Primary Mathematics: 10 day course

1. Primary Mathematics: 10 day course Developing mathematical thinking MEYL624 October 2007 Hampshire Mathematics Advisory Team in partnership with the Open University

2. Reflecting on….. • the nature of mathematical thinking; • the nature of mathematics; • how mathematics is learnt; • different ways that you might teach it; • how mathematics is used; and • how technology can influence all of these.  The Open University

3. Key themes • Mathematics • Mathematical Thinking • Learning Mathematics • Teaching Mathematics  The Open University

4. Knowing and doing  The Open University 2.1 Task 2b

5. Tasks from Module 1 Can a bank robber, working alone, take £5 000 000 from a bank in £5 notes? Estimate the number of piano tuners in the UK. You are sitting comfortably at home reading this module. A siren starts and the radio broadcasts a ‘red alert’. You have one hour to get as far away as possible. How far away from your home could you get? Someone has suggested that a quick way to add the first ten odd numbers is by squaring 10. Is this true? 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 might you prove that your answer to (ii) is correct?  The Open University

6. Reflecting on the tasks Are these really mathematical questions? • If you think they are mathematical, then what mathematics was involved? (In answering this, were you thinking of the nature of the questions, or the nature of your solutions?) - Would they be suitable questions in school mathematics lessons?  The Open University

7. Types of problems  The Open University 2.2 Task 2c

8. Which of these problems are ‘theoretical’ mathematics problems? • Which are practical or applied problems that model real situations? • Which are design problems where more information is likely to be needed?  The Open University 2.2 Task 2c

9. Alternative solutions Alternative solutions Alternative solutions Alternative solutions A farmyard contains both chicken and sheep. The farmer knows there are 26 heads and 74 legs. How many chickens and how many sheep are in the yard?  The Open University 2.2 Task 2d

10. Zios and Zepts 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? by Jenni Murray (NRICH)

11. Creepy Crawlies Ross collects lizards, beetles and worms. He has more worms than lizards and beetles together. Altogether in the collection there are twelve heads and twenty-six legs. How many lizards does Ross have? Thinking mathematically: John Mason, Leone Burton, Kaye Stacey

12. Mathematical powers • Imagining and expressing • Specialising and generalising • Ordering and classifying • Conjecturing and convincing Ref: John Mason

13. Being certain  The Open University 2.3 Task 2g

14. Always, sometimes, never?  The Open University 2.3 Task 2h

15. Thought experiment  The Open University 2.5 Task 2l