Chapter 4:
Presentation Techniques

Importance of Written and Oral Presentations

Mathematicians must present their work in written and oral form ⟶ papers & talks.

Otherwise: reinvention of the results is cheaper than to use available results from the literature.

Embed oneself into the scientific community of one's own field.

Types of Oral Presentations

Giving Mathematical Talks

Most important principle for the speaker:

Save the time of the audience !!!

Steps When Preparing a Talk

Analysis of Audience (see "Writing Papers")

Ask yourself:

Specification of Goals (see "Writing Papers")

A topic for a talk is not yet a goal !

Specify goals in the form of operational goals, i.e. by describing the operations (actions) the audience should be able to perform after having attended the talk.

Easy way to check the quality of one's own talk: If audience from the intended group of listeners are not capable of performing the operations specified as the operational goals then the talk does not meet the goals.

Clear operational goals give the audience a clear motivation to follow the talk, namely the desire to acquire the skills that are described by the goals of the talk.

Goals need to be structured (subgoals, prerequisites, independence).

Hierarchical structure of goals ⟶ hierarchical structure of the presentation.

Collecting Material (see "Writing Papers")

Literature needs to be studied:

Processing Material

Still a lot of work, because:

Goal of processing the material: Completely understand and master the topic !!!

Do not consider: Audience, psychological/pedagogical/methodological factors.

Interaction: Specification of goals  ⟷  Processing material. Start with specification of goals.

As often as possible: Elaborate your own ideas !!! (Examples, connections to other subjects, applications, etc.)

Preparation of the Presentation

Written preparation of Presentation:

Some Psychological Aspects …

Motivation

Motivation of the audience plays a crucial role.

How to motivate the audience?

Natural Structure for Oral Presentations

Learning Process Needs Time for Deactivation

Overlapping learning processes disturb each other.

Well–associated Information is Better Memorized

Therefore …

Alternating phases of:

Written Trace of the Presentation

Audience should have the possibility to obtain a written trace of the presentation.

Teaching Aids

Blackboard

For: Development of ideas.

Not for: Tables, diagrams, graphics.

Limited speed!

Overhead Projector

For: Presentation of information in one step.

Not for: development of ideas, proofs. (-> Uncovering part after part.)

Danger: Speed!

Laptop + Beamer

Can combine the advantages of both blackboard and transparancies.

Danger: Speed!

Accompanying Written Material

Summarize important information.

Graphics, pictures, tables, figures, etc.

Organizational Preparation of Presentation

Embed main part into

The Presentation

It is difficult to give general rules (taste!), but:

Some Hints

Auxiliary

learn[p_, col_] := {col, 
        Polygon[{p, p + {2, 0}, p + {1.5, 1}, p + {0, 1}}]}

Show[
      Graphics[{learn[{0, 0}, RGBColor[0.772549,  0.788235,  0.847059]], 
          learn[{1.7, 0}, RGBColor[0.501961,  0.517647,  0.576471]]}, 
        AspectRatio -> 1/3]]

Plot[{1/(0.7  x + 1), (E^(-2 x))}, {x, 0, 2}, 
      Ticks -> {{{1, "20 Min"}}, {{1, "100%"}}}, 
      Prolog -> {Line[{{1, 0}, {1, 1}}], 
          Text["well–associated info", {1.7, 0.55}], 
          Text["badly–associated info", {1.7, 0.1}]}, 
      PlotRange -> All]