November 20, 2006

Another math article

Do journalists have a false dilemma macro they use when writing articles about math?

This guy must.

Ron Lankford, as a boy growing up in Seneca, used reform math in the hay field without knowing it.

"I used to be able to look at a load of hay, and tell you just by looking at it how many bales were in there," Lankford told me. "I was thinking mathematically... there were four rows and each row had so many. I just knew it."

Yeah, 'cause you know you never learned such stuff in traditional math. Thank you, reform math.

I really like this hilarious typo.

What Lankford, now in his eighth year as superintendent of Webb City Schools, did instinctively has become a focal debate in public education. There is an ongoing shift from teaching math by rote, as in mesmerizing tables and formulas, to trying to impart concepts.

Reform math teaches you how to mesmerize tables and formulas instead of memorizing them.

That should be their slogan

Now meet the three horseman of the apocalypse.

The concept is broken into three major components: "Everyday Math" for grades kindergarten through fifth; "Connected Math," for the middle grades, and "Core-plus" for the upper grades. The goal is to use a cohesive method for teaching, using "spiraling" concepts that connect one idea to the next.


It gets better.

When Chicago University researchers dug into the problem, they concluded the fundamental issue was the way students were being taught - by memorizing facts and formulas, rather than being forced to understand and apply concepts. The difference is an auto mechanic knowing how to change the spark plugs in an engine, and knowing what the spark plugs do and what happens when they don't work.

What the knuckleheads at Chicago didn't realize was that the auto mechanic must still know how to perform the procedure for changing the spark plug if he wants to get the car to run again. And, unfortunately, the best way to do that is by practicing changing a lot of spark plugs.

Plus, as I recall, traditional math consisted of the teacher prattling away at the front of the class trying to teach understanding, not memorization. It didn't work all that well then and it doesn't work all that well now because novices don't really understand any topic when they first learn it. That comes later. At lest in the traditionally taught math, there was a coherent sequence of learning in which one skill builds on another. Think a computer program. In reform math, the sequence has largely been dispensed with in favor of presenting a series of unrelated problems to the student for discovering the answers. Imagine the computer programmer falling down on his way to class and dropping his punch cards and getting them all mixed up.

Georgianna McGriff, the Seneca curriculum director and a delightfully upbeat advocate for change, understands the frustration of teachers, parents and students. She acknowledges foibles in how the program was laid out in the district, and also agrees "no program" is perfect and that some adjustments may need to be made in how it is used in Seneca.

She notes that the way public education had been teaching mathematics was not keeping Seneca, Missouri or the nation competitive with the rest of the world. Doing nothing is not an option.

Yeah, but doing something stupid for the sake of change isn't the answer either.

Many employers, primarily manufacturing and technology, say some workers coming to them from public high schools and even colleges are not good at math. They know how to add, subtract, multiply and divide, but not how to think on the fly, to solve problems that require visualizing a logical sequence and then making changes to achieve the desired end.

In other words, how to think.

Except that in the reform math, kids aren't any better at solving problems than traditionally taught kids. If anything, the calculation skills of reform taught math kids have taken a nosedive. So, not only don't they solve problem any better, they don't
add, subtract, multiply and divide as well. Lose-lose.

Few disagree with the end result. We must be able to teach kids how to analyze, to critically examine a situation and come up with a unique solution. The debate is over how to do that.

Everyday Math has been the subject of dozens of contentious meetings around the country, and the issues are nearly identical. Parents are upset because they don't know how to help their children.

Let's take a look at the end results. Everyday math--61 studies. 57 were garbage. Out of the 4 that were OK, 3 had statistically insignificant results, the last study was performed by a researcher affiliated with Everyday Math who won't release his data set. Thus, the end result is that Everyday Math appears to be not the way "how to do that."

Webb City schools have used Everyday Math for several years and educators noticed early in its implementation that the elementary program failed to properly ground students in memorizing the multiplication tables. It is impossible to visualize higher concepts, such as counting a wagonload of hay in a single glance, without knowing that 4 times 12 is 48. Teachers began sending multiplication work home with the kids and urging parents to help them, which left more class time for teaching the concepts rather than memorization.

Oh wait, so you apparently still do have to memorize things in math. That's not what the authors of Everyday Math and the NCTM standards originally said. They thought that Understanding + Calculators = Math Bliss. Instead it's turned out that Understanding + Calculators = Math Failure.

So now the reformers are in a fighting retreat while doe-eyed educators are forced to hand out endless supplemental worksheets home (in addition to the normal homework) if they want kids to actually be able to do any math. This wouldn't sit too well with me if I were a kid. Lots more work for the same performance. Once again lose-lose. Compare this to a math program like Connecting Math Concepts where the practice is already built into the program by the curriculum designer. The result is that for most kids, all the practice is performed in class and there is no need for homework.

"No one math program is perfect," she told me. "This is a way of addressing a much larger problem."

Yes, but some are clearly better than others, so why not pick the ones that work?


Anonymous said...


What the knuckleheads at Chicago didn't realize was that the auto mechanic must still know how to perform the procedure for changing the spark plug if he wants to get the car to run again. And, unfortunately, the best way to do that is by practicing changing a lot of spark plugs.


Lets take a moment to think about this. How many people out there would take your car to a mechanic who doesn't know how to change spark clubs. I don't care how much he can spout off about the theory of internal combustion engines, if he can't turn a wrench then I am taking my car elsewhere.

I am so feeling you today!

Anonymous said...

In the Nov 19 Time Magazine, Claudia Willis opines and whines in an editorial called "How to End the Math Wars":

"So do we have a solution to the national math problem? We certainly have the correct formula. The question is, Can we apply it? Already the N.C.T.M.'s focal points are being called a back-to-basics movement, another swing of the ideological pendulum rather than a fresh look at what it would take to get more kids to calculus by 12th grade. If the script follows that of the Reading Wars, what comes next will be dreary times-tables recitals in unison, dull new books that fail to inspire understanding, and drill, drill, drill, much like the unhappy scenes in many of today's "Reading First" classrooms. And that would be just another kind of math fiasco--of the red variety. Kids will learn their times tables for sure, but they'll also learn to hate math."

Perhaps the people at NCTM hate math, but that doesn't mean that everyone taught in the so-called "traditional method" hates it. Journalists love the false dichotomy ending; it helps them write more concisely. Learning math = hating math. As to what it takes to get students to calculus in the 12th grade, look at what the students who make it to calculus by 12th grade have done. Ms. Willis doesn't care to look that far.