Jamar Pickreign, Ph.D. 2005 The Math "Wars" "Fuzzy" Math vs. "Parrot" Math.

Jamar Pickreign, Ph.D. 2005

The Math "Wars"

"Fuzzy" Math vs. "Parrot" Math

Information from various sources Jamar Pickreign, Ph.D. 2005

A Brief History of Math Education

Post WWII - war experience revealed much math illiteracy. Yet "orthodoxy" reigned.

Inadequately prepared teachers Use of "rule and rote" textbooks Computational "tricks" ruled

1957 Launch of Sputnik- mad dash to reform mathematics to respond

1960s 70s "new math"



"new math" ideas, however, were not "universally" successful in part because of difficulty "upgrading" teachers

Impossible to make every teacher a Max Beberman Also because of "sudden" transitions

Children having never experienced "new math" suddenly having it "thrust" upon them in a higher grade



Consequently, anxiety resulted in both children and their parents who never had such experience

Publishers began "jumping into" the "new math" but some were guilty of pasting "new math" onto "old" or calling "old math" "new"



School districts "hopped on to the new math bandwagon" but neglected to provide support and training to their teachers

Frightened "traditionalists" refused to budge. Some thought "new math" meant ignoring

basic skills and drill and practice



The expectation that "new math" would result in a miracle "quick fix" in the aftermath of Sputnik resulted in a lot of premature decisions which, not surprisingly, failed

So, came the "back to basics" cry in the mid 70s



1980: NCTM, still concerned about helping children "make sense" of mathematics, produced an "agenda for action"

1989: NCTM published "Curriculum and Evaluation Standards for School Mathematics"



Reminiscent of "new math" Standards-based mathematics has often been referred to as "new-new math" by those "back to basics" advocates. Despite the desire to help children "make sense", this standards-based math sometimes deserved this derision

1990s: the "math wars" rev up and become more politicized than they were in the 70s

2000s: ….


"Fuzzy" Math

Rooted in"constructivism" Math should "make sense" to learners Children should be thinkers, not "storage bins"

for thinking done by others


"Parrot" Math

Math in schools should be confined to arithmetic

Acquire facts (often out of any real context) first in the belief that these are necessary to become problem solvers

Memorization and rules, firmly established as successful by centuries of math, dominate (why "reinvent the wheel?")


Some Math Ed Myths and Facts

Myth:"Standard-based" mathematics has resulted in depressed test scores (NAEP, TIMMS)

Fact: Most students tested have received "traditional" instruction



Myth: "Reform-based" mathematics is untested

Fact: The research support for these methods and materials is vast.

(This myth of "untested" may be connected to the lack of presence of this type of math in classrooms.)



Myth: "Reform-based" math requires that teachers allow learners to "discover" everything on their own

Fact: "Reform-based" math allows learners to grapple with ideas, but this is guided.

"When you teach a baby to eat, there comes a point where they no longer want to be spoon-fed. They want to feed themselves. But parents still buy the food. They still cook it. They still put the baby in the highchair" (James Merlino, Director of the Greater Philadelphia Secondary Mathematics Project).



Myth: "Reform-based" math is based on a "radical" theory of "constructivism"

Fact: Promoting "understanding" is hardly "radical

This notion is probably rooted in a misconception of constructivism and the previous "myth"



Myth: "Reform-based" math ignores "basic skills"

Fact: NCTM describes a "worthwhile mathematical task" as one that, among other things, "fosters relevant skill development"



Myth: Mathematics content knowledge is sufficient for teachers of mathematics

Fact: Mathematics content knowledge is necessary for teachers of mathematics.



Myth: "Parrot Math" advocates and "Fuzzy Math" advocates have different goals for learners of mathematics

Fact: Both desire learners to develop computational fluency, problem solving ability and reasoning ability.


Goals for Students

Learn to value mathematics Become confident in their ability to do

mathematics Become mathematical problem solvers Learn to communicate mathematics Learn to reason mathematically


Shifts in classroom environmentfrom "traditional" to "reform"

Toward classrooms as math communities and away from classrooms as collections of individuals

Toward logic and math evidence as verification and away from teacher and textbook as source of authority

Toward math reasoning and away from mere memorization of procedures


Shifts in classroom environmentfrom "traditional" to "reform"

Toward conjecturing, inventing, and problem solving and away from emphasis on mechanistic finding of answers

Toward connecting math, its ideas, and its applications and away from treating math as a body of isolated concepts and procedures

Jamar Pickreign, Ph.D. 2005 The Math "Wars" "Fuzzy" Math vs. "Parrot" Math.

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