Reading the recent NY Times Editorial by Sol Garfinkel and David Mumford about how to fix math education, I was struck by the following line:
All this worry, however, is based on the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong.
Hmm. If so, then what math do people need to know? How do schools teach it? The next day I set my nine year old daughter and her two friends to work on making brownies. I handed them two boxes of brownie mix and told them to have at it. And did they. Boxes were opened and bowls pulled out of cabinets and then everything stopped. They looked to me and the other dad for what to do next. Busy in conversation we told them they could do it and left them to their own devices. We were helicopter parenting for sure, as we were in the kitchen, but trying to be a bit free-range too. I mean these were three smart kids- which is to say they are like all kids- who needed to be able to use their intelligence to solve the problem of turning a bag of brownie mix into brownies. To them this was a high stakes test.
They finally found the directions on the box and began to try to follow them- or more exactly to try get each other to follow them. I told them where things were- eggs, oil, ect- but stopped short of doing things for them. One little girl was known to bake with her mom, and caught fact that the other two had blown right through the first direction- turn on the oven. From there they divvied up the work, each cracking an egg and then cleaning the pieces of shell out of the bowl. And then came the question of how much water to add.
They had the measuring cups out and needed to add a quarter cup for each package- and there were two packages. The whole frenzy of activity ground to a halt, as they began to think about what that meant in terms of total water. I recalled that last year my daughter had brought home worksheet after worksheet where she had to add fractions. She had dutifully done them, but like much of the math she was learning had not really put together how fractions worked or how important and relevant they were to everyday life. Me telling her they were important had only made her eyes gloss over.
Anyways, the three girls began to go back and forth over how much water to add. “Two of these cups means one of those cups.” “No, we need to add one of these and then two of those.” The other dad and I looked at each other, the blades on our helicopters whirling loudly, and decided not to land in the midst of them. They continued to bat around how much they needed, one reading the box, one holding measuring cups, and the other waiting by the faucet. It became apparent that two had figured it out, while the third continued to hold out and want to add at least a quarter cup of water extra. This is brownies we are talking about, so I was having a hard time holding my tongue.
Then one of the girls took the measuring cups over to the sink and began filling the larger ones with the smaller ones to show that two quarters equal one half. The light bulb went on for the holdout, and the brownie making carried on. I thought about this later, over a brownie that could have turned out more like pudding, and realized that a lot of light bulbs had probably gone on in that moment of uncertainty. I don’t think that any of the three had a really good sense of the math behind the measuring cups, and had put it all together right then and there, assembling it like the brownies. They had to bat it around a bit, figure it out and convince each other, and then proceed. They wanted to get it right because it mattered to them- making brownies as a high stakes test.
School can be thought of facing a similar problem. We have this “knowledge” we want kids to know because we think it will help them in the future. The problem is we don’t know the future. What we do know is that a great deal of what we have already figured out- like math- can help us in the future. What we miss is how to get our children to realize this. We can try telling them- “This is math and important to your future!”- or we can try cramming it down their throats- “Here is math! Learn it because it will be on a test that will determine your future!”- or we can try something a bit different. We could look for and even try to set up situations in which math might matter. As Mumford and Garfinkel point out, we really don’t have to look too far, as mathematical applications are everywhere. They don’t come as worksheets but rather as real world problems often linked to larger questions or concerns- like making brownies.
My daughter does not like math, but she loves brownies. I am saddened that her education has pulled math out of life so much that she has to see it as a disembodied thing- a subject- rather than a tool to do and know things that matter to her. I can tell her math is everywhere, but to her it is a subject she has seven times a week in school because she needs to do well on high stakes standardized tests. How could we get education so backwards? I look forward to the day when we will see that in our rush to stuff knowledge into our children so they can spit if back to us as fast as possible on standardized tests that we are killing things like math for many of them. We are in effect immunizing them from their own ability to think, to problem solve, to love math as more than a school subject. We are feeding kids math as brownie mix instead of allowing them to learn it by making brownies.