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Community Math Forum Bellevue High School Bellevue, Washington Tuesday, April 25 2006. Co-Sponsored by Where’s the Math? and Washington State PTA. US K-12 Mathematics Education Reform 1989 – present Origins, qualities, controversy, results, and
Where’s the Math?
Washington State PTA
1989 – present
Origins, qualities, controversy, results, and
the implications for our children and our nation
Presentation by Elizabeth CarsonCo-Founder and Executive DirectorNYC HOLD Honest, Open, Logical Decisions on Mathematics Education Reformwww.nychold.com
“ Our nation is at risk. Our once unchallenged preeminence in commerce, industry, science, and technological innovation is being overtaken by competitors throughout the world.” We report To the American people that while we can take justifiable pride in what our schools and colleges have historically accomplished and contributed to the United States and the well-being of its people, the educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people.” If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exists today, we might well have viewed it as an act of war As it stands, we have allowed this to happen to ourselves.”
“In the area of setting national education goals, we unanimously agree that there is a need for the first time in this nation’s history to have specific results-oriented performance goals.”
President George Bush, Sr
Remarks at the Education Summit Farewell Ceremony at the University of Virginia, September 1989
Vision documents. Not mathematics content standards. Not grade specific articulation of goals for mastery.
Based in progressive education ideology. Constructivist learning theory. Discovery, student directed learning. Teacher is to be “a guide on the side, not a sage on the stage.”
Calls for radical departure from traditional mathematics content and sequence, and traditional classroom practices.
Susan Walton, “Add Understanding, Subtract Drill,” Education Week, July 27, 2983. National Science Board Commission on Precollege Education in Mathematics, Science and Technology, Education Americans for the 21st Century, excerpts reprinted in Education Week, September 14, 1983
Summary of Changes in Content and Emphasis in 5-8
source: NCTM document distributed to Manhattan District 2 parent community to explain basis for TERC Investigations and CMP
“It offers as its principal vision that school mathematics need not be difficult or dull and the cure was to remove the mathematical content from it leaving behind the mathematical concepts as a sort of Cheshire Cat grin.”
Ralph Raimi, Professor of Mathematics Emeritus, University of Rochester, a distinguished expert on domestic and international mathematics standards
Letters, Notices of the AMS, February, 2001
“The Council is now led by theoreticians from our Schools of Education, imposing policies that distort teaching and heavily impair the learning of school mathematics.”
“It [1989 NCTM Standards ] does not hold the properties of mathematics that make its study worthwhile. Mathematics is exact, abstract and logically structured These are the essential properties of mathematics.”
Frank Allen, Professor of Mathematics Emeritus, Elmhurst College and former president of the NCTM (1962-64) in “The NCTM Council Loses Hard Earned Credibility”
2000 Principles and Standards (PSSM)
The current, revised edition
“PSSM continues to abhor direct instruction in, among other things, standard algorithms, Euclidean geometry and uses of memory. “
“Almost anything in the way of content to be remembered can be omitted from a school mathematics program without running afoul of PSSM, providing the pedagogy is right and the process suitably “exploratory.” ‘Explore,’ ‘develop’ and ‘understand’ and their variants are much more prominent in the text than ‘know,’ ‘prove’ and ‘remember’.”
( excerpts from The article "52 x 8: The Importance of Children's Initiative ( The Constructivist, Fall, 1997) provided to Manhattan District 2 parents to explain the NCTM philosophy behind TERC Investigations and CMP )
Calculators in Elementary Math Class
W. Stephen Wilson and Daniel Q Naiman, “K-12 Calculator Usage and College Grades,” Educational Studies in Mathematics, 56:119-122, 2004
Influential Federal Funding Source for NCTM Based K-12 Reforms, since 1991
renamed Local Systemic Change Initiatives (LSC) (to implement the new NCTM math programs)
Eg: COMAP ARC UCSMP Everyday Math Center TERC MSPnet
NSF EHR Awards provide powerful funding incentives to colleges and universities and states and local school districts for research and development projects and K-12 reforms.
Testimony of James Milgram, US House Committee on Education and the Workforce, February 2, 2000
Michael McKeown, David Klein, Chris Patterson, “The NSF Systemic Initiatives, How A Small Amount of Federal Money Promotes Ill-Designed Mathematics and Science Programs in K-12 and Undermines Local Control of Education,” Chapter 13 in What’s At Stake in the K-12 Standards Wars, Sandra Stotsky, Ed (2000)
David Klein, Professor of Mathematics, California State University at Northridge
Richard Askey, John Bascom Professor of Mathematics, University of Wisconsin at Madison
R James Milgram, Prof of Mathematics Stanford University
Hung-His Wu, Professor of Mathematics University of California Berkeley
Martin Scharlemann, Professor of Mathematics, University of California, Santa Barbara
Betty Tsang, National Superconducting Cyclotron Laboratory, Michigan State University
Over 200 mathematicians and scientists, among them, our nation’s most distinguished, including seven Nobel laureates and winners of the Fields Medal, the highest award in mathematics, department heads at more than a dozen universities including Caltech, Stanford and Yale and two former presidents of the Mathematical Association of America.
