Showing papers by "Michael Schneider published in 2010"

Representations of the magnitudes of fractions.

Abstract: We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However, atypical characteristics of the presented fractions might have provoked the use of atypical comparison strategies in that study. In our 3 experiments, university and community college students compared more balanced sets of single-digit and multi-digit fractions and consistently exhibited a logarithmic distance effect. Thus, adults used integrated, analog representations, akin to a mental number line, to compare fraction magnitudes. We interpret differences between the past and present findings in terms of different stimuli eliciting different solution strategies.

The developmental relations between conceptual and procedural knowledge: a multimethod approach.

Abstract: Interactions between conceptual and procedural knowledge influence the development of mathematical competencies However, after decades of research, these interrelations are still under debate, and empirical results are inconclusive The authors point out a source of these problems Different kinds of knowledge and competencies only show up intertwined in behavior, making it hard to measure them validly and independently of each other A multimethod approach was used to investigate the extent of these problems A total of 289 fifth and sixth graders' conceptual and procedural knowledge about decimal fractions was measured by 4 common hypothetical measures of each kind of knowledge Study 1 tested whether treatments affected the 2 groups of measures in consistent ways Study 2 assessed, across 3 measurement points, whether conceptual and procedural knowledge could be modeled as latent factors underlying the measures The results reveal substantial problems with the validities of the measures, which might have been present but gone undetected in previous studies A solution to these problems is essential for theoretical and practical progress in the field The potential of the multimethod approach for this enterprise is discussed

The cognitive perspective on learning: ten cornerstone findings

Abstract: Michael Schneider and Elsbeth Stern place knowledge acquisition at the very heart of the learning process, albeit that the quality of the knowledge is as necessary as the quantity and that "knowledge" should be understood much more broadly than (but including) knowing facts. They summarise the cognitive perspective through ten "cornerstones". Learning: i) is essentially carried out by the learner; ii) should take prior knowledge importantly into account; iii) requires the integration of knowledge structures; iv) balances the acquisition of concepts, skills and meta-cognitive competence; v) builds complex knowledge structures by hierarchically organising more basic pieces of knowledge; vi) can valuably use structures in the external world for organising knowledge structures in the mind; vii) is constrained by the capacity limitations of human information-processing; viii) results from a dynamic interplay of emotion, motivation and cognition; ix) should develop transferable knowledge structures; x) requires time and effort.

The Numerical Stroop Effect in Primary School Children: A Comparison of Low, Normal, and High Achievers

Abstract: Sixty-six primary school children were selected, of which 21 scored low on a standardized math achievement test, 23 were normal, and 22 high achievers. In a numerical Stroop experiment, children were asked to make numerical and physical size comparisons on digit pairs. The effects of congruity and numerical distance were determined. All children exhibited congruity and distance effects in the numerical comparison. In the physical comparison, children of all performance groups showed Stroop effects when the numerical distance between the digits was large but failed to show them when the distance was small. Numerical distance effects depended on the congruity condition, with a typical effect of distance in the congruent, and a reversed distance effect in the incongruent condition. Our results are hard to reconcile with theories that suggest that deficits in the automaticity of numerical processing can be related to differential math achievement levels. Immaturity in the precision of mappings between numbers and their numerical magnitudes might be better suited to explain the Stroop effects in children. However, as the results for the high achievers demonstrate, in addition to numerical processing capacity per se, domain-general functions might play a crucial role in Stroop performance, too.

A digital road map analogy of the relationship between neuroscience and educational research

Abstract: At a recent meeting about neuroscience and education, an experienced teacher stated: ‘‘Over the last decades, in many countries school education has seen one reform after another. None of them really worked. Doesn’t this prove that we need neuroscience to make school instruction work?’’ While we politely smiled and nodded, we could not help noticing the irony in this proposal. It is certainly true that school education has seen many reforms come and go. Each of them was motivated by dissatisfaction with existing approaches and by the hope for a better future. However, in the end, dissatisfaction and hope alone are poor fundaments for educational reform. This young teacher expressed the same dissatisfaction with the status quo and the same vague hope for a better future when he argued for the necessity of a neuroscience approach to education. Did he ever ask himself if educational neuroscience might simply be yet another ‘‘scientific revolution’’, in a series of many such ‘‘revolutions’’, each leading to a brief period of disappointment, to be followed by yet another such ‘‘revolution’’ in 10 or 20 years? Scientists who believe that neuroscience should have a strong impact on education often claim that educational science is a soft science, which gives fuzzy, complicated answers that are based mainly on opinions, while cognitive neuroscience is a hard science, which gives clear and precise answers based on unambiguous empirical evidence. They hope that cognitive neuroscience will yield clear and precise answers to the question ‘‘What is effective instruction and how can it be implemented?’’ So far, educational science has not provided answers to everyone’s satisfaction. Opponents of this view paint a very different picture. They emphasize that neuroscience deals with biological processes in the central nervous system, while educational science deals with institutionalized learning of cultural competencies that can only be assessed by behavioral means, such as tests and conversations. As yet, brain imaging methods rarely reveal innovative insights into learning in real-world contexts. They have many technical and logistic constraints because the research must be done under restricted conditions in the laboratory rather than in the classroom. To avoid noisy data caused by body movements, participants must indicate their answers by pushing buttons, which limits social interaction. Further, because of the high measurement error, brain activation data must be averaged over numerous trials to gain an acceptable signal-to-noise ratio. When participants solve any task, almost their whole brain is active. Thus, activation differences between different experimental conditions can only be interpreted when the two experimental conditions are very similar to each other and differ only in one or two basic cognitive processes they evoke. This is hardly possible in real-life contexts with ecologically valid, complex learning materials. Given these two divergent positions, why should we have a special issue entitled ‘‘Cognitive neuroscience and mathematics education research’’? We believe that mathematics is a particularly suitable starting point for addressing scientific issues related to the interaction between the brain and learning. We will use an analogy to describe how neuroscience and educational research can complement each other. E. Stern M. Schneider (&) Institute for Behavioral Sciences, ETH Zurich, Universitaetsstrasse 41, 8092 Zurich, Switzerland e-mail: schneider@ifv.gess.ethz.ch