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Education Reporter

2 + 2 = 5: Fuzzy Math Invades Wisconsin Schools
Leah Vukmir
Leah Vukmir
Excerpts from Investigations In Numbers, Data and Space 
3rd Grade Worksheet
1. Suppose you can hold 150 beans in your right hand and 217 beans in your left hand. How many more beans are in your left hand? Write down how you figured this out.

2. Solve this problem three different ways. Using a calculator can be one way. Make notes about how you solved the problem. Be sure that others can understand what you did: 42+36+18=

First way:
Second way:
Third way:

From 3rd Grade Manual (Addition)
Birthday: Pantomime holding a newborn baby in your arms. Tell students that the baby was just born, and write today's date on the board. Explain that this is the baby’s birthday. Sing "Happy Birthday," and encourage students to sing with you. Ask for volunteers to sing the song in their native languages.

Students might also make a poster with the words "Happy Birthday" in all the languages spoken in the class. Have each student point to his or her birthday on the calendar. This is a good opportunity to make a graph of the months of students’ birthdays.

By Leah Vukmir

During nightly homework sessions with her children in the fall of 1997, Kathy Siegmann of McFarland, Wisconsin realized she had come face-to-face with what is commonly referred to as "new-new" or "fuzzy" math. The McFarland School District had recently adopted a new math curriculum called Investigations in Number, Data and Space, for grades three through five, which did not include textbooks. (see box) "I could not tell what my children were doing in math, nor could I look in a book to help them," she stated. Feeling frustrated and helpless, Kathy began to question school officials and to conduct her own research.

Fortunately, several other McFarland moms had also researched math programs and decided to pull their children out of school during math class and homeschool them for that hour using a more traditional math program. The parents informed the principal and teachers of their decision and, in December 1998, proceeded with their plan. Two more children subsequently joined the exodus, along with Kathy's 5th-grade son.

The children thrived under their parent's tutelage, scoring at the "advanced proficiency" level on the Wisconsin Student Assessment System (WSAS) math test. By the following school year, a total of eight families were involved in this endeavor. They did not pressure the school district to discontinue the new curriculum, but instead urged officials to consider offering a more traditional alternative that they felt would better serve all the children.

In January 2000, these parents received a letter from the school district informing them that their children would be in violation of school truancy laws if they continued to remove them from the school's math classes. The parents were allowed to finish the school year, but they faced uncertainty about the future.

'New-New' or 'Fuzzy' Math 
"New-new" math is based on the notion that children understand and learn only those concepts that they "construct" or discover on their own. In small "cooperative learning" groups, children use blocks, beads, sticks and other "manipulative" objects to solve mathematical problems. Students are expected to discover or "reconstruct" the ancient rules of mathematics using these objects with the guidance of peers who are equally in the dark. This practice often extends beyond the early grades and is even found in high school algebra classes.

Rote memorization of math facts, e.g. multiplication tables, is considered taboo and textbooks are virtually non-existent in these bold new classrooms. Correct answers are less important than the thinking processes exhibited by the students. Students write about math instead of practicing the fundamental rules of math. Calculators and "guesswork" are encouraged even in the early grades and the fundamental operations of math, known as algorithms, are left for the child to "discover."

Parental outrage and concern over fuzzy math is certainly not confined to McFarland. According to "Parents Raising Educational Standards in Schools," a Wisconsin-based grassroots organization, math education has become the number-one concern of parents who call for information and assistance. During the past two years, concern about math education has supplanted the "Reading Wars" and is causing parents across Wisconsin and the nation to organize and rebel.

Fuzzy Math's NCTM Origins 
In 1989, the National Council of Teachers of Mathematics (NCTM) published Principles and Standards for School Mathematics, a set of math standards viewed by many as the basis of today's "fuzzy" or "new-new" math curricula.

Embraced by teachers colleges long before its publication, Principles and Standards in essence became the bible for a progressive education theory known as "constructivism." According to critics, the document put a stamp of legitimacy on an approach to math education that had already invaded schools nationwide.

The California Experiment 
Armed with this new math education manifesto, teachers across the country pushed forward with a new sense of purpose and eagerly unleashed constructivist ideology in their classrooms. California bought into "new-new" math in the early 1990s and, by 1992, had released the California Mathematics Framework - a document based largely on the NCTM Standards.

