Elsbeth Stern

Individual differences in mathematical competence predict parietal brain activation during mental calculation

Functional neuroimaging studies have revealed that parietal brain circuits subserve arithmetic problem solving and that their recruitment dynamically changes as a function of training and development. The present study investigated whether the brain activation during mental calculation is also modulated by individual differences in mathematical competence. Twenty-five adult students were selected from a larger pool based on their performance on standardized tests of intelligence and arithmetic and divided into groups of individuals with relatively lower and higher mathematical competence. These groups did not differ in their non-numerical intelligence or age. In an fMRI block-design, participants had to verify the correctness of single-digit and multi-digit multiplication problems. Analyses revealed that the individuals with higher mathematical competence displayed stronger activation of the left angular gyrus while solving both types of arithmetic problems. Additional correlational analyses corroborated the association between individual differences in mathematical competence and angular gyrus activation, even when variability in task performance was controlled for. These findings demonstrate that the recruitment of the left angular gyrus during arithmetic problem solving underlies individual differences in mathematical ability and suggests a stronger reliance on automatic, language-mediated processes in more competent individuals.

Superior performance and neural efficiency : The impact of intelligence and expertise

Superior cognitive performance can be viewed from an intelligence perspective, emphasising general properties of the human information processing system (such as mental speed and working memory), and from an expertise perspective, highlighting the indispensable role of elaborated domain-specific knowledge and acquired skills. In exploring its neurophysiological basis, recent research has provided considerable evidence of the neural efficiency hypothesis of intelligence, indicating lower and more focussed brain activation in brighter individuals. The present EEG study investigates the impacts of intelligence and expertise on cognitive performance and the accompanying cortical activation patterns in the domain of tournament chess. Forty-seven tournament chess players of varying intelligence and expertise level worked on tasks drawing on mental speed, memory, and reasoning. Half of the tasks were representative for chess, while the other half was not. The cortical activation was quantified by means of event-related desynchronisation (ERD) in the upper alpha band. Independent effects of expertise and intelligence emerged at both, the performance and the neurophysiological level. Brighter participants performed better than less intelligent ones which was associated with more efficient brain functioning (lower ERD) across all tasks. Additionally, a high expertise level was beneficial for good task performance but exerted a topographically differentiated influence on the cortical activation patterns. The findings suggest that superior cognitive performance and the underlying cortical activation are not only a function of knowledge and domain-specific competences but also of the general efficiency of the information processing system.

Effects of Instructional Support Within Constructivist Learning Environments for Elementary School Students' Understanding of "Floating and Sinking"

In a repeated measures design (pretest, posttest, 1-year follow-up) with 161 3rd-grade students, the authors compared 2 curricula on floating and sinking within constructivist learning environments, varying in instructional support. The 2 curricula differed in the sequencing of content and the teachers cognitively structuring statements. At the posttest, both instructed groups showed significant gains on a test on understanding the concepts of density and buoyancy force as compared to a baseline group without instruction. One year later, the group of high instructional support was superior to the group of low instructional support on the reduction of misconceptions and the adoption of scientific explanations. Thus, instructional support within constructivist learning environments fostered elementary schoolchildrens conceptual change in the domain of physics.

Improving cross-content transfer in text processing by means of active graphical representation

Abstract The two studies presented investigate the conditions under which adults with different academic backgrounds (in terms of formal mathematical competencies and domain-specific knowledge in economics) use linear graphs as reasoning tools that can be transferred from one economic content area to another. In each of the studies, two groups of participants were presented with a text on stockkeeping. One group passively encountered a linear graph, while the other group was asked to actively construct this graph following the instructions provided. To control for transfer effects of content knowledge, a third group received a text on direct costing, a topic also dealt with in the transfer text. The groups were compared with respect to their transfer potential in processing a text dealing with the revenue functions and break-even points of two companies. Questions posed in this text could be easily answered by constructing a linear graph similar to that encountered in the stockkeeping text. Two studies with a total of 281 university and vocational school students confirmed that active graphical representation can be a powerful transfer tool.

