Discovering the Principles and Effects of the Discovering Math Series

In reading Robert Pondiscio’s “Suing Over Curriculum” (February 5, 2010), I was amused to find mention of a math text that I find generally flawed and illogical: Discovering Math. It is a text used locally, too, so I’ve had the stress of having to tutor some students who are subjected to the text’s cognitive torture. I feel sorry for them. Yes, of course, the texts have some good points, they do give some good or decent explanations of some things and there are a few good diagrams in them; but all texts must say 1 + 1 = 2, or the authors and publishers will be laughed out of society. The texts are so full of irrelevant pictures, it is hard to concentrate on the reading and the exercises. And the exercise sets do not at all allow students to learn, practice, and become proficient at concepts and methods. Very few students, I believe, could figure out what to do in some of the exercises, even if they had had practice in the basic concept being drilled. In an article about a court case involving the “Discovering” series, “Seattle Schools’ ‘Discovering Math’ curriculum risks a generation of students” (May 29, 2009 at 2:53 PM) by Cliff Mass (Professor of Atmospheric Sciences at the University of Washington), the Seattle Times said:

ON May 6, the Seattle School Board voted on the purchase of high-school math textbooks, and the results were both disappointing and tragic. In a 4-3 vote, the board adopted the Discovering Math series: “discovery-based” math texts that were found to be mathematically unsound by mathematicians working for the state Board of Education. As noted by Professor Jack Lee of the University of Washington, “definitions, computational algorithms, and formulas seem to be stated vaguely when they are stated at all.” These books are “discovery-based” or “reform” math texts in which discussion, group projects, manipulation of objects, use of calculators and inefficient “exploration” replace students acquiring of key skills, solving real-world problems and developing a strong mathematical foundation. At the core of this math series is the theory that unless students “discover” math facts themselves, they are unable to master and apply them effectively. The damage from “Discovering Math” is multiplied by Seattle’s previous selections of similarly weak “discovery” curricula in elementary (“Everyday Math”) and middle school (CMP2). During the roughly 10 years the Seattle Public Schools has used discovery-based math texts, the achievement gap for disadvantaged students has widened. Copyright © 2010 The Seattle Times Company

In “Looking at the decision” (seattle math group Blog, Friday, February 5, 2010, 12:06 AM), Martha McLaren writes:

Judge Julie Spector today announced her finding of “arbitrary and capricious” in the Seattle School Board’s May 6 vote to adopt the Discovering Math series of high school texts despite insufficient evidence of the series’ effectiveness. Judge Spector’s decision states, “The court finds, based upon a review of the entire administrative record, that there is insufficient evidence for any reasonable Board member to approve the selection of the Discovering series.”

The text itself, and the false theory behind it, should have been declared “arbitrary and capricious” and based on “insufficient evidence.” The effect of the texts are addressed above: cognitive failure, an inability to do math, and an inability to grasp the essentials of math. The principles behind the text are basically those of John Dewey: truth is a social construct; the “consensus” reigns supreme; “learning” is just verbal behavior; there are no objective absolutes; cognitive hierarchy and context don’t really matter. Update (9:00 PM):  On a related note, check out the site Mathematically Correct. They say about their site:

This web site is devoted to the concerns raised by parents and scientists about the invasion of our schools by the New-New Math and the need to restore basic skills to math education. Mathematics achievement in America is far below what we would like it to be. Recent “reform” efforts only aggravate the problem. As a result, our children have less and less exposure to rigorous, content-rich mathematics . The advocates of the new, fuzzy math have practiced their rhetoric well. They speak of higher-order thinking, conceptual understanding and solving problems, but they neglect the systematic mastery of the fundamental building blocks necessary for success in any of these areas. Their focus is on things like calculators, blocks, guesswork, and group activities and they shun things like algorithms and repeated practice. The new programs are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement. Concerned parents are in a state of dismay and have begun efforts to restore content, rigor, and genuinely high expectations to mathematics education. This site provides relevant background and information for parents, teachers, board members and the public from around the country.