At the beginning of preschool (M = 46 months of age), 197 (94 boys) children were administered tasks that assessed a suite of nonsymbolic and symbolic quantitative competencies as well as their executive functions, verbal and nonverbal intelligence, preliteracy skills, and their parents' education level. The children's mathematics achievement was…

If the principles of languages are applied to the learning of arithmetic, it appears that elementary grade pupils are being introduced to mathematical symbols at too early an age. (MP)

In a study of mathematics learning, taking a rule-oriented approach, students were taught to trade objects of type A for objects of types B and C. Children ranging from ages 7 to 9 were given rules for converting A to B and B to C and were then presented with the task of converting A to C. Of the 30, 6 succeeded. Of the 24 who failed, half were…