1. Chapter 3 Problem solving using mathematics

2. Chapter summary
This chapter gives an insight into how a problem solving approach can underpin all learning and teaching of mathematics.
It tackles the key ideas of communication, reasoning and problem solving
It introduces the big ideas of specialising and generalising

3. Starting point 1 3 5 7 … 2 6 10 14 4 12 20 28 8 24 40 56

4. International Baccalaureate
Learners should be:
Exploring, wondering and questioning
Taking and defending a position
Using critical thinking skills to defend a position
Making and testing theories
Experimenting and playing with possibilities
Solving problems in a variety of ways

5. Thinking mathematically
Everyone can think mathematically
Mathematical thinking can be improved by practising reflection
Mathematical thinking is provoked by contradiction, suspense and surprise
Mathematical thinking is supported by an atmosphere of questioning, challenging and reflecting
Mathematical thinking helps in understanding oneself and the world

6. Enquiry and problem solving
Look at the number line below
Look at chunks of the number line that contain consecutive numbers such as 4,5 or 11,12 and so on.
What do notice about the total. Do you think this is true for any pair of consecutive numbers? Why do you think this?
What about the sum of three consecutive numbers? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

7. Portfolio task
How many squares are there on a chessboard? The answer is not 1 or 64 or 65.

8. Observing problem solving using mathematics
How would you introduce this activity to a class?
What questions would you ask to scaffold the learning?
How would you ensure you left the activity open whilst ensuring it was accessible to all learners?
How would you encourage generalisation?

9. Reflecting on your learning
How confident do you feel in:
Supporting your learners in tackling an open investigation in mathematics?
Modeling being a mathematician?
Supporting children in articulating their thinking processes by articulating your own thinking process?