id: 06145555
dt: j
an: 2013b.00463
au: Speiser, Robert; Schneps, Matthew H.; Heffner-Wong, Amanda; Miller, Jaimie
L.; Sonnert, Gerhard
ti: Why is paper-and-pencil multiplication difficult for many people?
so: J. Math. Behav. 31, No. 4, 463-475 (2012).
py: 2012
pu: Elsevier, New York, NY
la: EN
cc: D70 F30
ut: urban schools; short term memory; difficulty level; mental computation;
neuropsychology; mathematical formulas; instructional innovation;
educational strategies; learning strategies; multiplication; problem
solving; teaching methods; representations; spatial schemata; working
memory; attention; algorithms
ci:
li: doi:10.1016/j.jmathb.2012.08.001
ab: Summary: 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.
rv: