Big Ideas in Numbers and Operations: for Future Teachers (Big Ideas in Mathematics for Future Teachers)

This book is part of a series of inquiry-based textbooks for math content courses to prepare future teachers for the mathematical work of teaching. This module focuses on Arithmetic, and is designed to serve as a first 4-credit course in mathematics for elementary teachers. Topics include mathematical thinking and behavior, sets and operations, place-value numeral systems, models and algorithms for arithmetic operations, integer arithmetic, elementary number theory, fractions, decimals, percents, ratios, rates, and proportional reasoning. As mathematicians we want to convey the beauty of our subject. We view mathematics as the study of patterns and structures. We want to show our students how to reason like a mathematician – and we want them to show this to their students too. This way of reasoning is just as important as any content they will teach. Mathematics isn’t a subject you can memorize; it is about ways of thinking and knowing. To do mathematics, 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 mathematics are not always easy – but they are fundamentally important for students to understand and so they are fundamentally important for future teachers to understand.Each section of our books begins with a Class Activity. This problem-based inquiry is designed for small-group work in class. Some activities may take as little as 30 minutes to complete and discuss. Others may take two or more class periods. The Read and Study, Connections to the Curriculum, and Homework sections are presented within the context of the activity ideas. No solutions are provided to activities or homework problems – students will have to solve them and discuss them themselves. Read more