What is a Klein vignette?

Vignettes are intended to give teachers a sense of connectedness between the mathematics of the teachers’ world and contemporary research and applications in the mathematical sciences. Thus it will start with something with which the teacher is familiar and move towards a greater understanding of the subject through a piece of interesting mathematics. It will ultimately illustrate a key principle of mathematics. The vignette must be written in a way to complete this journey.

A vignette is a short stand-alone piece of mathematical writing for secondary teachers of senior mathematics classes (STSMCs). It is not about pedagogy, but will inspire good teaching. It is not about curriculum, but will challenge teachers to reconsider what they teach. It is not a resource for classroom use, but source of inspiration upon which teachers can draw. The goal is to refresh and enrich teachers’ mathematical knowledge.

CHARACTERISTICS

Structure

A vignette will:

1. Be short (10 pages, normally less than 6 pages)
2. Be written in an expository style with a narrative flow appropriate for STSMCs, a minimum of formalised theorems and proofs. Mathematical detail is included where it is unusual, especially informative or constitutes the core point.
3. Contain some significant mathematics that would be new for most STSMCs.
4. Conform to scholarship standards in its physical characteristics (it is properly constituted as a piece of writing).
5. Be mathematically honest (correct in essence but not necessarily complete in all detail).
6. Direct readers to more information, e.g references (which will be accessible by teachers), web-links, or resource people.

Style

A vignette will have:

1. An opening paragraph (the hook) which will make a STSMC reader want to keep reading, or entice the reader to click “Continue reading” (normally including an illustration).
2. A mathematical point (illustrating some characteristic of mathematics greater than the subject of the vignette).
3. A connection to research or applications within the last 100 years, or a new light on classical mathematics. All themes are likely to have historical roots, but these will not normally make up the main part of the vignette.
4. A connection to the mathematics of the senior secondary classroom, helping teachers think about the mathematics they teach in a new light.
5. Appropriate illustrations.

A collaboration between a teacher and a research mathematician is a useful model for writing.