ABSTRACT
Like Georgine, many students today perceive mathematics to be a bunch of numbers that plug in to formulas to solve problems. More often than not, the problems they are asked to solve are not their problems, nor do they come close to something they are interested in pursuing. Georgine's experiences with mathematics are similar to those that I had as a mathematics student-the mathematics that I learned focused on finding the teacher's or the book's answer to a problem. But when I studied mathematics methods at Brooklyn College, my classmates and I explored a different kind of teaching and learning. Rather than lecture us about what we needed to know, Professor Geddes invited us to experience mathematics as a dynamic discipline that sometimes required tools such as toothpicks, geoboards, or mirrors to resolve thoughtprovoking problems. Her definition of mathematical competence clearly went beyond numbers and computations; she included in her definition of a mathematically competent person the ability to test a hypothesis, find patterns, and
communicate understanding-all of which are recommended today by the National Council of Teachers of Mathematics (NCTM) as essential elements of both teaching and learning mathematics. NCTM recommends that we teach and assess students in very different ways from the way Georgine is being taught. The new goals and directions are exemplified in the NCTM Curriculum Standards documents, which focus on K-12 curriculum and assessment, and in the professional development of teachers. The overall goal of the NCTM documents is to promote standards that will help teachers and curriculum developers better prepare students for the twenty-first century.
