This chapter contains sections titled:
Introduction
Bidirectional Collaboration
Converging ‘ME’ and ‘NS’
Bridging ‘ME’ with ‘NS’
From ‘MENS’ towards ‘Educational Neuroscience’
Acknowledgements
...References
Dyscalculia and mathematical learning disability (MD) are neurodevelopmental disorders characterized by difficulties in reasoning about numbers. Children with MD lag behind their typically developing ...peers in a broad range of numerical tasks, including magnitude judgement, quantity manipulation, arithmetic fact retrieval, and problem-solving. This chapter reviews current theories and knowledge of MD and its neurobiological basis from a systems neuroscience perspective. The chapter shows that MD involves processing deficits and aberrancies in multiple neurocognitive systems associated with non-symbolic and symbolic quantity judgment, visuo-spatial working memory, associative memory, and cognitive control. Convergent evidence from task and resting-state fMRI, along with morphometric and tractography studies, is used to demarcate distributed brain circuits disrupted in MD. The chapter examines neural mechanisms underlying intervention and remediation of deficits in MD, highlighting links between brain plasticity and response to treatment. The view that emerges is of a multi-component neurodevelopmental disorder, arising from aberrancies at one or more levels of the numerical information processing hierarchy.
Prospero Nowlan, Robert A.
Masters of Mathematics
Book Chapter
To solve problems, one must learn to be observant and ask the right questions. What follows are questions we need to have the answer to if we are to solve the problem that is the subject of this ...entry. Let’s test your number sense. What is number sense? What is a number? How do we know numbers exist? Do numbers exist? That is, do they have to be a physical quantity?
This chapter reviews the cognitive and neural mechanisms for numerical and mathematical development. It provides converging evidence that from a rudimentary, non-symbolic “number sense” ...representation that is assumed to exist even in non-human species, the human mind develops its unique symbolic representational system to accurately represent and manipulate numerical quantities. This process is non-trivial, it is slow, and it requires the push-and-pull of multiple neurocognitive systems. These include: (i) those supporting visual and verbal perception/decoding in the occipital and temporal cortices, (ii) regions of the frontal eye-fields and the posterior parietal cortex involved in active manipulation and updating processes, (iii) memory association processes within the medial temporal lobe, and (iv) executive control processes anchored in the frontal cortices. The present chapter proposes a neurocognitive model whereas the successful acquisition of our modern symbolic code for mathematics is gradually refined through the dynamic interaction of these neurocognitive systems throughout development. Depending on the specific cognitive weaknesses of the individual, training, intervention, and educational approaches should hence be designed to comprehensively “stimulate” part or all these neurocognitive systems to achieve the most optimal learning outcomes.
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A good aphorism can, in a few words, capture an essential truth. Of the many good aphorisms Paul Holland has coined over the years, I have found myself invoking the one above frequently enough to ...worry that I should be paying out royalty fees, so it is only fitting that I use it as the starting point for some ideas I wish to explore in this paper.
The gods were lazing around Mount Olympus, complaining that they got no respect anymore from human beings, who once feared them so much they went out of their way to appease the immortals. “It’s all ...your fault,” Hera says to her husband Zeus, king of the gods. “If you hadn’t given that silly jar to that female human Pandora and tempted her to open it and let out all the evils of humanity.” “I remember her she was a lovely woman, the first female I had created out of the mud.
This article provides a critique of the concept and role of 'number sense' in relation to students who have difficulties in numeracy. In a 1999 paper Gersten and Chard proposed that number sense ...might be to mathematics what phonemic awareness is to reading. They explained the role of phonemic awareness in reading acquisition and its influence on reading research and argued that an understanding of the concept of number sense could be equally influential in the field of mathematics, in particular for the population of students at risk of developing mathematical disabilities. The article examines this analogy between phonemic awareness and number sense in the light of existing literature in the area of number sense. The authors conclude that while the analogy may have some merit from a research point of view there are some inherent risks in its promotion, because, unlike phonemic awareness, number sense remains poorly defined, validated intervention procedures to develop number sense are lacking, and there is insufficient evidence that it is a prerequisite for mathematics success. Author abstract, ed
This article presents an investigation of the effectiveness of procedures undertaken to develop number sense and basic computational skills in learning disabled students. Twelve students in a K‐1 ...classroom who had been identified as learning disabled (LD) were presented tasks which required them to subitize (i.e., recognize the number of objects in a set without actually counting them). Consistent with other such studies in special education, a qualitative research methodology was employed, involving a case study of an intact group of LD students. Also consistent with many such studies in special education, observational rather than quantitative data were collected. At the end of a four‐week period, all students were consistently successful in recognizing and matching the numbers 0 through 5 and adding sums to five as determined on a teacher‐administered test. Increased time‐on‐task and pupil independence also are reported. Suggestions for further instructional research related to other arithmetic skills are presented.
