This week I received two comments on the Common Core math standards which are worth reading and understanding. This first is from Ze’ev Wurman, a former member of California’s Academic Content Standards Committee, and a U.S. Dept. of Education official under George W. Bush. Someone asked Ze’ev about Euclidean geometry in Common Core’s standards. This is his response:
“Common Core did not throw out Euclidean Geometry. Common Core replaced the way the fundamental theorems of Euclidean Geometry (relating to triangle congruence such as ASA, SAS, SSS) are supposed to be proven in the classroom to an experimental method with a track record of failure. Consequently, proving Euclidean Geometry theorems is bound to be no more than arm waiving under Common Core, and the beautiful edifice of logical air-tight deductive geometrical reasoning is bound to be lost. To add insult to injury, Common Core only lightly touches on traditional body of theorems relating to triangles and circles, making it’s geometry a shallow course.
In Common Core’s defense one could argue that many Geometry courses already today give a short shrift to logical proofs and to exploring geometrical relationships of triangles and circles. This is true for some courses, yet not for all of them. What Common Core does is that it codifies such shallow treatment of geometry to be the normative one, forcing even serious courses to be dumbed down to mediocre and shallow levels.”
This next comment is from Dr. Wayne Bishop, mathematician at California State University. Long time opponent of fuzzy math, he helped bring down the awful standards California adopted in the 90’s that devastated their state, and brought about their excellent 1999-2000 standards and framework which were among the best in the nation prior to their downgrading them for Common Core. This letter was in response to one of the questions on Governor Herbert’s recent survey. I don’t know which question this was a response to. Emphasis mine.
Although the words claim otherwise, the effect is highly pedagogical in support of a philosophy called “constructivism” that has a long history of repeated failure. I was very active in replacing California’s model of such in the 1990s with superb standards, the California Mathematics Content Standards with approved curricula and consistent assessments. Regrettably, California made the same mistake as Utah to “buy into” the misguided Common Core State Standards mirrored in the Utah ones. The words that the CCSS-M are tied to the best international standards are simply meaningless. FAR better would be to abandon the Utah form of the CCSS-M and replace the document with the far clearer and appropriate former California Mathematics Content Standards.
One of the problems is a deliberate, but disguised, avoidance of competence with arithmetic in the early grades. They are filled with nice-sounding words that are essentially content-free; pedagogy trumps specified/testable competency that is so critically important through ordinary fractions, percent, and ratio and proportion word problems. The lack of confirmation of arithmetic competence is dismissed by professional math education “experts” by ubiquitous, and inappropriate, access to calculators. By contrast, Japanese classrooms look very different:
“Students sit in rows and are expected to listen quietly. Teachers rely on direct instruction rather than investigative mathematics, but although they ask few questions, the questions they do ask are useful in guiding student understanding.”
The biggest surprise was a shocking lack of technology in Japanese classrooms. “Not a single student pulled out a calculator during class,” Drickey said. There were no overhead projectors, televisions, computers or laptops.
“But lack of reliance on technology may lead to higher scores for Japanese students,” she said. “The ability to think mathematically, without the aid of an outside source, could help students process mathematical problems more accurately and efficiently.”
As an experienced professor of mathematics who has taught our course designed to prepare prospective high school geometry teachers (Math 430 Modern Geometry), I am especially appalled the geometry standards that, again, echo the CCSS-M. To actually prove congruence (much less similarity) using transformations instead of the traditional sophomore Euclidean geometry approach, is something that no high school student is capable of doing without exceptional leadership, in part, because it is in none of the available books. Instead of making the subject harder (as an honest treatment would), the effect is the removal of proof from the high school mathematics curriculum. The very words in the CCSS-M and Utah Standards pass traditional sophomore proof on to college geometry which denies high school students the greatest gift of the ancient Greeks to modern human thought, semi-formal deductive logic. Sin has many forms but one of its more insidious ones is failing to educate students to the best of our ability under the misguided notion that if it’s especially challenging for some students, water it down so that everybody can “succeed”.
Professor of Mathematics
California State University, LA