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.

- Introducing mathematical argument, logic and proof
- Proof by deduction
- Proof by contradiction
- Proof by exhaustion
- Checking proof

- 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?

- Lesson Plan
- Presentation (PDF) (PowerPoint)

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

- Lesson Plan
- Presentation (PDF) (PowerPoint)
- Large bank of example proofs

- 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?

- Lesson Plan
- Presentation (PDF) (PowerPoint)
- Admissions Testing Service guide to proof (beyond A level but a useful reference)

- 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?

- Lesson Plan
- Presentation (PDF) (PowerPoint)

- 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?

- Lesson Plan
- Presentation (PDF) (PowerPoint)
- TMUA preparation (Paper two provides good proof extension material)

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The FMSP has been superseded by the AMSP