2+2=5: FUZZY MATH INVADES WISCONSIN SCHOOLS

LEAH VUKMIR

n the fall of 1997, Fortunately, Kathy Siegmann of Kathy was not alone. IMcFarland was Before long she was completely unaware joined by Kim Ujke, of the latest national another parent controversy brewing equally concerned over the teaching of + about the new cur- math to children. An riculum. After doing active mother of five their own exhaustive children, Kathy busily research into various attended to the many math programs, the tasks of running her moms decided to household, working pull their children part-time, shuttling out of school during children to extracur- math class and ricular activities and = instead homeschool lending an occasional for that hour using a hand during their more traditional evening homework math program. The sessions. It was dur- school's principal ing these nightly sessions that Kathy devel- and teachers were informed of their decision oped an uneasy feeling about what and how and, in December 1998, they proceeded with her son was being taught math. their plan. The next month Dawn Myers pulled her third grade daughter from the class. The McFarland School District had recent- Shortly thereafter Mary Turke's fourth grader ly adopted a new math curriculum for grades joined the exodus along with Kathy's 5th grade three through five that did not provide indi- son. vidual student . "I could not tell what my children were doing in math, nor could I The families quietly went about their home look in a book to help them," she stated. study courses and the children thrived under Feeling frustrated and helpless, she began to their parent's tutelage. All scored in the question school officials and she also did a lit- "advanced proficiency" level on the Wisconsin tle research of her own. It was then that she Student Assessment System math test. By the realized she had come face-to-face with what is following school year, a total of eight families now commonly referred to as "new-new" or were involved in this endeavor. They never "fuzzy" math, the latest educational fad to pressured the school district to discontinue the invade schools around the country. Her life Leah Vukmir is a visiting fellow at the Wisconsin Policy was about to dramatically change. Research Institute and President of PRESS (Parents Raising Educational Standards in Schools).

Wisconsin Interest 9 new curriculum, but instead urged officials to dren. Attempts to have teachers tailor the pro- consider offering a more traditional alternative gram to fit the children's needs led to frustra- that better suited their children and, they tion. Errors were found in "teaching packets" believed, many other children. and parents were asked to be patient as the "bugs" in the new program were worked out, In January 2000, their tranquility was bro- prompting one mom to emphatically reply in a ken when they received a letter from the parent survey, "Our daughter will only be in school district informing them that their chil- 3rd grade once. It is unfair to ask her to put her dren would be in violation of school truancy learning on hold." (See Figure 1 for examples laws if the parents continued to remove them from McFarland’s math program, Investigations from the school's math instruction. The parents in Numbers, Data and Space.) were allowed to finish out the school year, however, they now faced uncertainty about the This level of parental outrage and concern future. is certainly not confined to McFarland. According to Parents Raising Educational What is it about this new approach to Standards in Schools, a Wisconsin-based par- teaching math that so concerned these parents? ent organization, math education has become The “new-new” math classroom is based on the number one concern of parents calling for the notion that children understand and learn information and assistance. In the last two only those concepts that they "construct" or years it has supplanted the "Reading Wars" discover on their own. The teacher is discour- and is causing parents across Wisconsin and aged from providing information or imparting the nation to organize and rebel. knowledge, and is instead encouraged to act as a “facilitator” of learning. To fully understand the origins of this new approach to math education, one must look to In small “cooperative learning” groups, the National Council of Teachers of children use blocks, beads, sticks and other Mathematics (NCTM), and to the state of “manipulative” objects to solve mathematical California — often considered the nation's lab- problems. This practice often extends beyond oratory for educational fads. the early grades and is even found in high school algebra classrooms. The children are NCTM Origins expected to discover or “reconstruct” the For more than 75 years, NCTM, the ancient rules of mathematics using the objects nation's most influential organization of math with the guidance of peers equally in the dark. teachers, has been dedicated to "improving Rote memorization of math facts, e.g. mul- mathematics teaching and learning from tiplication tables, is considered taboo and text- preschool through post-secondary school." books are virtually non-existent in these bold NCTM boasts more than 110,000 members new classrooms. Correct answers are less worldwide.1 important than the thinking processes exhibit- In 1989, NCTM published Principles and ed by the children. Classroom time is filled Standards for School Mathematics, a set of math with projects such as writing essays about math standards seen by many as the basis of today's versus repeated practice of the fundamental "fuzzy" or "new-new" math curricula. This doc- rules of math. Calculators and “guesswork” ument put into print the philosophy of math are encouraged at even the earliest of grades, education noticed by the parents in and the fundamental operations of math, McFarland. Embraced by teacher colleges long known as algorithms, are left to the child to before its publication, Principles and Standards, discover in essence, became the bible for a progressive In McFarland, besides not understanding education theory known as "constructivism," the unconventional teaching methods, many and according to many critics put a legitimate parents found the pace too slow for their chil- stamp of approval on an approach to math

