Helen Billinge Jen Shearman NCP 4 Workshop 3 Helen Billinge Jen Shearman

Workshop 3 RW

Progression in Reasoning: a reminder Step one:  Describing: simply tells what they did. Step two: Explaining: offers some reasons for what they did. These may or may not be correct.  The argument may yet not hang together coherently. This is the beginning of inductive reasoning. Step three: Convincing: confident that their chain of reasoning is right and may use words such as, ‘I reckon’ or ‘without doubt’. The underlying mathematical argument may or may not be accurate yet is likely to have more coherence and completeness than the explaining stage. This is called inductive reasoning. Step four: Justifying: a correct logical argument that has a complete chain of reasoning to it and uses words such as ‘because’, ‘therefore’, ‘and so’, ‘that leads to’ ... Step five:  Proving: a watertight argument that is mathematically sound, often based on generalisations and underlying structure. This is also called deductive reasoning.

Workshop 3 Session 1: Feedback on Gap Task 2 “How does planning for student responses impact on students’ confidence to reason mathematically?” Find someone from another school What did you do? What was participation in your department like? What was the impact on students’ reasoning? Did students make progress in terms of the “5 steps”?

Workshop 3 Session 1: Feedback on Gap Task 2Conclusions, evidence, next steps “How does planning for student responses impact on students’ confidence to reason mathematically?” Can we draw any general conclusions about the research question? What evidence do we have? What might we do next?

The magic that is reasoning online 'mind reader' activity

Workshop 3 Session 2: Listening to reason: http://nrich.maths.org/7208

Workshop 3 Session 2: Listening to reason Challenge: Now can you use these proofs on similar problems (see NRICH notes for suggestions) - 10 mins Have a go in pairs with perhaps one person using Alison’s approach and the other Charlie’s approach to replicate the reasoning. (write down any key questions you think will support probing the reasoning from your partner – this will support you when working with pupils)

Workshop 3 Session 2: Listening to reason What skills might this problem develop with pupils? In what way does this task differ to reasoning activities in previous workshops? What potential might this approach have for developing pupils learning in different year groups– do we need videos? How might my department use the NRICH resources to support this type of learning?

Workshop 3 Session 3: Gap Task 3 Research Question: “How does comparing and discussing other students’ responses develop a students’ own ability to reason?” The task: http://nrich.maths.org/7208/ RW

Workshop 3 Session 4: Preparing for Workshop 4 Completed School Report RW

Other links Horizon: Fermat’s Last Theorem Elements of Mastery