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>I think the idea of focusing on concepts over computation 100% in the right spot.

Concepts over computation (or well, before computation) is probably right. But New math was about learning the abstract before the concrete. This was predictably an abject failure.

I think the best way to teach math is to follow the trajectory that humanity took when discovering it. The key that's missing is that math doesn't just come out of thin air, its just a systematization of precise quantitative thinking. If we motivate the concepts using real world examples, then explain how to abstract away the particulars into a general procedure, then these connections will get made that make math "real" and relevant.

Not even wrong. You think New Math refers to the current modifications of common core. New Math actually refers to a series of cold war changes made in response to perceived russian scientific dominance.

https://en.wikipedia.org/wiki/New_Math

Oops! Forgot about that. I assumed the OP was griping about Common Core.

BTW, "not even wrong" is a rather rude way to point out a misunderstanding.

yeah it is a bit rude..sorry! I just get very few opportunities to say it- and I was like yo- this is a good chance. Are you familiar with the history of the term? with pauli?

Yeah, I'm familiar. To be fair, it was a good opportunity. Well played :D

I disagree. I am not uncomfortable with math in general or the "new math". What I am uncomfortable with is the fact that my kids, and everyone else's kids, are essentially lab rats in a massive experiment. The result of which is 1+ generation of kids who can't calculate tax in their head or split a restaurant bill . They can't manage more than a few number without a calculator and are missing many of the basic blocks of math that are learned through rote.

I find it disheartening that I have to teach my kids basic fractions, ratios, and transformation cause the teachers don't or barely touch on it. Kids are supposed to "discover" and "explore" math, whatever that means. In my opinion it's all bullshit.

Math, in many ways, is like an engine, either it works meaning the answer is correct, or it doesn't.

You're confusing "New Math" with common core.

I know. I was replying to the comment and using the his/her terminology. It's actually a blended common core/discovery math hybrid.

Disagree. If you read the common core standards, they are very sensible and make no curricular or pedagogical recommendations. "Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph." CCSS.MATH.CONTENT.HSF.IF.B.6.

The way people are teaching math in the US is baffling and weird, but Pearson's textbook design has little to do with the common core per se. Most common core-labelled material is from something else with a new shiny CC cover slapped on.

I think you misunderstand, "New Math"[1] was a thing from the 60's, he clearly took it as an adjective talking about common core, the current "new math", but not the same as the "New Math" bitwize was saying had been tried and was a failure.

[1] https://en.wikipedia.org/wiki/New_Math

I know New Math from the 1960s; the sibling comment to my post indicates that ghettoCoder is talking about Common Core today and I disagree with his characterization of Common Core. New Math as practiced in the 1960s is a fascinating and very different failure case, although it probably had similar problems in implementation (poor teacher training and shoddy repackaged curricula).

idk, I studied higher level math very seriously, and even there, practicing computations is pretty key to understanding the underlying concepts. Concepts and abstractions are important, but they don't stick without practice.

I agree that it's an important part of the process, but I think it works best when it's connected with actual application, and not just a worksheet full of disembodied computations. I saw way too much of that as a student and as a teacher.

> I think the idea of focusing on concepts over computation 100% in the right spot

Concepts of what? Without intuitive understanding of basic computation procedures, what concepts can anyone build out of nothing?

Math is concrete. It's from observation of actual quantitative phenomenon.

And yet it's completely abstract as sets and numbers don't need a universe like ours to exists, they only need axioms.

Modeling the world is a job that math the tool was created for, but it certainly isn't concrete just because the world that needed it was or is.

You forcefully disintegrate concepts and physical world. All concepts have certain degree of abstractness for human understanding. It's not unique to Math. And it's not necessary that abstractions automatically alienate something from concreteness.

To split them, and think that, just because there is abstraction, and it's OK to develop the concept without the concrete substrates of actual experience is trying to make dream come true.

And I argue that no one should live in a dream. And it's obvious that only those dreams that have a strong connection with the real world have realistic chance of being made real.

Is it way too early, or has it produced a generation or two (or three!) of mathphobic Americans? How many generations of avoiding rote memorization would it take to judge an alternative, in your view?

Many problems that people have with math seem to stem from not having internalized the most basic facts about addition and multiplication. If you don't know at least to 10 by 10, each tiny step of working through a problem will tend to be interrupted by counting. Fluency requires memorization.

I knew a guy with a Physics PhD who would agree completely with bitwize, so I don't think it is just parental insecurity.