We all can recall with trepidation the last question on the math test; it was always the dreaded word problem. Most of us just immediately folded. The one brainiac smart girl in class had learned how to convert key phrases back into the required equation and found the word problem to actually be really easy. The one recluse kid in the back corner of the classroom could solve that problem without even writing anything down and, in fact, would refuse to do so because it was boring. So, out of a class of 25, two kids could solve the problem, but only 1 would get an A. Try as she might, and even though she explained the exact scenario using different characters, she could not get anyone in her class to be willing to even attempt the word problem. Most would just punt at the first sight of something that required any ounce of reasoning.
Nowadays, math classes are really pushing this concept. This is probably a good thing, although I am not sure about the methodology. Our children bring home a packet of complex word problems, scenarios that the young person has to figure out or fail on the pending test. As usual, the parent finds out about this the night before, and thus we find ourselves trying to explain how the word problem works. We are paying for the years in which we refused to do any word problems; now we are doing them at night with our kids.
It is almost as if that smart girl grew up and became an official in the state K-12 administration and fought hard to adopt a 100% word problem curricula to seek revenge on her 28 other classmates in high school algebra. Julie, please forgive me for shooting spit wads into your hair while you were finishing the math test. For the last time, I apologize. You can stop tormenting us now with your continuous production of word problems in your revenge plot.
There is a difference between procedural competence and conceptual understanding, and this is what the modern word problem is trying to achieve. Our children have the same reaction we did, which is the immediate recognition that conceptual understanding actually requires us to think and, like it or not, our brains are wired to avoid that level of thinking unless it is required for our immediate survival. Unless, of course, you are the black leather jacket, long-haired boy in the back of the room who was born with a passion to disregard all procedures in life and therefore wholeheartedly embraces high-order thinking.
A person can become very good at a procedure while still being unable to explain the underlying idea, adapt it to a new situation, troubleshoot when it breaks, or teach it to someone else. A good test of whether you have actually learned something is whether you can do four things: explain it in your own words, apply it in a different context, recognize when it does not apply, and modify the approach when conditions change.
I tried to explain this to my daughter last night; she just rolled her eyes, put her earbuds in, and said, "Dad, can you just give me the answer? The teacher is letting us use notes."
Thanks, Julie. You got me to do my word problems. When will the torture end?
