Saturday, January 21, 2017

Teaching Math

I was a big fan of Liping Ma's Knowing and Teaching Elementary Mathematics.  She asserted that Chinese elementary teachers had PUFM (profound understanding of fundamental mathematics) and too many American elementary teachers did not. (I've written several posts mentioning Liping Ma.)

There is a big difference between Shanghai teacher training and US/UK teacher training, just as there is a big difference between Shanghai elementary student math expectations and US/UK elementary student math expectations.  I was reminded of this after reading a BBC article:
When the Chinese city of Shanghai took part in the three-yearly Pisa test of 15-year-olds' academic ability in 2009 and 2012 it topped the table in maths, leaving countries such as Germany the UK and the US - and even Singapore and Japan - trailing in its wake. What is its secret?

The life of a teacher in a Shanghai primary school differs quite a bit from that of teachers in most other countries. For one thing each teacher specialises in a particular subject - if you teach maths, you teach only maths.

These specialist teachers are given at least five years of training targeted at specific age groups, during which they gain a deep understanding both of their subject and of how children learn.

After qualifying, primary school teachers will typically take just two lessons per day, spending the rest of their time assisting students who require extra help and discussing teaching techniques with colleagues.

"If you compare that to an English practitioner in a primary school now, they might have five days of training in their initial teacher training year, if they're doing the School Direct route, for example," says Ben McMullen, head teacher of Ashburnham Community School, London...

There are other differences too. School days are longer - from 07:00 until 16:00 or 17:00. Class sizes are larger. And lessons are shorter - each is 35 minutes long, followed by 15 minutes of unstructured play.

There is no streaming according to ability and every student must understand before the teacher moves on. In the early years of school basic arithmetic is covered more slowly than in the UK, says McMullen, who has travelled to Shanghai in one of the groups of British teachers sent every year by the Department of Education to watch and learn.

"They looked at our curriculum and were horrified by how much we were trying to teach," he says.

"They wouldn't teach fractions until year four or five. By that time, they assume that the children were very fluent in multiplication and division.

"This is essentially a 'teaching for mastery' approach: covering less and making smaller incremental movements forward, ensuring the class move together as one and that you go over stuff again and again until it's truly understood."
There's something to be said for this approach.  And if you believe that all children should learn, and you believe that education is the most likely approach to alleviating or eliminating the effects of poverty, then this should make sense.

"Spiraling" and "exposure" don't work as well as mastering it the first time.  On the other hand, I'm entirely against not allowing the brightest students to move forward at a faster pace.  While I want every student to have mastered the basic curriculum, I don't want every student to exit the curriculum at the same exact spot.


Ellen K said...

I've been reading studies on how people who memorized multiplication (and other) facts, actually use a different part of our brain to calculate which is sometimes more efficient. When I was in school, memorization of poetry every year was a staple. Now teachers are told rote learning is bad. But how much easier would it be to move to higher math (or other) skills if you already knew the basic level of information? I doubt that the Indians, Russian, Koreans or Chinese are handing out calculators to elementary school students telling them to just punch numbers and not talking about internalizing some of those facts. This may be why their students, even when they arrive here with little English language acquistion, often surpass our own in pure math and science calculations.

Anonymous said...

From what I have read, Shanghai is not typical of China. I understand that it is the financial heart and home to many high-performing families, but I have read that people who have come from elsewhere/rural areas, to work in Shanghai, Beijing and other cities are not allowed to live in those cities (special compounds outside, perhaps with walls/gates) and their kids are not allowed to attend the city schools. The Shanghai schools may be more like schools in Silicon Valley, Scarsdale NY, Winnetka ILor Potomac MD than any of our average schools. Not just exactly representative.