[Piaget, Vygotsky, Feuerstein, and the National Council of Teachers of Mathematics (NCTM) Principles and Standards]
The Seattle Times
December 15, 2005
The ongoing math wars: division by subtraction
By Niki Hayes
Special to The Seattle Times
As a math teacher, I believe that "basic skills" are more than competency in computation - they are the foundation for critical thinking and advanced learning.
Since my opinion is in the minority, I spent several weeks this past summer researching the "math-war environment" that disparagingly labels teachers like me "traditionalists."
Simply explained, there are two academic camps in math education. There are those who support including basic skills in math instruction, and those who don't. The second and dominant group - the so-called "progressive" bloc - believes conceptual understanding is interrupted by basic-skills instruction.
These two camps developed after the National Council of Teachers of Mathematics (NCTM), a private group, published a new set of curriculum standards in 1989.
Supported philosophically by the National Science Foundation (NSF), the council based its approach on the progressivism of John Dewey, the constructivism of Lev Vygotsky, and on modern cognitive-developmental research.
But, having studied in Israel with Prof. Reuven Feuerstein, a cognitive psychologist who worked with Jean Piaget and is an internationally recognized expert on Vygotsky, I saw, in reading some 30 articles this summer, little semblance between my understanding of Feuerstein's teachings and the NCTM program:
Cognitive psychology does not validate an anti-basic-skills attitude or many of the new and unreliably researched experimental programs in math education.
Feuerstein taught us to analyze a task (look at its basic parts and their relationships); assess the learner's prior knowledge; and understand the mental operations needed to complete the task as mediated by the teacher.
That means teachers guide learners in understanding principles - rules - and concepts of a subject, giving equal respect to both.
Learning is thus based on teacher direction, with student discovery encouraged at appropriate times and within designed boundaries.
Teacher and learner must understand the process for learning, but the process cannot become the product, which is NCTM protocol.
Common sense tells us learning mathematics is different from learning literary disciplines. Math requires precision and right and wrong answers. It's based on concrete solutions, not on "close enough" answers or opinions.
And, there is no need to rediscover or reinvent rich principles, many of which have been available to learners for several thousand years.
Students are always expected to explain their answers, whether in writing or orally; but learning the steps that caused incorrect answers is vital in mathematics.
Consequently, math-grading processes will be more exacting and often reflect "lower" scores if answers are graded according to accuracy, rather than subjectively or on student effort.
Math isn't hard. It just expects the use of principles and precision. That can make it seem hard.
Interestingly, more than 200 of the nation's top mathematicians and scientists, including Nobel laureates and Fields Medal winners, signed an open letter of protest in 1999, urging then-U.S. Secretary of Education Richard W. Riley to withdraw his endorsement of 10 experimental math programs.
Two of those are now used in Seattle: The "Connected Mathematics Program" is in middle schools and the "Integrated Mathematics Program" will be in at least two high schools. The "integrated math" curriculum supported by the NCTM is the basis for teaching mathematics in other schools.
There's something unbalanced about this math-war environment and the adult behavior that supports it. A group of private individuals decided it knew the best way to teach mathematics. The NSF funded these "progressive" programs, making them the "new, new math" in U.S. schools. This was quite a coup in education - a field notably resistant to change. An economic boon also resulted for authors and publishers promulgating this new curriculum. Now, many cash-strapped districts will have to keep those books and curricular materials, because they don't have the money to finance a move toward a more-traditional and balanced way of teaching math.
However, some movement has been stirring around the country. Parents in New York and California have fought since the 1990s to bring balance to math programs. A number of districts across the country are switching to Singapore Math, Saxon Math and other basics-oriented curricula.
The focus of those reviewing math programs for their districts is on how things can be done, not why they can't.
Frankly, it's time to make intelligence the greatest common factor between progressives and traditionalists, rather than the least common denominator. (Sorry ... I just couldn't help myself.)
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