Wilfried Schmid, Dwight Parker Robinson Professor of Mathematics, Harvard University on TERC:
“A TERC teacher doesn't explain, and a TERC teacher doesn't teach! I don't want to be misunderstood: group learning and discovery learning are parts of the tool chest of every accomplished teacher, but it is folly to turn these techniques into an ideology. If we mathematicians had to re-discover mathematics on our own, we would not get very far! And indeed, TERC does not get very far. By the end of fifth grade, TERC students have fallen roughly two years behind where they should be.“
“The TERC authors are opposed to the teaching of the traditional algorithms of arithmetic, such as long addition, subtraction with borrowing, and the usual pencil-and-paper methods of multiplication and division. Not only do they refuse to teach the algorithms, they make clear their preference not to have the students learn them outside of the classroom, either.”
Opening Remarks, “Are Our Schools Math Programs Adequate? Experimental Math Programs and Their Consequences,” Math Forum sponsored by NYC HOLD, NYU Law School, 2001
Jim Milgram, Professor of Mathematics, Stanford on CMP
“Overall the program seems to be very incomplete, and I would judge that it is aimed at underachieving students rather than normal or higher achieving students. In itself this is not a problem unless, as is the case, the program is advertised as being designed for al students.”
“Standard algorithms are never introduced not even for adding, subtracting, multiplying or dividing fractions”
“Precise definitions are never given.”
“Repetitive practice for developing skills, such as basic manipulative skills is never given. Consequently, in the seventh and eighth grade booklets on algebra, there is no development of the standard skills needed to solve linear equations, no practice with simplifying polynomials or quotients of polynomials no discussion of things as basic as the standard exponent rules.”
An Evaluation of CMP, R James Milgram
Constructivist curricula, such as TERC and CMP, forsake algorithms, postulates, and theorems (the foundation of mathematics) as well as teacher centered learning. Instead, they have students working among themselves in groups, loosely guided by the teacher in a drawn out attempt to "discover" mathematical truths A constructivist would argue that kids who memorize standard algorithms have no feel for numbers. This is a misconception. When taught properly, a student is first introduced to place value, then the distributive property. With these principles established, a teacher would introduce the standard algorithm and drill in a constructive fashion. Students gain mastery of an algorithm that solves all problems of its type. With that in place, students don’t have to struggle with simple calculations.
We who either teach or are parents of District 2 students know of the failures of these curricula. We send our kids to math tutors in record numbers. Intelligent, hard working kids have trouble doing simple math. We who have grown up with an understanding of elementary mathematics find that we can't help our kids; that many of the games they play and homework they do are so convoluted we either can't figure them out or don't see their significance. We're forced to sit by and watch our kids' frustration, both kids who are having great difficulty and kids who are so talented that they're terribly bored with their school mathematics. When we speak to school officials about our frustration we're condescendingly told that we just need to understand what they're doing. The truth is that many of us do understand what they're doing.
They're doing irreparable harm to thousands of kids.
Bruce Winokur, District 2 parent and Stuyvesant High School Mathematics Instructor, NYC
Over and over I've seen that the kids who can't calculate are the ones who don't get the concepts either. They don't know which operations to use; they don't know what numbers to punch into the calculator. The ones who know enough math to calculate the right answer are the ones who understand the concepts.
Some teachers don't like TERC & CMP but teach them because they have to. Others say they like the programs, but after a few enthusiastic sentences start mentioning how they need to be supplemented. The only people I know who completely support these programs are staff developers whose professional pride is at stake.
The students I test in middle and high school have not acquired the necessary math skills for higher level math using programs such as TERC. The proof is the number of referrals high schools receives for "math disabilities," when the only problem students have is prior content poor curricula . Every school administrator tells concerned parents "it will work out" or it will "all make sense". What Ms. McAdoo writes is true, “TERC is different from how most teachers learned math . . .“ But that is not what makes teachers and parents turn from this program; rather, it is the lack of content and rigor.
