We certainly do not argue that critical thinking and problem-solving skills are a waste of time, and neither does Garelick. He does wonder, though, if the so-called solution surpasses the traditional methods. “[T]he criticism of traditional math teaching is based largely on a mischaracterization of how it is/has been taught, and misrepresented as having failed thousands of students in math education despite evidence of its effectiveness in the 1940s, ’50s and ’60s. Reacting to this characterization of the traditional model, math reformers promote a teaching approach in which understanding and process dominate over content. In lower grades, mental math and number sense are emphasized before students are fluent with procedures and number facts. Procedural fluency is seldom achieved.”

In other words, they ponder how math works with many never mastering how to do it.

So, how many people pondered how their car works before learning to drive it? Did you know that many new cars have no mechanical connection between the controls the driver uses and the vital systems of the car, like the engine, steering and brakes? How does the engine actually work, and isn’t it quite amazing that it spins hundreds of times per second at cruising speeds? Do we bother pondering the suspension, transmission, or even the radio?

But, what if student drivers were encouraged to ponder a car before learning how to drive it?

There would be far fewer drivers on the road, that’s for sure. No, virtually all of us learn driving skills long before we learn auto mechanics. And don’t we all feel a little like we’re engaging mysteries of the universe when the technician says, “The mass air flow controller needs recalibration”?

However, let us return to math. Garelick quotes Johns Hopkins University mathematician Stephen Wilson, who said, “The way mathematicians learn is to learn how to do it first and then figure out how it works later.”

Right. Be able to add, subtract, multiply, and divide – even without understanding it, it will get most people pretty far in their lives with respect to math. Understanding can come later. In fact, the kind of thinking skills conducive to understanding math may actually come from other subjects – like philosophy, literature, and theology. The reasoning that goes on in these subjects – particularly in a classical curriculum school that employs the Socratic method – is a skill with universal applications. The skills of pondering and wondering and thinking are not precisely mathematical.

In a classical curriculum, all the subjects relate to each other. The skills learned in one enhance the experience of the others.

Garelick concludes, in part, “If in fact there is an increasing trend toward effective math instruction, it will have to be stealth enough to fly underneath the radar” of the powers that be who support what Garelick calls the “reform math.”

Or, it will mean that new schools will open who teach traditional math well.

So, how many people pondered how their car works before learning to drive it? Did you know that many new cars have no mechanical connection between the controls the driver uses and the vital systems of the car, like the engine, steering and brakes? How does the engine actually work, and isn’t it quite amazing that it spins hundreds of times per second at cruising speeds? Do we bother pondering the suspension, transmission, or even the radio?

But, what if student drivers were encouraged to ponder a car before learning how to drive it?

There would be far fewer drivers on the road, that’s for sure. No, virtually all of us learn driving skills long before we learn auto mechanics. And don’t we all feel a little like we’re engaging mysteries of the universe when the technician says, “The mass air flow controller needs recalibration”?

However, let us return to math. Garelick quotes Johns Hopkins University mathematician Stephen Wilson, who said, “The way mathematicians learn is to learn how to do it first and then figure out how it works later.”

Right. Be able to add, subtract, multiply, and divide – even without understanding it, it will get most people pretty far in their lives with respect to math. Understanding can come later. In fact, the kind of thinking skills conducive to understanding math may actually come from other subjects – like philosophy, literature, and theology. The reasoning that goes on in these subjects – particularly in a classical curriculum school that employs the Socratic method – is a skill with universal applications. The skills of pondering and wondering and thinking are not precisely mathematical.

In a classical curriculum, all the subjects relate to each other. The skills learned in one enhance the experience of the others.

Garelick concludes, in part, “If in fact there is an increasing trend toward effective math instruction, it will have to be stealth enough to fly underneath the radar” of the powers that be who support what Garelick calls the “reform math.”

Or, it will mean that new schools will open who teach traditional math well.

Excellent.

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