I have been busy these past couple of months writing some online training modules for early childhood practitioners about young children and math. These will eventually be available through the INCCRRA/Gateways training site and will be free of charge. Should be cool.
One of the things I keep reading about is how certain skills and competencies develop naturally and intuitively while others are less natural and come later. One of these is subtraction. Once children have an established sense of number, they begin to compose (add) and decompose (subtract) numbers. However, since we nearly always count forward with children, counting backward is much harder.
A child is passing out instruments from the instrument box. He gets to the bottom of the box and there are three children left without an instrument. The teacher asks, “How many more instruments do we need so that everyone has an instrument?” The child the counts the leftover children, “1,2,3. We need 3 more instruments.”
Two children bring some dolls to school to donate to the classroom. One child brings 3 and the other child brings 4. The teacher asks the children, “How many new dolls do we have for our classroom?” The children know that they can count the first set and then continue counting (we call this “counting on”) the next set until they arrive at 7. Counting from 1 to 7 is something children have been working on for a really long time, maybe even every day since they started talking. Counting forward is a fundamental mathematical skill.
It is much less usual for children to practice counting backwards. I’m sure there are other examples, but the only one that comes to mind, is when we count backwards from 10 when a rocket is about to take off. But then I thought of all of those songs we sing with young children that are about “taking away.” You know the ones I mean: 10 Little Monkeys Jumping on the Bed, 5 Little Ducks Went out One Day, 5 Little Pumpkins Sitting on a Fence, etc.
So, when you are singing these songs with the children, are you using mathematical language to highlight subtraction and take away? Do you say, “One little duck ran away so we take away one, and we have 4 left?” This is very important. It is not enough to believe that simply singing the songs will instill the concept of subtraction in children as they may not even be making the connection between the number of ducks in the song at all. To some/many children, this is just a song that they love to sing. Explaining the song, is the grown-ups job. The reason we sings songs like those above is because they are about subtraction.
Once your children can count forward, be sure to find opportunities for them to count backward. This will help dramatically when they begin to subtract and take away.