Peer Review

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations. The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will: • Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more. • Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete). • Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you’re right?” Practice asking these questions of yourself, of your professor, and of your fellow students. • Model with mathematics. You will demonstrate this skill by inventing mathematical notation and drawings to represent physical situations and solve problems. • Use appropriate tools strategically. You will be expected to use computers, calculators, measuring devices, and other mathematical tools when they are helpful. • Attend to precision. You will write and express mathematical ideas clearly, using mathematical terms properly, providing clear definitions and descriptions of your ideas, and distinguishing between similar ideas (for example “factor” versus “multiple”.)

Open (Access) Textbook

This book is useful for a 2-semester treatment of mathematics for elementary teachers.

The book can be used in any of the following formats

• a teacher can use it in class to introduce or deepen into a topic
• some portions of the book can be assigned as homework.
• some exercises can be done individually but then the teacher can switch to work in small groups. The book includes a section called THINK-PAIR-SHARE. This section may lead to group work.

Download as PDF from this site

Can also be used online in a Pressbooks format

Some of the book goals are that students will be able to

• make sense of problems
• persevere in solving them
• reason abstract and quantitatively
• Construct viable arguments and critique the reasoning ofothers.
• Look for and make use of mathematical structure

College Lower Division, College Upper Division

Some basic knowledge of mathematics and geometry

The user needs any type of browser and the book can be downloaded in PDF format.