9 THE MATHEMATICAL WORLD
Students' understanding of the Mathematical World has been extensively researched. The Handbook of Research in Mathematics Teaching and Learning. (Grouws, 1992) as well as the papers presented at the "research agenda conferences" on number concepts in the middle grades (Hiebert & Behr, 1988) and on the learning and teaching of algebra (Wagner & Kieran, 1989), reveal that there is a rich and growing research base related to Numbers, Symbolic Relationships, Shapes, and Uncertainty. There is still little research related to Reasoning, however. As in other domains, research has focused on what students understand about mathematical concepts at isolated points in time or on how this understanding evolves naturally in students. Research on instructional interventions that improve student understanding has received less attention.