ABSTRACT
Current discourse about the desirable ends of mathematics teaching and learning centers on the development of mathematical understanding and
mathematical power - the capacity to make sense with and about mathematics (cf. California State Department of Education, 1985; National Council of Teachers of Mathematics, 1989; National Council of Teachers of Mathematics, 1991; National Research Council, 1989). Learning mathematics with understanding, according to this view, entails making connections between informal understandings-about mathematical ideas, quantitative and spatial patterns, and relationships - and more formal mathematical ideas. Connections must be forged among mathematical ideas (Fennema, Carpenter, & Peterson, 1989). Students must develop the tools and dispositions to frame and solve problems, reason mathematically, and communicate about mathematics (National Council of Teachers of Mathematics, 1989).
