The purpose of the mathematics course is to build on your understanding and questions about mathematics and to demonstrate that mathematics can be rewarding to teach with effectively no barriers to success in learning and enjoying the subject. To this end we adopt an approach based, among other things, on exploration, collaboration, reflecting and writing about our experiences, problem-solving and problem-posing, games, history and applications. We will not be particularly concerned about covering a specific list of topics. Rather, the mathematics objectives will be achieved if you make significant progress in enhancing your own knowledge and attitudes towards learning mathematics.
We start by using a variety of exercises and discussion questions to reflect on our past experience, both positive and negative and, in particular to examine the common avoidance of the subject. We will then engage in 'authentic' mathematical activity, that is, mathematics as done by its practitioners, with much guessing and questioning. Through this approach, we hope you will revisit mathematics in a new way. We will create experiences and investigations which will structure your learning and guide your explorations. This will include problems which are not carefully stated, which do not submit to quick and obvious solution, and whose solution might take several hours of investigation.
We then move to working in small groups on investigations, initially chosen by the instructor. During this period, we expect you to develop your abilities to listen to each other, to use the vocabulary of mathematics, and to develop experience in talking mathematics. Eventually, you will pose your own questions. We will create an environment where you will be comfortable in situations you might meet as a teacher where, for example, you have to explain or convince, or where you are confronted by a student who had used a non-traditional approach to solving a problem. We will help you uncover the mathematics in the investigations we do, as well as in everyday situations and materials, for example, card tricks, games, 3-dimensional constructions, paper-folding, knotting.
Once this way of working together has become comfortable, you will be challenged to devise your own investigations which you can use in your classroom to teach curricular topics. Joint sessions in this phase will draw on the extensive curriculum experience of participating teachers to devise appropriate investigations.
Throughout the mathematics sessions, there will be an emphasis on the communication of mathematical ideas not just from instructor to students but from students to instructor and between students. We will use a variety of hands-on materials and involve you in the use of computers for both exploration and communication.
For more details on topics, assignments and expectations, please see the schedules for teachers and for teacher candidates. Topics listed are provided as a guide to the areas of mathematics in which we will anchor investigations although most of the mathematics content of the course will be arithmetic, algebra and geometry.
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revised August 23, 1995