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January 14, 2013

A Math Teacher on Common Core Standards

Stephanie Sawyer, via a kind reader's email:

I don't think the common core math standards are good for most kids, not just the Title I students. While they are certainly more focused than the previous NCTM-inspired state standards, which were a horrifying hodge-podge of material, they still basically put the intellectual cart before the horse. They pay lip service to actually practicing standard algorithms. Seriously, students don't have to be fluent in addition and subtraction with the standard algorithms until 4th grade?

I teach high school math. I took a break to work in the private sector from 2002 to 2009. Since my return, I have been stunned by my students' lack of basic skills. How can I teach algebra 2 students about rational expressions when they can't even deal with fractions with numbers?

Please don't tell me this is a result of the rote learning that goes on in grade- and middle-school math classes, because I'm pretty sure that's not what is happening at all. If that were true, I would have a room full of students who could divide fractions. But for some reason, most of them can't, and don't even know where to start.

I find it fascinating that students who have been looking at fractions from 3rd grade through 8th grade still can't actually do anything with them. Yet I can ask adults over 35 how to add fractions and most can tell me. And do it. And I'm fairly certain they get the concept. There is something to be said for "traditional" methods and curriculum when looked at from this perspective.

Grade schools have been using Everyday Math and other incarnations for a good 5 to 10 years now, even more in some parts of the country. These are kids who have been taught the concept way before the algorithm, which is basically what the Common Core seems to promote. I have a 4th grade son who attends a school using Everyday Math. Luckily, he's sharp enough to overcome the deficits inherent in the program. When asked to convert 568 inches to feet, he told me he needed to divide by 12, since he had to split the 568 into groups of 12. Yippee. He gets the concept. So I said to him, well, do it already! He explained that he couldn't, since he only knew up to 12 times 12. But he did, after 7 agonizing minutes of developing his own iterated-subtraction-while-tallying system, tell me that 568 inches was 47 feet, 4 inches. Well, he got it right. But to be honest, I was mad; he could've done in a minute what ended up taking 7. And he already got the concept, since he knew he had to divide; he just needed to know how to actually do it. From my reading of the common core, that's a great story. I can't say I feel the same.

If Everyday Math and similar programs are what is in store for implementing the common core standards for math, then I think we will continue to see an increase in remedial math instruction in high schools and colleges. Or at least an increase in the clientele of the private tutoring centers, which do teach basic math skills.

Related links: Math Forum.

Posted by Jim Zellmer at January 14, 2013 3:56 AM
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"Stephen Wolfram is the creator of Mathematica, the author of A New Kind of Science, the creator of Wolfram|Alpha, and the founder and CEO of Wolfram Research. Over the course of his career, he has been responsible for many discoveries, inventions and innovations in science, technology and business.

Born in London in 1959, Wolfram was educated at Eton, Oxford, and Caltech. He published his first scientific paper at the age of 15, and had received his PhD in theoretical physics from Caltech by the age of 20. Wolfram's early scientific work was mainly in high-energy physics, quantum field theory, and cosmology, and included several now-classic results. Having started to use computers in 1973, Wolfram rapidly became a leader in the emerging field of scientific computing, and in 1979 he began the construction of SMP—the first modern computer algebra system—which he released commercially in 1981." -- From Stephen Wolfram's site.

Wolfram gave an interesting TED presentation in which he gave very short shrift to practicing the algorithms, focusing instead on conceptual understanding and use of computers to help with that task.

This brilliant mathematician and scientist is not alone in his position. Alan Kay seems also in support, and I have heard other mathematicians say the same things. My experience with my daughter's education at MMSD schools, and my brief experience with middle school kids at Toki relying on calculators instead of knowing simple addition and multiplication has left me scratching my increasingly balding head.

I have no doubt, the use of computers and calculators in elementary school, middle school, and high schools are the primary cause of poor mathematics ability of students.

Wolfram's TED presentation, which I just saw again today, seemed so off-the-mark. I can't image how any student can learn even simple arithmetic and see interesting and important patterns, if the computers are doing the work.

If I recall from the last time I looked at NCTM, I've been disappointed in their positions. I never thought the T of STEM would mean replacing mental work of students with programmers' knowledge.

Is it case that those who are blessed with the capabilities of those like Wolfram have no clue about what it takes "normal" students to acquire math knowledge? Is there another answer? Whatever that answer is, I can't image how such mathematicians can be so wrong.

Posted by: Larry Winkler at January 14, 2013 7:04 PM

Along these lines, and perhaps somewhat at odds with Wolfram's position, Wolfram wrote these words on his blog regarding Richard Feynman, who he first knew when Feynman was 60 and Wolfram was 18. Here is a bit of what Wolfram says:

"It's kind of interesting to look at. His style was always very much the same. He always just used regular calculus and things. Essentially nineteenth-century mathematics. He never trusted much else.
But wherever one could go with that, Feynman could go. Like no one else.

I always found it incredible. He would start with some problem, and fill up pages with calculations. And at the end of it, he would actually get the right answer!
But he usually wasn't satisfied with that. Once he'd got the answer, he'd go back and try to figure out why it was obvious.

And often he'd come up with one of those classic Feynman straightforward-sounding explanations. And he'd never tell people about all the calculations behind it.
Sometimes it was kind of a game for him: having people be flabbergasted by his seemingly instant physical intuition. Not knowing that really it was based on some long, hard calculation he'd done.

He always had a fantastic formal intuition about the innards of his calculations. Knowing what kind of result some integral should have, whether some special case should matter, and so on.

And he was always trying to sharpen his intuition."

Posted by: Larry Winkler at January 14, 2013 8:16 PM
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