Three apparently unrelated developments have significant implications for the teaching of mathematics at the primary level. First, psychology labs specializing in child development report from Geneva that an operation is something that can be performed externally with concrete materials or internally with symbols representing those materials. It has been demonstrated that the probability of consistently performing internal operations accurately is increased by repeated experiences with the external, concrete models (Piaget [13], Bruner [3], and Flavell [5]*). Secondly, both the Woods Hole Conference (Bruner [3]) and the Kational Committee of the NEA Project on Instruction [11] have indicated that one of the most important considerations of instruction is that it should be based on the structure of the particular discipline being taught. Finally, in the 1964 Yearbook of the ASCD [1] it has been pointed out by Dehann and Doll that individual differences are based not solely on rate of learning, but rather on numerous factors, and that learning is both unique and personal.
On the Teaching of Mathematics in Elementary Schools, and its Continuity with the Teaching in Secondary Schools