Monday, December 23, 2013

Favorite comments of '13, cont: Barry Garelick, Anonymous and momof4

On Reform Math: is it just about the achievement gap?

Barry Garelick said...
As Robert Craigen, math professor at U. of Manitoba, has posted elsewhere, those who claim to support reform math talk a good game about "understanding" but they have little clue as to what a mathematician means by "understanding". In particular, the ability to articulate reasons -- that is, to prove things, is central. They think that saying "I used such-and-such strategy" is "articulating a reason" but it does not actually demonstrate understanding. Even the so-called "personal strategies" that students supposedly invent are rarely generated by them. A simple proof of this is that they are already sketched out to be evaluated, in the curriculum frameworks. If a truly original approach was used by a student most fuzzies would have no idea how to evaluate it to determine whether or not it is valid. And when it comes to the great theorems of elementary arithmetic, such as why ratios of integers always correspond to repeating decimals, they draw a blank -- generally these are reduced to inductive "explorations"; the deductive element is completely lost. So apparently, they have no clue.

Anonymous said...
I think it's true that traditional math is boring and baffling for great swathes of the population - like the clerk who was amazed at my mystical prowess in adding $5.50 to $1.75 in my head!! Just imagine what it's like for her to get a mortgage.

The problem with Reform Math is it throws the baby out with the bathwater: if math is boring and baffling, let's nobody learn math. Instead, let's all write little essays about number playtime.

The result, of course, is not that nobody is bored and baffled - plenty of kids are bored and baffled by Reform Math - but that the boredom and bafflement are more evenly distributed (at the expense of evenly distributed innumeracy). Rich and poor, smart and dumb alike are bored and baffled by TERC Investigations. Bye-bye Achievement Gap!

I think that one of the items you left out of your inventory of motivations behind Reform Math is subjectivity in assessment. In traditional math, there is a right answer, and it's easily seen who has arrived at it. This leads to quick perception of an achievement gap.

In Reform Math, adequate progress is nicely amenable to pencil-whipping, as the teacher gets to judge how much credit to extend for the explanation of how a wrong answer was reached. It could be an easy matter to make the achievement gap disappear in a third grade Reform Math classroom, as the matter under judgment becomes not accurate arithmetic but prowess at bullshitting the teacher. There's many a young fellow out there who can't add double digit numbers but is a whiz at making up stories.

momof4 said...
Yeah, they're doing such a great job at solving "real-world problems" that four HS grads were incapable of calculating sales tax with the aid of a calculator and had so little number sense as to be unaware that an answer of $16 for a $10 purchase, with 6% sales tax, had to be wrong. When I, a customer, walked them through the background (6% means six cents on each dollar) and the method, their awed reaction was, "Wow, you must be a math teacher!" No, I simply learned 6th-grade arithmetic.

While it is true that "mathematics" is beyond many people, basic arithmetic, fractions, decimals and percentages are not. In the days before calculators and cash registers that do all the calculations, ordinary people did these things by hand - and most were HS grads or less. It does, however, require effort and most people need explicit instruction and dedicated practice.

The whole spiral math disaster made more sense when I read that such curricula were specifically designed for the full-inclusion, heterogeneous classroom (not sure if it's true but it makes sense); because nothing has to be mastered, the pretense that all are learning is enabled. The fact that they are not learning won't become obvious until years later, when they are shut out of the math track that includes HS calculus, struggle with HS algebra and need college remediation; they can't learn those things without having mastered the fundamentals of arithmetic. There's no foundation under the math house and it will sink into the sand.

1 comment:

Anonymous said...

I thought you might like this article:

Children grasp place value earlier than previously thought