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Neural Correlates of Gender, Culture, and Race and Implications to Embodied Thinking in Mathematics

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Book cover Towards Equity in Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

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Abstract

In this chapter, I discuss neuroscience research and selected findings that are relevant to mathematics education. What does it mean, for example, to engage in a neuroscientific analysis of symbol reference? I also discuss various research programs in neuroscience that have useful implications in mathematics education research. Further, I provide samples of studies conducted within and outside mathematics education that provide a neural grounding of gender, culture, and race. The chapter closes with three brief implications of neuroscientific work in mathematics education research, in general, and in individual- and intentional-embodied cognition in mathematical thinking and learning, in particular.

Writing of this chapter has been supported by a grant from the National Science Foundation (DRL Grant #0448649) awarded to the author. The ideas explored and expressed in this chapter are those of the author and do not reflect the views of the foundation.

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Notes

  1. 1.

    Certainly motives behind interests in neuroscience outside education depend on stakeholder contexts. Hacking (2004) articulated medical interests as an example. Neuroscientific findings and programs in the in nonmedical issues that bear on national security (National Research Council 2008) are also of interest to federal and military agencies in the USA. In 2008, the NRC published the document, Emerging Cognitive Neurosciences and Related Technologies, in which an attempt is made to address ways in which neuroscientific knowledge could be used to eventually develop usable “future warfighting applications” (p. 14) for the intelligence community. Such applications would have neuroscience associated with the following tasks: (1) “read” the “cognitive states and intentions of persons of interest;” (2) “enhance” the “cognitive capacities” of soldiers (how to make them learn faster and process information more quickly and precisely than usual, how to help them make correct decisions when engaged in battle); (3) “control” the “states and intentions” of oneself (e.g., pain, fear) and others (e.g., “disrupt” an “enemy’s motivation to fight”), and: (4) “drive devices” via “cognitive states” (e.g., using white noise to impair senses, using neuropsychopharmacology to develop drugs that “target specific sensory receptors”) (pp. 16–17).

  2. 2.

    Sensory memory lasts for a few seconds and quickly keeps and discards copies of immediately acquired visual and auditory information. Short-term memory (STM) is a short-term storage of information transferred from sensory memory and does not manipulate the acquired information. STM provides a space for engaging in quick calculations and holds visual and auditory information. Working memory (WM) is the active operational component in STM. It actively processes information acquired in STM and is central in the development of language, reading, mathematics, and problem solving. WM also deals with attentional resources in STM such as the ability to concentrate on one aspect of a target object and shutting off others. Long-term memory (LTM) stores information over periods of time and is organized via schemes that join together to form new knowledge structures. Readers are referred to Menon (2010) for an extended discussion of the neuroanatomical correlates of working memory and other relevant cognitive processes relevant in the development of mathematical thinking and skills.

  3. 3.

    In particular, it is worth noting the interesting methodological reflections of Poldrack (2006) and Henson (2006) concerning ways functional neuroimaging data are employed in developing arguments that they term as forward and reverse inferences, which involve establishing relationships between cognitive functioning and brain activation; for ethical issues involving neural-based reverse inferences, see Poldrack 2008. Forward inferences are deductively valid, and proceeds from assessing neural activity on the basis of performing certain cognitive tasks. Reverse inferences are deductively invalid since they involve making conclusions about cognitive functioning on the basis of brain activation. For Poldrack (2006),

    cognitive neuroscience is generally interested in a mechanistic understanding of the neural processes that support cognition rather than the formulation of deductive laws. To this end, reverse inference might be useful in the discovery of interesting new facts about the underlying mechanisms. Indeed, philosophers have argued that this kind of reasoning (termed ‘abductive inference’ by Peirce), is an essential tool for scientific discovery” (p. 60).

    However, Henson’s (2006) point below is a reminder about being mindful of neuroscientific claims:

    [I]t is important to think carefully about the type of inferences that can be made from functional neuroimaging data… only by making these caveats and assumptions explicit, and criticizing them, will we be able to assess the real value of functional neuroimaging for cognitive science” (p. 68).

  4. 4.

    Kaufmann (2008) points out that current fMRI experiments are restricted to 5-year-old children and older because “fMRI technique requires participants to be awake and respond to stimuli presented in the (narrow and very noisy) scanner environment while simultaneously task-processing related changes in the blood oxygen consumption in different brain regions are recorded” (pp. 2–3).

  5. 5.

    See Varga et al. (2010) and Nieder (2005) for syntheses of research comparing human and animal competence involving concepts of counting, cardinality (numerical quantity), and order (rank) from neuroscientific and neurobiological perspectives. For fMRI comparisons between children and adults involving different aspects of arithmetical processing, see Rocha et al. (2005) and Kawashima et al. (2004). See Ansari (2009) for a review analysis of results drawn from various neuroscientific studies that focused on developmental disorders and difficulties involving numerical cognition and relevant mathematical processes.

  6. 6.

    Current interests in the implications of approximate number sense are linked to its possible reverse-inferential relationship to school mathematics achievement for both children and adults. For example, based on a longitudinal assessment of 64 14-year-old children with normal development that started in kindergarten, Halberda et al. (2008) established a strong correlation between individual children’s approximate number sense and their past scores on standardized school mathematics achievement tests. Mazzocco et al. (in press) established a strong correlation between domain-specific deficits in approximate number processing and persistently deficient mathematics achievement among children with mathematical learning disabilities (i.e. those who scored below the 10th percentile in a mathematics achievement test).

  7. 7.

    See Gentilucci and Corballis (2006) for an interesting and though-provoking neuroscientific-based account of the evolution of speech and language from manual gestures to vocal communications (i.e. “gestural-origins theory;” an account that differs from the typical sound-to-language perspective).

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  1. San Jose State University, San Jose, CA, USA

    Ferdinand Rivera

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  1. Fac. Education, Monash University, Wellington Road, Clayton, 3800, Victoria, Australia

    Helen Forgasz

  2. Dept. Mathematics, San Jose State University, Washington Square 1, San Jose, 95192, California, USA

    Ferdinand Rivera

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Rivera, F. (2012). Neural Correlates of Gender, Culture, and Race and Implications to Embodied Thinking in Mathematics. In: Forgasz, H., Rivera, F. (eds) Towards Equity in Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27702-3_47

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