So now OECD comes to the earth-shattering conclusion that students who do well in math are those given complex multi-step problems, and those who tend to do poorly are given so called “real world” problems. Those of us who’ve been bitching and moaning for years about the superficiality and uselessness of the “real-world” problems are now in a position to say “I told you so.” Yes, the real world problems are like a specific application that ignores the general underlying procedures of problem solving. Like teaching someone how to get from pt A to pt B in a specific city without teaching them how to use a road map.
Secondly, the real-world applied math technique tends to be taught to students from lower-income families while the students from higher income families reap the benefits of a more “pure math” approach. Of course, it could be that the techniques are the same for both, but that the students from higher income families have more access to tutors and learning centers which tend to teach in a more “pure math” style, but the OECD study doesn’t seem to delve into that.
Diane Briars, a former president of NCTM was asked about this trend; she touted Common Core as a solution to this problem:
“Briars added that the new Common Core standards are aimed at boosting conceptual understanding, and that’s one reason teachers are asking students to draw all those crazy pictures that are lampooned in the media.
” “There’s been a lot of push back in the media against these pictures and diagrams. The feedback in the media is, ‘Why don’t you just give them the rule?’ ” said Briars, “This report speaks to that. No, don’t just give them the rule. They need that conceptual understanding.” ”
Well, no, not exactly, Diane. The way CC has been interpreted is that the “rule” you seem not to like (aka standard algorithm) is delayed. The std algorithm for multidigit addition and subtraction for example, appears in the 4th grade, even though Zimba and McCallum, two lead writers of the CC math standards, say it can be taught earlier than 4th grade. What happens is students are given “strategies” requiring the drawing of pictures and diagrams for years before being given the “rule” in the belief that providing what they feel is “understanding” prior to the procedure gives the sufficient background. Otherwise, they believe, the standard algorithm eclipses why/how the procedure works. Which is nonsense. Procedures and understanding work in tandem.
This came to light when they looked at the PISA results–the exam given to students in various OECD nations:
“In the report, “Equations and Inequalities: Making Mathematics Accessible to All,” published on June 20, 2016, researchers looked at math instruction in 64 countries and regions around the world, and found that the difference between the math scores of 15-year-old students who were the most exposed to pure math tasks and those who were least exposed was the equivalent of almost two years of education. The research was based on how students answered survey questions that accompanied an international test, called the Programme for International Student Assessment, or PISA.
“The result was surprising for two reasons. First, the PISA exam itself is largely a test of applied math, not equation-solving. For example, one question asks students to calculate the length of a revolving door entrance that doesn’t let air get out. And yet the students with more pure math instruction were better able to handle this and other PISA questions.”
Well, I guess traditional math IS good for something. But don’t tell NCTM. They believe they are providing the conceptual understanding despite the fact that they aren’t.