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. In the book, the context index appears after the mathematical topics index. If they looked for the index in the same way I did ? namely, open the book to the last page and flip backwards ? they would encounter the context index first. So, if they assumed that there was only one index, then they may have been only guilty (in this instance, anyway) of shoddy scholarship, not pure hackery.

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. 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.

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