When I began this blog, I imagined and suggested that one of the common topics would be mathematics education. That has so far not turned out to be the case. But this past weekend, a rather disconcerting opinion piece in the Howard County Times got my attention that I think warrants review and discussion.

(Normally, I would simply say that disconcerting opinions are in abundant supply and leave it at that. However, this particular opinion was written by H. Jean Thiebaux, the current chair of the Mathematics Advisory Committee for the Howard County Public School System in Maryland. When the disconcerting opinion is held by someone in a position with some significant influence, it is time to pay attention. I encourage you to read the article first before I cloud your judgment.)

Before diving into the article, I submit two main points that may at first seem contradictory. First, I think very few people need even basic mathematics to function in their daily life, let alone in their jobs. That may sound strange coming from a mathematician; shouldn’t I be a champion of my field? Isn’t mathematics everywhere? Yes I am, and sure it is. But not everyone needs to be a mechanic to drive a car. Having said that– and this is my second point– understanding mathematics is useful to everyone, as a *mode of thought*. That is, mathematics should not be treated as a vocational skill that some need and others do not, but instead as a teachable, testable, “cleanroom” environment in which *everyone* can learn to *think critically*, a skill that I think everyone should have.

In the article, Ms. Thiebaux suggests that “consumer mathematics” should be considered sufficient mathematics education for those students “who do not aspire to becoming mathematicians and scientists.” As an example of the core mathematical competency that should be expected of such non-mathematicians or non-scientists, she provides a list of “practical questions to illustrate situations in which any of us might find ourselves needing to use basic mathematics.” Following is one of those questions from the article:

For dinner for two at a pleasant restaurant, the kitchen bill might be $52 and the bar bill $28, before tax and service are added. With a 20 percent tip and 5 percent tax, what will the total be? Quickly, without using your calculator!

My main objective here is not to pick apart these problems. But highlighting the issues with this one will hopefully serve to make my first point, namely that we simply don’t need much mathematics here. When was the last time that you encountered a restaurant bill that didn’t provide an itemized total including tax (which, by the way, is 6% in Maryland, not 5%, making the “quick without a calculator” business a little iffier)? Also, the specific numbers in this question suggest that a nice, round $100 is the intended solution. But this is only if you tip on the pre-tax bill (i.e., if you add instead of multiply the tax and tip percentages); if you do this, you are a cheapskate with more mathematical ability than you let on. Yes, you.

Another example question asks for the monthly payment on a car loan. The only skills necessary to answer this question involve not mathematics, but the use of a computer to navigate the dozens of web sites with loan and investment calculators that can provide this information.

So, why bother teaching any more than “consumer” mathematics? Why struggle with algebra or geometry if most of us will never use either, if most of us will get whatever mathematical information we need in our lives and jobs from tables, handbooks, or calculators? I feel this is a critical question, the answer to which we must not get wrong. Learning mathematics shows us how to find logical paths to truth, how to unambiguously describe those paths to others, and how to recognize descriptions of faulty paths that lead in the wrong direction or in circles. A young budding journalist may have no aspiration to mathematics or science; but does he or she not also need the tools to think critically?

I strongly recommend Underwood Dudley’s very interesting (and somewhat cynically amusing) article on this subject; as he eloquently puts it, to teach mathematics is “to teach the race to reason.”