Someone criticized me the other day for trashing a book he wrote that I hadn’t read. I have many failings and yes, trashing books I haven’t read is one of them. I bring this up because of a book I read about here: “Reimagining the Mathematics Classroom: Creating and Sustaining Productive Learning Environments, K-6.”
The title alone tells me it’s a book I won’t like. I’m tired of being told to “reimagine” things as if such things desperately need to be reimagined. In this case, what he reimagines in terms of math education in K-6 are (I’m guessing) the conventional or traditional mode of teaching math which the author of the book describes in the interview:
For most teachers, myself included, K-6 grade mathematics emphasized following procedures to get answers without much concern for how or why these strategies worked, were related or could be adapted to new problems.
One can find by examining textbooks from previous eras, such as the 50’s and 60’s evidence that there were explanations for procedures or strategies, as well as many problems for students to apply such knowledge. Something that does not get talked about in articles such as this, is that over almost three decades, math in K-6 has undergone a transformation thanks in large part to the 1989 math standards of the National Council of Teachers of Mathematics (NCTM) (revised in 2000, and then clarified to little avail in 2006).
Such standards as well as those adopted by states which imitated them carried an underlying message that “Memorization is bad; struggle is good”. This message has been extended somewhat by the Common Core math standards, which carry the “dog whistles” of math reform, as Tom Loveless of Brookings Institution refers to them. The result is that K-6 math education has become a no-STEM zone, in which understanding is given priority over learning procedures. If anything needs to be “reimagined” perhaps it is what has emerged as a result of the previous reimagining. If a child cannot explain their reasoning, the child is held to not understand underlying principles. Students are given one-off problems that do not generalize well, but appear to be “mathy” and real-world like. Traditional problems are held in disdain for being predictable, easy, and not teaching students to “think like a mathematician”, this last despite the fact that they are novices, not experts, and have to think like children, just as mathematicians once did.
I’m also tired of people who hold in disdain the very things they have benefited from. When pressed on this by pointing out that they seemed to do all right with the down-trodden and eschewed traditional methods, they will respond that “Yes, but there were plenty that did not” without providing much in the way of evidence other than “Look how many people say they hate math” or “Look how many adults cannot do _____” in which the blank is generally some procedure that they may not have used for many years. (I myself have to brush up on certain math procedures that I haven’t done in years; it usually comes back fairly easily. Oh, right, that’s me, and I’m the exception.)
What they offer to replace the methods that helped them succeed are summarized in this statement:
The methods I used in the 1990s, which led to significant improvement in my students’ outcomes in mathematics, are becoming more widely adopted today. These include giving students opportunities to productively struggle with an unfamiliar task designed to extend and/or challenge their prior knowledge, requiring students to communicate with peers about their mathematical reasoning, and using students’ mathematical ideas as the basis for calling attention to key mathematical relationships and properties.
Well, these sound an awful lot like the coveted Standards for Mathematical Practice (SMPs) contained in the Common Core math standards. These purport to teach students to think like mathematicians and are frequently implemented by teaching “habits of mind” of, say, algebraic thinking, well outside of any proper algebra course in which such habits would arise as a result of what’s being taught and practiced. On the subject to the SMPs and thinking like a mathematician, I rely more on the wisdom of a real mathematician, Steve Wilson of Johns Hopkins, who provided this perspective:
There will always be people who think that teaching kids to “think like a mathematician,” whether they have met a mathematician or not, can be done independently of content. At present, it seems that the majority of people in power think the three pages of Mathematical Practices in Common Core, which they sometimes think is the “real” mathematics, are more important than the 75 pages of content standards, which they sometimes refer to as the “rote” mathematics. They are wrong. You learn Mathematical Practices just like the name implies; you practice mathematics with content.
You’ll forgive me then if I choose not to read this book or to write a nuanced review of same.