10 Winter 2001 FIGURE 1EXAMPLES 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. education that had already invaded schools The web site docu- nationwide. ments the history of today's "," cri- tiques NCTM standards, analyzes a variety of The California Experiment math texts and programs (see Figure 2), and Armed with a new math education mani- provides parents with a multitude of resources festo — the NCTM Standards — teachers to fight "fuzzy" math in their own communi- around the country pushed forward with a ties. In a strong and authoritative voice, the new sense of purpose and eagerly unleashed mathematicians and scientists who run the site the constructivist ideology in their classrooms. warn parents that: California heavily bought into "new-new" Although there are many variations in the math in the early 1990s, and by 1992 had methods of these new programs, they have released the California Mathematics one clear characteristic in common — they Framework — a document based largely on are weak in mathematics. The expectations the NCTM Standards. for our students are seriously undermined. And, as the mathematics is leeched out of Before long, this unorthodox approach to the textbooks, the opportunities for our teaching math was noticed by a group of students to learn is withering away. California parents. Largely hailing from scien- tific fields, these parents believed their own They found that this problem is not limit- children would never be able to function in ed to the elementary schools, or to the four professions similar to their own with the scant operations of mathematics. The combination skills and weak foundation they were develop- of new methods and "low content levels" are ing in their new math classrooms. Calling present in many high schools and even in col- themselves "Mathematically Correct," these lege calculus. Incoming college freshmen are parents organized through the Internet and showing a decline in math achievement, caus- mounted a fierce opposition to California's ing concern over the quality of future teachers. NCTM-modeled math standards.

Wisconsin Interest 11 FIGURE 2“FUZZY” MATH PROGRAM RATINGS: The following is a partial list of programs reviewed by Mathematically Correct. Other reviews can be found at: www.mathematicallycorrect.com Second Grade Investigations in Numbers, Data and Space by Dale Seymour F by Everyday Learning Corporation (The University of Chicago Mathematics Project) C Fifth Grade Investigations in Numbers, Data and Space by Dale Seymour F Everyday Mathematics by Everyday Learning Corporation (The University of Chicago Mathematics Project) C- Seventh Grade by Dale Seymour F

Math Thematics by McDougal Littell D+ (Book 2)

They conclude: Language Learning and Integrated Science), and mathematics reform in particular." The Now we are faced with an inadequate sup- ply of teachers who are really qualified to conflict pitted the so-called mathematics teach mathematics, with new curriculum reformers from the schools of education materials that lack the content our students against parents and a significant portion of the 4 need, and with poor achievement com- university mathematics community. pared to our international competition, all wrapped in glowing rhetoric about the The combined forces of parents and math- 2 new directions in . ematicians began an information campaign that ultimately led to the development of a The Mathematically Correct parents faced revised set of state math standards adopted by an arduous task when they decided to take on the California Board of Education in December California's education establishment. 1997. The new blueprint, "California Nevertheless, they were buoyed by an undis- Mathematics Academic Content Standards," puted fact: California kids scored among the delineated benchmark standards for each lowest in the nation on the 1996 National grade level. Gone were the prescriptions for Assessment for Educational Progress (NAEP) constructivist teaching methods. Finally, a set math test. More than half of California's fourth of standards that emphasized the development graders scored below the basic proficiency of basic math skills! level and 49% of the state's eighth graders had "below basic" math understanding. Overall, Mathematically Correct maintains a vigi- California's fourth graders ranked fourth worst lant watch over California's math instruction in the nation, tying with Louisiana and trailed and adoption. The group also serves only by Mississippi, Guam and the District of as a resource to parents in other states who are Columbia.3 starting to notice the invasion of "new-new" math in sleepy towns across Middle America. According to Dr. David Klein, Professor of Mathematics at California State University– Wisconsin Joins The New World Of Math Northridge, California experienced "a backlash McFarland is just one of the many sleepy at the grass-roots level against the general edu- Wisconsin towns choosing to adopt "fuzzy" cation reform movement (including Whole

