PD3: Looking at learning activities

1. PD3: Looking at learning activities

2. Aims of the session This session is intended to help us to: • explore the different types of mathematical activity contained in the resource. • Classifying mathematical objects. • Interpreting multiple representations. • Evaluating mathematical statements. • Creating problems. • Analysing reasoning and solutions.

3. 1. Classifying mathematical objects • Learners examine and classify mathematical objects according to their different attributes. They create and use categories to build definitions, learning to discriminate carefully and to recognise the properties of objects. They also develop mathematical language.

4. In each triplet, justify each of a, b, and c as the ‘odd one out’

5. Classifying using 2-way tables

6. Classifying using 2-way tables

7. 2. Interpreting multiple representations • Learners match cards showing different representations of the same mathematical idea. • They draw links between different representations and develop new mental images for concepts.

8. 2. Interpreting multiple representations

9. 3. Evaluating mathematical statements • Learners decide whether given statements are always, sometimes or never true. • They are encouraged to develop: • rigorous mathematical arguments and justifications; • examples and counterexamples to defend their reasoning.

10. Always, sometimes or never true?

11. Always, sometimes or never true?

12. Always, sometimes or never true?

13. True, false or unsure?

14. 4. Creating and solving problems • Learners devise their own mathematical problems for other learners to solve. • Learners are creative and ‘own’ the problems. • While others attempt to solve them, learners take on the role of teacher and explainer. • The ‘doing’ and ‘undoing’ processes of mathematics are exemplified.

15. Developing an exam question

16. Developing an exam question

17. Doing and undoing processes Kirsty created an equation, starting with x = 4. She then gave it to another learner to solve.

18. Doing and undoing processes

19. Doing and undoing processes

20. 5. Analysing reasoning and solutions Learners compare different methods for doing a problem, organise solutions and/ or diagnose the causes of errors in solutions. They begin to recognise that there are alternative pathways through a problem, and develop their own chains of reasoning.

21. Comparing different solution strategies Analysing reasoning and solutions

22. Analysing reasoning and solutions Correcting mistakes in reasoning. • In January, fares went up by 20%. • In August, they went down by 20%. • Sue claims that: “The fares are now back to what they were before the January increase.” • Do you agree?

23. Analysing reasoning Putting reasoning in order