Two of the most striking and informative results from recent research on children's mathematics learning are the following. On the one hand, many children possess a surprising degree of competence with mathematical situations outside of school. For example, before beginning school, most young children can solve simple addition and subtraction stories, such as “Mary has 8 pennies. She gives 3 pennies to Roger. How many does she have left?” (Carpenter and Moser 1984; DeCorte and Verschaffel 1987; Riley, Greeno, and Heller 1983). In other words, before children have been taught how to add and subtract, they can solve addition and s ubtraction problems. Similarly, older children, as well as adults, can solve a variety of real-world problems using strategies that they have not learned directly in school (Carraher, Carraher, and Schliemann 1987; Lave, Murtaugh, and de Ia Rocha 1984; Scdbner 1984).
James Hiebert is especially interested in how children make sense of written mathematical symbols.