The Power Habit Lab
From Test Maven
Have you ever dwelt on a problem or task for a long time without getting anywhere? Why do some people seem to move quickly to the finish line on things that others can't even get started with?
One big difference between getting things done and spinning your wheels is the all-important question, "What can I ignore?" Whether it's writing a report or solving an SAT math problem, you'll be overwhelmed from the beginning if you let all the information wash over you like a wave of live cats.
Instead, ask yourself what finishing this task looks like. What counts as doing it? Your goal should be to accomplish that and nothing else. In software this is called the "Good enough" principle. It has nothing to do with cutting corners or shrugging your shoulders at defects you can "get away" with. It's not about mediocrity. Rather, it's about identifying the precise definition of excellence and accomplishing exactly that. Nothing more, nothing less.
Anything that you don't need to do to reach that definition of excellence, every superfluous bit of information or insight or research question, is a distraction from achieving your goal. Free your attention up to focus intensely on just what you need, and let everything else get out of the way.
To get things done, ask "What can I ignore?"
Take today's SAT Problem of the Day as an example:
Holy crap. There are eight named vertices, two unnamed intersections, three intersecting triangles, two smaller triangles inside the larger triangles, four trapezoids, a rhombus, a bajillion line segments, and another bajillion angles. And they only give you the measure of one angle? How are you even supposed to process this?
Well, that's exactly the point. Only on one level is this a question about parallel lines, angles, and isosceles triangles. More fundamentally, it is a challenge to your ability to focus your attention on precisely what matters in solving a complex problem.
As in many situations, the best way to focus your attention is to approach the problem systematically. Aristotle knew this when he described practical reasoning as a process of working backwards from a desired outcome to an action. We can do the same thing here by focusing our attention on the question: what is the value of ϴ? In a way, the question is a sign pointing the way to the answer. It tells us what we need to pay attention to. We can work backwards, step by step, from the question to the information that will bring us to the answer.
In this case, if we want to know the value of ϴ, the first thing we should do is ask what we would have to know in order to get that value. For now, nothing else in the figure matters. Well, ϴ is just a snooty geometry name for the number of degrees in the measure of an angle, in this case, angle JFH. So we need to find out the measure of that angle.
Okay, great; that's one step backwards. So now how do we find the measure of that angle? What would we need to know? Here we have to shift our attention away from the angle itself, and look at it as part of the bigger picture. This angle is one of three angles which together make up the larger angle AFB. So let's look at that angle and ignore everything else. Ignore the large triangles, the small triangles, the triangles as big as your head. Whatever. Just ignore everything else.
(Side note: I'm not yanking your chain here; I know AFB looks like it's just a straight line segment, not an angle, but put on your Math Goggles for a second and look at it a different way with me. If you take an angle and open it up until it's so wide open that it's just lying flat like an open book, it doesn't magically stop being an angle at that moment. It's just a 180° angle. You could have stopped at 179° or keep going on to 181°, but you didn't, because you're just not that kind of cat. 180° is the only way for you, and you're not going to let some small-minded geometer tell you you can't have a 180° angle just because it happens to look like a line segment, are you? Be your own person! Fight for your right to 180°!)
So where does that leave us? If the angle AFB has a measure of 180°, why is that interesting? Well it gives us another way of looking at the measure of angle JFH. We can now define that angle as having a measure of 180° minus the sum of the measures of the other two angles that make up angle AFB (AFJ and HFB).
Great. So what do we need to know in order to find the measures of those two angles? With every question we ask, we have to shift our attention to what matters now, what we were ignoring before. Now we don't care about angle AFB anymore. That's last week's lasagna, baby. So let's stop looking at AFJ as a part of that angle, and think of it as a part of something else. It's also part of the isosceles triangle AJF, so we know it has the same measure as the angle JAF.
We won't go through the whole thing. Suffice to say that we creep step by step, with the cunning of a spider crossing its web, ever closer to the one piece of information we were given at the beginning: the measure of angle AEI. Eventually we figure out that we can use that angle to find the measure IEG, which is the same as JAF, which in turn is the same as JFA and HFB, the two angles we needed in order to get the measure of JFH. (Check the College Board's SAT Practice app for a full explanation.) The point is not the details of the proof, but how we directed our minds as we proceeded. At every step, we systematically ignored almost everything about the figure, and applied a laser-like focus to the one aspect of it that we needed.
There's no habit of mind more important for the SAT than being able to shift your focus to different aspects of a figure or situation or sentence or passage. But it's not one of those things that only makes you better at solving problems on a test. It's a crucial life skill, too! Future leaders need to be experts at focusing on the most relevant aspect of a situation and ignoring everything else, methodically shifting their attention to look at things from different points of view, one at a time, until a path to action becomes clear.
To become an excellent problem-solver, don't try to pay attention to everything all the time. You'll never be able to do that, and you'll only get overwhelmed! Instead, learn to be "good enough" at paying attention by focusing intently on just what matters and nothing else. It's just a matter of practice.