Petition to Upgrade Maryland's Mathematics Standards

We are alarmed that the State of Maryland's mathematics standards:

· prescribe "pretend algebra" that is actually 5th or 6th grade arithmetic;

· neglect the math skills and conceptual understanding that are essential for real algebra;

· promote defective and inaccurate mathematical reasoning;

· reflect the absence of any meaningful coordination with mainstream university math courses; and

· debase the curricula of local school districts.

Maryland's math standards deny students the essential skills and understanding they need for college level mathematics -- not just for high-tech careers in science and engineering, but also for business, law, social sciences, and especially for elementary education.

Accordingly, we recommend that:

The State of Maryland should:

· initiate a review and revision of the State's mathematics standards and web-site content by a panel representing the views of mainstream university mathematicians; and

· align the Maryland Content Standards with the most rigorous international and state content standards available, such as Singapore and California.

School districts in Maryland should:

· align their mathematics curricula with the most rigorous international and state content standards available, such as Singapore and California.

RATIONALE:

• Maryland's math standards prescribe "pretend algebra" that is actually 5th or 6th grade arithmetic, and they neglect the math skills and conceptual understanding that are essential for real algebra.

Jerome Dancis, associate professor of mathematics at the University of Maryland, College Park (UMCP), served as the mathematics advisor for the California edition of Harcourt's new grade 6 math textbook. After reading all of the sample questions for the Maryland High School Assessment on Algebra he concluded:

The main knowledge needed for this pretend algebra test is reading, common sense and simple arithmetic (with reading including the reading of numbers off tables, charts and graphs). Calculation with symbols (x's and y's) -- the core of Algebra -- is not included. What Maryland calls "algebra" is not even pre-algebra; it is sixth-grade preparation for algebra.

Yet even in arithmetic, Maryland's expectations are low. The Maryland high school standards do not even demand that children be able to perform simple arithmetic calculations, as students may use graphing calculators on this test.

Teaching to such a low standard will increase the already high number of students taking remedial math in college. In Prince George's County, about one student in three needs remediation even among the better students – i.e., those who completed three years of math in high school. About half the students in the engineering calculus class at UMCP need tutoring in algebra and trigonometry.

Full article at http://groups.yahoo.com/group/GTAletters/message/2003 See State test at: http://www.mdk12.org/mspp/high_school/look_like/algebra/intro.html

Montgomery County parent John Hoven

compared questions on the Maryland algebra 1 exam for ninth graders with questions on an [arithmetic] exam given in Singapore to fifth graders. "By world-class standards, the Maryland algebra exam is grade-school math," he recently told a state commission. Two college professors -- W. Stephen Wilson, of Johns Hopkins University, and Jerome Dancis, of the University of Maryland -- checked the math and agreed.

-- Washington Post, June 12, 2001. Details at: http://groups.yahoo.com/group/GTAletters/files/Math/MCPS_vs_Singapore.htm

• Maryland's math standards promote defective and inaccurate mathematical reasoning.

R. James Milgram, Professor of Mathematics at Stanford University, describes Maryland's recommended mathematical reasoning as "dangerous and destructive":

I went through all three mathematics reasoning exemplars at http://www.mdk12.org/practices/support_success/mspap/mathematics/math_processes.html. It was appalling. No, it was worse than that. All three exemplars are incorrect, and not just for one reason . . . .[These exemplars are] dangerous and destructive for students. Students who get the idea that this represents mathematical reasoning are doomed when they get to college. Details at: http://groups.yahoo.com/group/GTAletters/files/Math/Milgram_MD_and_MCPS.htm

UMCP Professor Dancis concurs:

The Maryland Content Standards ask students to "recognize, describe and/or extend patterns" with no mention of algebra, geometry, or science to confirm the pattern, and no deductive proof. This is unjustified speculation, not mathematics. It trains students to make rash, often incorrect, projections about the future. Because of what they have been taught, they can LESS readily see through the faulty reasoning so often presented in the media and by politicians. Details at:

http://groups.yahoo.com/group/GTAletters/message/2209

• Maryland's math standards reflect the absence of any meaningful coordination with mainstream university math courses.

High school mathematics is preparatory for college mathematics, since the majority of Maryland's high school graduates will go on to college and take more mathematics there.

The deficiencies and mathematical inaccuracies noted above flow from the absence of any meaningful and consistent partnership between the mainstream mathematics community of Maryland's universities and colleges and the State. Professors of mathematics were not a major voice (in fact, hardly a voice at all) in the Keys to Math Success: A Report from the Maryland Mathematics Commission. http://www.msde.state.md.us/Special%20Reports%20and%20Data/keys.pdf

Perhaps that explains why the Commission report disparages "the narrow pre-calculus curriculum that is traditional fare in United States schools," and urges a shift in emphasis toward "significant content" in data analysis, statistics, probability, and discrete mathematics. Most of the traditional pre-calculus curriculum is real algebra, of the type avoided on Maryland's Algebra test. The other main component of "the narrow pre-calculus curriculum" was serious training in logical thinking in a deductive-proof based Euclidean Geometry course. This real algebra and logical thinking are the basis for doing serious data analysis, statistics, probability, and discrete mathematics, as well as high school physics. Without "the narrow pre-calculus curriculum" as background, only superficial courses in these subjects are possible. "For our discrete math course," UMCP math professor Dancis says, "we replaced a very good textbook with a dumber one in order to accommodate the weaker algebra background of our students."

Rather than rely on mainstream mathematicians, the commission sought advice from consultants like Steve Leinwand, who supports a policy that fails to prepare students for college mathematics:

It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous.

