Numeracy Teachers in London, 22/10/2008 Woburn House Joan OHagan, Consultant 1 Positive approaches to mathematics Joan OHagan 075157 02991 [email protected].

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 1

Positive approaches to mathematics

Joan O’Hagan075157 02991

[email protected]

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 2

I’m inviting you to look at two questions:

•How far can E3 maths take you?

•How can we create culture change ?to storm in a tea-cup

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 3

E3 maths doesn’t look all that impressive on paper.

For example, you don’t have to do any of the following - they’re all L1)

• recall the 6, 7, 8 or 9 times tables

• work with numbers greater than 1000

• know that 50% = ½

• use the 24 hour clock

• interpret information from tables or diagrams

• do anything with probability

• calculate averages

• though you are expected to be able to use a calculator to

solve problems in context back to prev

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 4

Storm in a tea-cup? Maths to the rescue!

I used to work in an adult residential college with about 50 staff and 100 students. We took our tea-cups everywhere – into classrooms, bedrooms, the garden, the Common Room etc. And every so often the kitchen staff would come to an all college meeting and plead with us to bring the cups back. And we would all nod sympathetically and promise to co-operate. But things didn’t really improve, and one day the discussion got quite heated – as family discussions often do.

“We should have about 250 cups and we’re down to about 100”, the kitchen staff complained. “How are we supposed to manage?”

We all looked at each other.

Who had stolen 150 cups?

“Not me”, we each thought, smugly.

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 5

Then a (history!) tutor had a blinding insight.

“Who has stolen 150 cups? Nobody!

How many of us have dozens of cups secreted away, gathering fungus, in our rooms? None of us.

But how many of us has just one cup sitting on our desks or on the bedroom floor?”

About 150 people blushed and pleaded guilty.

A little mathematics goes a long way.

NIACE Power of Maths Stories.

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 6

My mother told me about a lively discussion she’d had with some friends about washing-up liquids.

The TV ad story was that one where somebody washes stacks and stacks of plates with a single drop of a super-concentrated liquid, but only manages a few plates with a single drop of the cheaper liquids. The super-concentrated, - and more expensive - liquids wash more dishes than the ordinary - and cheaper varieties; so the cost per dish works out less with the super-concentrated ones.

My mother, and her friends, accepted the basic facts. Therefore, said her friends triumphantly, we should buy the super-concentrated ones.

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 7

My mother argued however that if you are doing small amounts of dishwashing, the TV ad scenario doesn’t apply. In the ad, people are doing hundreds of dishes at a time, but she and her friends were usually only washing a few cups and saucers each time.

She realised that there is a minimum amount of liquid which you use each time - a function of the size of the hole in the lid and of the squeeziness of the plastic bottle - and she suspected that this minimum amount – let’s say a single drop - of the super-concentrated stuff was far more than was needed at each of her washing-up sessions, whereas the same quantity of the ordinary stuff was just about right.

Therefore, she hazarded, you’d be wasting the “superness” of the expensive liquids by in effect under-using them; super-concentrated manufacturers (like mustard makers) were making money from the stuff you throw away.

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 8

Sophisticated thinking

“easy” procedures “hard” procedures

Less sophisticated thinking

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 9

“Which way? Which way?” said Alice

Sophisticated thinking

“easy” procedures “hard” procedures

Less sophisticated thinking

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 10

Good starting points for a culture shift ?

• Use the maths we’ve got.

• Use it more often.

• Be our usual sophisticated, clever selves.

This is E3 for grown-ups!

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 11

Two tips:

Ask questions you really would like answered.

Start some of your questions with “What if....?”

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 12

What if....

more people defaulted on their mortgages than the business models predicted?

football teams got 4 points, not 3, for a win, and 2 for a draw?

the programme weightings for the employer-responsive model and the adult learner-responsive model were the same?

we didn’t have a zero?

the public’s votes counted for more than the Strictly judges?

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 13

Are your times tables in good shape?

Joan O’Hagan07515702991

[email protected]

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 14

10

2

3

45

6

7

8

9

Ask 10 people to make a circle, spaced out like this, like a clock with ten numbers.

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 15

You’re going to play with your multiplication tables, starting with the 2 times table.

Give a ball of wool to Zero.

Zero holds one end and throws the ball to Two.

Two pulls the wool tight, wraps it round her finger or holds onto it, and throws the rest of the ball to Four. (If this explanation doesn’t make sense, have a look at the picture below)

Four pulls the wool tight, holds on and throws the ball to Six.

Who throws it to Eight.

Who throws it to ....there isn’t any Ten; but Zero could count as Ten, so Eight throws it to Zero.

Zero would like to throw it to Twelve, but there isn’t any Twelve, so Zero throws it to Two.

And so you go on until it gets either interesting or boring.

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 16

Now try some other tables. Start again at Zero each time. (or take a risk...what if you started somewhere else?) Before you know where you are, you’ll be trying to anticipate what shape each of the multiplication tables will have. You’ll be wondering why Seven is so unpopular. You’ll be trying to work out whether some tables have the same “shape” as others, and if so, why. Or you might just be enjoying making pretty pictures. See over....

Numeracy Teachers in London, 22/10/2008 Woburn House Joan O’Hagan, Consultant 17

Picture reproduced with the kind permission of colleagues at a workshop organised by the Basic Skills Cymru National Support Project, November 07.