Dh. Uttal et al., MANIPULATIVES AS SYMBOLS - A NEW PERSPECTIVE ON THE USE OF CONCRETE OBJECTS TO TEACH MATHEMATICS, Journal of applied developmental psychology, 18(1), 1997, pp. 37-54
This article offers a new perspective on the use of concrete objects t
o teach mathematics. it is commonly assumed that concrete manipulative
s are effective because they allow children to perform mathematics wit
hout understanding arbitrary, written mathematical symbols. We argue t
hat the sharp distinction between concrete and abstract forms of mathe
matical expression may not be justified. We believe instead that manip
ulatives are also symbols; teachers intend for them to stand for or re
present a concept or written symbol. Consequently, research on how you
ng children comprehend symbolic relations is relevant to studying thei
r comprehension of manipulatives. We review evidence that ma ny of the
problems that children encounter when using manipulatives are very si
milar to problems that they have using other symbol systems such as sc
ale models. Successful use of manipulatives depends on treating them a
s symbols rather than as substitutes for symbols.