Friday, February 21, 2014

Math problems of the week: 4th grade 1920s math vs. Everyday Math

Two approaches to multidigit multiplication:

I. From Hamilton's Essential's of Arithmetic, First Book, published in 1919:

II. From the Everyday Math 4th grade Student Math Journal, Volume 1, published in 2002:


Auntie Ann said...
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Auntie Ann said...

We sent this in a letter to our school when we were trying to get them to switch our kid's class to SM. The school had decided to make the switch, but only for the class behind our kid:

>> Everyday Math presents multiple algorithms for solving arithmetic problems. For multiplication, four different methods are presented. The program does not emphasize standard algorithms, so these are not mastered. [...] Using too many methods leads to a great deal of confusion. Many of the algorithms taught (lattice multiplication being a prime example) are not robust enough and do not scale to more difficult problems. Try doing a lattice multiplication problem with four or five digit numbers, or with decimals; it quickly devolves into a mess. Using the classic algorithm for such problems—or even harder ones—is straight forward, and you don’t have to waste time drawing the lattice. The Everyday Math Teacher’s Reference Manual actually states that the lattice method was originally added for its “recreational value and historical interest,” not it's mathematics value, and that, “It is not easy to understand exactly why lattice multiplication works.” (K-3 Edition, 2001, pg 107.) In other words, it’s something to play with, but is hard to understand and not worth spending the kind of time that the school spends on it—time which could be spent actually working to master a robust algorithm. Obviously, Singapore doesn’t teach this at all. I won't even talk about long division; the problems with Everyday Math are well known.<<

I think each of our kids spend several months of their schooling doing lattice.

Allan Folz said...

I was shown lattice math for the first time ever last weekend. It was one of seven(!!!) "artifacts" for performing multiplication. Of the seven, it was also the most inscrutable. All the others I could figure the process, convoluted and unscalable as they were, but lattice really took me a few minutes and a lucky "aha" moment to see what was going on.

It certainly seems sinister. Of all the methods for performing multiplication, it just so happens these texts chose the most confusing one?