A great way to think about conceptual variation is to ask children when something doesn’t fit into a specific set of criteria – knowing not only the properties of a maths topic but being able to explain why particular objects don’t belong in that topic too is a feature of maths mastery.
Conceptual variation means the opportunity to work on different representations of the same mathematical idea. This might be, for instance, looking at multiple representations of a number with Diennes equipment, place value counters, Gattegno grids, place value grids, arrow cards etc. These numerous representations demonstrate to pupils the different conceptual ideas that underpin a mathematical concept.
So, in the context of place value, some will reveal the quantity or value of a digit, some will show the importance of the position of a digit, others will support the order of the number and some will reveal the additive or multiplicative nature of place value.
The use of conceptual variation can be applied to all areas of the mathematical curriculum.
One website I’ve found to aid in this aspect of conceptual variation is nonexamples.com.
The site has a range of mathematical topics to choose from and will display a variety of appropriate images of both examples and non-examples relating to it. There are two modes currently: question and compare.
I feel the initial question mode would be useful for opening lessons, possibly mid-way through a unit of work. They would also be a wonderful resource to develop and assess children’s reasoning skills.
Compare mode, however, is something I would use to introduce a new concept – perhaps even just displaying examples and non-examples side by side as above and asking children what they notice.