Book Review: Another Sort of Mathematics: Selected Proofs Necessary to Acquire a True Education in Mathematics

Recently I was invited to take a look at J. Jacob Tawney's new book, Another Sort of Mathematics: Selected Proofs Necessary to Acquire a True Education in Mathematics. While so much of the work I do is in elementary education, it was a nice invitation to read a book that would challenge me mathematically and encourage me to look at mathematics as a whole. Having heard Tawney speak at the National Symposium for Classical Education (where I will also be speaking in February), I was familiar with Tawney's love for mathematics and was excited to explore more examples.

Diving Into Another Sort of Mathematics

The book is divided into four sections:

1. The Nature of Mathematics

2. 10 Proofs Everyone Ought to Know

3. 10 Theorems Worth Knowing (Though the Proofs Are Difficult)

4. 10 Unsolved Problems Worth Knowing

The first part of the book really resonated with me and the work that I do. Tawney spends time defining true mathematics and its nature. In a world where mathematics has just become a subject to check off from a list, I was excited to read more about the beauty of mathematics. All math educators should recognize this big picture of mathematics as something much more than a list of objectives to help understand why we teach it, and Tawney does a great job of explaining it.

The second part of the book dives into ten proofs that all educators should know. Many of my professional development sessions try to help teachers understand why algorithms, formulas and procedures work. These ten proofs are an excellent place to start to develop that type of thinking. They helped me consider how math fits together across grade levels, and why it matters that we as teachers understand not just what we’re teaching, but why it works.

The third and fourth parts were more advanced as Tawney describes more difficult proofs. They reminded me of the proofs I studied in college-level math theory and activated parts of my brain I haven’t used in a while working primarily with K-8 educators. However, it was completely worth the time to go to that depth. These are the kinds of problems you may need to read, step away, and return to later in order to really engage with them.

Using this Book for Your Own Professional Learning

Educators spend so much time learning their own math curriculum without looking at the full picture of mathematics. It's worth the time to take a few minutes to refresh what you learned about mathematics theory to make the most of your own curriculum.

If I were to read this book alongside my peers in a book study, I would almost break it into three sections:

• Part 1: The Nature of Mathematics would be an ideal part to talk about why we teach mathematics and to come up with a common definition within a school. It would help educators to have some meaningful conversations about their own experiences with mathematics and how students should interact with it.

• Part 2: 10 Proofs Everyone Should Know has a perfect title. All educators from K-12 really should understand these proofs. I almost wanted this section to be a workbook where I could write and solve with Tawney with my own notes. I could see a group of educators folding paper, drawing models and using manipulatives to really understand these proofs.

• Parts 3 and 4 would definitely be an extension. As someone who likes to read and then process information, it took me a lot longer to work through those proofs. I wanted to truly process them and consider other examples.

Final Thoughts

Jacob Tawney’s passion for mathematics is clear throughout this book. He writes to help educators and learners alike develop not just mathematical knowledge, but mathematical thinking. If you’re ready to be challenged, this book will do that. And it will leave you thinking differently about how you teach mathematics.

Disclosure: I was provided a copy of this book by Jacob Tawney in exchange for an honest review. This post contains an affiliate link. If you choose to purchase through the link below, I may earn a small commission at no extra cost to you.

👉 Click here to purchase Another Sort of Mathematics on Amazon (affiliate link)