Algebra Handshake

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    • 00:05

      [MUSIC PLAYING]

    • 00:14

      ISAAC ANOOM: The fun bit is the prediction.The fun bit is the getting the answer with confidence, OK?

    • 00:20

      NARRATOR: Isaac Anoom, Mr. Numbervator,was invited into Mount Pleasant Lane Schoolto take a year six class in algebra.

    • 00:28

      ISAAC ANOOM: Let's shake hands.How many handshakes can two people make?One.OK.Right.If there's three people, how many handshakescan three people make?

    • 00:38

      FRAN BRADSHAW: Isaac, we asked you to do a lesson on algebra.How did you think that the handshake problem addressedthe issues?

    • 00:44

      ISAAC ANOOM: What I was looking atwas this idea of pattern spotting.And the fact that the children wereable to sort of record their observations,and then actually identify the pattern, explain the pattern,and talk about the pattern.And so that was my way in to the actual session and lessonitself.Four people.How many hands?[ALL] Eight.

    • 01:05

      ISAAC ANOOM: How many handshakes?[ALL] Six.

    • 01:07

      ISAAC ANOOM: Right.Look at what I've written on the board.Can anyone have a little think?We know this column here.We know that we're doubling, because this boy, here, said,we're going to times it by two because of the number of hands.But look at this column here.Can anyone see what is happening here?

    • 01:24

      STUDENT: It's adding one, then adding two, and then addingthree.

    • 01:28

      ISAAC ANOOM: Right.So, Sammy, then can you tell me, if all Ihave got five people, how many hands will there be?

    • 01:37

      STUDENT: 10.

    • 01:38

      ISAAC ANOOM: The number of handshakeswill be how much, then?

    • 01:41

      STUDENT: 10.

    • 01:42

      ISAAC ANOOM: How did you know it's going to be 10?

    • 01:44

      STUDENT: Well, because you've added one, then you add two,then you add three, so you must add fouronto six, which means 10.

    • 01:51

      ISAAC ANOOM: Right.Excellent answer.Well done.The problem is, I need to know how many handshakeswill 10 people make?And 15.And 20.

    • 02:06

      FRAN BRADSHAW: I loved their different methods of recording.If you noticed, particularly the girls were perfectly neatin their recording.And the boys who grasped the pattern spotting immediately,simply wrote the answers, and simply wrote the list,as it went through.But what interested me most was the young boywho thought he came up with a generalization--

    • 02:26

      FRAN BRADSHAW [continued]: that he could double the pattern--and I found that fascinating.And I particularly loved the way you handled that.

    • 02:33

      STUDENT: Once I got to 20, I just doubled it to 40,then doubled 40 to 80.

    • 02:38

      ISAAC ANOOM: Right.So do you think we're just doubling all the time?

    • 02:42

      STUDENT: Mmm, sometimes.

    • 02:43

      ISAAC ANOOM: What was the answer for Number 5?Five people, how many handshakes?

    • 02:46

      STUDENT: Um, 5 were 10.

    • 02:48

      ISAAC ANOOM: Right.So if I double the answer for five,what's your answer there for 10?

    • 02:53

      STUDENT: Oh.

    • 02:54

      ISAAC ANOOM: So it's not doubling, is it?

    • 02:56

      STUDENT: No.But listen.You had an idea.We tested it out.It didn't work.So now you can move on again independently, can't you?

    • 03:03

      ISAAC ANOOM: And he didn't feel that he was wrong.He didn't feel that he made a mistake,or someone was going to look at him.He just knew, automatically, that hehad to go back and revise his answer.

    • 03:13

      DAVID FUNNELL: And that's the sort of thingI want to encourage within the class--that the children are aware that they are allowedto make mistakes, because they will learn from those mistakes.And it's the children that made the mistakes thatwere determined to go on and succeed.

    • 03:26

      FRAN BRADSHAW: The other thing I noticedwas that the children were all incredibly quick at observingthe pattern, and then repeating the patternon their white boards.But you stopped them at one stage,because in order to get them to think algebraically,you are wanting them to go to the next level.And that's when you brought them out to the front,

    • 03:47

      FRAN BRADSHAW [continued]: and used them physically to get the task of the observation--if there were 6 of them, the pattern would go 5 plus 4,plus 3, plus 2, plus 1.And that generated something which was really exciting.Do you remember that, David?

    • 04:04

      DAVID FUNNELL: Yes.The one that said, oh, it's minus one.

    • 04:07

      FRAN BRADSHAW: Fantastic.

    • 04:08

      DAVID FUNNELL: And he took one step towards algebra.

    • 04:11

      ISAAC ANOOM: Yes.

    • 04:11

      STUDENT: Well, since you've already, like,you're missing one child.You won't count himself.So every it will go around, he'll be missing,like, himself.So each time, it will go minus 1.

    • 04:24

      ISAAC ANOOM: It's always going to be minus 1.So minus 1 is coming to this.It's always going to be minus 1.We're looking at number, we're looking at algebra.And when you mentioned minus 1 to me,this is what comes into an actual equation.It comes into algebra.You are talking in terms of representing numberswith people, and people we've numbers.

    • 04:46

      FRAN BRADSHAW: As a year 6 teacher,David, do you find teaching algebra tricky?

    • 04:52

      DAVID FUNNELL: I think there are thoseat the top of the group who will find it great.They love it.They enjoy it.They want to get involved.They know it's a next step for them.And there are those that are towards the middleand the lower end of the group who find it really trickytoo grasp the idea.But I think by applying it to this idea of a pattern,then they will be able to think to themselves,

    • 05:12

      DAVID FUNNELL [continued]: OK, it's not just "n" we're putting in.We're putting in "n" because we don't know what number it is.And if we applied it to this pattern each time,we could find the answer in every occasion.I think they will link the two in much better now.

    • 05:25

      FRAN BRADSHAW: So I think that there'squite a bit of work that needs doing on, certainly,the empty box bit, much lower down the school,so they get used to that-- that they're not alwaysgoing to know a quantity.So once you progress them from the empty box, the spottingof patterns, the coming up with predictions,the generalizations, the moving into the function

    • 05:47

      FRAN BRADSHAW [continued]: machine where they're giving you a rule.And once they can spot the rule that's happening,then I think we're on the way to making algebraeasier for children to grasp.

    • 05:58

      ISAAC ANOOM: Definitely.[MUSIC PLAYING]

Algebra Handshake

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Abstract

Isaac Anoom uses pattern spotting to introduce algebra in a year 6 math class.

Algebra Handshake

Isaac Anoom uses pattern spotting to introduce algebra in a year 6 math class.

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