What is the difference between equal sharing and equal grouping and why is it important?
The difference between equal sharing and equal grouping boils down to what the quotient represents. When sharing, the quotient represents the quantity of shared objects in each group. When grouping, the quotient represents the amount of groups within the shared quantity.
At the start of teaching division, teachers often focus on sharing, but not always on grouping. At this stage, it’s important to give equal, or more, emphasis on grouping when pupils are first getting their heads around multiplicative structures.
One rationale for this belief is that sharing is more intuitive and it’s likely that pupils already have a notion of sharing — although not necessarily a very deep one.
Grouping is conceptually more difficult and it’s less likely that pupils will have a strong notion of it. Letting them struggle early on with grouping before moving on to the simpler notion of sharing is more likely to create the necessary relational depth.
Encouraging them to think of the less-intuitive representation of division as grouping helps them stretch to accommodate this less-familiar concept alongside their pre-existing and more child-like understanding of division.
If you do the opposite and let children spend time playing with, structuring and later practicing the notion of sharing before they spend any time thinking about grouping, their understanding of division may become fixated on the sharing model. This can make it harder to relate the notion of grouping with division, causing difficulty later on.
