id: 06367015
dt: a
an: 2014f.00029
au: Clements, McKenzie (Ken) A.
ti: Fifty years of thinking about visualization and visualizing in mathematics
education: a historical overview.
so: Fried, Michael N. (ed.) et al., Mathematics and mathematics education.
Searching for common ground. Dordrecht: Springer (ISBN
978-94-007-7472-8/hbk; 978-94-007-7473-5/ebook). Advances in
Mathematics Education, 177-192 (2014).
py: 2014
pu: Dordrecht: Springer
la: EN
cc: A30 D20 D40 C30
ut: visual image; visualization; mathematics learning; problem solving; item
response theory; verbal-analytic processing; visual processing
ci: ME 1992a.00416; ME 1992a.00418
li: doi:10.1007/978-94-007-7473-5_11
ab: Summary: This chapter surveys meanings given to the term “visualization"
in mathematics, mathematics education, and psychology, and considers
the evidence for the oft-heard assertion that mathematics learners tend
to prefer to think algorithmically rather than visually. The analysis
reveals that students who do very well on pencil-and-paper
“visualization" tests often prefer not to use visual methods when
attempting to solve mathematical problems; and those who do not do well
on standard visualization tests often describe themselves as “visual
thinkers", and prefer to use visual methods when attempting to solve
mathematics problems. The influence of various mathematics educators,
and especially Alan Bishop ‒ who thought of visualization in terms of
a person’s use of visual images when posing and solving mathematics
problems ‒ of Norma Presmeg, and of a group of mainly Israeli
mathematics educators who developed the construct “concept image", is
also examined. Views of some mathematicians are also taken into
account. In the early 1990s, {\it W. Zimmermann} (ed.) and {\it S.
Cunningham} (ed.) [Visualization in teaching and learning mathematics.
Washington, DC: Mathematical Association of America (1991; ME
1992a.00416)] wrote of how David Hilbert had spoken of two tendencies
in mathematics ‒ one that sought to crystallize logical relations,
and the other to develop intuitive understanding, especially through
“visual imagination". In addressing that theme, {\it T. Eisenberg}
and {\it T. Dreyfus} [in: Visualization in teaching and learning
mathematics. Washington, DC: Mathematical Association of America.
25‒37 (1991; ME 1992a.00418)] spoke of mathematics students’
preference for “algorithmic over visual thinking". The paper draws
special attention to the work of two lesser-known mathematics education
researchers, Nongnuch Wattanawaha and Stephanus Suwarsono. It was
Suwarsono who devised and applied a method whereby learner preferences
for visual or verbal thinking, as well as the “visualities" of the
mathematics tasks themselves, could be measured and calibrated on the
same scale, using item response theory.
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