The purpose of this book is to explain the reasons for the main rules learned in middle school and high school mathematics (i.e., for 6th through 12th grade), and this ebook contains the entirety of the first two chapters.

Dr. Kelley's goal throughout the book is to explain why the rules work the way they do. Applications to real world problems are also sometimes mentioned, but the focus here is on the math itself. For most rules, instead of giving rigorous proofs, Andrew explains the essence for why the rules work. He focuses on the heart of why they are true. This book was written as a supplement to traditional curriculum.

The present ebook sold on leanpub contains the entirety of the first two chapters. The first is on fractions, and the second is on pre-algebra.

Reviews of Understand Math:

Andrew's "process is the same as that used by excellent teachers interacting with students to help them develop understanding." Cathy Duffy, homeschool curriculum reviewer

"I thought the fractions chapter was quite clear and easy to understand and follow." - Elizabeth Mayner, former homeschool mom

"I completed chapter 1 and really enjoyed the process of relearning and better understanding fractions! Your examples are easy to identify with, your explanations are clear, and your conversational style made me feel like I had the help of a tutor via the text." - Gayle Meredith, senior library associate

"Dr. Andrew Kelley's Understand Math: Reasons for the Rules is a delight to read." Elizabeth Trotter, homeschool mom and blogger

"So far, I’m loving it!...I really like your descriptions and how you develop ideas/concepts, especially in discussing the inherent properties of seemingly simple ideas (which, of course, are not usually simple)...I also very much like how you explain the logic and thought processes behind each concept. You present so much more than a set of rules ..." Erica Hastert, PhD, college math teacher

"Most math teachers (and students!) are deeply familiar with the common impulse in mathematics education to “just learn the formula,” apply it, and move on. After all, that’s the goal, right? Well, actually no, not if you really want to learn mathematics. What I so appreciate about Andrew Kelley’s work is his relentless emphasis on understanding real mathematics – the ‘why’ behind the formula – and his skillful explanation that makes those beautiful concepts accessible to the student. I believe Andrew’s work can turn what many students experience as dull and dry manipulation of indecipherable symbols into a delightful exercise in finally understanding the beauty, usefulness, and design of mathematics. You won’t be disappointed." - Jim DeKorne, retired math teacher and former principal of Colorado Springs Christian Schools

You can find more reviews at the author's website. There you can also find a free sample of the whole book, containing parts of all twelve chapters. (The ebook sold on leanpub instead is the entirety of the first two chapters.)

https://UnderstandMathRules.com/

At that website, you can also find comparisons with other math textbooks, a FAQ, links to YouTube math videos, and the author's email.