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Mathematical ideas taught in the elementary school can be represented by at least two types of models: concrete (manipulative or enactive) and symbolic. Although there has been much theoretical discussion concerning the value of concrete models in enhancing learning (Kieren, 1969), empirical data are just beginning to accumulate that give some information concerning the efficacy of concrete models (Kieren, 1971), and such data are far from conclusive.
Élizabeth Fennema (Wed,) studied this question.