Phylogeny and Ontogeny of Mathematical and Numerical Understanding

2015 ◽  
Author(s):  
Elizabeth M. Brannon ◽  
Joonkoo Park
Keyword(s):  
Individual Differences ◽  
Mathematics Education ◽  
Numerical Cognition ◽  
Mathematical Mind ◽  
Key Questions

This navigator chapter situates the chapters that comprise the section on the phylogeny and ontogeny of mathematical and numerical understanding. How is number represented in the absence of language? What are the key questions that arise as we map out the continuities and discontinuities between non-human and human numerical cognition? What can we learn from studying individual differences in numerical cognition? How do the initial representations of quantity in the infant give rise to the uniquely human mathematical mind? Can we use the knowledge we are gaining about how the preverbal mind represents and manipulate quantity to improve mathematics education?

The visual number world: A dynamic approach to study the mathematical mind

2018 ◽  
Vol 71 (1) ◽  
pp. 28-36 ◽  
Author(s):  
Matthias Hartmann ◽  
Jochen Laubrock ◽  
Martin H Fischer
Keyword(s):  
Numerical Cognition ◽  
Mental Arithmetic ◽  
Simultaneous Presentation ◽  
Language Research ◽  
On Line ◽  
Arithmetic Performance ◽  
Mathematical Mind ◽  
The Mind ◽  
Visual Number

In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the “visual number world”-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements.

scholarly journals Modeling the latent structure of individual differences in the numerical size-congruity effect

2020 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Kristen Bowman
Keyword(s):  
Individual Differences ◽  
Numerical Cognition ◽  
Congruity Effect ◽  
Numerical Magnitude ◽  
Data Sets ◽  
Comparison Task ◽  
Physical Size ◽  
The Individual ◽  
Size Congruity Effect ◽  
Individual Size

When people are asked to choose the physically larger of a pair of numerals, they are often slower when relative physical size is incongruent with numerical magnitude. This size-congruity effect is usually assumed as evidence for automatic activation of numerical magnitude. In this paper, we apply the methods of Haaf and Rouder (2017) to look at the size-congruity effect through the lens of individual differences. Here, we simply ask whether everyone exhibits the effect. We develop a class of hierarchical Bayesian mixed models with varying levels of constraint on the individual size- congruity effects. The models are then compared via Bayes factors, telling us which model best predicts the observed data. We then apply this modeling technique to three data sets. In all three data sets, the winning model was one in which the size-congruity effect was constrained to be positive. This indicates that, at least in a physical comparison task with numerals, everyone exhibits a positive size-congruity effect. We discuss these results in the context of measurement fidelity and theory-building in numerical cognition.

scholarly journals Global Visual Motion Sensitivity: Associations with Parietal Area and Children's Mathematical Cognition

2016 ◽  
Vol 28 (12) ◽  
pp. 1897-1908 ◽  
Author(s):  
Oliver Braddick ◽  
Janette Atkinson ◽  
Erik Newman ◽  
Natacha Akshoomoff ◽  
Joshua M. Kuperman ◽  
...  
Keyword(s):  
Individual Differences ◽  
Brain Development ◽  
Numerical Cognition ◽  
Visual Motion ◽  
Dorsal Stream ◽  
Motion Processing ◽  
Intraparietal Sulcus ◽  
Global Motion ◽  
Visuomotor Integration ◽  
Motion Sensitivity

Sensitivity to global visual motion has been proposed as a signature of brain development, related to the dorsal rather than ventral cortical stream. Thresholds for global motion have been found to be elevated more than for global static form in many developmental disorders, leading to the idea of “dorsal stream vulnerability.” Here we explore the association of global motion thresholds with individual differences in children's brain development, in a group of typically developing 5- to 12-year-olds. Good performance was associated with a relative increase in parietal lobe surface area, most strongly around the intraparietal sulcus and decrease in occipital area. In line with the involvement of intraparietal sulcus, areas in visuospatial and numerical cognition, we also found that global motion performance was correlated with tests of visuomotor integration and numerical skills. Individual differences in global form detection showed none of these anatomical or cognitive correlations. This suggests that the correlations with motion sensitivity are unlikely to reflect general perceptual or attentional abilities required for both form and motion. We conclude that individual developmental variations in global motion processing are not linked to greater area in the extrastriate visual areas, which initially process such motion, but in the parietal systems that make decisions based on this information. The overlap with visuospatial and numerical abilities may indicate the anatomical substrate of the “dorsal stream vulnerability” proposed as characterizing neurodevelopmental disorders.

Synaesthesia as a Model System for Understanding Variation in the Human Mind and Brain

2020 ◽  
Author(s):  
Jamie Ward
Keyword(s):  
Individual Differences ◽  
Human Mind ◽  
Model System ◽  
Mind And Brain ◽  
Way Of Thinking ◽  
Key Questions

The aim of this article is to reposition synaesthesia as model system for understanding variation in the construction of the human mind and brain. People with synaesthesia inhabit a remarkable mental world in which numbers can be coloured, words can have tastes, and music is a visual spectacle. Synaesthesia has now been documented for over two hundred years but key questions remain unanswered about why it exists, and what such conditions might mean for theories of the human mind. This article argues we need to rethink synaesthesia as not just representing exceptional experiences, but as a product of an unusual neurodevelopmental cascade from genes to brain to cognition of which synaesthesia is only one outcome. Specifically, differences in the brains of synaesthetes support a distinctive way of thinking (enhanced memory, imagery etc.) and may also predispose towards particular clinical vulnerabilities. In effect, synaesthesia can act as a paradigmatic example of a neuropsychological approach to individual differences.

