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shalteir:

Never in my full time career, did my class ever "recite" tables. On supply I've followed a few plans to do this. On supply, of late, I've found children run through the sequence: 4,8,12,16,20,24 etc. Then I've asked them what is, say, 4x4, and I got blank faces. 

Unison voice is a powerful tool.  

Did they show you the early Dave Hewitt videos (which preceeded grid algebra) in 'Developing Mathematical Thinking'?.  If you look in your DVD resources you may find it.  You can see him talking about and using unison voice there.  (It's the one of him circa' 1980s with a 'tash).  

When students are scaling they are very rapidly picturing the 'size' of the result in a way which is not repeated addition (because of the speed with which things are said and the rapid checking which goes on)  I think unison voice supports the learning of how to do this in a way which is not just the memorisation of facts.  

One way to think about it is like thinking about music.  If I gave you a note and asked you to sing a fourth above it, you could sing up the notes (repeated addition) or you could know the interval, if you have learned to hear the ratios of the pitches of the notes.   You can train music students to do either and it is best to train them to do both.  Similarly I think you can train students to do multiplication through repeated addition or you can teach them to picture the relative size of quantities.

shalteir:

My OU course ran 1986-1988, (including the co-ordinator module), it predated dvds, I'm not sure I had the videos either, some things were on early morning tv, not much of it though. I've still got the books, somewhere. I had Y4 then.

Hmmm, well I'll try and summarise the video so you can imagine it, but if that doesn't work do say and I'll either try harder or give up depending on what you say.

Basically, as an introduction to grid algebra, Dave Hewitt is doing consecutive numbers.

 He has a stick which he taps on the wall and says one.
He takes a step to his left (their right), taps the wall and say two.
He takes another step to his left, taps the wall and gestures to the class.  They say three.
and so on for four. 
then he says dot dot dot as he walks a few paces to his left, taps the wall and then he says 200. 
Step to the left, gesture to the class.....
Step to the right, gesture to the class....
Step to the right, gesture to the class  ... let them stumble as they puzzle out 199

and so on, exploring e.g. the boundary between 1,000,000 and 999,999(nasty one)
and then back into negative numbers.  Watch them struggle with the left and rights and the nasty boundaries now.  They stuggle but they enjoy it.

It's a lovely demonstration of unison voice in teaching and how it forces students to estimate answers very quickly and how a huge amount of mental checking goes on by everyone when one voice is out of synch.

If you want to find out more about grid algebra here's a video Dave made after I badgered him to.

http://www.youtube.com/watch?v=SYVW60KQjss

Thanks Dave - it helps so much!  

weebecka:

Here's the reference:

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Bed time reading Mr Gove?  Or perhaps you feel you already understand all these issues having spent a few days in China.

 

weebecka, I'm impressed. Thanks also for the time you've taken over matters in your posts.

weebecka:

sheltair

shalteir:

Btw,my user name is shalteir, (not shelteir)

shalteir:

But no hard feelings about the spelling

shalteir:

as said earlier I did deliver the approaches of the Developing Mathematical Thinking

https://www.ncetm.org.uk/community/thread/73300

Developing Mathematical Thinking at KS3 is still a very good course 

shalteir:

at least up to the NC, when prescription over-ruled some of previous practice

most obviously the art of extracting awarenesses from concrete experience.  Here in Cumbria it wasn't the NC that did it, it was all the stuff that came with it which made it a weapon not a guide.