
06367015
a
2014f.00029
Clements, McKenzie (Ken) A.
Fifty years of thinking about visualization and visualizing in mathematics education: a historical overview.
Fried, Michael N. (ed.) et al., Mathematics and mathematics education. Searching for common ground. Dordrecht: Springer (ISBN 9789400774728/hbk; 9789400774735/ebook). Advances in Mathematics Education, 177192 (2014).
2014
Dordrecht: Springer
EN
A30
D20
D40
C30
visual image
visualization
mathematics learning
problem solving
item response theory
verbalanalytic processing
visual processing
ME 1992a.00416
ME 1992a.00418
doi:10.1007/9789400774735_11
Summary: This chapter surveys meanings given to the term ``visualization" in mathematics, mathematics education, and psychology, and considers the evidence for the oftheard assertion that mathematics learners tend to prefer to think algorithmically rather than visually. The analysis reveals that students who do very well on pencilandpaper ``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. 2537 (1991; ME 1992a.00418)] spoke of mathematics students' preference for ``algorithmic over visual thinking". The paper draws special attention to the work of two lesserknown 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.