My sister gets nervous sometimes when we are at the store together. She is afraid (rightfully so) that she may have to witness me give a math lesson at the cash register. I can see why it might be embarrassing to her and I can also see why it infuriates people behind me in line, but sometimes I just can’t help myself. As a math teacher, it frustrates me that the cashier can’t figure out the change when I give her a twenty, a one and a nickel for a bill that is $11.05.
Now, one could argue that the reason why the cashier can’t do this is because he or she did not receive enough instruction on the traditional algorithm for subtraction. Maybe he or she used calculators too much in class instead of doing lots of “drill and kill” exercises.
But I don’t think that having lots and lots of practice with the traditional subtraction algorithm would help in this case.
The truth is, I don’t often use traditional algorithms when solving math problems in real life. I do use a lot of mental math.
I count up or I count down when adding or subtracting. I break numbers apart when multiplying. I rarely think about multiplying 25 times 6 in my head using a traditional algorithm. Instead, I think of 20 x 6 plus 5 x 6 or I think about 25 x 4 plus 25 x 2. It is just easier. To figure out a 15% tip, I usually find 10% and then half it and add the two together. Or most of the time I double it because waiters and waitresses really deserve that 20%.
I bet a lot of you operate the same way. You don’t take out a pen and paper in the store or restaurant.
Yet as I mentioned in a previous post, some people still think that traditional algorithms are the only way to teach math.
As you may expect, I disagree. How much more valuable is it to work flexibly with numbers? To be able to calculate things in your head quickly. To have a sense of whether an answer is way off base. I think this is the way we should approach math in the early grades. It certainly would make my experiences at the grocery store less traumatic.
So what does the research say? Two researchers (Fosnot and Dolk, 2001) reported on a program called “Mathematics in the City” in which teachers fostered mental math computation strategies in children between the ages of 4 and 8. They showed how these students developed a deep understanding of number and the operations of addition and subtraction.
Now is there a place for learning traditional algorithms? I think there is. But I think it’s often more valuable to do after students have had experience working flexibly with numbers.
So how do we begin to do this in our classrooms? That I’ll talk about in my next post. But feel free to write any suggestions you have in the comments below.
Want to know more?
Check out the Mathematics in the City site here.
Check out Fosnot and Dolk’s book: Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction.