Representing Mathematical Concepts to Two- and Three-Year-Olds Through Action, Image, and Word: An Experimental Comparison of Teaching Methods.

Three experiments concerned with methods of teaching mathematical concepts to 2- and 3-year-olds were carried out. The first experiment, in which 12 children were taught the concepts "fat" and "skinny," showed that (1) explicit verbal representation of the concepts was a more effective instructional technique than formulation in terms of an extrinsic reinforcer, and (2) a variety of concrete examples has an adverse effect on learning when the number of exemplars exceeds the minimum necessary for complete logical definition of a relational concept. The second study, in which 16 children were taught the concept "round," investigated the effects of different amounts of teacher verbalization and different forms of child action; none of the experimental variables significantly facilitated learning. The third study, in which 18 children were taught the concept "square," compared the effectiveness of different forms of verbal representation when combined with visual and proprioceptive feedback. The two instructional variables were number of verbal contexts and use of contrastive terms in the correction procedure. For children who had already learned the meaning of "round," round-square confusions were reduced when the terms were contrasted. A contrastive term did not help a child who did not already know its meaning. Confusions between square and shapes other than round were reduced when the teacher presented the term "square" in a variety of verbal contexts and the child responded by using a square object in a number of action contexts. (Author/SS)