Elizabeth Green’s Why do Americans Stink at Math? didn’t go far enough, writes Dan Willingham. Improving math instruction is even harder than she thinks.

The nub of her argument is this. American stink at math because the methods used to teach it are rote, don’t lead to transfer to the real world, and lead to shallow understanding. There are pedagogical methods that lead to much deeper understanding. U.S. researchers pioneered these methods and Japanese student achievement took off when the Japanese educational system adopted them.

. . . Traditional classrooms are characterized by the phrase “I, We, You.” The teacher models a new mathematical procedure (“I”), the whole class practices it (“We”), and then individual students try it on their own (“You”). That’s the method that leads to rote, shallow knowledge. More desirable is “You, Y’all, We.” The teacher presents a problem which students try to solve on their own (“You”). Then they meet in small groups to compare and discuss the solutions they’ve devised (Y’all). Finally, the groups share their ideas as a whole class (“We”).

Reform math comes around every 30 years, but never gains traction, writes Willingham. Green blames “lack of support for teachers, and the fact that teachers must understand math better to use these methods.”

Green’s take is that if you hand down a mandate from on high “teach this way” with little training, and hand it to people with a shaky grasp of the foundations of math, the result is predictable; you get the fuzzy crap in classrooms that’s probably worse than the mindless memorization that characterizes the worst of the “I, We, You” method.

True enough, writes Willingham. But there’s more.

Green’s preferred method requires teachers to make quick decisions in class when a group gets on the wrong track. “Do you try to get the class to see where it went wrong right away, or do you let them continue, and play out the consequences of the their solution? Once you’ve decided that, what exactly will you say to try to nudge them in that direction?”

Japanese teachers discuss individual lessons in detail to prepare for this. They agree on the best way to teach each lesson down to what numbers are best for examples. And they expect all students to learn the same content with no regard for individual differences.

U.S. teachers are used to teaching autonomy.

The Japanese people are very different from Americans. It is naive to think thay what works well for them will necessarily work well in US schools.

Agreed…

Of course, we could stick to traditional math and go back to what actually worked 30-40 years ago, that is knowledge of basic facts, etc.

Sigh

Don’t know who did that graphic, but the quadratic formula isn’t even correct ~

Yes, you’re right. And at the lower right corner we have the limit as delta t goes to oo of an expression involving ln(e – delta t) which won’t be defined when delta t exceed e. I guess we do stink at math.

I’ve used “Singapore math” for years for the very reasons you point out in the article. They have an American version (which includes American instead of Singapore dollars and an extra page or two inserted on the Ft/Mile/pound/inch etc measurements in addition to the metric system) and it has helped all my children actually learn the foundations of math through grade 6.

Singapore, Saxon, and Kumon are all methods of learning math which are far superior to anything related to Common Core, plain and simple.

They cut out the garbage and get to the math, whereas common core (and other idiotic methods) are more interested in getting students to write about feelings towards math, rather than actually DOING math.

Egad!

Japanese teachers spend half their days in planning and collaboration.

A report from the US Department of Education says:

“Compared to the teachers in the U.S. case study schools, teachers in the Japanese schools have only a little more planning time each week–an average of 1.25 hours more. Although the Japanese teachers do not have significantly larger amounts of planning time, they have more sustained blocks of planning time. This time occurs after students have left school for the day, so teachers are available for collaborative and individual planning.

‘This difference in the structure of planning time appears to be due to two key factors: (1) a relatively longer work day (by 1 to 2 hours) than U.S. teachers; and (2) variable student dismissal times over the course of the week. On at least one day each week students are dismissed early so that teachers have several hours of planning time after the students had left the school building.”

http://hub.mspnet.org/index.cfm/9148

Of course, like most government publications, it was not peer reviewed.

Ironically, a good deal of Japanese collaborative time is devoted to creating lessons that are relatively scripted. American teachers (and union leaders and ed school professors) tend to hate scripted lessons. Perhaps it is different when you have developed them with your colleagues, or perhaps Japanese teachers are more conformist and group-oriented. Or, perhaps, some of both.

In Project Follow Through, Englemann’s Direct Instruction was the most successful, and has been pretty much ignored for the last 40+ years – partially because it’s heavily scripted.

East Asians are definitely more conformist, group-oriented and respectful of authority.

They also have above-average IQs. Their schools are far more homogeneous than ours and I’m betting that the significantly-handicapped aren’t mainstreamed and that disruptive kids (either spec ed or otherwise) are not tolerated in the classroom. The latter two factors used to be true in the US, with the severely disabled never entering schools.