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| To Prospective Teachers In this course you are the student. However, this is an important time for you to begin thinking like the teacher you will become. This is the time to begin thinking about the nature of mathematics and about teaching and learning mathematics. You can do this by monitoring your own thoughts and feelings as you explore and investigate, and by making notes about how you might change or adapt an activity for use in an elementary or middle school classroom. This book was written to help you experience some of the mathematical ideas you will soon be teaching and to provide methods for teaching them to your students. You will construct models, use manipulatives, work cooperatively, explore, investigate, discover, make conjectures, and form conclusions. You will find that the models and manipulatives that accompany this book can be used with children. When you have opportunities we encourage you to try appropriate activities with children and, by observing and asking questions, try to understand how they are thinking about mathematics. Eleanor Duckworth used her observations of children learning in her book, The Having of Wonderful Ideas and Other Essays on Teaching and Learning, where she makes these comments: 1 So what is the role of teaching, if knowledge, must be constructed by each individual? In my view, there are two aspects to teaching. The first is to put students into contact with phenomena related to the areas to be studied--the real thing, not books or lectures about it--and to help them notice what is interesting; to engage them so they will continue to think and wonder about it. The second is to have the students try to explain the sense they are making, and, instead of explaining things to students, to try to understand their sense. These two aspects are, of course, interdependent: When people are engaged in the matter, they try to explain it and in order to explain it they seek out more phenomena that will shed light on it. 1New York: Teachers College Press, Columbia University, 1987, p. 123. |