ABSTRACT
Psychologists, mathematicians, and mathematics educators are all interested in mathematics learning, but the questions they ask and the perspectives they take sometimes differ in important and even fundamental ways. Mathematicians of course are deeply versed in the content and in the practice of mathematics; educational psychologists are interested in mechanisms and processes involved in learning; mathematics educators are interested in tools and methods to facilitate learning mathematics in particular. Mathematicians talk about "nice problems." The distinction between problems and exercises is important if teachers are interested in problem solving as described by National Council of Teachers of Mathematics during the Standards-based movement. Effective scaffolding in mathematics takes the child's prior knowledge into account so that the support is appropriate for that child. In order to support children learning mathematics with meaning, Jerome Bruner believed that the way ideas were represented should change over time. He described three modes of representation through which students should move as they learn new topics.
