variation trees

Experiencing difference against a background of sameness enables learners to discern critical aspects.

When certain aspects of a phenomenon vary when its other aspects are kept constant, those aspects that vary are discerned (Lo, Chik & Pang, 2006)

What’s the same, what’s different and why?

The same tree is shown in four different seasons.  Attention is drawn to the season because the tree is the same in all four pictures.

It ensures that attention is drawn to the different seasons and not the tree.

Conceptual variation can be broken down into positive and negative variation or examples and non examples.  

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

  1. What it is (both standard and non-standard examples) – positive variation;
  2. What it is not – negative variation.

Standard examples have two straight lines that cross at a vertex.

Non-standard examples have more that two lines coming from the same vertex or are contained in a larger diagram e.g. parallel lines.

Negative examples show lines that share a common vertex but they are not straight lines.

Standard examples are the obvious examples of the concept in its most basic form.

Non-standard examples often show the concept in another context.

Negative variation examples are often referred to as non-examples and can be used effectively to address misconceptions. this website has lots of examples of non-examples.

cv birds

I love this image to show the conceptual variation.

Standard birds that have feathers and wings, non-standard birds – feathers and wings but doesn’t fly and non – bird that has wings and can fly but is not a bird.

Standard and Non-standard Variation

  • cv4
  • cv2
  • cv3
  • cv5