Red flags rise everywhere. Elementary students cry because they can’t comprehend homework problems. New math workbooks omit instructional reference materials. Children are dependent on parents for instruction. There’s too much group work. Kids can’t grasp concepts through discovery and walk away without the intended fundamentals. Math concepts aren’t retained because they aren’t practiced sufficiently to be ingrained. Students receive inflated math grades that don’t equate to their actual knowledge in the areas of study. It’s common practice in middle school to resubmit failing tests for revision credit to bolster grades thus creating a dilemma for parents who see grades that reflect high achievement, yet the skills are absent. Many families supplement with tutoring services to assure coverage. Students who once thrived in traditional math programs are disheartened to forfeit leisure time for remediation. Some well-known universities acknowledge that high school graduates from reform math curriculum are unprepared as compared with pupils from traditional programs.
Our children deserve a choice in their math curriculum.
Claudia Loy, excerpt of letter to the editor, Penfield (NY) Post, 3/17/05
While I totally understand the need to apply math facts and how critical that is to the advanced math, I do not feel that totally abandoning traditional teaching methods is the wisest plan. I also do not understand why someone seems to think that our country’s children will learn better and be able to be compared to foreign children and compete at higher levels in a program that is nothing like how they are being taught. While change can be great, thorough and multifaceted research with a randomized cross-cultural cohort is the only way to know if that method of teaching even has promise. I do not see that in the studies that have been proudly given to me to read. I have read and evaluated their quality and found them to be less than adequate. Put simply, as a nurse practitioner, which I now am, if I applied a treatment to my patients based on these studies, I would be risking my license if not someone’s well-being or life.
Whole Language” was a failure. .Why are we trying “Whole Math?” This is lunacy and I am ashamed to have my children participating in it.
I am a physician who was initially a mathematics major in college. I just found your website today, and wish I have known about it 6 years ago when my oldest daughter began kindergarten in District 2. It was not till late in third grade that I realized just how little math she was learning, and how behind she was in basic skills. According to her teachers everything was fine, but then, no testing or assessment was done other than the state wide tests.
We recently moved here from Miami and enrolled our daughter in the second grade at a District 2 school. We're very happy with the teacher and the school, except, of course, for the level of math instruction. Our daughter already is capable of carrying over in both addition and subtraction, and she can also do simple multiplication and division. Her class is nowhere near this level; they are still doing TERC to compute 2-digit addition. When my daughter attempts to do it the normal way, the teacher tells her that she cannot. This is not only slowing her down, it is actually causing her to regress. She is developing an aversion to the normal methods.
The inadequacies of the math program in my daughter's middle school came into clear focus when I sent her to Kaplan to prepare for the Science High School tests. Her instructor was sufficiently perplexed to call me up and ask why she was unaware of so many of the math concepts that were supposed to have been covered in her school. It turned out that only the private school students were adequately prepared to take the entrance examination for a public high school. this was shocking.
My younger son is currently in 4th grade at PS --, and last year the school implemented the TERC curriculum-- and that alone. What I have seen (and I have my older son's old homework books to prove it) is that he is WAY behind where my older son was at this point in 4th grade. He and many of his classmates are bored and frustrated by the curriculum.
My husband and I both work with computers (coming from arts backgrounds) and know that the fewer steps involved, the fewer chances for error. TERC takes just the opposite approach. It is not clean, it is not simple or elegant, TERC is just plain fuzzy…While it may be true that 76% of District 2 students meet state standards, the dirty little secret is that our scores are skewed because parents are resorting to private tutors... I would suggest that you take a close look at the teaching methods of new math, best illustrated by the diagram in the Post this week. Take a really close look, go to some classrooms, ask some fifth graders to multiply 36 x 75, or to do a math problem involving decimals or fractions, but do so as a prospective parent. Would you put your children into this math program? District 2 children are a year behind in instruction compared to most private schools and now, in addition, they are saddled with a lack of basic math skills. Mr. Levy, many of us are stuck. The private schools are full and expensive, we made a commitment to public school in good faith and now those of us who want out cannot get out.
Susan Erlanger, Excerpt of letter to NYC Schools Chancellor Harold Levy
We feel that our daughter has lost a sense for basic math facts and we have seen her confidence, as well as basic skills deteriorate especially within the last year, as a 5th grade student. We spend hours helping her learn but find this program cumbersome and difficult for us as parents to follow. Though we are college educated parents, with a reasonable understanding of mathematics we are very concerned with the momentum that this system of teaching has gained. I have yet to read anyone in academia who endorses this program. I have spoken to a number of parents who either don't understand what is happening to their children or are absolutely livid with this system of teaching.
