The Battlestar Galactica Theory of Math Education – Math with Bad Drawings

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Last month, as I check out Christopher J. Phillips’ gripping and short The New Math: A Political History, I discovered myself reciting the threatening line from Battlestar Galactica:

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Early in my mentor profession, I invested a great deal of time and life-force railing versus the imperfections of a rote mathematics education. The meaningless adjustments. The paper-thin understanding. The absence of important idea. I saw it as my task to name (and blame, and embarassment) these patterns.

As the years passed, I recognized these reviews were not as fresh as they felt. Individuals like me had actually been decrying approaches like those not simply for years, however for centuries. Such reviews did not actually interfere with the system; they were a longstanding component therein.

Far from challenging the status quo, I was playing a comfy function within it.

These ideas came hurrying back as I check out Phillips’ powerful and pithy history. There is absolutely nothing brand-new under the sun– a minimum of, not in our viewpoints of mathematics pedagogy. The arguments simply go round and round.

Witness this passage, about the competing books of Pike and Colburn:

Pike stressed the value of remembering math guidelines and after that using them to different examples …

Colburn’s [approach] was to reverse guideline and example: rather of providing guidelines, he provided easy examples in an effort to lead kids to form guidelines on their own …

Contemporaries comprehended the distinctions in between the books to be about distinctions in thinking …

[One critic] announced … that rule-based approaches stopped working due to the fact that a trainee would not have actually “been hired, in this procedure, to work out any thinking, judgment, or discrimination …”

[Another critic] declared that inductive approaches would … eventually weaken authority by removing the standard grounding of extensive understanding in guidelines.

Is this about the Common Core fights of the 2010s? Sure seem like it.

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But no, it’s about the New Math debate of the 1960s. ?

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Wrong once again. Colburn released his book in the 1820s. Pike composed his in the 1780s.

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All of this has actually taken place before. All of this will occur once again.

As Phillips clarifies, a quiet presumption underlies both sides of the Colburn/Pike argument. “Even– maybe particularly– at the most primary levels,” he composes, “assessing mathematical approaches required presumptions about the virtues of intellectual training.”

Let me spell that out: the shared presumption, the axiom that both sides accept, is that mathematics education forms the intelligence Math is not simply math. You handle matters of reproduction, that’s how you’ll likewise approach matters of democracy.

In the 1960s, New Math reformers stressed that rote drill would reproduce blind deference to authority. They hoped rather to produce a society of mini-professors, seeing the world in regards to versatile, abstract structures.

In the 1970s, “back to essentials” counter-reformers held the opposite hope, and the opposite worry. They thought rote drill instilled discipline and diligence, which the New Math would reproduce a feckless generation that was permanently complicated real with incorrect, ideal with incorrect.

The competing camps preferred opposite type of minds, and opposite type of mathematics. They shared a deep concept:

Math makes minds

I’ve long run on this very same concept. Essential to a successful and complimentary intelligence– and hence, to a totally free and successful society– is excellent mathematical thinking, whatever that is. At the minute, I can’t assist questioning if we’ve all got it incorrect. Possibly mathematics education isn’t about wider intellectual routines. Possibly it is not, as 17

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December 18, 2023(*) December 5, 2023(*)

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