Chapter 3 Problem solving using mathematics

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

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

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

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

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

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

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?

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?