My family and I were recently discussing what makes people good at math. My son Nathaniel, who’s in his early thirties, brought up something he read in Malcolm Gladwell’s book Outliers. Gladwell talks about a woman in her mid twenties named Renee who’s trying to solve a math problem as part of a research project. Renee is sitting at a computer that allows you to type in x and y axis values to produce a curve. It’s basic rise over run math stuff that we all learned in junior high school or high school (but nearly all of us have since forgotten).
If you’re like me and you’ve forgotten, Gladwell provides a brief example. If the value of the rise on the y axis = 5, and the value of the run on the x axis = 5, then the slope = 1. Because the rise over run is 5 over 5, and 5/5 = 1.
So this woman Renee is sitting at the computer trying to solve a problem. And while she’s doing this, a Cal Berkeley professor and researcher named Alan Schoenfeld is sitting next to her. Schoenfeld knows the problem Renee is trying to solve is impossible. But she wasn’t told that it’s impossible. What she was told, was to enter values that will create a line that is perfectly vertical. But the problem is impossible because a vertical line requires a rise value of infinity and a run value of 0. And infinity divided by 0 doesn’t produce a number.
So she’s sitting there at this computer. And she starts entering in values. And she fiddles around. And she enters some more values. And then she fiddles some more. The whole while she’s talking to herself. And as she fiddles and experiments, her values for y get larger and larger. And the larger they get, the closer the line gets to the y axis. But no matter how large a value she assigns to y it never gets there.
Finally, after twenty-two minutes of trial and error, Renee experiences a eureka moment and she says, “Oh… A vertical line is anything divided by zero, and that’s an undefined number. Now I see.”
Schoenfeld videotapes these sessions and Renee’s is Schoenfeld’s favorite video, because Renee best exemplifies the secret to math.
Schoenfeld has observed countless students working on math problems. And most of them, when presented with a problem like Renee’s, give up–within 30 seconds. What they typically do is they stop. And then they declare to Schoenfeld that they don’t get it. And they say they need him to explain it to them.
But Renee didn’t give up after 30 seconds. In fact, Renee didn’t give up at all, and that’s what made the difference.
What’s funny is our perception of those who are good at math is that they have some sort of innate ability that’s absent from those who aren’t good at math. But Schoenfeld disagrees. According to Schoenfeld, and Gladwell, the real secret is persistence. Persistence, and a willingness to work hard, even if it takes a long time, is the real secret to solving the problem. (Gladwell)
Jesus’ Secret To Prayer
It’s interesting to see that Gladwell used a woman to demonstrate his secret to math, and Jesus uses a woman to illustrate his secret to prayer.
There she was, before the judge again. And he wasn’t a good judge either. He had no fear of God, and he had no respect for men. But she was there–again. And she said, “Give me legal protection from my adversary.”
And at first he said, no.
And for awhile, he continued to say no.
But she just kept coming. And finally he said, “Even though I don’t fear God or respect men, I’ll give her what she wants, because she won’t stop, and she makes me weary.”
He told us that parable to show us we should pray all the time, as the widow petitioned the judge. And that we should not lose heart. Even if it takes a long time. (Luke 18:1-5)
Jesus also said to “ask and it will be given to you; seek, and you will find; knock, and it will be opened to you.” (Luke 11:9) And sometimes answers to prayers do come quickly. We ask and just as Jesus says, God gives to us. But other times there’s seeking and knocking involved. And we have to not give up even as Renee did not give up until she figured out Schoenfeld’s impossible problem. We have to pray all the time, persistently, in the same way the widow petitioned the judge.
So don’t lose heart. Even if it takes a long time before your answer comes.
Don’t lose heart.
And never give up.
“Hear what the unrighteous judge said; now, will not God bring about justice for His elect who cry to Him day and night, and will He delay long over them? I tell you that He will bring about justice for them quickly. However, when the Son of Man comes, will He find faith on the earth?” -Jesus Christ, Luke 18:6-8
Persistence wasn’t the only secret to math that Malcolm Gladwell wrote about in his book. Culture and language were also cited. But persistence was the foremost reason.
Malcolm Gladwell, Outliers, Little, Brown and Company, November 18, 2008
Image via Jeremy Lim – Creative Commons