This concerns two math problems my third-grade son brought home yesterday. The two problems he couldn't complete baffled me and my husband. Not to boast, but he [husband] holds two math degrees (Master's in statistical analysis) plus an EE. As an experienced software developer, complex problem solving is his forte. While a teenager in the Soviet Union, he was required to study -- like every other high school student there -- science and math subjects I didn't see until my junior year at CSUN. I myself have a Bachelor's in math, and before motherhood worked under contract to the US Navy as an analyst (mathematician, really), designing complex math models for dynamic simulation. If the two of us cannot solve a third-grade math problem, just what the heck is going on with this "wonderful" math program our school district's adopted?!
The curriculum approaches the absurd, teaching multiple (five!) ways of doing simple multi-digit subtraction. It has left my son with exposure to five ways, and mastery of none. ..Why is the school teaching them to use calculators while I am left to teach them long division? As someone with a deep appreciation and a strong background in mathematics, it pains me to see the material taught this way. In the short term I will be providing tutoring for my own kids to make up for what I feel to be a hole in their educations. In the longer term, my wife and I are also looking into private schools for this reason alone.”
My daughter is in 4th grade and cannot multiply, cannot divide, cannot do fractions or decimals, barely adds well, and struggles with subtraction yet her math grade is 4 out of 5. I do not understand nor do I want to understand that. Now how was she supposed to understand and do this investigative math with out the basic skills? I guess that is my job now. I feel sad that I pay my taxes and put immense trust in the quality teachers that this school district has, only to see their hands tied and the tongues tied on this issue.
14 years of NSF EHR funded K-12 mathematics research and development:
No conclusive scientific research to support any of the NCTM based NSF EHR funded programs
“On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations,” National Academies' Mathematical Sciences Education Board, National Research Council (2004)
Findings: “Evaluations of mathematics curricula provide important information for educators, parents, students and curriculum developers, but those conducted to date on 19 curricula (which included all 13 NSF funded K-12 math programs) fall short of the scientific standards necessary to gauge overall effectiveness.” ( press release National Academy Press)
Key findings of “The State of State Math Standards,” by David Klein, with Bastiaan Brahms, William Quirk,Wilfried Schmid and W Stephen Wilson, Fordham Foundation, 2005
Most state math standards are content poor, and closely aligned with the NCTM “vision.”
2005 State National Assessment of Education Progress (NAEP)
vs State Exams reveals low standards in the majority of state assessments.
NAEP 40% proficient
NAEP 36% 4th proficient
see: state-by-state comparisons in 4th and 8th grade for math and reading in “Achieve Quick Facts NAEP vs State Proficiency 2005”
Since 1989 a national mathematics education reform movement led by the NCTM and education theorists in our Schools of Education has swept our nation’s schools. The results:
2005 US 4th grade: 36% at or above proficient; 8th grade 30% at or above proficient
Washington State 4th grade: 42% at or above proficient 8th grade 36% at or above proficient
2003 No change in the average math and science scores of U.S. fourth graders between 1995 and 2003, while U.S. eighth-graders improved their averages in math and science in 2003 compared to 1995
US 4th and 8th grade ranks still far from the top. 12th and 15th in 4th and 8th grades respectively
Top performing nations: Singapore Korea Hong Kong Chinese Taipei Japan
2003 24 out of 29 participating nations With 10 nonmember participating nations added (including a number of developing nations) : US tied Latvia for 27th place
Top performing nations: Finland and Japan
2005 “New Study Finds US Math Students Consistently Behind Their Peers Around the World”
“Reassessing US International Mathematics Performance: New Findings from the 2003 TIMSS and PISA” (AIR)
12 nations participated in TIMSS 4th and 8th grade, and PISA (15 year olds)
US ranking: TIMSS Grade 4: 8 TIMSS Grade 8: 9 PISA : 9
Top performing: Hong Kong, Japan, Belgium, Netherlands, Latvia, Hungary, Russia rank higher in all three
The National Academy of Sciences (NAS) observed in a recent report. "Although many people assume that the United States will always be a world leader in science and technology, this may not continue to be the case inasmuch as great minds and ideas exist throughout the world. We fear the abruptness with which a lead in science and technology can be lost - and the difficulty of recovering a lead once lost, if indeed it can be regained at all.“
The report "Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future." Committee on Science, Engineering, and Public Policy (COSEPUP) a joint unit of the National Academy of Sciences, National Academy of Engineering, and the Institute of Medicine. 2006 A committee of leading scientists, corporate executives and educators oversaw the drafting of the report.
To spur American innovation, its recommendations include enhanced math and science education in grade school and high school.
The report cites China and India among a number of economically promising countries that may be poised to usurp America's leadership in innovation and job growth.
"For the first time in generations, the nation's children could face poorer prospects than their parents and grandparents did," the report said. "We owe our current prosperity, security and good health to the investments of past generations, and we are obliged to renew those commitments.“