“I met a young man who had recently graduated from high school, where a mathematics teacher had labeled him a ‘bigot’ for thinking it was important to get the right answer.” (Nancy Pearcey, Total Truth: Liberating Christianity from Its Cultural Captivity)
We're in 15th place
If you’re wondering why your child finds math akin to reading Sanskrit on fossilized bark, the culprit could be “reformed math.”
In 1989, the National Education Summit established goals for public education. Among them: “By the year 2000, United States students will be the first in the world in mathematics and science achievement.” Soon afterward, the National Council of Teachers of Mathematics (NCTM) crafted and unveiled new standards for math instruction.
In contrast to the traditional methods aimed at computational accuracy and individual mastery using time-tested algorithms, reformed methods emphasized group participation and thought processing. The NCTM standards also called for “mathematical equity”; namely, that the goals for math instruction reflect social justice issues, like the politics of race and gender.
Today, with over a decade of experience using the reformed methods, it is reasonable to ask how effective they have been in meeting the 1989 goal.
In late 2003, a study of math proficiency ranked U.S. students 15th among their peers in 45 countries. Another study, with a different set of countries, placed the U.S. 24th in math literacy and 26th in problem-solving capabilities.
Whether ranked 15th or 24th, it is clear that the U.S. woefully lags the industrialized world in math achievement. To understand why, it may help to see how the national recommendations have been implemented in state educational standards.
“Dysfunctional beliefs”
In 2000, the Department of Public Instruction in Washington state published “Teaching and Learning Mathematics—Using Research to Shift From the ‘Yesterday’ Mind to the ‘Tomorrow’ Mind.” According to the document’s author, Dr. Jerry Johnson, substandard math proficiency is linked to dysfunctional beliefs, including:
“The goal of mathematical activity is to provide the correct answer to given problems, which always are well defined and have predetermined, exact solutions.” (I wonder if Dr. Johnson has shared this insight with the banker who calculates his checking account balance.)
“The nature of mathematical knowledge is that everything (facts, concepts, and procedures) is either right or wrong with no allowance for a gray area.” (What a breeze third grade multiplication would have been had Miss Scarborough understood that “41” falls within an acceptable “a gray area” as a solution to six times seven!)
Criteria for assessing teaching effectiveness are contained in the more recent document, “Washington State Professional Development IN ACTION.” Among the “below standard” indicators defined in that document is this: “Students believe there are right and wrong answers to questions and work to determine what those are.” The corresponding “above average” indicator is that “students know [that] their ability to construct understanding and think reflectively about a problem is more valuable than correct answers" (emphasis added).
I suspect that families who lost loved ones in the Minneapolis bridge collapse would strongly disagree. A structural engineer who is more concerned about reflective thinking than the right answer to a load calculation is a dangerous person. Even more dangerous is one who believes he can “construct” his own answer, rather than calculate the correct one.
Considering context
In a recent post on The Point, a reader took me to task for not considering the context of these documents. He pointed out that, oft-times, an engineering analysis results in no bright line that separates a right answer from a wrong one. Because of the inherent uncertainties in a problem, calculations frequently require error analyses that bound answers within acceptable ranges and tolerances.
I agreed that context is important. And had the guidelines been restricted to mathematically mature students undertaking advanced courses in fluid mechanics, statistical analysis or quantum theory, I wouldn’t be quibbling about them. But they’re not. The context is basic math instruction for kids in grades K-12 who have trouble doing long division, calculating fractions, and knowing where to put decimal points.
From my 30-year career as an engineer, I also understand that uncertainty is an unavoidable feature in many engineering problems. But calculational uncertainty is not due to the underlying math; it’s the result of imprecise measurements, unknown quantities, and contingencies that must be accounted for to ensure that the engineering requirements will be met. With precise inputs, an engineer has every confidence that the applicable mathematical algorithms will give correct results, every time.
A concerned mother
M. J. McDermott is a meteorologist who returned to college in the late 1990’s for a degree in atmospheric science. While taking classes in advanced math and physics, McDermott observed some unsettling things about her colleagues, most of whom were 20 years her junior.
