You’re An Idiot, Dept.

Another article mischaracterizing the way math has been taught, as well as how it should be taught, as well as misrepresenting what Common Core requires. For starters:

“Subjects that are vibrant in the minds of experts become lifeless by the time they’re handed down to students. It’s not uncommon to hear kids in Algebra 2 ask, “When are we ever going to use this?” and for the teacher to reply, “Math teaches you how to think,” which is true — if only it were taught that way.”

I realize that my experience doesn’t count as “evidence” but when I give my algebra students the math word problems held in disdain by people like the author of this article, they are actively trying to solve them. Those that aren’t doing so need additional instruction/guidance which I provide. Students generally ask “When are we going to use this?” when they’re frustrated and don’t know how to do something, and/or because it is played up so much on TV shows and other media. Perhaps we do a disservice by saying that “you will use this later in life” because that is not necessarily true.

The author goes on:

“To say that this is now changing is to invite an eye roll. For a number of entrenched reasons, from the way teachers are trained to the difficulty of agreeing on what counts in each discipline, instruction in science and math is remarkably resistant to change.”

Interesting that he thinks math is being taught in the same old ways. Where has this author been the last 25 years with many parents complaining about the “new” ways of teaching basic arithmetic in the lower grades? It’s true that middle school and high school math have not changed too very much, except for the fact that algebra has been almost totally expunged of any kind of word problem of value, as has the requirement to do proofs in geometry. But generally, high school still offers a more traditional means of delivering instruction rather than the various pedagogical gimmicks employed in the lower grades that pass as effective practices.

Also, in articles of this type, there is no attention paid to how students who go on to STEM majors learn their math.  Many students receive help from home, from tutors, or from learning centers–something that didn’t occur that much in the days when “traditional math failed thousands of students” as the reformers like to say. It was possible for many students to make it all the way through calculus without aid of tutors or help at home–something that even today’s brightest kids are finding hard to do. Many need help in the lower grades when foundational math skills are necessary to move on.

The author goes into some history, particularly of the 60’s new math and says “Later manifestations of the impulse away from rote instruction include curricular standards created by the National Council of Teachers of Mathematics in the 1980s and the enthusiasm for “inquiry-based” science in the 1990s.”

Let me skip my usual tirade against the use of “rote instruction” as the main method by which traditionally taught math in the past is portrayed. Instead, I find it interesting that he leaves out the fact that NCTM distanced themselves from the 60’s new math when it fell out of favor, but when they came up with their infamous standards in 1989, they kept the inquiry-based practices that were being tried out in the 60’s new math. So they didn’t hate it all that much, it seems.

The article delves into how well CC approaches the concept of proportionality, and how it connects ratio to rate to proportion and ultimately slope.

“What they’re learning is: The way you find the fourth number is by setting up this gadget called a proportion,” Daro said. “That’s not really learning anything about proportionality, that’s learning how to get answers to problems in this chapter.

I’ve worked with middle school students using texts that emphasize this connection. The connection may be obvious to the teachers who have had the benefit of working with these concepts for many decades, and obvious to the authors who put together the text books. But most students want to know how to do the problems. As far as “cross multiplying”, I and others I know do teach how to calculate “the fourth number”, but in the end, the kids end up with cross multiplying because it is the way they know how to do it–and ironically, when students are coached for Math Counts competitions and standardized tests, there are short-cuts galore that they are taught.

Phil Daro, for those who don’t know the name, was the force behind the shoddy pre-1995 California standards that were responsible for atrocities like MathLand being introduced in schools, and resulting in parent outcries in areas like Palo Alto. He’s back and was one of the driving forces behind the CC math standards.

While the CC standards can be interpreted in ways that are sensible and useful, (see for example this article) one has to work to do so. One also has to ignore all the textbooks that ascribe to the reform-minded interpretations to which these standards have leant themselves.

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