## Saturday, 4 June 2011

### How do the Chinese do it? Part 5

If I was teaching a lesson on long multiplication or long division, I would set an SDPQ starter which contained one of the toughest questions they would face.  It was fascinating to see them trying to wrestle out an answer.  The method I was teaching that lesson would then become closely contextualised into their existing thinking as this existing thinking was now active, rather than being developed somewhere separate in their mind.

They didn't object to doing a lesson on long multiplication or division even if they could do the initial example, because by now they understood the validity and power of having multiple methods and of revisiting structural methods.  But, of course, in general I found they needed far less teaching on basic operations, because we were covering it very effectively through these starters.

One structural lesson I would never miss would be counting the squares in rectancles which leads to grouping them in hundreds tens and unit in a visual representation of the grid method for multiplication, because this so beautifully scaffolds the expansion of quadratic brackets and more.

How do the Chinese do it?  Links to my other blogs in this series.

1. What grade level do you use this with?

Are you attached to calling it SDPQ? I personally don't care for using special terms for the answers, and would be inclined to call this PMTD or ASMD for the process.

2. Hi Sue, I'm a secondary maths teacher who taught age 11-18. I used this with all my students (but particularly 11-16 - there's more to come which explains the relevance to higher attaining older students) and have also used it with trainee teachers.

It's not just that I'm not particularly attached to any particular name for this, I would positively encourage anyone to rename, redesign, extract elements and just in general remain completely in charge of whatever they do in the classroom, taking only what they want from this idea.

And then of course to feedback on what happened if you've got time! :)

3. Did you have a reason for choosing those terms, or is it just what came to you? I've never seen this idea elsewhere. I'm imagining that you dreamed it up while thinking about Ma's accounts of Chinese math education.

I teach math at a community college. I'll point this blog out to the two people who teach the basic skills classes. Would you use this in an algebra course?

4. The task was just something I started to do long before I read Ma Sue. When I read her work I was struck by the similarities in the mathematical structures the Chinese teachers used and I started to use with my students because of this task so I decided to make that link in the blog title. In essence I'm saying I think we can do what the Chinese do and here's here's a good task you can try for yourself to see if you believe me or not.

Sum, difference and product are core vocabulary in the English National Curriculum so I named it that deliberately to force students to become fluent in this vocabulary which picks them up key marks on English exams.

Yes I would use this in an algebra course. Since you raised it I'll make sure I write part 6 this weekend which will give better insight into how.

5. Is this a series of starters that you have run over a period of lessons or is it one lesson's worth of work? I will be trying this idea with a few sets without a doubt!

Getting them using the correct terminology for anything mathematical is always a pain, see integers for example!

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7. This is definitely a series of starters. It would be dull to do this for a big chunk of a lesson. When I'm first teaching them it I sometimes set a couple in one lesson so that they can feel they've got the hang of it.