How Mathematics Propels the Development of Physical Knowledge

Three studies examined whether mathematics can propel the development of physi-cal understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Dis-crete quantities led to age typical performances. Continuous quantities caused per-formances like those of 5-year-olds. In Experiment 2, 11-year-olds solved problems with feedback. They were encouraged to use math or words to justify their answers. Children who used math developed an understanding superior to most adults, whereas children who used words did not. In Experiment 3, 9-year-olds solved prob-lems with or without prompts to use math. Children encouraged to use math exhib-ited greater qualitative understanding, even though they were unable to discover met-ric proportions. The results indicate it is possible to design symbolic experiences to propel the development of physical understanding, thereby relating developmental psychology to instructional theory. Mathematics, diagrams, and other explicit representations help scientists discover and organize complex empirical relations and this also may be true for the develop-ing child. The proposal that external representations and organizing activities con-tribute to development comes from Vygotsky’s (1978) foundational insight that