Rebecca Zook - Math Tutoring Online

Have you ever looked at the explanation box in your math book and just felt more confused than you did before?

Words: “For any real numbers a and b, if a^2=b, then a is a square root of b.”

Huh? I can tease the definition apart if I slow my reading speed down to about one mile per hour. But usually things make sense to me a lot faster if I see an example.

Example: “Since 5^2 =25, 5 is a square root of 25.”

Phew… so much better!

What I like about Glencoe Mathematics Algebra 2 book is that it includes both kinds of explanations in the explanation box—Words, Example, and when appropriate, Symbols and/or a Model. I love how this maximizes the chances that students can see the kind of explanation that makes sense to their own brain!

For example, I was working with a student from a very progressive high school, but her Algebra 2 book only had verbal explanations, with no symbols or examples. We pulled out the Glencoe book and found the “explanation box” for the concept we were discussing, and it made SO much more sense to her than just the words did.

This book doesn’t go as far as to include examples for tactile or kinesthetic learners (like Math U See does) but it’s definitely a step in the right direction!

Disclaimer: The sequencing in this book has been confusing to many students, so it’s not perfect.

Related Posts: The Best Algebra Book In the World?
I am SO excited about Math U See!

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In my seven years as math tutor, I’ve probably worked with twenty algebra books. Hands down, no contest, this is the absolute best I have used: Algebra: Structure and Method, Book 1. (Brown, Richard G. et al. McDougal Littell, Evanston, Illinois: 2000.)

This book doesn’t have a ton of frills—there are barely any pictures or “extras.” But
what makes this book exceptional is its GREAT sequencing. It does an excellent job of breaking the math down without dumbing it down. The problems get harder very incrementally. There are so many practice problems to choose from that you can really practice until each procedure becomes second nature. And the book only introduces new concepts once you’ve already mastered the prerequisite skills.

For example, when this book introduces factoring trinomials, it introduces each pattern that you might encounter one at a time. You practice that pattern extensively before facing a new pattern. Once you’ve practiced all the different patterns separately, THEN it mixes all the different patterns together in one problem set. But by now you know how to recognize the different patterns and what to do differently for each pattern. So when faced with a page full of different types of factoring patterns, you can just think, “OH—difference of squares!” or “OH—perfect squares!” instead of having to do trial and error until you erase a hole in your paper!!

The students I’ve used this book with acquire very, very strong algebra skills without getting bored or frustrated. And I think it’s because the sequencing forces students to learn how to “chunk,” a concept I learned from Daniel T. Willingham’s book, Why Don’t Students Like School?

For example, take two algebra students. One is still a little shaky on the distributive property, the other knows it cold. When the first student is trying to solve a problem and sees a(b + c), he’s unsure whether that’s the same as ab + c, or b + ac, or ab + ac. So he stops working on the problem and substitutes small numbers into a(b + c) to be sure he’s got it right. The second student recognizes a(b + c) as a chunk and doesn’t need to stop and occupy working memory with this subcomponent of the problem. Clearly the second student is more likely to complete the problem successfully. (p 31)

Thank you, thank you to those who wrote this book so chunk-fully: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, and William L. Cole!