## Multiple Mathematical Intelligences
The report, ``Sources of Mathematical Thinking: Behavioral and Brain-Imaging Evidence'', demonstrates that there are at least two different loci in the brain involved in arithmetic and that the two loci do different things. - Exact calculation is accompanied by a ``large and strictly left-lateralized activation in the left inferior frontal lobe''.
- Approximate calculation tasks activate a region in the bilateral inferior parietal lobule.
The mathematical mind: exact calculation locus in the left inferior frontal lobe; approximate calculation locus in the bilateral inferior parietal lobule. These two loci are also associated with other mental activities: - The left inferior frontal lobe is also activated during verbal association tasks; the behavioral aspect of this research, a set of experiments with bilingual subjects, shows that in fact exact calculation is language linked, whereas approximate calculation is not.
- The authors remark that bilateral inferior parietal loci are also activated during visually guided hand and eye movements and mental rotation. In an essay in the same issue of
*Science*, Brian Butterworth points out that the proximity of the areas that control finger movements and approximate calculations ``raises the possibility that these brain regions contribute to finger counting and finger calculation ... and prompts the suspicion that the parietal lobes, in the course of development and learning, come to support the digital representation of numbers.'' Presumably this refers to a preverbal ideation of number, with the first three fingers coming to represent the equivalence class 3, etc.
The report concludes with a discussion of the evolutionary difference between exact calculation and approximate. - ``Symbolic arithmetic is a cultural invention specific to humans, and its development depended on the progressive improvement of number notation systems.'' i.e., of mathematical language.
- ``Approximate arithmetic, in contrast, shows no dependence on language ... An interesting, though clearly speculative, possibility is that this language-independent representation of numerical quantity is related to the preverbal numerical abilities that have been independently established in various animal species and in human infants.''
- ``Together, these results may indicate that the human sense of numerical quantities has a long evolutionary history, a distinct developmental trajectory, and a dedicated cerebral substrate. In educated humans, it could provide the foundation for an integration with language-based representations of numbers. Much of advanced mathematics may build on this integration.''
Dehaene goes deeper into the philosophical, humanistic, and pedagogical implications of his research in an
-are each ``a capacity, with its component processes, that is geared to a specific content in the world (such as musical sounds or spatial patterns)''. This quote is from his Reflections on Multiple Intelligences: Myths and Messages, where he also mentions that ten years later he proposes adding to the list an eighth intelligence, that of the naturalist. The experimental results of Deheane, Spelke, and their collaborators strongly suggest that mathematical ability must involve at least three of Gardner's intelligences: the logical-mathematical (by definition), the spatial, and the linguistic. The concept of multiple mathematical intelligences was put forth, almost at the same time, in a work called
When I came across Burns's book I was very pleased to see explicitly written out, for the first time, what I had felt as a mathematician for many years: there are different kinds of mathematical minds. Besides helping me make sense of a career spent in departments with logicians, analysts, and algebraists, it made me very receptive to the ``rule of three'' as propounded by the members of the Harvard Calculus Consortium, which has become the Rule of Four in the second edition of their -- |
Welcome to the These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics. Search Feature Column Feature Column at a glance |