More educational malpractice: the sad legacy of Everyday Math, II

Here's a follow-up post to my first "sad legacy of Everyday Math" post, in which I concluded by saying that

You can’t blame the mathematical deficiencies of these 4th and 5th graders on their parents: both the private school and the after school program select for parents who care about education. You can’t blame it on the kids: my kids, who clearly wanted to learn, had been admitted [to our after school program] in part based on their behavior.

Picking up from there, the second post proceeded as follows:

You also can't blame it on language problems; these kids are fluent in English. In fact, there's really only one thing outside the Everyday Math curriculum that one can possibly point a finger to, and that is that these immigrant parents (many of them don't speak English) don't realize what many native-born parents already know: namely, that they can't count on the schools to fully educate their children.

So these kids are a case study in what happens when you leave math instruction entirely up to Everyday Math practitioners. And the answers to this question are slowly coming in.

For several of the 5th graders I work with, it turns out that not only do they not know how to borrow across multiple digits; they also don't know their basic addition and subtraction "facts." In other words, they don't automatically know that, say 5 plus 7 is 12, or that 15 - 8 is 7; instead they count on their fingers.

This got me thinking about addition and subtraction "facts." Back in my day, there was no issue of kids  learning these facts as such. Yes, we memorized our multiplication tables. But we never set about deliberately memorizing that 5 plus 7 is 12. Why? Because the frequency of the much-maligned "rote" calculations we did ensured that we, in today's lingo, constructed this knowledge on our own.

Back in my day, a typical third grade arithmetic sheet looked something like this:

And a typical fourth grade arithmetic sheet looked something like this:

But in Reform Math programs like Everyday Math, such pages filled with calculations are only occasional, and each problem involves a much shorter series of calculations. Here's a set from 4th grade Everyday Math:

Each multi-digit addition problem amounts to a series of simple addition problems. For example, adding two two-digit numbers involves adding at least two pairs of numbers; three if one is regrouping. Adding three three-digit numbers can involve 8 iterations of simple addition. Some of the problems in the second traditional math sheet involve as many as 17 iterations of simple addition.

In the traditional 4th grade math scenario, we may have had 25 problems per day like those in the first two sheets above, 5 days a week. With Everyday Math, you might get, at best, 25 problems like those in the second two sheets above per week.

Putting it all together, the resulting difference in the amount of practice with basic addition "facts" is quite large.  5 (days) times 25 (problems) times (say, as an average of iterations of simple addition) 10 for the traditional math curriculum versus 1 (day) times 25 (problems) times (average iterations) 3 for the Everyday Math curriculum. Assuming I'm not screwing up my arithmetic, that's 1,250 vs. 75 basic addition calculations per week. No wonder so many of those who are educated exclusively through Everyday Math don't know their "addition facts" by grade 5!

Ah, but surely their "conceptual understanding" is deeper. Note the calls for "ballpark estimate" at the bottom of each Everyday Math problem, where traditional math simply has you calculate. Stay tuned: in my next post on this topic, I'll discuss the state of conceptual understanding in my Everyday Math mal-educated 5th graders.

Does progressive education have to mean watered down math?

One of the most common criticisms of "progressive math", aka "reform math", is that the math itself is highly watered down--a natural consequence of the inefficiencies of child-centered discovery learning.

But every once in a while, I'm reminded that there are other incarnations of "progressive education" in which the math is anything but watered down.

My mother, for example, attended a self-proclaimed progressive private school in the 1950s where she got a very solid education in math (not to mention English, French, and history). In fact, a number of the algebra problems I've excerpted in my math comparison problems (comparing traditional U.S. math with Reform Math) came from her algebra book.

Now we have a very interesting article from this week's New Yorker about 3rd grade math at a progressive school in Chengdu, modeled after John Dewey. Here is one of the third grade math problems the author's twin took home with them:

While multiplying one two-digit number by another two-digit number, Little Sloppy misreads 22 as 25, and as a result his answer is higher than the correct answer by 69. What is the correct answer.

How many American 3rd graders can do this problem--no matter how "progressive" (or not) their math classes are?

Two years later, when the family returns to the U.S. but the twins continue to learn Chinese math through a remote tutor, they're doing problems like:

A certain number, when divided by 3, leaves a remainder of 2; when divided by 4, leaves a remainder of 3; when divided by 5, leaves a remainder of 4. What is the smallest that this number could be?

“Math is virtue"; “Math is a way to cultivate yourself," the author quotes the third grade math teacher as saying. 

America's "progressive math" proponents seem to see things differently.