How Mathematics Propels the Development of Physical Knowledge

Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances 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 problems with or without prompts to use math. Children encouraged to use math exhibited greater qualitative understanding, even though they were unable to discover metric 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.