Advanced Math for Young Students

Phil Keller sent me a copy of his beautiful new book Advanced Math for Young Students.

(Here's his blog. And here's an early review!)

I told Phil, as soon as I laid eyes on the book, that it has the look and feel of an authored work, nothing like the many-authored splendor of a typical commercial textbook.

Plus (and I have to say this) the cover and pages are creamy and smooth, a throwback to the physical beauty of books pre-crash (although of late I've had the sense that decent paper may be making a comeback).

The book is so compelling I may have to buy a second copy to work through myself so the other one can stay on the coffee table.

From the Introduction:

For 26 years, I have been a high school physics teacher. I work in an excellent, well-regarded high school and I have been fortunate to have many talented students who soak up all the physics I can teach them, and more. But every year, I also teach students who struggle to master the topic, despite their great efforts and mine. And I know from discussions with colleagues, both within my school and arose the country, that we are not the only ones struggling. There is something getting in our way. Maybe this will seem obvious to anyone who has struggled in physics, but here's what I think: I think it's the math.

Physics applies math. It's all about finding relationships and solving the puzzles that the laws of physics present. For the most part, this work is done in the language of mathematics, and more specifically, the language of algebra. So to be comfortable learning physics, a student has to be fluent in that language. Algebra cannot just be a memorized set of procedures for finding 'x'. It has to be a symbolic way of representing ideas. But for many students, that level of fluency is not attained unjust one year of algebra--which is all that many students have had when they start studying physics. It's no wonder that some struggle.

It is not only physic students who struggle. For even more than 26 years, I have been teaching students how to prepare for the math portion of the SAT. What I have seen over the years is that most students are not fluent enough in algebra to successfully apply algebra on the SAT. One goal of my SAT course is to teach alternative, non-algebraic approaches to SAT problems. It is also a major theme of my math SAT book, The New Math SAT Game Plan. And I will tell you something you may find surprising (or even distressing): on the SAT, these non-algebraic methods work very nicely. They won't get you to an 800, but they will take you pretty far. And even my top scorers report that they like to mix in the non-algebraic methods along with the standard approaches (which, as top students, they also know how to use).

The non-algebraic methods, however, won't get you very far in physics. In fact, a student who does not really learn the language of algebra is going to struggle in all later math and science classes: physics, statistics, computer science and beyond. That STEM door is swinging closed because one year of algebra class did not lead to sufficient fluency. So why spend only one year? Why not start earlier?

I am not saying every 7th grader should be in a high-school version of Algebra I. But I am saying that every middle school student should, over the course of the middle school years, start learning about and thinking about the ideas of algebra (even some ideas that won't reappear until Algebra II or Pre-calculus). These are ideas that take some time to ponder.