I have many wonderful books to recommend.
Not least my own. If you’re reading this and do not own a Teacher Edition for Which One Doesn’t Belong? I need you to fix that situation before reading further. Because clearly you’ve found value in the words and ideas on this site, and the book is a better, more focused version of those ideas.
But I’m not here today to push my book. No, I’m here to get another thing on your reading list. First a prelude.
People (well some people, who are not me anyway) like to carry on about differences between elementary school math and high school math. When they do, they fall into one of two camps.
- You have to commit the facts and techniques of arithmetic to memory before you can use them to think, and to do real math.
- You can play around with the early, intuitive ideas of math, but when you get to algebra (or trigonometry, or calculus, or whatever) the game changes and you need to be told stuff. Then you need lots of practice with what you’ve been told.
That these two make opposite assumptions about elementary math, and also about secondary math should suggest to us that people are just choosing to look at things from a perspective rather than describing the true nature of the discipline.
Whatever the eventual fate of the Common Core State Standards for Mathematics, hopefully one of its lasting legacies will be an understanding that mathematics as a discipline is more than content, and that this should be represented in school mathematics. Where this appears in the standards is the Standards for Mathematical Practice (SMP).
Aside…true story: I once spoke at length to a producer at a semi-famous radio show as she did background on the question How Much Math Should Everyone Know? 20 minutes of conversation before it became clear that this person hadn’t read the SMP. Andrew f-ing Hacker was going to be on the program assailing the state of mathematics teaching in this country and the producer hadn’t read the Standard for Mathematical Practice. I was livid. But back on task now…
An important thing to know about the Standards for Mathematical Practice is that they pertain across all levels of mathematical activity. These are K—12 standards, but they describe the kinds of activity that distinguish math as a discipline.
But I’m here today to tell you that Mike Flynn has taken the high road and done the much more challenging job of treating each of these standards right.
Flynn structured his book Beyond Answers around the Standards for Mathematical Practice—one chapter per standard. He illustrates each with a vignette from his own life demonstrating the utility of the practice in his own daily life, with vignettes from classrooms, and with clear writing demonstrating the very real and important mathematical work of which young children are capable.
On its surface, this is a book about elementary children doing mathematics. But it’s really a book about people doing mathematics. If you’re a secondary or post-secondary teacher, and you read this book without seeing important connections to the work that you do, I’ll buy you a cup of coffee so we can talk about that.
Ultimately, my own critique of the SMP was about them being too numerous to remember, and about them overlapping in ways that make it difficult to communicate their individual importance. I still have those critiques. Flynn doesn’t convince me (nor does he try) that this is the perfect set of such standards. But he doesn’t need to do that.
These are the standards we have. They resonate at all levels of mathematical activity, and in Beyond Answers, Mike Flynn shows convincingly that young children’s mathematical work is not fundamentally different from that of older students. Mathematics as an intellectual discipline is alive and well.