Professional Development Videos: Reasoning and Proof

These videos show various ways that ideas relating to reasoning and proof can be used in A level Mathematics/Further Mathematics lessons. Each video is approximately five minutes in length and demonstrates a different idea.

The videos were filmed at Beechen Cliff School in March 2017.

Videos



Introducing mathematical argument, logic and proof


Questions for reflection

  • How can you help students to appreciate the level of rigour required?
  • What are the possible advantages/disadvantages of a discussion/pair based approach to this sort of task?
  • What questioning strategies are useful to help ensure that students feel confident about their answers?

Related resources



Proof by deduction


Questions for reflection

  • How does the structure of the task in the video help students to engage with the question?
  • What methods could be used to assess students’ understanding of how to structure a proof?
  • What would be the next steps in helping students to construct their own proofs?

Related resources



Proof by contradiction


Questions for reflection

  • What relevant vocabulary might students lack when meeting proof for the first time?
  • What can you do to support students who might struggle with the abstract nature of proof?
  • Are there ways of integrating proof and reasoning techniques into your teaching of other parts of the syllabus?

Related resources



Proof by exhaustion


Questions for reflection

  • What are the possible advantages/disadvantages of a discussion/pair based approach to this sort of task?
  • How can you help students to develop systematic ways of working?
  • What sorts of questions do students need to be able to ask themselves to succeed with this sort of task?

Related resources



Checking proof


Questions for reflection

  • What questioning strategies are useful for this sort of task?
  • What are the common flaws in proofs with which students should become familiar?
  • Do the techniques developed through reasoning and proof have applications elsewhere in the syllabus?

Related resources



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