12 Winter 2001 math. But how did a West Coast math craze Figure 3 make its way into the heartland of America's Midwest? Can a national organization of math Math Programs Endorsed by the United teachers wield that much power over the local States Department of Education decision making processes of small Wisconsin October 1999 school districts? What factors are responsible 1. Cognitive Tutor Algebra for the invasion of "new-new" math in 2. College Preparatory Mathematics Wisconsin and how entrenched is this ideolo- (CPM) gy in our schools? To answer these questions we must look to three sources: 3. Connected Mathematics Program (CMP) 1. Federal Math Program Recommendations 4. Core-Plus Mathematics Project 2. Wisconsin Model Academic Math 5. Interactive Mathematics Program Standards (IMP) 3. Wisconsin Academy Staff Development 6. Everyday Mathematics Initiative 7. Federal Math Program Recommendations 8. Middle-school Mathematics through In October 1999, a United States Education Applications Project (MMAP) Department "panel" released a controversial 9. Number Power list of 10 "exemplary" or "promising" mathe- 10. The University of Chicago School matics programs to a captive audience of edu- Mathematics Project (UCSMP) cators attending a national conference. The programs reflected the pedagogical approach- Two hundred mathematicians wrote to Education es to math outlined in the NCTM standards. Secretary Richard Riley asking to withdraw his With one swift wave of a wand, the federal recommendation of these programs that they found to have “serious shortcomings.” education "experts" gave educators their bless- ing to proceed down the road to "Fuzzy Mathdom." (See Figure 3) too deep to find the NCTM influence on the state standards. The introductory paragraph Fearing the effects of such an endorse- cites the NCTM Curriculum and Evaluation ment, a group of 200 highly respected univer- Standards for School Mathematics as a resource sity mathematicians and scholars, including document used during standards deliberations. several Nobel Laureates, sent an open letter to Under the heading of "Goals and Instructional Education Secretary Richard Riley urging him Practice," the introduction continues: to withdraw the recommendation.5 Warning that the programs had "serious shortcomings," Classroom practice geared to the attain- they urged local districts to "exercise caution in ment of the Wisconsin Standards should be choosing mathematics programs." The educa- aimed at creating a community of learners and scholars, a place where the teachers tion establishment has largely ignored these and students actively investigate and dis- warnings. Many local districts in Wisconsin cuss mathematical ideas, using a wide vari- continue to cite federal recommendations in ety of tools, materials, and technology. their push to embrace the new math curricula. Classes should engage students in more high-level mathematical thought and Wisconsin Math Standards emphasize conceptual understanding, 6 A second influencing factor can be found in more so than in the past. the Wisconsin Model Academic Math Sound familiar? Strains of constructivism Standards, adopted in 1997. One need not dig echo throughout the entire document.

