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July 04, 2005

New Math

Kevin Drum writes:

The Washington Monthly: MATH FOLLOWUP.... Normally I'd just post this as an update, but it seems like it deserves a separate post of its own. Yesterday I excerpted a Diane Ravitch op-ed about mathematics textbooks from the Wall Street Journal. One of the paragraphs in the op-ed was this one:

In a comparison of a 1973 algebra textbook and a 1998 "contemporary mathematics" textbook, Williamson Evers and Paul Clopton found a dramatic change in topics. In the 1973 book, for example, the index for the letter "F" included factors, factoring, fallacies, finite decimal, finite set, formulas, fractions and functions. In the 1998 book, the index listed families (in poverty data), fast food nutrition data, fat in fast food, feasibility study, feeding tours, ferris wheel, fish, fishing, flags, flight, floor plan, flower beds, food, football, Ford Mustang, franchises and fund-raising carnival.

That sounded pretty amusing indeed, but last night I got the following via email:

The 1998 "contemporary mathematics" textbook referenced [by Ravitch] actually has two distinct indexes -- one is called Index of Contexts, the other is called Index of Mathematical Topics. Now, let's see, in which index might a discerning reviewer look for a list of mathematical topics that start with the letter "F"?

This seems to be a hard question for Ravitch, Evers, and Clopton. They chose to look in the Index of Contexts. Let's use a bit more insight and look in the Index of Mathematical Topics. Under the letter "F" we find the following topics listed for this integrated mathematics textbook: Faces, Face-views (3-D drawing), Finding equations (using points, using regression, using situation, using slope and intercept), Five-number summary, Formula (area, perimeter, surface area), Four-color problem, Fractal, Fractional exponents, Frequency table, Front view (3-D drawing), and Function.

I don't know if Ravitch is an innocent victim of deliberate deception by Evers and Clopton, or if she knew what they were up to and passed it along anyway. In either case, it seems as if she and the Wall Street Journal owe their readers a retraction.

And the follow-up:

The Washington Monthly: ALGEBRA TEXTBOOK FINALE....Thanks to reader MH, we now have a definitive answer to last night's algebra textbook question: it turns out that Contemporary Mathematics in Context does indeed have two indexes, a "topic" index and a "context" index. The "F" section of the topic index is shown on the right, and it appears to have a fairly standard collection of high school math entries. A scanned image of both the topic and context indexes is here (warning: large PDF).

MH also provides a possible explanation for the initial citation of the wrong index by Evers and Clopton:

It is possible that Evers' and Clopton's error was inadvertent.... If they looked for the index... [by] open[ing] the book to the last page and flip[ping] backwards... they would encounter the context index first...

That could be. In any case, it appears that Evers and Clopton highlighted the index primarily as a substitute for a fair discussion of the books themselves. In fact, their main substantive complaint was about CMiC's lack of emphasis on factoring polynomials, and a reader who has contributed to CMiC emailed to explain that this was deliberate:

[Older texts use] what we would call a theory of equations approach (aka traditional with heavy emphasis on factoring)....That is, everything that you do is directed towards writing x= __.

....[CMiC] and other NSF funded projects...generally take approaches called the functions-based approach. The idea there is that you think about functions and analyze the relationship between input and outputs. It is only in the context of functions that you start to ask: where does this function hit the x-axis? Or, how can I make a function that hits the x-axis in these places (we'd call that interpolation)?

So, traditionally, students were exposed to page after page of 'how to factor this specific form' whereas in [CMiC] students are expected to make use of factoring, but it's not a huge focus.

I don't have any independent opinion about which approach is correct, since that's obviously a pretty technical pedagogical question. [Let me put in my two cents' worth: in the fifteen-year-old's--excellent--Algebra 1 course, they put a little too much emphasis on factoring and a little too little on functions and where they hit the x-axis.] Regardless, citing the context index as a measure of frivolity while ignoring the topic index is clearly unfair and misleading. Ravitch, Evers, Clopton, and the Wall Street Journal owe their readers a retraction.

But is it possible at this date for Diane Ravitch to be an "innocent victim of... deception" in her use of people from the Cato-Heritage-AEI-Hoover Republican smoke machine as sources? I think not. Surely nobody normal presumes that the Republican smoke machine is especially competent, or cares about playing it straight, or even knows what it is to work carefully.

Whenever you have good reason to suspect that your sources may be misleading, you have a duty to verify. Ravitch is old enough to know this.

Posted by DeLong at July 4, 2005 02:04 PM