# The Path To Competence

Sorry. If you’re here for a “get rich quick” scheme, you’ve come to the wrong place. You know what I’m referring to… those: “Read this book of tricks and see your score go up 200 points!” or the “Just plug in some values to see which formula is right,” or even the “Practice 10 minutes a day while you’re riding the bus!” (Seriously, don’t do that.) As I’ll explain below, these strategies alone will fail you.

That’s not to say there aren’t certain strategies that are essential to succeed on the SAT. There are some, and my colleague Jack discusses some of those here. However, what I’d like to recommend instead is what I call the Path to Competence. Its design is pretty simple: Better mathematical skills = better SAT results.

I don’t think I need to convince you of the veracity of this statement, as it is pretty self-evident. However, what I’d also like to demonstrate is that the Path to Competence also has broader implications for better preparing you for the more advanced math courses at the college level and for the careers of the near future.

Before we really get into the Path to Competence, however, let’s first discuss some of the other popular test strategies and explain why they will fail you over time.

## Why Most SAT “Tricks” Fail

First,  The College Board, the company that develops the SAT, works very hard to defeat every strategy other than substantive competence – and they are very good at it! Why though? Are the evil or something? Quite the contrary, the College Board has a vested interest in making a fair test.

The “why” is simple. Colleges looking at students would like to have an honest assessment of the student’s ability to succeed at their respective level. In other words, while admissions offices are interested in finding out how good a student you were in high school and how well you’ve learned high school mathematics, they are far more interested in estimating your chances of college success. And it’s the College Board’s job to deliver a test capable of making an accurate prediction. Are they successful at it? Yes! Studies show that SAT scores are, in fact, good predictors of college success. So, kudos to the College Board!

And what is it that makes one successful at the college level? Is it possessing a handful of tricks? Knowing how to narrow down multiple choices on some problems? How about picking up disparate problems from using an app 10 minutes a day? No, no and No! What will define a successful college career is the ability to acquire competence in a particular subject. Competence is King.

But how does the SAT test achieve the goal of assessing competence? After all, it can only test a narrow range topics, typically not exceeding sophomore-level mathematics. Take a moment and think about how hard it is to write this test. The authors have to predict how good the student will be at learning college level Calculus by testing how good the student is at Algebra! That’s like a college basketball recruiter trying to see if you will have the skills to play for the D1 basketball by looking at your ability to make free throws alone. If that’s all the recruiter could observe, I could be a contender… and that would certainly not be good for the team.

So over the years, the College Board has found an effective solution. First, let’s discuss what we mean by competence. Competence is more than basic knowledge, it’s more than being able to do routine exercises correctly, and it’s far more than memorizing all of the “tips and tricks” SAT gurus push.

Competence means having the ability:

1. To tie mathematical concepts into real-life situations
2. To apply one’s knowledge in unfamiliar scenarios
3. To use logic on new kinds of problems
4. To extract essential information from complicated data
5. To see simplicity in complex problems
6. To overcome complexity in simple problems
7. To recognize concepts in various formulations, and finally
8. To dismiss non-essential data, and more!

These are all pretty hard to fake, and the College Board takes full advantage of this fact. Yes, they are only able to test a narrow range of topics, but they are not at all limited in the ways in which they ask questions. So they often ask questions in a way that would expose any lack of competence on the student’s part. This is not very hard to do in mathematics! In fact, it’s very easy to take a simple problem and pose it in several different ways in order to root out those who are competent in the concept and those who are not.

#### Let’s try an example

Consider the following four questions:

1. For the function $$f(x)=3x^2+11x+6$$, find the endpoints of the range of the values of $$x$$, whereas $$f(x)>0$$.
2. For the function $$f(x)=3x^2+11x+6$$, find the values of $$x$$ where $$-|f(x)|$$ attains the maximum.
3. For the function $$f(x)=3x^2+11x+5$$, find the values of x where the function $$\frac{1}{f(x)+1}$$ is undefinied.
4. Solve the quadratic equation $$3x^2+11x+5$$.

If you are comfortable with the quadratic formula, you will find Problem 4 quite straightforward. However, the other three are the exact same problem in slightly different variations! Did any of them throw you? If you understand quadratic equations inside and out, I doubt it.

In summary, the folks at the College Board have mastered the art of asking questions in a way that exposes any lack of thorough understanding or, as we call it, competence. This cannot be overcome with rote repetition, tricks or any other strategy meant to avoid mastering the substantive content.

In addition, you should know that the authors of the problems are fully aware of the strategies that are advertised as a way of “beating” the test. For instance, it was once believed that when you have no idea how to approach a problem, that choosing B) increased your chances of getting it right. I assure you that, even if it ever was true, it no longer is. Plugging in values to assess the correctness of each of the multiple choices? Questions like that can hardly be found on the test anymore, especially in the New SAT.

## So Where Does That Leave You?

In a wonderful place as a matter of fact! It leaves you with the one strategy: taking the Path to Competence. This method increases your substantive understanding of the Math itself, makes you feel great about yourself, develops your problem-solving abilities in an array of different topics, enriches your life and actually prepares you for College and your career beyond.

If you feel overwhelmed, like you are way behind and will never recover, do not give up. Instead, develop a plan based on the strategy I’ve laid out here. If you spend a little bit of time on the substantive content, it will help a little. If you spend a lot, it will help a lot. That’s the very nature of learning: you can only get back what you put in.