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1. Why is paper-and-pencil multiplication difficult for many people?

Author

Speiser, Robert, Schneps, Matthew H., Heffner-Wong, Amanda, Miller, Jaimie L., and Sonnert, Gerhard

Subjects
*PENCILS, *PAPER, *MULTIPLICATION, *SCHOOLS, *ALGORITHMS, *COGNITIVE learning theory, *SHORT-term memory
Abstract

Abstract: In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in neuroscience, we trace the flow of arithmetic information to emphasize demands on visual working memory and attention. We predict that algorithms that make moderate demands on memory and attention will work better than others that make stronger demands. We suggest that the judicious use of spatial schemas can reduce such cognitive demands. Experimental evidence from children in an inner-city school supports this claim. Our work suggests new ways to think about instruction. The goal should be to minimize demands that present obstacles and maximize instead what human eyes, bodies, and brains do well. [Copyright &y& Elsevier]

Published
2012
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2. Intraoperative mapping of the cortical areas involved in multiplication and subtraction: an electrostimulation study in a patient with a left parietal glioma

Author

R Van Effenterre, L Cohen, Dominique Denvil, F.M. Gasparini, Laurent Capelle, Hugues Duffau, and M. Lopes

Subjects
Paper, Adult, medicine.medical_specialty, Brain mapping, Angular gyrus, Postoperative Complications, Neuroimaging, Parietal Lobe, medicine, Humans, Attention, Dominance, Cerebral, Problem Solving, Mathematics, Cerebral Cortex, Brain Mapping, medicine.diagnostic_test, Brain Neoplasms, Parietal lobe, Subtraction, Magnetic resonance imaging, Glioma, Magnetic Resonance Imaging, Electric Stimulation, Psychiatry and Mental health, Surgery, Multiplication, Female, Neurology (clinical), Radiology, Occipital Lobe, Occipital lobe, Neuroscience, Follow-Up Studies
Abstract

Objectives: Advances in neuroimaging studies have recently improved the understanding of the functional anatomy of the calculation processes, having in particular underlined the central role of the angular gyrus (AG). In this study, the authors applied this knowledge to the surgical resection of a glioma invading the left AG, by localising and sparing the cortical areas involved in two different components of calculation (multiplication and subtraction), using direct electrical stimulations. Methods: A calculation mapping was performed in a patient without deficit except a slightly impaired performance for serial arithmetic subtraction, during the resection under local anaesthesia of a left parieto-occipital glioma invading the dominant AG. After somatosensory and language mappings, cortical areas involved in single digit multiplications and subtractions of seven were mapped using the method of electrostimulation, before glioma removal. Results: Distinct sites specifically involved in multiplication or subtraction were detected within the left AG, with a precise spatial distribution and overlapping. All the eloquent (somatosensory, language, and calculation) areas were surgically spared. Postoperatively, the patient had a transient complete deficit for arithmetic subtraction, without either multiplication or language disturbance. The tumour removal was complete. Conclusions: These findings suggest: firstly, the usefulness of an intraoperative calculation mapping during the removal of a lesion involving the left dominant AG, to avoid permanent postoperative deficit of arithmetic processes while optimising the quality of tumour resection; secondly, the possible existence of a well ordered and dynamic anatomo-functional organisation for different components of calculation within the left AG.

Published
2002