This unorthodox approach to teaching math was assailed by a group of California parents working largely in the mathematical and scientific fields. These parents believed their children would never be able to follow in their footsteps, given the weak skills they were developing in new-new math classrooms. Calling themselves "Mathematically Correct," these parents organized through the internet and mounted a fierce opposition to California's NCTM-modeled math standards. Their Mathematically Correct web site documents the history of the "Math Wars," critiques NCTM standards, analyzes a variety of math texts and programs, and provides parents with a multitude of resources to fight "fuzzy" math in their communities.

The mathematicians and scientists who run the site warn parents that the combination of new methods and "low content levels" found in elementary schools are present in many high schools and even in college calculus. Incoming college freshmen show a decline in math achievement, causing concern about the quality of future teachers.

The Mathematically Correct parents faced an arduous task when they decided to take on California's education establishment. Nevertheless, they were buoyed by an undisputed fact: California kids scored among the lowest in the nation on the 1996 National Assessment for Educational Progress (NAEP) math test. More than half of California's 4th-graders scored below the basic proficiency level and 49% of the state's 8th -graders had "below basic" math understanding.1

The combined forces of parents and mathematicians ultimately led to the development of a revised set of state math standards adopted by the California Board of Education in December 1997. The new blueprint, "California Mathematics Academic Content Standards," delineated benchmark standards for each grade level. Gone were the prescriptions for con-structivist teaching methods. Finally, a set of standards that emphasized the development of basic math skills!

Mathematically Correct maintains vigilance over California's math instruction and textbook adoption. The group also serves as a resource to parents in other states who are experiencing the invasion of "new-new" math.

Wisconsin Discovers Fuzzy Math 
McFarland is but one of many sleepy Wisconsin towns choosing to adopt fuzzy math. But how did a West Coast math craze make its way into America's heartland? Does the NCTM wield that much power over local decision-making processes? What factors are responsible for the invasion of "new-new" math in Wisconsin and how entrenched is this ideology in our schools?

To answer these questions we must look to three sources: Federal math program recommendations, the Wisconsin Model Academic Math Standards, and the Wisconsin Academy Staff Development Initiative.

In October 1999, a U.S. Education Department "panel" released a controversial list of 10 "exemplary" or "promising" mathematics programs. These programs reflected the pedagogical approaches to math outlined in the NCTM standards. With this list, federal education "experts" gave educators their blessing to proceed down the road to "fuzzy" math.

Fearing the effects of such an endorsement, a group of 200 highly respected university mathematicians and scholars, including several Nobel Laureates, sent an open letter to Education Secretary Richard Riley urging him to withdraw the recommendations. (See Education Reporter, March 2000) Warning that the programs had "serious shortcomings," they urged local districts to "exercise caution. . ."

The education establishment has largely ignored these warnings. Many Wisconsin school districts continue to cite federal recommendations in their push to embrace the new math curricula.

Wisconsin Math Standards 
A second contributing factor is the Wisconsin Model Academic Math Standards adopted in 1997. One need not dig too deep to find the NCTM influence on these standards. The introductory paragraph cites the NCTM Curriculum and Evaluation Standards for School Mathematics as a resource document used during standards deliberations.

Under the heading "Goals and Instructional Practice," the introduction states: "Classroom practice geared to the attainment of the Wisconsin Standards should be aimed at creating a community of learners and scholars, a place where the teachers and students actively investigate and discuss mathematical ideas, using a wide variety of tools, materials, and technology. Classes should engage students in more high-level mathematical thought and emphasize conceptual understanding, more so than in the past."2

Similar strains of "constructivism" echo throughout the document.

Perhaps the most powerful influence on Wisconsin's move toward "fuzzy" math is the Wisconsin Academy Staff Development Initiative (WASDI). Most Wisconsin citizens are likely unaware of this $6-million dollar project funded by a National Science Foundation grant. However, WASDI is a very familiar resource for Wisconsin math and science teachers. The goal of WASDI is "To totally transform the way technology education, mathematics and science are taught. It's not just reading the chapter and memorizing terms and filling in the blanks at the end of the chapter. It's hands-on learning."3

To that end, WASDI sponsors a series of one-week summer "academies" throughout Wisconsin where participants can earn graduate credits for learning new approaches to math, science and technology instruction. Over 2000 teachers participate in these workshops each year at 11 sites across the state.

