"A college graduate ought to be able to count to 20 without taking his shoes off. ....The Irascible Professor.

Commentary of the Day - March 1, 2012: College - Numeracy, is it Important?   Guest commentary by J.J.S. Boyce.

In one of those shocking twists of irony headline writers just can't resist, four-time Florida school board member, Rick Roach, took and failed his state's major standardized test.  The story was told on the Washington Post website by Marion Brady, who initially withheld the board member's name.

Mr. Roach took this year's version of the Florida Comprehensive Assessment Test for tenth graders, and was quoted, summarizing his results: "The math section had 60 questions.  I knew the answers to none of them, but managed to guess ten out of the 60 correctly.  On the reading test, I got 62%."  He did earn a low pass on the reading section, but his math score is an unambiguous failure and that is what I'd like to focus on here.

The most significant fact in this story is not that a person with one bachelor's and two master's degrees in education was completely lost with his state's tenth grade mathematics curriculum.  What strikes me instead is his reaction to the results.  There's the obligatory "Aw, shucks!" moment of semi-embarassment, but then both Mr. Roach and Mr. Brady go on the offensive.  They reason that, since Mr. Roach is a successful person (as measured by his educational credentials and the nice, big house he owns), whatever sort of knowledge it is that the FCAT tests for is clearly irrelevant.  A quote from the school board trustee later on in the article includes this rationalization:

"I have a wide circle of friends in various professions.  Since taking the test, I've detailed its contents as best I can to many of them, particularly the math section, which does more than its share of shoving students in our system out of school and on to the street.  Not a single one of them said that the math I described was necessary in their profession.”

Before we go any further, it would be nice to see what kind of math we're actually talking about here.  The most recent version of the tenth grade math section of the FCAT available on the official website is the one administered in 2006.  Looking it over, it's pretty much what you'd expect.  There are questions requiring arithmetic, basic algebra, reading graphs, and the standard geometry fare -- some area and volume calculations and some simple trig (every formula is provided).  A small sample of the questions from that test is below:

11) An artist sells earrings from a booth at a fair.  Rent for the booth is $250.  The artist makes $6 from each pair of earrings sold.  The profit in dollars, P, can be found using the following equation, where n is the number of pairs of earrings sold.

P = 6n - 250

How many pairs of earrings must the artist sell to earn a profit of $500 ?

17) The number of shoppers at a Fort Myers flea market ranges from an average of 55,000 per weekend during the tourist season to an average of 18,000 on a summer weekend.

What is the percent of decrease, to the nearest whole number, in the number of shoppers at the flea market from the tourist season to a summer weekend?

21) A toy company manufactured 12,000 model race-cars.  Alisha, who works in the quality control group, chose 250 of the model race-cars at random and had them checked for defects.  Of the 250 race-cars, 212 were found to have NO defects.  Assuming this ratio held true for all 12,000 model race-cars, how many of the race-cars had defects?

Some of the test questions (number 17, for example) are multiple choice. Even the putative algebra or formula applications can mostly be solved using guess-and-check, plugging in different numbers until one fits, so the only truly essential requirements to get through the Math FCAT are the basic operations of multiplication, addition, subtraction, and division, including the related concepts of ratios, fractions, percentages and averages, plus the ability to interpret simple graphs.

These are not only very basic but also very practical math skills. What interests me is that Mr. Roach defends his failing grade by saying he has never had to use these skills, but he's really begging the question.  If he lacks these skills in the first place, it goes without saying that he can't apply them in his everyday life.  That in itself implies little about their relative usefulness.

By most measures, Mr. Roach could be categorized as an innumerate adult, a person suffering from a kind of illiteracy specific to dealing with numbers and their relations.  Traditionally illiterate adults, those lacking proficiency reading text, usually get by using various compensating strategies: navigating by visual landmarks in lieu of street signs; memorizing the form of the most common words or phrases like "STAFF ONLY" or "DO NOT ENTER"; carefully observing other people's behaviour in order to determine what public information or instructions say; guessing the basic content of writing based on its context.

Innumerates have to make the same adjustments.  Once upon a time, shop-keepers wrote out order receipts, including taxes, by hand.  Anyone and everyone was required to have this skill.  When I was a teenager, a fellow employee had to take a hand-calculator with him during food deliveries since he couldn't perform the simple subtraction in his head to figure out a customer's change.

