We've all been there, right? Driving is usually what psychologists call an associative task. Associative tasks are things we do like brushing our teeth, washing the dishes or driving in normal conditions. We can simultaneously wash dishes and sing along with a familiar song on the radio because each task uses up almost no cognitive resources. In fact, scientists have recently learned that habits are controlled by the basal ganglia and not the pre-frontal cortex, the part of brain involved with higher level reasoning. Habits just sort of happen. We don't actively think about putting toothpaste on our toothbrush we just do it. We are on autopilot. Our brains are free to think other thoughts.
The other type of task is called a cognitive task. Cognitive tasks are jobs or activities that require concentration. Calculus. A 30 foot putt for par. Writing a research paper. We can't sing a song and write a research paper. At least I can't.
Driving on a sunny day on dry roads is an associative task for most adults. But once the snow hits driving turns into a cognitive task.
So what's this got to do with math? Some math tasks are associative mostly the ones that we have committed to long-term memory or algorithms that we have practiced so much that they have become second nature.
But some math tasks are cognitive. It is my job to make sure that students are doing only one cognitive task at a time.
I am supposed to be the snowplow driver clearing the roads. Scaffolding math problems is the educational analog of the snowplow. Scaffolding provides answers or near answers for sub-tasks so that the only job remaining is the essence of the day's lesson.
Consider long division.
For a fifth grader, or for anyone, this is an incredibly complicated set of steps and calculations. Each individual step seems to be governed by an arbitrary rule whose application requires a difficult calculation which is then followed by another arbitrary rule whose application requires another difficult calculation. As you can see above this chain of "WHAAAAAAAT?" can go on for a number of steps. Imagine trying to do this if you are like most fifth graders and your single digit multiplication facts are still a little shaky. It's a nightmare!
This week we are metaphorically clearing the roads of snow. We are scaffolding long division. We are providing students enough support so they can fully focus on the logic and steps of the long division algorithm. Below you will see part of a worksheet from 5th grade that gives students arrows, colors and a list of math facts to point the way down the previously hidden and slippery highway. Blue numbers from above are used in the blue blocks below. Yellow blocks have a similar correspondence.
When the intellectual clutter is cleared I hope that what they see before them is a crisp and cogent schema of the standard algorithm for long division.
