You aren’t going to like the answer, I’m afraid. They way to become an expert is to really work at it. I’m not being glib. Malcolm Gladwell explains (brilliantly, as usual) in his new book, Outliers, which I highly recommend.
Gladwell builds a very convincing argument that math skill is much more closely related to persistence and hard work than any innate ability. Bottomline: The more you do math, the better you get at math.
Most convincing study: Every four years, elementary and junior high students around the world take the TIMSS test of math and science. The test begins with a long, boring series of 120 questions designed to get the students’ background–parents level of education, home life, views on science, etc.
That’s a load of questions for an elementary kid and many don’t finish those 120 questions, even though they aren’t actually part of the test. Erling Boe, an educational researcher at the University of Pennsylvania, noticed that if you ranked countries by how many of these initial questions their students tended to complete–in effect, ranking their persistence in completing boring tasks–and then compared that to their international rank on the math portion of the test, the two ranking were exactly the same! In other words, you can predict math ability by measuring persistence (at least on an international scale among school kids).
The lesson for us is, if you want to get better at math, keep working at it. That “aha!” insight sometimes comes only after hours or days of trying to figure out a single math concept. Once it comes, the concept is easy. Before that, it’s nearly impossible.
Here are ten tips to help you maximize your math abilities…
- Get help. A good teacher (book, website, tutor, etc.) can ramp you up in a hurry. Think coaching; a good coach can steer you in the right direction and tell you exactly how to practice, but it’s still up to you to put in the time and energy to gain mastery.
- Don’t stop studying it just because the teacher stopped teaching it. For you to master a particular concept may take days or weeks longer than the rest of the class, while in other areas you may be much quicker. Your brain doesn’t grasp concepts on anyone else’s schedule.
- Don’t skip a concept. Much of mathematical knowledge is cumulative, building on prior concepts. That means, if you fail to understand a concept this year, it can have big consequences for years afterward.
- Missed questions on the test are the key. When you take a test–whether it’s a calculus test in college, an SAT practice test, or a test of your multiplication tables–the ones you missed are the key to future mastery. They tell you where your understanding is lacking. Go back and spend time figuring out why you missed what you missed. Your goal is to never miss that type of question again. While the ones you get right determine your test grade, the ones you get wrong determine your future grades. Master them, and it will be smooth sailing. Ignore them and your just costing yourself in the long run.
- Persistence pays. Some math concepts come quickly and easily, but some only come after long hours of continued contemplation. If the concept isn’t sinking in, stick with it until it does. I personally have spent two hours trying to figure out a single SAT problem. My roommate in college, an engineer, often spent days on a single math problem. As much as I like study shortcuts, sometimes the quickest way to get it done is via hard work over time.
- Don’t memorize a single method. Math is like travel. There are thousands of different ways to get to College Station, Texas. Some are slower. Some are faster. Some are scenic. Some not so much. Getting the correct answer to a math problem is the same way. There are many, many, different ways to get the correct answer. Learning a particular method is only telling you one of the many ways. That method is just a reliable crutch to use until you really grasp the concept. Aim for being able to solve any problem in several different ways. Example: What is 3/5 of 200? I can divide 200 into 5 parts of 40 each. Three of those parts would equal 120. OR I could lay out 200 cents in the form of 20 dimes. I then divide the dimes into 5 equal piles of 4 each. Three of the piles then equal 120 cents. OR I could convert 3/5 into 6/10 which is 60%. I multiply 200 by .6 to get 120. OR, etc. etc.
- Play with it. Math problems are really just puzzles. If you see them as work you have to do for school, they can be dry and boring. If you change your perspective and view them as mental puzzles to do for kicks when your bored… I was never fond of math as a kid, but after college, I had to spend a lot of time driving for work. As a way to pass the time, I followed my father’s advice and began playing mental games with different numbers I saw on the side of the road. Example; 55 mph. What is 55 squared? Cubed? What’s the square root of 55? If I’m travelling 70 and the next town is 22 miles away, exactly how many minutes will it take me to get there? Bonus: SAT and GRE students, carry some practice problems around with you and work on them whenever you get bored. Avoiding boredom can take you a looong way!
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