Integrated math-was that really necessary?

Bowen wrote in the comments recently:

Hey, speak for yourself, we dumped FOIL in our high school books. I guess that means we’re not mainstream!

I replied, with respect to CME, which is the FOIL-dumping curriculum to which he refers.

Is this news to you, Bowen? Is it bad news?

This got me thinking about high school curriculum-mainstream and non. Look back at the NSF-funded high school curricula of the 1990’s and the associated Math Wars. One major sticking point in the brouhaha was the idea that these programs were integrated. That is, they were not Algebra I, Geometry, Algebra II/Trig, PreCalculus/Statistics sequences. They were First Year, Second Year, etc. programs in which each year integrated algebra with geometry and statistics, etc.

And I have to ask, was that really necessary?

In hindsight, I’m not sure I really get the motivation for it. Wouldn’t it have been enough to improve high school pedagogy and content within each traditionally organized course? Did we have to try to blow up the whole structure at once?

I’m just asking.


3 responses to “Integrated math-was that really necessary?

  1. Well, perhaps for CME Project, this is good news, because we got NSF funding partially by specifically wanting to NOT be an integrated curriculum. The programs you cite, in general, have not had the national impact NSF was hoping for, partially because of this integrated sequence.

    I can go on for some time about why CME wanted to not be integrated (algebraic and geometric habits of mind take time to develop). Some of our success in district adoption has come from the fact that our books “look and feel” like existing series.

    I think there can be good reasons to do it one way or another. Why does CMP space out the Bits & Pieces books instead of doing them all back-to-back? I think curriculum can be designed in a lot of good ways, as long as there is a method behind the decisions. The NSF integrated curricula do a better job than some other books that pretended by calling themselves “integrated” when, in reality, they were just reordered and incoherent. You’d have to ask the other programs’ authors whether they felt their integration was a necessary part of their philsophy, or just a selling point — and if it was just a selling point, ho boy did that backfire.

    So, did we win? Is FOIL gone yet?

  2. Bowen asks:

    So, did we win? Is FOIL gone yet?

    FOIL gone from the American curriculum? Have you been living under a rock? No. As a present-day teacher of College Algebra, I can assure you that it’s not gone yet. Indeed, I can assure that it’s not gone from my college’s adopted developmental mathematics textbook.

    Sorry. Got a little worked up there.

    But FOIL’s gone from Common Core. It never appeared in the Connected Math quadratics unit (nor elsewhere, for the record).

    Suddenly I am curious (and do not know) whether FOIL ever made it into a set of state standards.

    The NSF integrated curricula do a better job than some other books that pretended by calling themselves “integrated” when, in reality, they were just reordered and incoherent.

    And how. The Integrated part was the easy part to fake.

    The other piece of research I need to do here (and which will be much easier to do than the 50-state FOIL scavenger hunt) is to revisit the 1989 NCTM Standards. I have a feeling that’s the real source of this integrated business. I recall discussion of a “Core Curriculum” that may have involved breaking down artificially constructed barriers between algebra and geometry. (From this came the name “Core Plus”, for instance).

    And now we have the Common Core. This core metaphor seems to be important in some circles. I’m not sure I quite get the metaphor. Don’t cores melt down? Or get composted when you’re done eating the rest of the apple?

  3. Oh, I was just kidding, I know FOIL hasn’t gone anywhere… Of course, I wish it would, and so do the writers of Common Core, specifically calling it out as an object that contributes to the “mile wide, inch deep” phenomenon of teaching independent topics. Sure, FOIL works this week for this topic, but then dies a horrible, horrible death. I did not find it in a quick search of state standards, which is fortunate, but that doesn’t stop it from being the most frequently presented method in (others’) textbooks.

    Wish I could find it, someone wrote a nice piece complaining about how once students learn FOIL, they want to use it in ridiculous situations that are nowhere near its intended application. FOIL seems important: heck, it’s got an acronym, it has to be important! What a disaster.

    I think you’ll have to go further back in time to find the first debate about integrated math versus segmented courses. I still find it weird that after algebra and geometry come “Algebra 2” and “Precalculus” even though a lot of it is about the connections between algebra and geometry and the analysis and synthesis of key concepts from both.

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