She noticed students fresh out of high school, enrolled in college calculus, who had trouble with basic math skills like algebra, trigonometry, and even arithmetic; whose understanding of symbolic math and application of mathematical logic was poor; who had difficulty working independently; and whose dependence on calculators was so entrenched that many relied on their TI-83’s for simple multiplication tasks, like calculating 4 times 6.
As a concerned mother of young children, McDermott was provoked to investigate the instruction offered in today’s schools. What she found in grades K-6 was reformed math, or, as it is more fittingly referred to, “fuzzy” math.
In textbooks like Everyday Mathematics, students are encouraged to reason through problems, rather than rely on time-proven methods. Instead of helping students gain mastery over the simple, effective, and 100-percent-accurate algorithms, students are given a toolkit of methods that encourage group work over individual effort.
For simple double-digit multiplication, students are shown the “cluster method,” the “partial products method,” and the “lattice method,” all of which yield valid results if done correctly, but are highly inefficient and at least as prone to error as the traditional method. After watching a demonstration, I understand why group work is an integral part of “fuzzy” math.
Intolerant math
In her book Total Truth, Nancy Pearcey references a curriculum, funded by the National Science Foundation, instructing educators to teach students that “mathematics is man-made, that it is arbitrary, and good solutions are arrived at by consensus among those who are considered expert.” Pearcey also draws attention to a Minnesota document that advises teachers to be tolerant of “multiple mathematical worldviews.”
Can you believe it? Mathematics, of all things, is man-made and arbitrary, and alternate mathematical worldviews are to be tolerated? Does that apply to the viewpoint of a student who prefers to believe that two plus two equals five? Probably so, as long as he demonstrates “reflective thinking.”
Then there’s the educator who told Pearcey that he graded his students not on whether they obtained “right” or “wrong” answers, but whether their answers were the result of cooperative effort and consensus. I shudder to think that, sometime in the future, I could board a plane designed by one of his students.
Clearly, reformed math is the direct result of four decades of postmodern thought. The notion that truth, even in hard disciplines like math, is a product of popular opinion rather than a statement of objective reality comes straight from the architects of postmodernism: Foucault, Derrida, and Rorty.
G.K. Chesterton saw this coming a century ago. In his classic work, Orthodoxy, Chesterton predicted, “We are on the road to producing a race of men too mentally modest [read, cynical] to believe in the multiplication table.” Laying the blame squarely on the malignant skepticism of his day, Chesterton continued, “we have largely destroyed the idea of that human authority by which we do a long-division sum.” One hundred years later, we see how prophetic his predictions were.
There is more than a touch of irony here; for while there is tolerance for differing answers in math class, down the corridor in biology class there is one and only one acceptable answer: Darwinism, a belief system that transcends reflective thinking and popular opinion, at least according to the NSF and the educational establishment. As to alternative theories for the origin and complexity of life; they are neither taught, critiqued, nor tolerated.
Only through the looking glass of reformed education, could alternative answers to a multiplication problem be viewed acceptable; while alternatives to a theory that has been controversial for 150 years be viewed inadmissible for class discussion. It appears that the reformers have succeeded in constructing an educational Oceania, where academic proficiency and critical thinking have been replaced by groupthink and indoctrination.
So if your college-aged son or daughter hasn’t mastered the multiplication tables, take heart; they’ve got their TI-84 Plus, and knowledge of peppered moths, drug-resistant bacteria, and the Urey-Miller experiment—textbook “proofs” for the most sacrosanct theory of our day—that is sure to please their professors. Feeling better?
Regis Nicoll is a freelance writer and a Centurion of the Wilberforce Forum. His "All Things Examined" column appears on BreakPoint every other Friday. Serving as a men’s ministry leader and worldview teacher in his community, Regis publishes a free weekly commentary to stimulate thought on current issues from a Christian perspective. To be placed on this free e-mail distribution list, e-mail him at: centurion51@aol.com.
Posted with permission from the Center for Christ & Culture