Wisconsin Interest 13 Wisconsin Academy Staff Development According to Sparks, WASDI has trained Initiative 337 "Lead" teachers in the past six years. He explained that the National Science Perhaps the most powerful influence on Foundation (NSF) has been a leader in advanc- Wisconsin's movement toward "fuzzy" math ing new math approaches across the country can be found in the Wisconsin Academy Staff by providing grants to groups willing to write Development Initiative (WASDI). Average math curricula that match the NCTM Wisconsin citizens are likely unaware of this Standards. Currently, 13 NSF-sponsored cur- six-million dollar project funded by a National ricula are available to local districts.8 Science Foundation grant. WASDI is, however, a very familiar resource to Wisconsin math Sparks could best be described as a stan- and science teachers. Aimed at improving K-12 dard bearer for constructivist math in mathematics, science and technology educa- Wisconsin. Indeed, it is difficult to speak with tion in Wisconsin, the goal of WASDI is: Dr. Sparks without sensing his fervor to this cause. In September 2000, Sparks spoke at a To totally transform the way technology education, mathematics and science are public forum held in the McFarland School taught. It's not just reading the chapter and District. He gave an impassioned presentation memorizing terms and filling in the blanks entitled, "Mathematics Education: Past, at the end of the chapter. It's hand-on Present, and Future." In it he described the phi- 7 learning. losophy behind the district's recent adoption of To that end, WASDI conducts a series of "Investigations in Numbers, Data and Space," one-week summer academies throughout the controversial NCTM-based math program Wisconsin at which participants can earn grad- that spurred the McFarland parents into uate credits for learning new approaches to action. teaching math, science and technology. Over During his talk, Sparks outlined his own 2000 teachers participate in these workshops personal odyssey toward constructivist math. each year at 11 sites located across the state. He reflected on his student days in a tradition- WASDI also takes an active role in devel- al mathematics classroom that, in his view, oping teachers as future leaders through its only allowed certain students to excel in math. "Lead Teacher Institute." According to the "Today, we need a curriculum for all, not just WASDI web site, teachers completing this the select God-chosen few, " Sparks explained. eight-week "Institute" will be able to: Dr. Spark's presentation was replete with 1. Serve as local, state, and regional state comments showing his deep commitment to resources to their school, other districts the constructivist philosophy: and state associations. • "Math programs should be presented in a 2. Present a core curriculum at the summer fashion where there is exploration first. academies, specifically one that "uses a Exploration should proceed convention, constructivist approach to teaching." rule and formula." 3. Network with other "Lead" teachers • "Math programs need to incorporate group throughout the state. activities. Within groups, children learn from each other and learn the value of the At the helm of this ambitious project that contributions of others. This is what hap- infuses Wisconsin districts with "new-new" pens in the workplace." math is Dr. Billie Earl Sparks, Co-Project Director of WASDI. A math professor at the • "I am not a fan of acceleration of children University of Wisconsin-Eau Claire, Sparks and grouping of children by ability levels. also teaches math "content" to the university's If we put the brightest kids in one group, education students. the other kids will never get the benefit of their strategies for learning."

14 Winter 2001 To many this may sound more like sociolo- • At the 5th grade level, curriculum is more gy than math. Yet, Sparks is a true believer. He than two years behind the Singapore cur- emphatically asserted that math skills should riculum not be taught in isolation. This is the "old" way Dr. Schmid described a situation where his of learning where teachers demonstrated a daughter, Sabina, was not allowed to add two- skill and students were expected to under- digit numbers by carrying tens, despite the fact stand the skill through repetition, and rote that she knew perfectly well how to do so. memory. In classrooms today, students are Instead, her teacher insisted that she demon- expected to explore with their classmates until strate her work with blocks or by counting on they find the skill that will solve the problem. her fingers. "So Sabina is reduced to drawing As they explore, teachers intervene and teach 39 little men to solve problems like 39 minus skills as they arise. This is how math becomes 14."11 Today Schmid is a vocal critic of con- meaningful, he believes, and how children will structivist math programs. more likely remember the skill.9 Based on international testing data from According to Harvard University Math the Third International Professor, Dr. Wilfried Mathematics and Science Schmid, there is some Study (TIMSS) conducted value in the practices that in 1995, it appears that Sparks describes. "These Schmid's concerns are not are used by good teachers unfounded. Considered all over the world. The At the 5th grade level, by far the most compre- problem comes when hensive and rigorous these ideas are pushed to curriculum is more than comparisons of interna- the point of becoming an tional math achievement ideology — as they are in two years behind the ever to be conducted, the the 'Investigations in Singapore curriculum study involved 42 coun- Numbers, Data and tries and assessed chil- Space' math program. dren at three grade levels. Many teachers using this Although American 4th program manage to do a graders scored above the good job, by using their international average, the own judgment to filter study found that: out the ideology. When the manuals are taken literally, then you get • U.S. 12th graders scored below the interna- into trouble.”10 tional average in math and were ranked 19 out of the 21 nations that tested high Dr. Schmid ought to know. Last year, his school seniors. Only Cyprus and South second grade daughter was enrolled in the Africa scored below the U.S students. same math program being used in McFarland. He lists the following problems with the • Among students taking advanced math "Investigations" program: courses, U.S. students ranked 15 out of 16 tested. • Mathematical substance is very shallow • U.S. 8th graders scored below the interna- • Memorization is discouraged tional average.12 • Students are kept dependent on mental A follow-up study just released in crutches (fingers, blocks, clock faces) December revealed even more troubling • Intellectual level is demeaning to bright results. Conducted in 1999, the TIMSS-Repeat students assessed students at the 8th grade level and found that U.S. 8th graders were well below

