Physics professor Chad Orzel’s child (“SteelyKid”) started school in 2013, which was close to the peak of the freakout over Common Core Math:
The inscrutability of the new standards for elementary school math was an endlessly recurring topic in late-night talk show monologues and frustrated Facebook rants from high-school classmates whose kids are a bit older than mine. Nobody seemed able to understand what was now deemed to be third-grade math, and everybody was pissed about it.
As is often the case with issues touching on STEM in schools, I found this a little puzzling. As SteelyKid started to get into the math curriculum, I thought it was great — not just the endless algorithmic chugging I dimly remembered from my own childhood, but something much closer to actual math. Students were being asked to get answers by multiple methods, check them against each other, and explain how they knew their final answers were right. These are all things I struggle to get college frosh to do in intro physics, and here it was built right into the elementary school math curriculum.
So, on reflection, I guess it’s pretty obvious why everybody else hated it…
What a lame and pointless boast. The smart guy who loves math and does it for a living prefers a free-wheeling and conceptual approach to teaching arithmetic over drilling the same old time-tested algorithms. Big surprise. If I were teaching an elementary school arithmetic class to physics professors, yeah, that would probably be the way to do it. But for kids who haven’t been doing math for decades, and who probably are neither as smart as this guy nor anywhere near as interested in math as him, it was a disaster.
This emphasis on rigor and verification strikes me as a good thing. That said, not every kid is cut out to be a rocket scientist.
Seems that it would be appropriate to get the basics in place before going to some alternative analysis.
Many students/people would have difficulties understanding the basic problem, let alone coming up with several ways of getting a solution.
Rote learning is the foundation that equips the student for analysis when they have higher brain function later. If they can’t memorize they will never be able to analyze.
I know nothing about Common Core Math, but it stands to reason that it wouldn’t be terrible. Math is foundational to the education of reliable technicians, which are forever in short supply. The question is always, where aren’t you looking? You can’t see what isn’t in your field of vision. Similarly, what isn’t there?
In schools, the question is therefore not what is in the schools but what isnt.
I suggest that the liberal arts — in other words, the classics — are essential to producing a citizenry capable of governing itself. And naturally, a body politic capable, and not only capable but demanding, of self-governance is by far the most salient threat to any incipient occupational class. Nothing else comes close.
Ask, therefore, why Greek and Latin aren’t in the school. Ask why, if they are, they suck balls. Ask where the Great Books are in the school library. Ask where, when, and how the school teaches the students to organize themselves into a coherent body capable of making resolutions, and passing them, and keeping them.
Really, to ask the questions is to answer them.
I worked with Common Core graduates years ago, and what I saw depressed me. They were totally hopeless at any kind of math. They could not calculate sales tax with a calculator. These weren’t the smartest people I’ve ever worked with, but they weren’t notably stupid, either. I have no doubt that if they had been taught the traditional algorithms through repetition and memorization, they would have been far more competent. Wang Wei Lin is right: memorization of the very basics is the foundation. It’s not trendy, and it’s boring to teach, but for most students it’s the best way.
Business math and engineering math are two very different things. And we need both. Just not in the same student.
Don’t talk to me of the evils of specialization. It’s a moot point. Kids come specialized. Teach according to the students’ aptitude. Some of them will sell widgets. Others will make moon rockets out of those widgets. It will all sort itself out.
In England they speak of maths in the plural. They may have the right idea.
Not coincidentally, math is much like music or a foreign language. You have to learn the basic chords, etc. before you can actually begin to play. You have to learn the basic grammar and vocabulary before you can converse. You can’t expect someone who was never drilled in chords to suddenly be playing Chopin or jazz improv, or who has limited vocabulary and grammar to suddenly write French poetry.
Rote learning is nothing more than learning to give rote responses to rote questions. It’s a skill, and it’s the wrong skill. The problem with a catechism isn’t so much that they you all the answers. It’s that they give you all the questions. That’s no way to learn what you need to know.
(By the way, I find most FAQs to be a waste of time.)
Ultimately the only way to learn something is to do it. The way to learn the foundations is to do the foundations. From which it follows that the way to teach the foundations is to drill the foundations. Not some stupid catechism of question-and-response, but actual application of the fundamentals to simple problems that approximate – in simplified form – real world situations.
The way to learn a language is to use the language. The way to learn a branch of math is to use the branch. The way to learn music is to play it.
Language: Start with a limited vocabulary and a fairly comprehensive grammar. Practice all the sentence structures this way. Learn pronunciation and hearing comprehension this way. Then add vocabulary to deal with ever more real world situations. The great bulk of vocabulary is specific to a domain. The vocab you need depends entirely on what you want to talk about.
Business math: Start by adding a column of numbers. From this progress to a ledger, and then to a balance sheet… your graduation exercise will be to start a business.
Engineering math: Start with exponential notation and algebraic notation. Then some canned algebraic equations to predict results of simple lab experiments. Check your math by doing the lab experiment. Then go on to more complicated machines that call for more complicated calculations. Here’s where you bring in algebra and calculus.
Number theory: Fiddle with cryptographic algorithms and data structures. Or else don’t bother.
Music: Start with an instrument that’s easy to play – a keyboard instrument. Learn the chords by playing the chords. Learn the keys and modes by playing the scales. Then learn improv by noodling. Not too much drill – that will slow you down. Skill will come in its own time, but learn the basics now by doing the basics now. And maybe switch to guitar at some point.
What of abstract knowledge, you ask? Screw abstract knowledge. It’s not actually about anything, is it?
Tellers, von Neumanns and Newtons would probably learn arithmetic just fine with common core. They would do just fine without it, too.
If your child is normal-ish, he needs repetitive drill, and he will not learn anything by being encouraged to “explore.”
90+% of the population wants to be told THE answer, and will not, cannot think successfully.
“Wang Wei Lin is right: memorization of the very basics is the foundation. It’s not trendy, and it’s boring to teach, but for most students it’s the best way.”
It isn’t mentioned but they made the same mistake with whole language, I think it was called, instead of phonics. They taught kids to read with hieroglyphics of the whole word instead of the basics. Phonetics are the main big advantage over graphic whole symbol based writing systems and they ignored it.
I think what they were trying to do was to mimic the people who read fast by seeing the whole word as one but that doesn’t work for everyone and probably doesn’t work as well if you skip the phonics part.
I wonder if the “new” math essentially did the same. Study accomplished math students and try to replicate their performance by skipping steps.
I once heard Pierre Deligne say that his children stopped asking him for help with their homework because he would suggest many different ways to solve a problem. Regression to the mean.
But even Von Neumann said that in mathematics, you don’t understand things, you just get used to them. A hyperbolic truth.