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Mathematical Examples Generator#

See also: casa

Origins#

In teaching Mathematics examples are important. Especially in certain forms of explicit teaching. learner-generated-examples are very useful, but often come after teacher-generated examples used as part of explicit teaching.

Poor examples limit learning. Confuse students, increase cognitive load, fail to reveal essential mathematical structures (e.g. across-the-grain). Generating examples can be difficult in both

  1. Design - creating effective examples of learning mathematical concepts.
  2. Implementation - transforming those designs into artefacts (PowerPoints, images in Canvas, Word documents etc) that can be effectively used in specific L&T situations.

For example#

Recent observations of a lesson on interior alternate angles includes lots of examples. Most using the same image of parallel lines with a transverse line forming a set of angles. Visually these angles are all the same, but for the examples the degree values for the angles were changed. Resulting in students looking at an acute angle labelled 125 degrees. Cognitive dissonance.

In a related class, there was the challenge of the example not having a quick visual connection or scaffold to the names and definitions of certain mathematical concepts. e.g. a teaching having to skip between an activity for the students and basic definitions that should be in their other resources (which they don't have)

Possible design approaches#

  • Leverage something like manim to write Python code that can generate visual examples.
    • Though manim appears more focused on animations - but does support other formats - so possible.
    • Also has a large community which could be useful
  • Use ideas from variation theory etc to in the code designing the examples.