Updating The Map

The limits students face, and how they transcend them

It’s the hardest conversation to have with parents: Their son (or daughter) is dreaming of a really high score. He’s willing to work really hard for months. Can he reach his goal? Sometimes the answer is…and it’s painful to even write this word…No.

There is nothing wrong with my students or their efforts. This is just the nature of skill acquisition – there are limits. I see those limits in our Mathchops data, in my students, and in my own life. There actually is a way to transcend those limits. It’s very simple. And it’s not about getting smarter, hiring a better tutor, working harder, or setting up more sessions. But it’s extreme.

Before I describe this ‘way’, I should describe what the limits look like. Our Mathchops data indicates that student progress usually slows a little after a 100 point increase on SAT Math (roughly 1 standard deviation), and progress becomes very difficult after 150 points. I’ve seen these soft limits with my own students too, on both sides of the test. There is almost always a way for a student to improve his or her scores by 200 points in total, but it’s very difficult to earn a 300 point jump. And I’ve never had a student improve 400 points.

These scores are directly related to skills, and it’s very hard to develop a comprehensive skill set quickly. We see this in every domain. For example…My sister and I both grew up in the same environment, with roughly¹ the same abilities. We did not take Spanish in high school. Today, she is fluent in Spanish, and I know maybe 10 words. Can I achieve her level of Spanish fluency in 6 months?

Unfortunately, I can’t. And it doesn’t matter how hard I work. She spent many years living in Spain, working as a pediatrician. She’s back in the U.S. now, but she still speaks Spanish with most of her patients. Her husband also speaks Spanish fluently. There is simply no way for me to catch up to her in such a short period of time, even if I speak Spanish all day for 6 months. Any high-quality test we both took would reflect that.

Now consider the verbal (R/W) portion of the SAT. Students can make tremendous progress by practicing questions that appear frequently and implementing good question-answering processes. But suppose one student loves to read. She reads Jane Austen for fun! She’s excited when she discovers a new word. She reflexively analyzes the motivations of characters and the arguments of authors. Now suppose another student hates to read. She only reads books that are required by her school. She works hard in other domains and is just as talented as the other girl, but she just hasn’t spent much time with books. And as a result, the first girl is much better at reading. Every high-quality test will reflect this, and no pile of practice tests and exercises will change it.

Something similar happens on the Math side of the test as well. I’ve noticed that really good math students have a habit of ‘updating the map’. Whenever they see a new math wrinkle, they stop and try to reconcile it with their current model of math. Sometimes you can hear them working it out: “Oh…right…because when you multiply you add, so when you divide you would subtract. Okay!” They love math, so they do this all the time. In school, of course, but also when they’re walking around the grocery store, playing fantasy football, or estimating when their car ride will be over. They may even join a math club or look at math puzzles for fun. Math is an enjoyable part of their everyday life, and the hard SAT math questions are just an extension of that.

So that is the simple ‘way’ I mentioned earlier: you have to love the subject and engage with it every day for a long time, updating your mental model of it every time you encounter something new. Readers do this with words, sentences, arguments, and plots. Math kids do this with numbers, puzzles, and patterns. They keep updating their maps – adding roads, destinations, landmarks; noticing solution paths, creating new ones.

There is no shortcut, no quick way to replicate all of that map-making. And really…would it be fair if there was?

1. although maybe she is a little smarter :)