ABSTRACT
The Institute for the Learning and Teaching of Mathematics is located at the University of Illinois in Chicago. Chicago is a large city with a diverse population — culturally, ethnically, racially and economically. This diversity is reflected in the schools. Most teachers’ major experience of a classroom is that of a transmission line where the teacher is the center, the source of knowledge that is to be transmitted to the students, and the students are passive receivers. The initial objective of the Institute, then, was to provide teachers with the opportunity to experience mathematics as an activity, something you do rather than something you learn, a way of thinking, and a way of looking at and solving problems. We believed that we must present mathematics to teachers so that problem-solving and mathematical thinking are integral components of concept development. If teachers are to recognize that there are many problems in mathematics that have more than one answer and usually many different paths to arriving at an answer, then they need to meet problems of this nature. We must provide them with experiences in problem-solving that require them to use all of their mathematical resources, including executive control and other metacognitive skills. If we want them to understand how children learn and how that learning can be facilitated, we must give them a context to observe these processes in action. Moreover, if we want them to adopt a classroom model different from the transmission model then we must provide them with the experience of the classroom as a dynamic learning environment involving the interaction of three interrelated components — the learner, what is to be learned, and the learning facilitator. They must understand: how learning takes place; mathematics, the nature of the content under study; and how the learning of the mathematics is facilitated. This can only be achieved by experience, in the context of developing and doing mathematics.
