Predicting long-term growth in students' mathematics achievement: the unique contributions of motivation and cognitive strategies

This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long-term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; Mage = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies.

Poisoning the mind: Arsenic contamination of drinking water wells and children's educational achievement in rural Bangladesh

Bangladesh has experienced the largest mass poisoning of a population in history owing to contamination of groundwater with naturally occurring inorganic arsenic. Prolonged drinking of such water risks development of diseases and therefore has implications for children's cognitive and psychological development. This study examines the effect of arsenic contamination of tubewells, the primary source of drinking water at home, on the learning outcome of school-going children in rural Bangladesh using recent nationally representative data on secondary school children. We unambiguously find a negative and statistically significant correlation between mathematics scores and arsenic-contaminated drinking tubewells at home, net of the child's socio-economic status, parental background and school specific unobserved correlates of learning. Similar correlations are found for an alternative measure of student achievement and subjective well-being (i.e. self-reported measure of life satisfaction), of the student. We conclude by discussing the policy implication of our findings in the context of the current debate over the adverse effect of arsenic poisoning on children.

Don’t aim too high for your kids: parental over-aspiration undermines students’ learning in mathematics

Previous research has suggested that parents’ aspirations for their children’s academic attainment can have a positive influence on children’s actual academic performance. Possible negative effects of parental over-aspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German schoolchildren and their parents (N = 3,530; grades 5 to 10), we showed that parental aspiration and children’s mathematical achievement were linked by positive reciprocal relations over time. Importantly, we also found that parental aspiration that exceeded their expectation (i.e., over-aspiration) had negative reciprocal relations with children’s mathematical achievement. These results were fairly robust after controlling for a variety of demographic and cognitive variables such as children’s gender, age, intelligence, school type, and family SES. The results were also replicated with an independent sample of US parents and their children. These findings suggest that unrealistically high parental aspiration can be detrimental for children’s achievement.

Breaking the double-edged sword of effort/trying hard: developmental equilibrium and Longitudinal relations among effort, achievement, and academic self-concept

Ever since the classic research of Nicholls (1976) and others, effort has been recognized as a double-edged sword: whilst it might enhance achievement, it undermines academic self-concept (ASC). However, there has not been a thorough evaluation of the longitudinal reciprocal effects of effort, ASC and achievement,in the context of modern self-concept theory and statistical methodology. Nor have there been developmental equilibrium tests of whether these effects are consistent across the potentially volatile early-to-middle adolescence. Hence, focusing on mathematics, we evaluate reciprocal effects models over the first four years of secondary school, relating effort, achievement (test scores and school grades), ASC, and ASCxEffort interactions for a representative sample of 3,421 German students (Mn age = 11.75 years at Wave 1). ASC, effort and achievement were positively correlated at each wave, and there was a clear pattern of positive reciprocal positive effects among ASC, test scores and school grades—each contributing to the other, after controlling for the prior effects of all others. There was an asymmetrical pattern of effects for effort that is consistent with the double-edged sword premise: prior school grades had positive effects on subsequent effort, but prior effort had non-significant or negative effects on subsequent grades and ASC. However, on the basis of a synergistic application of new theory and methodology, we predicted and found a significant ASC-by-effort interaction, such that prior effort had more positive effects on subsequent ASC and school grades when prior ASC was high—thus providing a key to breaking the double-edged sword.

Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Models, mathematics and meaning in interdisciplinary research

Interdisciplinary research presents particular challenges for unambiguous communication. Frequently, the meanings of words differ markedly between disciplines, leading to apparent consensus masking fundamental misunderstandings. Researchers can agree on the need for models, but conceive of models fundamentally differently. While mathematics is frequently seen as an elitist language reinforcing disciplinary distinctions, both mathematics and modelling can also offer scope to bridge disciplinary epistemological divisions and create common ground on which very different disciplines can meet. This paper reflects on the role and scope for mathematics and modelling to present a common epistemological space in interdisciplinary research spanning the social, natural and engineering sciences.