WASDI also takes an active role in developing teachers as future leaders through its "Lead Teacher Institute." According to the web site, teachers completing this eight-week "Institute" serve as local, state, and regional state resources to their schools, other districts and state associations. They present a core curriculum at the summer academies, specifically one that "uses a constructivist approach to teaching,"and network with other "Lead" teachers throughout the state.

At the helm of this ambitious "new-new" math project is Dr. Billie Earl Sparks, co-project director of WASDI. A math professor at the University of Wisconsin-Eau Claire, Sparks also teaches math "content" to the university's education students.

According to Sparks, WASDI has trained 337 "Lead" teachers over the past six years. He explained that the National Science Foundation (NSF) has been a leader in advancing new math approaches across the country by providing grants to groups willing to write math curricula that match the NCTM Standards. Currently, 13 NSF-sponsored curricula are available to local districts.4

Dr. Sparks can best be described as a standard bearer for "constructivist" math in Wisconsin, and his fervor for the cause is evident. In September 2000, he gave an impassioned presentation entitled "Mathematics Education: Past, Present, and Future," at a public forum at McFarland School. He described the philosophy behind the district's recent adoption of Investigations in Numbers, Data and Space, (see box), a controversial NCTM-based math program that spurred Kathy Siegmann and the McFarland parents into action.

During his talk, Sparks emphatically asserted that math skills should not be taught in isolation. In classrooms today, students are expected to "explore" with their classmates until they find the skill that will solve the problem. As they explore, teachers intervene and teach skills as they arise. This is how math becomes meaningful, Sparks believes, and how children will more likely remember the skill.5

According to Harvard University Math Professor, Dr. Wilfried Schmid, there is some value in the practices Sparks describes. "They are used by good teachers all over the world. The problem arises when these ideas are pushed to the point of becoming an ideology - as they are in the Investigations in Numbers, Data and Space math program."

Dr. Schmid ought to know. Last year, his 2nd -grade daughter, Sabina, was enrolled in this program. He said she was not allowed to add two-digit numbers by carrying tens, despite the fact that she knew perfectly well how to do so. Instead, her teacher insisted that she demonstrate her work with blocks or by counting on her fingers.6 Today, Dr. Schmid is a vocal critic of constructivist math programs.

As fuzzy math gradually encroaches into more and more Wisconsin school districts and the debate rages on, Wisconsin parents are not waiting idly for the experts to reach a consensus of opinion. Time does not stand still for young children at critical ages when fundamental math principles must be learned. Parents are finding their own ways to deal with the flaws they see in the new curricula.

In McFarland, some parents have enrolled their children in private schools. Others have left the district or hired private tutors. Still other parents have been forced to put their children back into the very math classes that started the controversy. These parents hope to counter the negative effects of "fuzzy" math by tutoring their children at home.

For Kathy Siegmann, the "new-new" math curricula has become more than a personal issue. She is concerned about its long-term effects on the entire community and has decided to stand up for her beliefs, even if it means being "a lone voice on the school board." Only three families from the original group of parents continue to fight in McFarland. Sadly, it appears that their children's fate may ultimately lie in the hands of a court rather than in the hands of parents.


  1. NAEP scores can be found at the National Center for Educational Statistics web site: www.nces.ed.gov/index.html. 
  2. Wisconsin Model Academic Standards Home Page: 7. www.dpi.state.wi.us/standards/index.html. 
  3. www.wasdi.org. 
  4. Information obtained in a phone conversation with Dr. Sparks, December 2000. 
  5. Taped presentation, McFarland School District, September 2000.  
  6. Anemona Hartocollis, "The New, Flexible Math Meets Parental Rebellion," New York Times, April 27, 2000.

Leah Vukmir is a visiting fellow at the Wisconsin Policy Research Institute and President of PRESS (Parents Raising Educational Standards in Schools). This article was excerpted from the Winter 2001 issue of Wisconsin Interest.

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