Primary Mathematics: Primary Mathematics: 10 day course10 day course

Developing mathematical thinkingDeveloping mathematical thinkingMEYL624MEYL624

October 2007October 2007

Hampshire Mathematics Advisory Team Hampshire Mathematics Advisory Team in partnership with the Open Universityin partnership with the Open University

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Reflecting on…..Reflecting on…..

the nature of mathematical thinking; the nature of mathematical thinking; the nature of mathematics; the nature of mathematics; how mathematics is learnt; how mathematics is learnt; different ways that you might teach it; different ways that you might teach it; how mathematics is used; and how mathematics is used; and how technology can influence all of these. how technology can influence all of these.

The Open University

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Key themesKey themes

Mathematics Mathematics

Mathematical Thinking Mathematical Thinking

Learning Mathematics Learning Mathematics

Teaching MathematicsTeaching Mathematics

The Open University

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Knowing and doingKnowing and doing

2.1 Task 2b

The Open University

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Tasks from Module 1Tasks from Module 1

Can a bank robber, working alone, take £5 000 000 from a bank in £5 notes?

Estimate the number of Estimate the number of piano tuners in the UK.piano tuners in the UK.

You are sitting comfortably at home reading this module. You are sitting comfortably at home reading this module. A siren starts and the radio broadcasts a ‘red alert’. A siren starts and the radio broadcasts a ‘red alert’. You have one hour to get as far away as possible. You have one hour to get as far away as possible. How far away from your home could you get?How far away from your home could you get?

Someone has suggested that a quick way to add the first ten odd numbers Someone has suggested that a quick way to add the first ten odd numbers is by squaring 10. Is this true?is by squaring 10. Is this true?Is there a similar rule for any numbers other than the first ten odd numbers? Is there a similar rule for any numbers other than the first ten odd numbers? How would you convince someone that your reply to (ii) is correct?How would you convince someone that your reply to (ii) is correct?How might you prove that your answer to (ii) is correct?How might you prove that your answer to (ii) is correct?

The Open University

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Reflecting on the tasksReflecting on the tasks

Are these really mathematical questions?Are these really mathematical questions?

- If you think they are mathematical, then what If you think they are mathematical, then what mathematics was involved? (In answering this, mathematics was involved? (In answering this, were you thinking of the nature of the questions, were you thinking of the nature of the questions, or the nature of your solutions?)or the nature of your solutions?)

-- Would they be suitable questions in school Would they be suitable questions in school mathematics lessons?mathematics lessons?

The Open University

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Types of problemsTypes of problems

2.2 Task 2c

The Open University

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Which of these problems are ‘theoretical’ Which of these problems are ‘theoretical’ mathematics problems? mathematics problems?

Which are practical or applied problems Which are practical or applied problems that model real situations? that model real situations?

Which are design problems where more Which are design problems where more information is likely to be needed? information is likely to be needed?

2.2 Task 2c

The Open University

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Alternative solutionsAlternative solutions

A farmyard contains both chicken A farmyard contains both chicken and sheep. The farmer knows and sheep. The farmer knows there are 26 heads and 74 legs. there are 26 heads and 74 legs. How many chickens and how How many chickens and how many sheep are in the yard?many sheep are in the yard?

Alternative solutionsAlternative solutionsAlternative solutionsAlternative solutionsAlternative solutionsAlternative solutions

2.2 Task 2d

The Open University

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by Jenni Murray (NRICH)

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico, who first discovered the planet, saw a crowd of Zios and Zepts. He managed to see that there was more than one of each kind of creature before they saw him. Suddenly they all rolled over onto their backs and put their legs in the air. He counted 52 legs. How many Zios and how many Zepts were there?

Zios and ZeptsZios and Zepts

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Creepy CrawliesCreepy Crawlies

Ross collects lizards, beetles and Ross collects lizards, beetles and worms. He has more worms worms. He has more worms than lizards and beetles together. than lizards and beetles together. Altogether in the collection there Altogether in the collection there are twelve heads and twenty-six are twelve heads and twenty-six legs. How many lizards does legs. How many lizards does Ross have?Ross have?

Thinking mathematically: John Mason, Leone Burton, Kaye Stacey

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Mathematical powersMathematical powers

Imagining and expressingImagining and expressing

Specialising and generalisingSpecialising and generalising

Ordering and classifyingOrdering and classifying

Conjecturing and convincingConjecturing and convincing

Ref: John MasonRef: John Mason

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Being certainBeing certain

2.3 Task 2g

The Open University

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Always, sometimes, never?Always, sometimes, never?

2.3 Task 2h

The Open University

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Thought experimentThought experiment

2.5 Task 2l

The Open University