The opening to this article about students in Wake County, North Carolina, was almost enough to get me to stop reading, but apparently I felt the need to punish myself, so I pressed on.
Wake County students taking high-school-level math courses are now finding that getting the right answer isn’t always as important as the process they use to solve the problem.
Yes, as a math teacher, I often give partial credit on test questions where a student has made a numerical error but has set the problem up correctly. But I do like right answers, and from what I’ve seen, the definition of “process” varies from teacher to teacher. Drawing pictures amounting to a time consuming and inefficient process is sometimes considered to be just fine. In a high school level math course, in my opinion it is not just fine.
Wake began rolling out this school year new classroom materials from the Mathematics Vision Project, a nonprofit education group that provides resources designed to align with the Common Core learning standards. Wake school leaders and teachers say the new materials have led to major changes in how math classes are run to shift from lecturing to having students work in groups to learn concepts through problem solving.
“We have to teach failure as a part of learning,” said Brian Kingsley, Wake’s assistant superintendent for academics. “If we’re going to be college and career ready, the answer isn’t always the most important thing.
Well, to be college and career ready, let me just say that the right answer is a lot more important than what Mr. Kingsley and others of his ilk seem to think. Learning how to work with algebraic expressions may seem like senseless manipulations of meaningless symbols to those subscribed to the group-think this article extols. But to the rest of us, it’s rather important to learn how to factor, and work with algebraic fractions. Students will undoubtedly make mistakes, so if “failure” is a goal of these people, the traditional method they hold in such disdain provides opportunities to make mistakes. Making mistakes is not the province of the “new way of teaching math”, I can assure you.
Math I students got workbooks this school year, but a lot of what they experienced was unexpected. Instead of students copying what their teachers write on the board, they’re working in groups to solve problems such as how long it would take to drain water from a pool. Teachers are guiding the students instead of lecturing them on subjects like quadratic functions.
“Instead of me saying, ‘Here is a linear equation: It’s y=mx+b,’ it’s much more, ‘Let’s get to this equation,’ ” Herndon said. “It’s very much a different approach. Rather than me giving them all the answers, they’re having to work towards them themselves.”
The opinion of those who believe traditional math has never worked is that teachers give the students all the answers, and students do not do any work for themselves. There is general belief among the prevailing educational forces that initial worked examples with plenty of practice is nothing more than “rote memorization” of procedures and that the process produces “math zombies” who cannot think for themselves.
I have observed the teaching methods described in this article. A problem about how long to drain water from a pool is rather straightforward, but I’ve seen problems like this take the better part of a class period when with proper direct instruction and worked example, it should take about 10 to 15 minutes. I’ve seen a class in which students worked on slope, graphing and the connection to linear equations for five to six weeks. There is no reason for taking that long and I wonder what evidence there is that such students have “deeper understanding” (a term that remains undefined, but generally means a “rote understanding” of explanations that students learn to give the teacher in order to satisfy them) than students taught in the traditional manner.
Do the people in the article have any evidence that their methods are producing better results than the methods they hold not to work? I mean other than their opinions and seeing what they want to see.