Math education: It’s not about numbers, it’s about learning how to think

I was talking about conceptually expressive power. Symbols have no conceptually expressive power at all, we assign meaning to them by describing what they do using familiar language, and previously defined symbols. The transitive definition of any symbol is completely and only defined from first principles via familiar language.

That obviously hasn't worked as most people are quite awful at math and society at large hates it. Memorizing times tables has been a spectacular failure as has memorizing formulas.

Math is about problem solving, not memorizing answers to common things; it's the focus on memorization that's made so many people bad at math to begin with. Common core is an attempt to address this by focusing on how the problem is solved rather than what the answer is, it's freaking parents out, but it is a better approach if you're actually trying to teach math.

Maybe I didn't make my point clearly. I'm not arguing against the use of notation or symbols. I'm asking whether Greek specifically is slowing learning down or intimidating people from starting. I'm asking whether learning the symbols with the concepts is the most efficient way to learn math, not whether it's the most efficient way to do math.

Maybe the laborious way is better if more people are comfortable starting that way, and easing more slowly into symbolic syntax.

Maybe there's a more compelling story about math that will get more people interested in it than teaching what symbols do.

If Greek is intimidating enough that many people never start, it doesn't matter how actually laborious the symbols are or not, the battle is lost.

No it wasn't, at least writ large in the USA.

And that's not what New Math was. Explaining what multiplication is doesn't demand an introduction to set theory.

If we read Feynman's CRITICISM of New Math, we actually find that he ADVOCATES for exactly what your parent is suggesting ("cobbled together.. in order to solve real-life problems"). So clearly, your parent isn't describing "New Math". Or perhaps Feynman is just a raving lunatic.

So I'm no advocate for "New Math", but I do oppose the argument you're making here, in which "New Math" is taken to mean "anything other than memorizing times tables" and is then denigrated on face. Without regard to the fact that the most vocal opponents of "New Math" were in fact advocating for exactly what your parent post is suggesting.

> Spectacular failure

So brief was the new math intervention that, to this day and despite all of the hoopla, we don't have a good empirical basis for claiming new math worked or did not work.

New Math was barely attempted, and its primary opponents were mathematically illiterate parents and teachers. This is just true, even if there were mathematically literate opponents to New Math, e.g., Kline or Feynman.

(But also note Meder’s reading of Kline. It's also worth noting that Mathematicians are maybe not the ultimate authority when discussing secondary pedagogy, especially in the mid 20th century. I have no basis for this belief, but IMO lots of mathematicians who weighed in on New Math were very possibly waging a sort of proxy battle as part of a larger war over the future of their own field -- pure vs applied.)

> Do you want to know what worked? Memorizing times tables.

Is this satire (honest question)? For all the things we don't know about math ed, we know that this doesn't work. Students who memorize times tables are routinely incapable of multiplying 12 by 13 or 55 by 55.

> There's just no way around the fact that drilling is key to early mathematical learning.

No, there isn't. But there's also no way around the fact that drilling without understanding is why a whole bunch of students who are "good at math" can't get through even the most dumbed-down versions of proof-based courses in college, or in some cases can't even get through a full calculus sequence. But they're "good at math" because they can rattle off 12*7 real fast!

New Math advocates (and their opponents!) were all at least correct about one thing: we REALLY SHOULD seriously ask what good is learning "math" if the student does not become a better problem solver. It's not 1417 anymore -- problem solving is important, but human calculators don't pull down living wages.

Probably the answer is that we should all be equal opportunity critics: memorization without understanding is intellectually lazy and limits growth potential, while understanding without practice is for most learners a contradiction in terms.

imagine a kid learning to speak 'stop just memorizing words, you need to understand how language was derived before you learn how to speak it'.

its completely counter intuitive to how creatures learn. learn easy things, especially those that relate to problems we deal with, and then get deeper into the subject if necessary.