How should we teach elementary mathematics? This is a subject close to my heart and once again the focus of fierce educational warfare. As a student, parent, and spouse of an elementary school teacher I have been exposed to a few of these battles, and it's always presented as a contest of the good new way versus some obsolete old bad way. The latest episode is the battle over so-called "Math Investigations," published by Pearson, developed by a nonprofit called TERC, based, perhaps very loosely, on standards from the National Council of Teachers of Mathematics.

It has attracted a lot of hostility from parents, including some highly mathematically literate parents. It seems to have considerable support for the educational establishment, and is the flagship product of a publishing behemoth.

The basic content, in so far as I can tell, is an emphasis of student discovery of problem solving methods, a strong de-emphasis on memorization, heavy use of calculators, and a role for the teacher as facilitator rather than leader. Students encourage to try different problem approaches like drawing pictures, using manipulables, and counting on their fingers.

The WaPo has this story on some rumbling of parental revolt. A couple of foci for parent anger are the lack of textbooks and wholesale discarding of much traditional nomeclature, and especially, painful experience.

Greg Barlow, an Air Force officer in the defense secretary's office at the Pentagon, was helping his 8-year-old son, Christian, one recent night with a vexing problem: What is 674 plus 249?

The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned. Applying lessons from his school's new math textbook, "Investigations in Number, Data, and Space," Christian tried breaking the problem into easier-to-digest numbers.

But after several seconds, he got stumped. He drew lines connecting digits, and his computation amounted to an upside-down pyramid with numbers at the bottom. His father, in a teacherly tone, nudged him toward the old-fashioned method. "How would you do that another way?" Barlow asked.

A personal pet peeve for me is the de-emphasis memorization. For some reason, modern education has an absolute fetish against it, but memory is probably the most fundamental human talent, and children are very, very good at it.

Defenders of TERC say that they are teaching understanding, not memorized algorithms made obsolete by the calculator.

Carol Knight, Prince William's math supervisor, said that when children break down numbers into multiples of 10 and 100, their understanding of place value and "number sense" increases.

"Memorization will only carry you so far," Knight said. "With 'Investigations,' kids understand the real values of the numbers and are not doing shortcuts. When they multiply 23 times 5, they'll do five 20s to get 100, and then add five 3s to get 15, and they put that all together and get 115. What they've done is made actual use of the numbers."

Sounds reasonable, alright, but it gets a bit messy if you want to multiply, say, 1024 by 319, since you get twelve terms in your sum with up to seven digits in each. Which is why we have calculators.

The battle has been taken to youtube. Anti TERC (and another somewhat similar program called Everyday Mathematics) is represented by : Math Education, an Inconvenient Truth while the case for the defense is presented in here.

If you watch them, I would be interested in your reactions.