The spring issue of Education Next has a forum on whether changes are needed in No Child Left Behind. Check out the graph on the variation in reading and math standards among the states: It’s a lot easier to reach proficiency in some states than others.
Christine Rossell writes about magnet schools, which remain popular. The first magnet opened in Tacoma in 1968 as a desegregation tool.
Barry Garelick writes about what he learned about math education as a tutor of proof-less geometry students, the father of a second grader who wasn’t being taught addition and a government analyst temporarily assigned to a senator’s staff.
The National Council of Teachers of Mathematics “recommended that students learn ‘strategies’ for learning number facts rather than memorize those facts.” Calculators were emphasized; teachers were urged to decrease time on paper-and-pencil computations, including long division and fractions, the use of rounding to estimate, rote memorization and practice and direct instruction by the teacher. Instead, students were supposed to discover math concepts for themselves.
Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned. There is little argument that learning is ultimately a discovery. Traditionalists also believe that information transfer via direct instruction is necessary, so constructivism taken to extremes can result in students’ not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering and taking ownership of the wrong answer. Additionally, by working in groups and talking with other students (which is promoted by the educationists), one student may indeed discover something, while the others come along for the ride.
Texts that are based on NCTM’s standards focus on concepts and problem solving, but provide a minimum of exercises to build the skills necessary to understand concepts or solve the problems. Thus students are presented with real-life problems in the belief that they will learn what is needed to solve them. While adherents believe that such an approach teaches “mathematical thinking” rather than dull routine skills, some mathematicians have likened it to teaching someone to play water polo without teaching him to swim.
Garelick wanted the senator he was advising to question the National Science Foundation’s funding of “fuzzy” math curricula. But Lynne Cheney, then a fellow at the American Enterprise Institute, was campaigning against fuzzy math, and he was working for a Democrat.
I told (Democratic staffers) about the open letter from the two hundred mathematicians and urged them not to confuse the message with the messenger. “This is a real issue,” I said. “Kids aren’t learning the math they need to learn.”
Garelick wanted to brief the senator on the issue. The staffers said it was impossible: The Democratic senator couldn’t be on the same side of the math debate as the Republican vice president’s wife.
Update: Thanks to Steve in Comments for mentioning the American Institute for Research report which compares math curricula in the U.S. with high-scoring Singapore. AIR praises the U.S. “emphasis on 21st century thinking skills, such as reasoning and communications, and a focus on applied mathematics,” but notes the U.S. students “must begin with a strong foundation in core mathematics concepts and skills, which, by international standards, they presently lack.”