Big Ideas in Mathematics for Future Teachers

Big Ideas in Mathematics for Future Teachers is a series of inquiry-based textbooks written by UW Oshkosh Mathematics faculty for mathematics content courses for pre-service teachers.

The Texts

We wrote these inquiry-based textbooks for our math content courses at UW Oshkosh to prepare future elementary, middle, and high school teachers for the mathematical work of teaching.

The first two books in the series can be used in a standard two-course sequence of mathematics for elementary teachers, while the other four books in the series are intended for mathematics teaching major and minor programs.

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.


We make these textbooks available for free to support inquiry-based learning and teaching in classes for pre-service mathematics teachers. We frequently update these texts to respond to our student needs. Click on the links to download the PDFs for the most current version of each text.

The Big Ideas in Mathematics for Future Teachers series has six textbooks.The first two books in the series can be used in a standard two-course sequence of mathematics for elementary teachers:

The subsequent four books in the series are intended for use in mathematics teaching major and minor programs:

There is also an Instructor’s guide for this series, which explains the pedagogical theories being the texts, provides some analysis of the class activities from the first text in the series so you can see what mathematical processes and concepts can arise out of working on and discussing these problems. This guide is available to Instructors by contacting the authors at

Printed Copies available on Amazon

We also plan on making these texts available through Amazon as an on-demand printing service for you and your students to purchase a printed hard copy at cost. Currently the following titles are available:

New College Algebra Text

We have also written an inquiry-based textbook for College Algebra, which takes a similar approach as our Big Ideas series, adapting many of the same activities from the Modern Algebra textbook, but aimed at a general College Algebra audience. This text is available for download here:

And is available for on-demand printing on Amazon at


These works are licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. To view a copy of this license, visit

In short, you are free to share (copy and redistribute) these material in any medium or format, under the following terms:

Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests that we endorse you or your use.

NonCommercial — You may not use the material for commercial purposes.

NoDerivatives — If you remix, transform, or build upon the material, you may not distribute the modified material.


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Department of Mathematics
University of Wisconsin Oshkosh
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Oshkosh, WI 54901


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Developmental Math Lab
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