1.4 Workshop 4 (Communication)

Mathematicians often share their ideas with others. Explaining a proof to others not only helps their understanding. It also increases your own understanding of the proof because it forces you to organise your thoughts and be flexible in the way you explain to help others understand (take a look at the Feynman technique). In this workshop, you’ll practice verbally sharing your proofs to the problems you worked on in the Construction workshop with those in your group.

NOTE: This forms some of your preparation for the dialogic assessment so it is very important that you engage in this workshop.

Task 1.19 (15 min).

Warm Up

  1. 1.
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    Allocate a number to each of the remaining non-assessed problems from the Construction workshop for this block.

  2. 2.
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    Create a random list (using e.g. https://www.random.org/lists/) to allocate each member of your group a random number from 1 to 6 inclusive. No number should be allocated to more than one person. The number you get indicates the problem whose proof you’ll be explaining.

  3. 3.
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    For each person in your group, allocate another person to be their “Encourager”. When a speaker is talking about their proof, their encourager must:

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      highlight at least one positive aspect of the speaker’s proof/explanation.

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      ask at least one question.

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      invite questions from the other listeners.

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      keep an eye on time. Each speaker should not spend more than 14 mins before moving onto the next speaker.

  4. 4.
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    Remind yourselves of the “Guidance for the Communication Workshops” on the IMU Learn course.

  5. 5.
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    Use this time to familiarise yourself with the proof you’ll be explaining to the group. What are the key steps? How will you structure your explanation.

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    If there’s time, practice explaining your proof to the person next to you.

Task 1.20 (85 min).

Communication Time!

  1. 1.
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    Decide amongst yourselves which order each of you will explain your proofs in.

  2. 2.
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    Take it in turns to talk about your proofs.

Suggestions for Questions to ask

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    Questions regarding the mathematical objects that appear in the proof and their definitions

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      Can you remind me of the definition of…?

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      What does that theorem state?

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      Can you explain why that theorem can be used in this context?

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    Questions regarding the logical links between parts of the proof

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      Can you explain why you can assume that?

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      Can you give a bit more explanation about why that step follows?

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    Questions regarding the key ideas of the proof

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      Where in your proof do you use this property/assumption?

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      What are the key steps in this proof?

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    Questions regarding the proof and its links to the main ideas seen in the course.

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      Are there other proofs in the course that use a similar proof technique/idea? Can you briefly describe them?

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      If we changed this [object, assumption, conclusion], how would your proof change? Would the statement still be valid?