PPublished by EducationNews.org — Methods are about HOW to solve problems, not solving problems themselves.
Back in the 1990s, circumstances so maddened Dr. Matthias Felleisen, he felt forced to create Program by Design (PxD) to bring life back to computer science and algebra, both. Since then, thousands of students have used it to learn the elements of programming, with or without a teacher. Even I could understand its free, online textbook. The PxD target audience were first-year college students, but Felleisen’s team wanted it to be accessible to clever 10-year-olds. The NSF and other major funders continue to be impressed.
The final straw for Felleisen’s frustration was his children’s 10th-grade babysitter, when he was a young computer-science professor at Rice University. The girl was floundering miserably in math, as so many students do. He offered to help and found her gratefully receptive to his methods.
Felleisen is German by birth, so his own training was quite different than what’s available here. In the U.S., “Teachers hand students the functions, but students do not know where they came from or what they are, really. Algebra problems are terribly boring because teachers just use numbers. Algebra can manipulate pictures, or even words. I have nothing against numbers, but I asked if I could help (the sitter) make functions of her own that could that make a movie or a game.”
Animation helps beginning students see how math makes a computer DO something.
“Of course it worked with her, so I knew then that I could and should change algebra.”
“Multiple choice is about right answers.”
Felleisen’s much bigger issue were his frustrating college students. It seemed they’d been taught to drive straight to right answers with virtually no attention to the methods by which answers emerge. No real-world context engaged students in why the problems were intriguing — contexts like animation, Census data, aerospace calculations or video games. What really excites him are the methods or processes that help students work through problems. He gets impassioned, even a bit snarky about American teaching methods, using the word “boring” a lot.
“I grew up in Germany where I was taught by ex-engineers. They were excited because they had no limits on their imaginations. My textbooks were one-tenth the size of American textbooks. They just had the methods for how to solve problems. My math teachers put the subject in context.”
American textbooks, on the other hand, “are huge, filled with big color pictures of all kinds of objects that may convey the idea of a function (a manual meat grinder), or an alternative view of functions (an image of a graph and a rule with arrows in between). They might describe several uses of functions (economics, biology, or programming), often with one-page stories on a person. None of this reaches the kids. In particular, it fails to bring across why a functions are needed and how they are created systematically. Instead, they have pages of practice problems. My training had no multiple-choice. It was always about the method and not the right answer.”
Felleisen gives his students zeros if they get the correct answer, but don’t show work that lets him see their methods and thinking. They get full credit, though, “if your answer is wrong, but your methods are right and you made a small mistake. Yes of course I had math drill, but only early on, when I was very young. From then on it was all about the methods, for algebra, geometry…”
The drive to get the right answer seems to have wiped out most students’ sense of the possibilities and power of both math and the computer.
“A computer is a dumb piece of engineering.”
After the baby-sitter experience, Felleisen gathered a team to develop a curriculum that turned the computer into the learner. “The student, then, is the teacher who tells the computer what to do. The creative person is the student.”
In his own class, his first lesson teaches students how to get a computer to move a cat across a screen. The cat is on the left, positioned in relation to the “x” and “y” axis.
He says, “You construct a function from the little ingredients. When you understand the relationships in your function, the numbers are just incidental. Mathematicians know this. Functions are just little machines. They’re often written as tables where the function of time is to place the cat image at X distance from the right. Every time I make this picture I change the Time and the coordinates. Yes, these are numbers, but pictures are involved.”
Methods are about HOW to solve problems, not solving problems themselves.
So the driving question ought to be: what problem do you want to solve? What real-world context is engaging? When right answers become too important, math is all plug-n-play with functions and not creative acts of imagination.
Worse still, the bee-line drive to right answers cripples the American student’s imagination and appetite for solving problems in all sorts of ways. And that, in turn, produces way too many wrong answers on the all-important tests. Ironic, no?
Julia Steiny is a freelance columnist whose work also regularly appears at GoLocalProv.com and GoLocalWorcester.com. She is the founding director of the Youth Restoration Project, a restorative-practices initiative, currently building a demonstration project in Central Falls, Rhode Island. She consults for schools and government initiatives, including regular work for The Providence Plan for whom she analyzes data. For more detail, see juliasteiny.com or contact her at firstname.lastname@example.org or c/o GoLocalProv, 44 Weybosset Street.