Friday, December 12, 2014

Math problem of the week: Common Core-inspired first grade arithmetic


From an article in last week's Education Week, entitled Parents Get schooled on New Math Standards.

Here's more:
Jennifer Bonds, a parent at Old Orchard Elementary School in north-central Toledo, said she was watching her 3rd grader do math problems last year, "and I was like, wait a minute, I don't understand what you're doing!" The boy was calculating multi-digit addition and subtraction starting from the tens or hundreds place, and working down to the ones.

"I said, 'You can't do math from left to right,' " Ms. Bonds said.

She soon found out that, actually, he could. By attending parent math days held last year and this year at the school, Ms. Bonds learned that the common standards encourage students to add and subtract in a variety of ways other than the vertical carry-and-borrow methods she was taught, including by separating the tens and the ones.[Emphasis added.]  
Common Core advocates generally don't mention this, but alternative methods of adding have been around for a very long time. Nor are they incompatible with the standard vertical carry-and-borrow algorithms. One way to add a long column of digits in the ones (or tens, or hundreds, etc.) place, after all, is to make tens out of pairs and triplets of those numbers (and then to carry those tens over to the next place). I did that all the time as a kid.

What's changed is that, ever since the dawn of Reform Math in the early 1990s, these alternative methods have been crowding out rather than supplementing the standard algorithms.

What hasn't changed, meanwhile, is the fact that the standard algorithms, for arbitrary, arbitrarily large numbers, are by far the most efficient and the least prone to user errors. They are also, arguably, the best way to explore the subtleties of place value.

Finally, they are often easier to carry out than the alternative algorithms. Here's Ms Bond's take on the alternative method of adding: "It makes it look more difficult than it actually is."

Perhaps that's why American Reform math falls so far behind Singapore math and other more traditional curricula--even by the end of first grade.

1 comment:

Anonymous said...

"What hasn't changed, meanwhile, is the fact that the standard algorithms, for arbitrary, arbitrarily large numbers, are by far the most efficient and the least prone to user errors"

Which is why (like phonics for reading) they must be eliminated, lest the little people be able to read and calculate.