I think that I shall never c
A # lovelier than 3;
For 3 < 6 or 4,
And than 1 it’s slightly more.
All things in nature come in 3s,
Like … , trio’s, Q.E.D.s;
While $s gain more dignity
if augmented 3 x 3 —
A 3 whose slender curves are pressed
By banks, for compound interest;
Oh, would that, paying loans or rent,
My rates were only 3%!
3² expands with rapture free,
And reaches toward infinity;
3 complements each x and y,
And intimately lives with pi.
A circle’s # of °
Are best ÷ up by 3s,
But wrapped in dim obscurity
Is the square root of 3…
– John Atherton
Does the poem above make you feel like you’re reading Chinese?
When you look at numbers do you feel like your head is spinning?
Are you just so glad that your student days are behind you and that you never have to take another math test again?
A lot of adults (and children) feel that they will never understand math. That’s how Barbara Oakley felt until she was twenty-six. Now, she’s a professor of system engineering and has a PhD in the field of mathematics. Oakley recently wrote a book called A Mind for Numbers: How to Excel at Math and Science (Even if you Flunked Algebra) to explain how she overcame her failure in math and emerged as a leader in the field.
Oakley explains that math builds on itself, so if you miss a concept at a key moment, you can fall helplessly behind. This can happen because of a two-week long bout with the flu, a teacher who mistakenly skips a topic, zoning out during class time because you were thinking about your parents’ divorce, or switching schools. Then, suddenly, you find yourself behind and unable to catch up.
This happened to Oakley as a child, growing up in a poor school district with teachers who chose to kick kids out of the classroom rather than teach them the concepts they didn’t understand. Thus, Oakley grew up believing that she was terrible at math. Luckily, she had other skills. She quickly learned Russian and joined the military as a translator. She got many promotions within the army, but realized that the only way she would have a successful career outside of the army as a translator was if she also had experience with technology. This scared her immensely. After all, she was terrible with numbers. In the end, though, she decided that even though it might be impossible she was going to “train her brain” to understand math.
And, that’s just what she did! At twenty-six, she went back to school, got a second Bachelors degree, a Masters degree, and a doctorate, all in math. Oakley’s whole philosophy is that anyone can train his/her brain to understand math.
Below, I’ve included ten tips that Oakley suggests to help train your brain for math. In reality, these tips can work for any discipline that you are studying.
Use recall. After you finish reading a page or concept, look away and say the main ideas aloud to yourself. If you can recall the ideas on your own, then you’ve been actively taking in the information. If you can’t, then you’ve been passively reading and not truly gaining anything.
Test yourself. Use flashcards, use online quizzes, and test yourself on everything you are studying all the time. Without these tests, you will never know what you understand or what critical piece you are missing.
Chunk your problems. Once you understand a complex problem, practice it so many times that all of the different steps involved become a “chunk” of memory. That means that instead of needing to remember 10 steps to solve the quadratic equation, you have recall of it with one chunk.
Space your repetition. Don’t study for five hours one night. Instead, study for one hour over five nights. Think of your brain like a muscle. Would you start run a marathon without training before?
Alternate different problem-solving techniques during your practice. Study guides and textbooks are rarely set up this way, but test yourself on different types of problems throughout your study sessions. This will allow you to feel comfortable knowing when and how to use the different techniques.
Take breaks. If you hit a brick wall, take a break and do something else. Giving your brain time to focus on something else will allow it to subconsciously work on the problem you were struggling with before.
Use explanatory questioning and simple analogies. Once you understand something think about how you would explain it to a ten-year-old. Then, say it out loud or write it down. These acts will solidify your newfound understanding.
Focus. Set a timer for a manageable amount of time (20-40 minutes) and turn off all distractions. Then, focus completely on the material you are studying. When the timer goes off, give yourself a reward.
Eat your frogs first. The novelist Mark Twain once said that if you have to eat a live frog, you might as well eat it first thing in the morning so that you know that the worst part of your day is over. Start with the thing that you are most dreading. Once you get that over with, the rest will be easy as pie!
Make a mental contrast. Think about where you’ve come from and where you’d love to be at the end of your studies (an astrophysicist, a better homework helper for your sixth grader, an interior designer). Use that contrast to propel yourself through the tough times.
Can everyone be the next Einstein? Of course not. But, maybe you don’t have to be bad at math.