ESE scores were associated with higher test scores, while females exhibiting higher levels of ESE were also more confident and less anxious about mathematics, believed intelligence to be malleable, were more persistent and were learning goal oriented. Moderated regression analyses confirmed mathematics anxiety as a negative predictor of test performance in males and females, but also revealed that in females EI and ESE moderate the effects of anxiety on test performance, with the relationship between anxiety and test performance linked more to emotional management (EI) than to ESE.