Models and mathematics

Although there is reasonable agreement about which mathematical ideas should be taught in the elementary school (Begle 1966) and that these ideas should be taught meaningfully (Dawson and Rud-dell [a] 1955), there is little agreement on how learning environments should be structured to facilitate this learning. One reason for this lack of agreement is an inadequate recognition of the role that concrete and symbolic models can and should play in facilitating the learning of mathematical ideas.