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.

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?

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

-Mark Roulo

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.

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.

I got angry with my son once because I thought he was ignoring his EM homework in his fifth grade “Study Links” workbook. I turned my back for just 5 minutes. He said: “I did it already.” There were only 8 simple problems they had to do. Simple if you knew how to do the problem already. If you didn’t, then good luck trying to track down an explanation. Good luck for a parent who tries to help. If you talk to the teacher, you will probably be told that it’s OK, they will see the material again. No! It won’t be OK.

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.

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?