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Big Ideas in Mathematics for Future Elementary and Middle Grades Teachers

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Big Ideas in Mathematics for Future Elementary Teachers and Big Ideas in Mathematics for Future Middle Grades Teachers and Math Specialists 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 teachers for the mathematical work of teaching.

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. Click on the links to download the PDFs for the most current version of each text.

The Big Ideas in Mathematics for Future Elementary Teachers series has three textbooks:


The Big Ideas in Mathematics for Future Middle Grades Teachers and Math Specialists series has four textbooks:




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.


We frequently update these texts to respond to our student needs. The texts for Elementary Number and Operations and for Middle School Algebra will be revised this summer, and the new versions should be "published" by August 1, 2018. The PDFs for these texts will be updated at that time.

We also plan on making these texts available through an on-demand printing service (such as for you and your students to purchase a printed hard copy at cost. That option should be in place by the end of Summer 2018.


Please email for inquiries on using these texts in your math class for preservice teachers.

by Kuennen, Eric W last modified Jun 21, 2018 10:33 PM
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