We often say things in the Maths class without fully thinking them through. Having just finished the Early Years Subtraction package I think I am super sensitive to all things subtraction.
I listened to a teacher this week explain how she teaches young students the concept of subtraction: “I show students some objects and then I take some away and then I tell them when you take something away it is gone. Students then model subtraction with objects remembering to take things away to find how many left.”
On the surface this doesn’t seem too bad but …
Think about situations where the objects ‘taken away’ have not gone or at least not gone far.
For instance, if I have 6 strawberries to decorate some cakes and I put 2 on one of the cakes I might ask: “How many are left for the other cakes?” All 6 strawberries are still visible.
Even in this picture from the Mem Fox classic, Ducks Away, the duck that fell off the bridge is still visible (thank goodness)!
Which brings us to the fact that addition undoes subtraction (the inverse operation is an important concept).
“If I take the 2 strawberries off the cake and put them back with the originals I now have a group of 6 again.”
It is only after such experiences that students are going to connect known addition facts with subtraction and vice-versa.
So we need to rethink the contexts and vocabulary that flags subtraction.
Some will actually match the ‘they’re gone’ statement. If I ate 4 lollies I would consider them gone but if I filled 3 glass out of 6 with juice, I still have 3 left to fill, they haven’t gone away.
This incident reminded me of one of my favourite articles, 13 Rules that Expire, from the NCTM
The article identifies sayings and rules that we teach students and which are, essentially, gobbledygook. I wish every teacher of subtraction would read and consider 13 rules that Expire.