Math Education

Abbas’s top-notch post about innumeracy in the US led Lindsay to fish an article in the Washington Post about reforming math teaching (though in a comment on Appletree, SLC beat Lindsay to the link by 24 minutes).

Maryland math leaders meet today — and D.C. math educators gather tomorrow — to discuss Curriculum Focal Points, a new document from the influential National Council of Teachers of Mathematics that could profoundly influence math instruction in the region and nationwide.

It says the typical state math curriculum runs a mile wide and an inch deep, resulting in students being introduced to too many concepts but mastering too few, and urges educators to slim down those lessons.

Some scholars say the American approach to math instruction has allowed students to fall behind those in Singapore, Japan and a dozen other nations. In most states, they say, the math curriculum has swelled into a thick catalogue of skills that students are supposed to master to attain “proficiency” under the federal No Child Left Behind mandate.

The Focal Points document can be accessed from here; the article only gives a teaser of the entire curricular reform idea. In a nutshell, it’s very much like New Math, in the sense that it orders a lot of things in the way professional mathematicians think about them rather than in the way kids do. That’s not necessarily a bad idea – New Math’s problems were in its excesses, which Focal Points has none of – but using the word “cardinality” in the section on counting for kindergarteners doesn’t inspire much confidence.

Whereas the primary goal of New Math was to introduce rigor and pure math into schools, which had taught math using only applications up to that point, the primary goal of Focal Points is to sequentialize math teaching more. One of the greatest problems of math curricula in the US is that they tend to introduce too many concepts too early – for example, they introduce probability before the kids have even learned about fractions.

At that goal, Focal Points succeeds. It simplifies the multitude of goals of state curricular standards while barely stepping over the line of oversimplifcation, and, more importantly, creates something approaching unified national standards. Since one of the problems in the US is the incoherence resulting from non-uniform standards, centralization alone would make things better – for a start, a federal Board of Education will have an easier time saying “no” to TI instead of letting its calculators take over the entire curriculum.

However, Focal Points ends up dumbing things down too much. Traditional math education had people knowing how to multiply in first or second grade and memorizing the entire multiplication table by third grade; Focal Points doesn’t even introduce multiplication and fractions until third grade, and doesn’t expect mastery until fifth or sixth grade. Nowhere does the document mention percentages, which merit at least a mention in a section on fractions or decimals. While teaching probability in first grade makes no sense, neither does waiting until eighth grade to start talking about averages and until high school to teach probability.

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