A different co-worker constantly asked me to work out phone orders for her.  She would mistype something and end up with a delivery meal for two costing $250.  She lacked even the number sense to pick up on an order of magnitude error, so she unabashedly left the writing of delivery receipts to others.

Whenever I receive a bill, I give it a quick once-over to see that the final amount makes sense.  I don't need to recalculate everything to the penny, just perform some simple mental estimations to ensure the presented total is within a couple of dollars of what I'd expect.  In the grocery store I calculate unit prices to find the best deal (most stores now include unit prices of products since this is a vanishing skill).  When out with friends, I determine my share of the bill based on fractions (including tip).  I look at fees and brokerage costs when determining which and how much of a stock to purchase, or whether to invest in a mutual fund.

The innumerate cannot do these things, so unless they can find someone to do it for them, they have to get along without such information.  While illiterate adults, especially in developed countries, tend to be deeply aware of their own shortcomings, the same stigma doesn't apply here to those with undeveloped math skills.

Somehow, math and science have become the two areas of knowledge of which it is totally acceptable to profess complete ignorance.  Mr. Roach, I'm sure, is not a stupid man.  He could have mastered the basic feats of numeracy found on this test at the age of fifteen, but for whatever reason, he didn't.  The pervasive American belief that numbers, unlike the ability to read and write, just aren't for everyone, has allowed this one-time educator and current policy-maker to consider and then reject the correct response to his test results: shame.  As a result, he could only conclude that the educational standards themselves are at fault.

It's probably easier for Mr. Roach to get by than it is for a traditional illiterate, since he doesn't have the added difficulty of hiding his deficiency.  He'll gladly pass on tasks he should be able to do himself to an underling, his accountant, the bank employee, and still believe himself to be an educated person.  But there's a problem when this obliviousness leads a state school-board trustee to make a public statement like this:

“It makes no sense to me that a test with the potential for shaping a student's entire future has so little apparent relevance to adult, real-world functioning.  Who decided the kind of questions and their level of difficulty?  Using what criteria?  To whom did they have to defend their decisions?  As subject-matter specialists, how qualified were they to make general judgments about the needs of this state's children in a future they can't possibly predict?”

I'm no fan of high-stakes testing. I think we can and should do assessment better.  But there's nothing wrong with the assertion that every future citizen can and should understand graphical data, measurement calculations, and ratio reasoning.  Mr. Roach does a great disservice to his students when he suggests they can disregard these skills.  Those who cannot do the math will be left to the mercy of those who can.

© 2012, J.J.S. Boyce.
J.J.S. Boyce is a free-lance writer and former science teacher from Canada.  He publishes "The Back of the Envelope" blog.

The Irascible Professor comments: There are two issues here.  One is the issue of depending too heavily on standardized tests to measure student achievement, and the other is the issue of how innumeracy affects the individual and society at large.  The IP took a look at FCAT math test that is available online.  As Mr. Boyce points out it is not a very challenging test.  Most of the questions don't involve sophisticated mathematical reasoning, but they do require a student to have some basic understanding of what I would call practical mathematics.  This is the mathematics that you need to understand simple graphs you might encounter in the newspaper or on a web news site, or to determine if the advertised price of a particular item or service is a good deal, or the math that you might need to run a small business.  The test is written in such a way that memory is not vey important.  And, a standard basic calculator is provided for each student taking the test.  The necessary formulas needed to solve the problem are given for most of the problems.  A few of the questions do require the student to remember basic theorems of geometry.  But one just has to be comfortable with some of the basic ideas of arithmetic, first-year algebra, and geometry to solve most of the problems.  An adult walking into the test cold probably is not going to do as well as the average student who has taken math classes more recently, but the IP would expect that a college graduate like Mr. Roach would be able to solve more than half the questions on the test correctly.  The fact that Mr. Roach was able to answer only ~17% of the questions correctly, suggests that he is a true innumerate.  Frankly, the IP does not think that a person who is truly innumerate should be sitting on a school board where judgments about budgets, contracts, and bond issues have to be made.

That said, the FCAT is not a great test to determine a student's math skills.  The IP would hope that it would be used as one tool among many to measure the progress of students in math at the secondary level.

Irascible Professor invites your  .

© 2012 Dr. Mark H. Shapiro - All rights reserved.
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