Brief Reports: Some Aspects of Individual Differences in Mathematics Instruction

1979 ◽  
Vol 10 (5) ◽  
pp. 359-363
Author(s):  
Hendrik Radatz
Keyword(s):  
Information Processing ◽  
Individual Differences ◽  
Mathematics Education ◽  
Learning Process ◽  
Social Factors ◽  
Demographic Characteristics ◽  
Situation Specificity ◽  
Treatment Interaction ◽  
Aptitude Treatment Interaction ◽  
Research In Mathematics Education

For some years individual differences in learners and teachers have played an important part in educational research in general and especially in research in mathematics education. There are a multitude of studies on the importance of abilities, demographic characteristics, and various cognitive, affective, and social factors to the learning of mathematics or, more precisely, to achievement in mathematics. Three developments in particular seem to have increased interest in individual differences: information-processing psychology. aptitude-treatment-interaction (ATI) research. and an increased awareness of the content- and situation-specificity of the learning process.

scholarly journals Integrating numerical cognition research and mathematics education to strengthen the teaching and learning of early number

2019 ◽  
Author(s):  
Zachary Hawes ◽  
Rebecca Merkley ◽  
Daniel Ansari
Keyword(s):  
Mathematics Education ◽  
Teaching And Learning ◽  
Numerical Cognition ◽  
School Context ◽  
Intervention Group ◽  
Number Line ◽  
Control Group ◽  
Number Line Estimation ◽  
Teachers And Students ◽  
And Mathematics

This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for K-3 educators (N=45) and their students (N=180). A central goal of the PD was to better integrate numerical cognition research and mathematics education. The results of the first iteration (Year 1), indicated that compared to a control group, both teachers and students benefitted from the intervention. Teachers demonstrated gains in self-perceived and actual numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on a measure of self-perceived numerical cognition knowledge, but no gains in actual numerical cognition knowledge. At the student level, there was some evidence of gains in numeration. Given the mixed findings, questions remain as to why the model may be effective in one school context but not another.

scholarly journals Motor plans under uncertainty reflect a trade-off between maximizing reward and success

2021 ◽  
Author(s):  
Aaron L Wong ◽  
Audrey L Green ◽  
Mitchell W Isaacs
Keyword(s):  
Individual Differences ◽  
Trade Off ◽  
Study Behavior ◽  
Reward Seeking ◽  
Movement Strategies ◽  
General Response ◽  
Key Questions

When faced with multiple potential movement options, individuals either reach directly to one of the options, or initiate a reach intermediate between the options. It remains unclear why people generate these two types of behaviors. Using the go-before-you-know task (commonly used to study behavior under choice uncertainty), we examined two key questions. First, do these two types of responses reflect distinct movement strategies, or are they simply examples of a more general response to choice uncertainty? If the former, the relative desirability (i.e., weighing the likelihood of successfully hitting the target versus the attainable reward) of the two target options might be computed differently for direct versus intermediate reaches. We showed that indeed, when exogenous reward and success likelihood (i.e., endogenous reward) differ between the two options, direct reaches were more strongly biased by likelihood whereas intermediate movements were more strongly biased by reward. Second, what drives individual differences in how people respond under uncertainty? We found that risk/reward-seeking individuals generated a larger proportion of intermediate reaches and were more sensitive to trial-to-trial changes in reward, suggesting these movements reflect a strategy to maximize reward. In contrast, risk-adverse individuals tended to generate more direct reaches in an attempt to maximize success. Together, these findings suggest that when faced with choice uncertainty, individuals adopt movement strategies consistent with their risk/reward-seeking tendency, preferentially biasing behavior toward exogenous rewards or endogenous success and consequently modulating the relative desirability of the available options.

scholarly journals Disciplinary differences between cognitive psychology and mathematics education: A developmental disconnection syndrome. Reflections on 'Challenges in Mathematical Cognition' by Alcock et al. (2016)

2016 ◽  
Vol 2 (1) ◽  
pp. 42-47 ◽  
Author(s):  
Daniel B. Berch
Keyword(s):  
Mathematics Education ◽  
Research Agenda ◽  
Quantitative Methods ◽  
Numerical Cognition ◽  
Mathematical Cognition ◽  
Disconnection Syndrome ◽  
Theoretical Perspectives ◽  
Open Questions ◽  
Mathematics Education Researcher ◽  
And Mathematics

As the participants in this collaborative exercise who are mathematics education researchers espouse a cognitive perspective, it is not surprising that there were few genuine disagreements between them and the psychologists and cognitive neuroscientists during the process of generating a consensual research agenda. In contrast, the prototypical mathematics education researcher will mostly likely find the resulting list of priority open questions to be overly restrictive in its scope of topics to be studied, highly biased toward quantitative methods, and extremely narrow in its disciplinary perspectives. It is argued here that the fundamental disconnects between the epistemological foundations, theoretical perspectives, and methodological predilections of cognitive psychologists and mainstream mathematics education researchers preclude the prospect of future productive collaborative efforts between these fields. [Commentary on: Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., . . . Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41. doi:10.5964/jnc.v2i1.10]

From Single-Cell Neuropathology to Mathematics Education

2015 ◽  
Author(s):  
Roi Cohen Kadosh
Keyword(s):  
Mathematics Education ◽  
Single Cell ◽  
Numerical Cognition ◽  
Future Directions ◽  
Research Directions ◽  
Non Invasive ◽  
Exciting Line ◽  
Productive Research ◽  
Exciting Application

One of the most productive research directions in numerical cognition is its combination with neuroscience. This navigator aims to provide the current outlook to this exciting line of studies, together with future directions. I will cover here studies from single-cell neurophysiology in monkeys, to non-invasive neuroimaging studies in children and adults, and will end by discussing a particularly exciting application of neuroscience to education.

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