“What can I eat for lunch?” A potentially loaded question when coming from anyone but certainly of high priority when coming from one’s pregnant wife. The other day I fielded this very question and in my “husband of the year” role, began to list out every edible thing I noticed in our pantry and refrigerator before finally moving on to the freezer.
The response back was underwhelming. Nothing sounded good. “That all sounds like snacks… not lunch!”
I again dutifully went through the list again (looking in each door like something magically had appeared since the last food roll call). “You could have, cheese… bread… an apple…”. Still nothing. It was beginning to look dire. And then it dawned on me. I had said bread AND cheese. “You could have a grilled-cheese sandwich.” And with that, my wife’s eyes lit up and I regained my hero husband footing.
WHAT in the WORLD does this have to do with mathematical mindsets you ask (hopefully after going to get yourself a grilled cheese)? It dawned on me as I was making the sandwich just what had happened. My wife in her hunger was focused on the problem – she needed to eat! Both times I ran through the food items, she missed the ingredients that would bring her a yummy treat!
How often do students seem to do the same thing in Math? A problem or two show up and they immediately focus on “solving it” (or more accurately… getting the right answer). They see the algorithm and not the numbers. They don’t look at the ingredients but are zeroed in on an outcome.
This is one aspect of my math instruction that I am trying to change. I want my students dissecting the numbers, thinking about potential strategies and considering reasonable outcomes all before they focus on the algorithm (if they ever need to do so in the first place). When my students see numbers, I want them to see pairs and compliments and understand the sense they make (ingredients).
To that end, we’ve been doing work with number strings a bit, estimating target answers to check reasonability and using quite a bit of increased DOK questions like those discussed by Robert Kaplinsky on his site. I was excited to see this type of thinking also presented at a recent district math workshop. It was eye opening to see how many students were going through procedural motions with trading during subtracting when they were given a problem with missing digits. Almost none of my students saw the path through the algorithm… YET!
But some did start to see math wasn’t just a set of rules or steps to follow and conquered the problem. I’m hopeful as the year continues, more and more will start to think this way first.
If we don’t get our students to think past the problem on the page, how will they ever grab hold of that mathematical grilled cheese?