The Case for Everyday Mathematics is made by Andy Isaacs of the University of Chicago Mathematics Project in response to Barry Garelick’s critique.

Isaacs writes:

The highly efficient paper-and-pencil algorithms that have been traditional in the U.S. may no longer be the best algorithms for children in today’s technologically demanding world. Today’s elementary school children will be in the workforce well into the second half of the 21st century and the school mathematics curriculum should reflect the technological age in which they will live, work, and compete.

I’m not sure what that means. That kids should use calculators all the time? Or something quite different?

Isaacs defends spiraling:

Research shows that students learn best when new topics are presented at a brisk pace, with multiple exposures over time, and with frequent opportunities for review and practice.

The program offers more supports for teachers and parents, he writes.

Lots of comments, including a response from Garelick on whether research supports EM’s effectiveness.

Education “experts” love to make broad statements about “technology” and use them as justification for their programs. I wonder how many of them actually know anything substantive about key technologies and the ways in which they are applied in business and government.

As an IT worker, I find that argument nothing short of infuriating. If you don’t understand pencil&paper math algorithms, you cannot understand computers. Computers implement those same algorithms in hardware, and if you can’t understand that, you have to treat them as a magic box.

Which is how educrats regard computers.

I often use calculators or Excel to solve math problems. But because I can do it by hand if I need to, I am able to recognize when I’ve made an input error. It’s easy to transpose digits when entering in large numbers, leading to a “whoa, that cannot possibly be the right answer” moment. How are students taught EDM going to be able to recognize when the calculator/spreadsheet gives a “garbage” answer like that?

Oooo, “research shows….” I do love it when they start with that line.

Spiraling is not logical. It may be effective because we don’t teach logical reasoning but I’d say the better cure is to introduce and teach deduction earlier.

As a computer science professor, I find Isaacs’ claim that “The highly efficient paper-and-pencil algorithms … may no longer be the best algorithms for children in today’s technologically demanding world.” simply baffling. Modern technology is built on a foundation of highly efficient algorithms. If anything, the highly efficient algorithms we’ve been using for centuries are MORE important now than they ever have been.

Of course, living up here in the ivory tower teaching the next generation of technocrats, my worldview is a bit skewed. But notice the glaring weasel words in Isaacs’ claim. They “MAY no longer be the best”? There’s a reason you can’t figure out what he means; he isn’t actually saying anything! Excuse me for prying, Mr. Research-Shows, but are they the best or aren’t they? Doesn’t the research you so gleefully cite say something about whether they are the best or not? Aren’t you supposed to be the expert?

One of my favorite comments reads:

I teach math (test prep) to fifth graders in the early morning program. The workbooks are based on Everyday Math. My students found the problems too easy and the topics too brief. I had to make up more difficult problems for them. I also had to drill them in some basics. They needed more basics and more challenge.

The students kept asking for something harder. So when the test was well behind us, I brought them some Euclid. I helped them understand Euclid’s definitions and figure out the first postulate. They were fascinated. But they need challenges of that order in their regular curriculum–not necessarily Euclid, but problems they can wrestle with over and over until they become easy.

According to Isaacs,

“The highly efficient paper-and-pencil algorithms that have been traditional in the U.S. may no longer be the best algorithms for children in today’s technologically demanding world.”For a mathematician, this is unusually fuzzy language. An algorithm is a set of steps which, followed correctly, will produce the correct answer.

Whether you use paper and pencil or a computer program is irrelevant. So what does Isaacs mean by his reference to paper and pencil? Is he claiming that there are better ways (“algorithms”) to do math? If so, what are they?

Also, a look at his CV is quite puzzling. Although he apparently got a couple of degrees in maths, his research and dissertation seem to deal with teaching, not maths.

Very odd.

(Susan): “Oooo, “research shows….” I do love it when they start with that line.”

You beat me to it. Professors of Education call their marijuana-induced hallucinations “research”. Doctor Paul Dumand, of the University of Hawaii College of Education, claimed that “research” demonstrated the superiority of discovery methods in Math education. I asked what research demonstrated this, and he gave me a reference. I read that study, and found that the authors determined that “discovery” methods work based on the rate at which teachers who volunteered to participate in their “discovery” Math program later volunteered to continue. It had nothing to do with improved student performance.

Usually the constructivist/progressive/discovery folks mean “use a calculator” or “estimate” instead of paper-and-pencil multiplication or long division.

-Mark Roulo

Oh, no. It’s worse than you think. It’s not that students are encouraged to use calculators. No, in EM (or Houghton Mifflin Math) they still use paper and pencil to make whatever elaborately confusing diagram will help them answer the question. Sometimes it makes sense, as when a student draws sets to answer a multiplication question. Sometimes they waste a lot of time creating confusing drawings that don’t help them at all.

JeffE: The one problem with memorizing the efficient pencil and paper algorithms, which I did nearly fifty years ago, is that no teacher ever explained why they worked. I doubt that any teacher before 7th grade understood that, so when I needed to implement multi-byte multiplication and division on an 8 bit microcontroller, I had to find some relevant books and figure out how that algorithm worked for myself. But I was certainly better off than if I hadn’t known the algorithm even by rote. And since good mathematicians will always have much better job opportunities than teaching elementary school, it’s better to teach something that is effective, than trying to “guide” the kids to discover something that the teacher might well be unable to fully comprehend…

Memorizing and performing the arithmetic algorithms by rote may help in developing programming skills later in another way – it’s what computers do! A computer doesn’t understand the problem or the solution, but it can still find the solution by precisely following the prescribed steps.