Pattern Recognition

Many students do quite well in school but are then mystified by why they can't match that performance on standardized tests. There's a good reason. When you learn a subject like Geometry in school, it's pretty clear what topic you are in at the moment. So when you take a test, all of the problems are going to revolve around your mastery of that topic, making it clear what rule or technique you need to apply to solve it. Standardized tests aren't usually like that, however. There are still a limited number of topics, but they are often combined in unfamiliar ways. Being able to break down a problem in this context is more than just a simple matching game.

So it makes a lot more sense to teach a student thought patterns. Follow the same path, and you will reach the same destination. But if you know why you took that path, then not only can you find your way back, but you can blaze your own trail. For example, a student might learn that the value for Pi is 3.14159... but never question why. It becomes an abstract piece of trivia, just a number to plug into a formula. How do we know its value, though? Who discovered it, and how did they do it? It's much more effective to learn that you can approximate a circle with a square, get a little closer with a hexagon, closer still with an octagon, etc., until we have so many sides that it might as well be a circle. It’s literally re-inventing the wheel. Since each side is straight, we can measure it easily. And since we can always add more sides, that measurement can become more and more precise. Pi is really just a limit. Once students understand Pi as a process, the end result - the number - becomes obvious.

Applying this principle to test prep, we batch related problem-types together, filtering them into broader problem-categories. This process aids pattern recognition because it forces the student to focus on similarities between problems, rather than differences. It helps them become quicker at identifying possible solutions because they are mapping "solution groups" to "problem groups", rather than individual solutions to individual problems. My goal is to demonstrate that although there may be 50, 60, even 70 questions in a section, they aren't all different problems. This builds confidence and helps avoid "paralysis by analysis" - the bane of every decision-maker.