Desperately Seeking Numeracy in Fayette County

December 13, 2005

From today's Lexington Herald-Leader:

Last night, Vision 2020 groups began presenting recommendations based on six months of research to Fayette County school board members. Groups used computer presentations, skits and anecdotes to relay the information. The group on mental health and well-being encouraged everyone to stand up and stretch as part of their presentation.

It sounds like they had some fun with their presentations, but we were interested in the actual results, so we visited the group's website.

At first we didn't notice a report for Mathematics, but they've labeled it "Numeracy" (report available in MS Word format). The report contained seven specific recommendations (paraphrased here):

1. Require four years of math in high school.
2. Decrease math class size to 25 students.
3. Lengthen the math period to one hour, daily. Below-grade level students will receive an extra half-hour.
4. Hire a math specialist for every elementary school.
5. Develop professional development for administrators to help them evaluate math programs.
6. "Fully fund the use of technology to support mathematics instruction."
7. Evaluate the math track record for the past 5 years for every school in Fayette County.

It doesn't look like these well-meaning 2020 folks understand the problem. For starters, with sole exception of #6, all of these recommendations don't have anything to do with math! (Replace the references to "math" with "English" or "Science" to see how generic the recommendations are.) Plus, the recommendations are of the conventional-wisdom variety.

We have nothing against, say, 4 years of 1-hour per day math in high school, but they're dreaming if they think they can effect the length of a math session in period-oriented schools like middle or high schools.

And class size is a sore point with us, homogeneity is far more important! If students were promoted to the next grade (more importantly, to the next math course in the sequence) only upon the mastery of previous skills, then there wouldn't be a big problem with 30-odd kids in a class.

Getting back to their recommendations, the only reference to how math is specifically taught is contained in #6, embracing "technology" (a euphemism for calculators).

While it's no secret that we're no fan of calculators in K-12 math classrooms (see "Calculators are like Bicycles"), it's interesting, but sad, to read how the 2020 folks defend their recommendation, as in the following paragraph (emphasis ours):

Technology allows teachers to teach some traditional topics in a new way as well as teach new topics that are not accessible to students without the technology. For example, fraction calculators permit students to choose a common factor to reduce improper fractions to simplest form; graphing calculators allow students to look at where a quadratic function crosses the x-axis as another way to solve a quadratic function; graphing calculators show students connections between algebra and analytic geometry.

It is shocking that they'd suggest that these three skills are not accessible without technology! To reduce fractions (improper or otherwise) we can either have students be familiar with the multiplication table, or we can buy them all fraction calculators and then train students how to use them. To find where a quadratic crosses the x-axis we can, oh, set the function equal to zero maybe? And since Analytic Geometry can be defined as the marriage of Algebra and Geometry, it's not clear how calculators would "show connections" any better than say their everyday work in this course!

Did the authors of these recommendations even pass high school mathematics themselves?

If they took the name of their report seriously, they'd promote numeracy: the fluency and facility with numbers and mathematics. This begins by not shying away from what has worked famously in the past: memorization (and utilization) of basic skills, such as the multiplication table, to name one set of facts.

Memorization isn't the end point (as the drill-and-kill critics claim), but rather the beginning. When someone has mastered the basic skills, that student can look at ever more complicated problems and simply recognize--without thinking about it--patterns that are essential to the solution. For example, factoring a quadratic equation requires the student to simultaneously consider both sums and products, a fairly hopeless endeavor if one hasn't memorized the old-fashioned multiplication table.

Promoting calculators as a tool for numeracy is like embracing text-messaging shorthand as a tool for literacy.

cu L8r ok?