Don Sevcik is the Creator of the fastest math tutor on the planet, MathCelebrity. He’s a best-selling author of 5 books and also consults on SEO and mental models.
A math student sits down in class, pulls out a pencil, and begins a math exam. On every question, one of two things will happen. The student will get the correct answer. Or they will get an incorrect answer. To improve our score, we must reduce the number of incorrect answers. But how?
In 20 years of math tutoring, I’ve seen two types of math students. The top 10% and the other 90%. If grades separate the top 10% from the other 90%, what’s the difference? The top 10% think differently. To break down the top 10% thinking, we start with the three ways to get a math problem wrong.
- The student had no clue how to start a problem.
- The student knew the type of problem but forgot crucial formulas and shortcuts.
- The students knew the type of problem and all the formulas but made a silly mistake in their work.
To reduce the incorrect answers we get, let’s explore how to solve these three situations.
How To Start A Problem
The top 10% excel by using pattern recognition. When they see a new math question, their brain scans for patterns. Consider these examples:
- 98 mod 2
- 98 % 2
- What is the remainder of 98 divided by 2?
If you’re familiar with modulus problems, you know these 3 questions mean the same thing. Which means they have the same answer. And it all comes down to patterns. The abbreviation mod means modulus. The percent sign between two numbers comes from the programming world. It also means modulus or remainder when 98 is divided by 2. Question 3 is self-explanatory.
Pattern recognition helps you respond faster to math problems. Once you have the pattern, you can drill down to the steps. The steps lead you to the answer. If you can’t recognize what type of problem you’re looking at, you can’t find the right steps to finish the problem.
How do you develop pattern recognition? Start by reading problems in the math book. Look for patterns or common phrases which give clues to the type of problem it is. Also, cut extraneous information. Here’s an example:
John Smith lived in Canada. His trailer can hold 500 pounds. He has a box of watermelons which each weigh 10 pounds. How many watermelons can the trailer hold?
If you’ve fine-tuned your pattern recognition skills, you’ll notice two things. First, the trailer weight capacity. Second, the weight of watermelons. John Smith living in Canada means nothing. So you cross that sentence out of your mind. And the important parts of the problem are left over. Once you have strong pattern recognition skills, the next skill reveals itself.
The Steps Require Reps
A pattern should trigger two things in your head: formulas and shortcuts. Formulas come from words and symbols in the pattern. In the example earlier of 98 mod 2, we have 2 steps:
- Divide 98 by 2
- Get the remainder (modulus)
Easy enough. But the top 10% of students take it a step further. 98 is even. 2 is even. If you know about even numbers, you know any even divides an even with no remainder. It doesn’t matter how big or small the even numbers are.
You’ll find another classic example of formulas and shortcuts in two-step equations. Consider the equation 2x – 9 = 41. The average student adds 9 to each side, simplifies. Then they divide each side by 2. The top 10% know a shortcut for any two-step equation:
x = (c – b)/a
For 2x – 9 = 41, we have a = 2, b = -9, c = 41. Using the shortcut, we have:
x = (41 – -9)/2 = 50/2 = 25
This one shortcut shaves 5-10 seconds off the time it takes to solve the problem. Find enough shortcuts, and you give yourself back more time on an exam. More time gives you a chance to fix the third type of mistake on math problems…
Avoid Silly Mistakes.
In Simon Rano’s book, Extraordinary Tennis Ordinary Players, he talks about the difference between professional and amateur players. Professionals win points whereas amateurs lose them. What do we mean by this? Amateurs make lots of unforced errors. Unforced errors happen when you make a correctable mistake with no outside cause. Unforced tennis errors include hitting the ball out of bounds or into the next. Professional players set up situations where amateurs give away points.
In essence, the professional avoids losing points. And they do this by avoiding unforced errors. Amateurs give away points to pros by making unforced errors.
Warren Buffett’s partner, Charlie Munger said it best. “All I want to know is where I’m going to die so I’ll never go there.” In math class and life, we can gain a large advantage through inversion. Inversion is a mental model which forces you to think backwards. For math class, think about what will hurt your progress, and then eliminate it.
For instance, how would I be a poor math student? I’d get less sleep for poor cognitive function. I wouldn’t read the syllabus, so I’d miss out on foreknowledge. I’d eat a poor diet to hurt my brain power. And I wouldn’t check my work to avoid silly, unforced errors. You see, taking away bad behaviors is so much easier than adding good new ones. Think of it as addition by subtraction. Take away the bad and the good shines through.
3 Steps Revisited
To break through to the top 10% of math students, you must develop these 3 skills. First, master pattern recognition. Use patterns to identify the type of problem. Second, the pattern comes with formulas and steps. Build relationships between patterns and formulas. Use shortcuts when you can. And last, avoid silly mistakes. You can’t win when you take yourself out of the game.