What Makes Certain Arithmetic Word Problems Involving the Comparison of Sets So Difficult for Children

Arithmetic word problems with an unknown reference set, such as «John has 7 eggs. He has 4 eggs fewer [more] than Peter. How many eggs does Peter have?» are considerably more difficult for children than problems with an unknown compare set (second sentence: «Peter has 4 eggs more [fewer] than John.») Six experiments with 1st graders and kindergartners investigated reasons for this finding. Experiments 1-4 revealed that neither difficulties in processing the personal pronoun nor the use of key word strategies could explain the difficulty differences. Experiment 5 and 6 indicated that the lack of access to flexible language use is what makes compare problems with an unknown reference set so difficult.

When intelligence loses its impact: Neural efficiency during reasoning in a familiar area

Several studies have revealed that persons with a lower IQ show more cortical activity when solving intelligence-related tasks than more intelligent persons do. Such results are interpreted in terms of neural efficiency: the more intelligent a person is, the fewer mental resources have to be activated. In an experiment with 31 experienced taxi drivers of varying IQs (measured by Ravens advanced progressive matrices test), we investigated cortical activation by measuring the amount of event-related desynchronization in the electroencephalogram during a familiar task (thinking about routes to take in their city) and a novel task (memorizing routes of an artificial map). A comparison of participants with lower and higher IQs (median split) revealed higher cortical activation in the less intelligent group for the novel task, but not for the familiar task. These results suggest that long-term experience can compensate for lower intellectual ability, even at the level of cortical activation.

The role of situational context in solving word problems

Abstract Word problems depicting the comparison of quantities have been shown to be difficult for elementary school children in several studies. One reason for this may be that young children lack situational understanding because they are not familiar with the quantitative comparison of sets. To test this assumption, we presented 45 first graders with “compare” problems that were embedded in a familiar situational context. The results showed that children who received compare problems following stories that induced situational understanding of qualitative comparisons performed better than children who received compare problems following stories that had nothing to do with the comparison of sets. The data suggest that most first graders have access to the mathematical problem-solving knowledge necessary to understand and solve compare problems only when these problem are embedded in a familiar situational context.

The Inverse Relation of Addition and Subtraction: A Knowledge Integration Perspective

A number of mathematical concepts and computational procedures are linked to the inverse relation of addition and subtraction on an abstract mathematical level. In this discussion article for the special issue on subtraction-related principles, we suggest that the mainstream of research on inversion is conducted from a Knowledge Dissociation Perspective in which researchers show that children often fail to see abstract relations in the domain. Implicit rationale of the studies is that seeing these inter-relations occurs naturally and that we have to find the cognitive processes that can explain exceptions from this rule. Based on a review of key findings from cognitive research on knowledge acquisition we argue that a Knowledge Integration Perspective would be more adequate in which children acquire different concepts and procedures in different situations. Only experts but not children who are new in a domain can see their abstract mathematical inter-relations. Thus, research should shift its focus from merely describing dissociations between childrens concepts or procedures to looking for causal mechanisms and instructional approaches that help children to integrate their knowledge by seeing the underlying deep structures of mathematical principles and problems.

In Search of the Benefits of Learning Latin

The authors studied whether Latin or French as a foreign curricular language is a better preparation for learning Spanish. Fifty native German speakers who took a university Spanish course concluded their course with a translation test. English was the 1st foreign language for all students, whereas half of them had learned French and the other half had learned Latin as their 2nd foreign language at school. Participants who had learned French at school made markedly fewer grammar errors and slightly fewer vocabulary errors in the Spanish test than participants who had learned Latin. Knowledge of Latin is probably not an optimal preparation for modern language learning.

Abstract reasoning with mathematical constructs

Mathematical constructs have a dual role because they can be used as instruments to model real world situations and events, but they can also become an object of reasoning. Mathematics is a particularly abstract domain because the affordances and constraints underlying the use of mathematical constructs may be different from the affordances and constraints in real-world situations. We argue that this makes the acquisition of quantitative schemata a difficult task but also accounts for the potential to extend our understanding of the world by mathematical means. We refer to developmental, educational, and experimental studies supporting the view that new understandings and powerful ways of reasoning become possible on the basis of culturally mediated mathematical constructs.