Variation

The central idea of teaching with variation is to highlight the essential features of the concepts through varying the non-essential features.

– Gu, Huang and Marton (2004)

When giving examples of a mathematical concept, it is useful to add variation to emphasize:

  1. What it is (as varied as possible);
  2. What it is not.

When constructing a set of activities or questions it is important to consider what connects the examples and what mathematical structures are being highlighted.  Constructing a set of activities or questions takes time, careful thought and discussion. This discussion allows ideas to be shared and different perspectives to be addressed. It is also important to think through how the children will answer a set of activities in order to ensure that they notice the key concept.

Variation is not the same as variety – careful attention needs to be paid to what aspects are being varied (and what is not being varied) and for what purpose.


Procedural VariationsConceptual VariationOne Problem

Useful links:

https://link.springer.com/article/10.1007/s11858-017-0858-4

https://www.sensepublishers.com/media/3027-teaching-and-learning-mathematics-through-variation.pdf

https://londonshanghaimaths.files.wordpress.com/2015/11/variation-theory-mike-askew.pdf

http://www.elementsofmastery.org/productivity/

http://www.glowmathshub.com/uploads/7/0/2/3/70232199/annewatson_variation_booklet_version_2.pdf

http://www.pmtheta.com/uploads/4/7/7/8/47787337/variation_2007.pdf

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