Math as Critical Thinking?
In the March 2016 issue of The Atlantic, education expert Peg Tyre writes of "The Math Revolution" that is quietly taking place, among some educators in the US, emphasizing not drills but conceptual thinking in teaching math, and she tells of Daniel Zaharopol, "founder and executive director of Bridge to Enter Advanced Mathematics" (BEAM), who is intent on locating minority kids with math skills, as in the following anecdote about a kid he found in Middle School 343:
Five years ago, when Zaharopol entered M.S. 343, a boxy-looking building in a rough section of the South Bronx, and sat down with a seventh-grader, Zavier Jenkins, who had a big smile and a Mohawk, nothing about the setup was auspicious. With just 13 percent of kids performing at grade level in English and 57 percent in math, M.S. 343 seemed an unlikely incubator for tomorrow's tech mogul or medical engineer.Now, that's progress! I wish I'd been taught that way in my early school years. I did have one outstanding middle-school math teacher, though, and his name was Jerry Moody. I still remember the math formulas that he insisted we learn. I've always wanted to thank him for his successful methods, but I somehow never got around to it . . . so, if you're out there somewhere, Mr. Moody, "Thank you!"
But in a quiet conversation, Zaharopol learned that Jenkins had what his siblings and peers considered a quirky affinity for patterns and an inclination toward numbers. Lately, Jenkins confided to Zaharopol, a certain frustration had set in. He could complete his math assignments accurately, but he was growing bored.
Zaharopol asked Jenkins to do some simple computations, which he handled with ease. Then Zaharopol threw a puzzle at Jenkins and waited to see what would happen:
You have a drawer full of socks, each one of which is red, white, or blue. You start taking socks out without looking at them. How many socks do you need to take out of the drawer to be sure you have taken out at least two socks that are the same color?"For the first time, I was presented with a math problem that didn't have an easy answer," Jenkins recalls. At first, he simply multiplied two by three to get six socks. Dissatisfied, he began sifting through other strategies.
"I was very encouraged by that," Zaharopol told me. "Many kids just assume they have the right answer." After a few minutes, he offered to show Jenkins one way to reason through the problem. The energy in the room changed. "Not only did Zavier come up with the right answer" - four - "but he really understood it very thoroughly," Zaharopol said. "And he seemed to take delight in the experience." Four months later, Jenkins was living with 16 other rising eighth-graders in a dorm at the beam summer program on Bard College's campus in upstate New York, being coached on number theory, recursion, and graph theory by math majors, math teachers, and math professors from top universities around the country. With some counseling from BEAM, he entered a coding program, which led to an internship at Microsoft. Now a high-school senior, he has applied to some of the top engineering schools in the country.
Ah, almost forgot! Math as critical thinking! "Inessa Rifkin, a co-founder of the Russian School of Mathematics . . . [in] the United States" wants "children to ask difficult questions, to engage so it is not boring, to be able to do algebra[, for example,] at an early age, . . . but also to see it for what it is: a tool for critical thinking." Readers interested in Rifkin's views can look further into the article.