Big Ideas in Infinite Processes: For Future Mathematics Teachers (Big Ideas in Mathematics for Future Teachers)

This book was written to prepare future teachers for the mathematical work of teaching. The focus of this module is infinite processes, and this means we are going to eventually get to the big ideas of calculus. We know that right about now you’re thinking, Calculus? I’m not going to be teaching calculus to my seventh grade class. Okay, probably not. But the types of ideas that lead to calculus and the kind of thinking required will be a part of your middle grades curriculum, and we have the examples to prove it. The ideas in this book are fundamentally important for your students to understand and so they are fundamentally important for you to understand. In addition, the ideas of calculus are truly stunning and beautiful. Just you wait and see.

As mathematicians, we try to convey to you the beauty of our subject. Mathematicians view mathematics as the study of patterns and structures. We want to show you how to reason like a mathematician – and we want you to show this to your students too. This way of reasoning is just as important as any content you teach. When you stand before your class, you are a representative of the mathematical community; we will help you to become a good one.

No one can do this thinking for you. Mathematics isn’t a subject you can memorize; it is about ways of thinking and knowing. You need to do examples, gather data, look for patterns, experiment, draw pictures, think, try again, make arguments, and think some more. The big ideas of probability and statistics are not always easy.

Each section of this book begins with a Class Activity. The activity is designed for small-group work in class. Some activities may take your class as little as 30 minutes to complete and discuss. Others may take you two or more class periods. No solutions are provided to activities – you will have to solve them yourselves. The Read and Study, Connections to Teaching, and Homework sections are presented within the context of the activity ideas.