Wisconsin Interest 15 average when compared with countries that For Kathy Siegmann it means becoming a were included in both the 1995 and 1999 stud- member of the McFarland School Board. The ies. Additionally, the TIMSS-Repeat was specifi- "new-new" math curricula has become more cally designed to provide information about than a personal issue for her. Now she is con- changes in the math achievement of a cohort of cerned about the long-term effects of this pro- students over the past four years. Most signifi- gram on the entire community. She has decid- cant was the finding that U.S. 8th graders ed to stand up for her beliefs, even if it means dropped from 9th to 12th place among the 17 being "a lone voice on the board." nations tested, indicating that American stu- Only three families from the original dents are falling behind their international peers group of parents continue to fight on in the longer they remain in our school system.13 McFarland. Sadly, it appears their fate may lie Wisconsin education officials are quick to in the hands of a court — instead of the hands note that Wisconsin students consistently rank of parents. in the top five on NAEP math tests, often Notes referred to as the "Nation's Report Card." This is no consolation given the country's overall 1. www.nctm.org. international rankings. At the same time, DPI 2. www.mathematicallycorrect.com. officials state that one-third of Wisconsin 3. NAEP scores can be found at the National Center for school districts are shifting toward some type Educational Statistics web site: 14 of new math curricula. With the gradual www.nces.ed.gov/index.html. encroachment of "fuzzy" math into more and 4. Dr. Klein's essay entitled "Big Business, Race, and more Wisconsin school districts, it may only be Gender in Mathematics Reform" is found in How to a matter of time before Wisconsin slips further Teach Mathematics by Steven Krantz, American in the national rankings. Mathematical Society, January, 1999. 5. Mathematically Correct web site. While the debate regarding math rages on, one thing remains certain: Parents in 6. Wisconsin Model Academic Standards Home Page: 7. Wisconsin are not idly waiting for the experts www.dpi.state.wi.us/standards/index.html. to come to a consensus of opinion. Time does 7. www.wasdi.org. not stand still for young children at critical 8. Information obtained in a phone conversation with ages when fundamental math principles must Dr. Sparks, December, 2000. be learned. Parents are finding their own ways 9. Taped presentation to McFarland School District, to deal with the flaws they see in the new cur- September, 2000. ricula. 10. Obtained from email correspondence with Dr. In McFarland, that means that some par- Schmid, December, 2000. ents have enrolled their children in private 11. Anemona Hartocollis, "The New, Flexible Math meets schools. Others have left the district entirely. Parental Rebellion," The New York Times, April 27, Some children are being privately tutored. Still 2000. others have been forced to put their children 12. The National Center for Educational Statistics Home back into the very math classrooms that started Page: www.nces.ed.gov/. this controversy in the first place. Parents hop- 13. Ibid. ing to counter the negative effects of “fuzzy” 14. Valeria Davis-Humphrey, "McFarland finds some math tutor these children at home. successes in math program," Wisconsin State Journal, September 24, 2000.

16 Winter 2001