-- Steve Leinwand, "It's Time To Abandon Computational Algorithms," Education Week on the Web, February 9, 1994, http://www.edweek.org/ew/1994/20lein.h13

• Maryland's math standards debase local school districts' curricula

Maryland's deficient standards debase local school districts' instruction. For example, in July 2001 at the recommendation of Superintendent Jerry D. Weast, the Montgomery County Public Schools (MCPS) adopted verbatim the Maryland Content Standards as its statement of "what every student should know" and aligned its entire K-8 curriculum towards those standards. In effect, the entire MCPS curriculum and instructional practices have been geared towards the State's pretend algebra test. ("One purpose [of the new curriculum], officials explained, is to emphasize state standards to ensure that students are ready for high-stakes high school assessment exams that the state will be requiring in a few years." Editorial, The Washington Post, August 5, 2001)

The following commentaries on the MCPS action illustrate the harmful effect of the State's standards:

"The most important and most fundamental elements of grade school mathematics appear as an afterthought. . . . This curriculum denies children the very grounding they need to master more advanced math skills in the upper elementary grades, pre-algebra and algebra."

-- Wayne Bishop, Professor of Mathematics, California State University, Los Angeles

"The development of both numerical skills and mathematical reasoning is weak. Unlike the California standards, the MCPS framework mandates fuzzy math pedagogy such as "developing strategies" for multiplication." -- James R. Milgram, Professor of Mathematics, Stanford University.

See these and other commentaries at http://groups.yahoo.com/group/GTAletters/files/Curriculum/aim-low.htm

When major school districts like Montgomery County Public Schools adopt 6th grade arithmetic as their statement of what children should know in "algebra," and reject benchmarking to the best national and internationally competitive standards, education in the state of Maryland is in serious trouble.

Suggestions by State Superintendent of Schools Nancy Grasmick that "people are ready to look at a state curriculum … [and] it is going to be a state structure that will drive instruction" (Washington Post, 8/2/01 page PG 6) underscore the damage that will result unless the Standards are revised to ensure mathematical accuracy, reasoning and rigor.

• Recommendation: Maryland's math standards should be benchmarked to international standards

All of Maryland's students, from the highest to the lowest achievers, deserve to be challenged at world-class levels. The Third International Mathematics and Science Study's 1999 Benchmarking Report (TIMSS-1999) states that "the world-class performance levels in mathematics were set essentially by five Asian [school systems]'' - Singapore, Korea, Taipei, Hong Kong and Japan. In contrast, Maryland's performance was average, well below these top performers. http://www.timss.org/timss1999b/mathbench_report/t99b_math_report.html

In Montgomery County, the entire spectrum of students, from low-achievers to high-achievers, performed well below their Singapore counterparts. http://groups.yahoo.com/group/GTAletters/message/2148

The Illinois First in the World Consortium modeled its mathematics standards against Singapore, Hong Kong and California's highly rated standards. http://www.ncrel.org/re/fitwsp/ It is preposterous for anyone to suggest that we should set our math standards lower than world-class levels. We should set our math standards at world-class levels. Tying curriculum to state standards that dumb down our students is just plain dangerous to the future of our local economy.

Accordingly, we recommend that:

The State of Maryland should:

· initiate a review and revision of the State's mathematics standards and web-site content by a panel representing the views of mainstream university mathematicians; and

· align the Maryland Content Standards with the most rigorous international and state content standards available, such as Singapore and California.

School districts in Maryland should:

· align their mathematics curricula with the most rigorous international and state content standards available, such as Singapore and California.

For further information contact:

Jerry Dancis, University of Maryland College Park – jnd@math.umd.edu

Steve Wilson, Johns Hopkins University – wsw@math.jhu.edu

Jack Morava, Johns Hopkins University – jack@math.jhu.edu

Disclaimer: All signatures represent the personal and professional opinions of the individuals, not the opinion of their employers.

Signers of Petition from University of MD, College Park (UMCP)

Michael Fisher,

Professor of Physics and Distinguished University Professor and Regents Professor.

Michael F. A'Hearn

Professor of Astronomy and Distinguished University Professor

Stuart Antman,

Professor of Mathematics and Distinguished University Professor

David C. Levermore

Professor of Mathematics and

Director of Applied Mathematics and Scientific Computation (AMSC) Program,

Benjamin Kedem

Professor of Mathematics and

Director of Statistics Program

Mark Freidlin

Professor of Mathematics and Distinguished University Professor

John Millson

Professor of Mathematics

David Hamilton

Professor of Mathematics

Joel Cohen

Professor of Mathematics

Leon Greenberg

Professor of Mathematics

Peter Wolfe

Professor of Mathematics

Paul Green

Professor of Mathematics

Michael Brin

Professor of Mathematics

Michael Jakobson

Professor of Mathematics

Harland M. Glaz

Professor of Mathematics

Carlos A. Berenstein

Professor of Mathematics

Jeffrey Cooper

Professor of Mathematics

Eric V. Slud

Professor of Mathematics

Daniel Sweet

Professor of Mathematics

Ryszard Syski

Professor Emeritus of Mathematics,

Seymour Goldberg

Professor Emeritus of Mathematics

John Horvath

Professor Emeritus of Mathematics

Jerome Dancis

Associate Professor of Mathematics

Robert Warner

Associate Professor of Mathematics

Marshall Cohen

Visiting Professor of Mathematics

Thomas Murphy

Associate Professor of Chemistry and Bio- Chemistry, UMCP

Bruce Donaldson,

Professor of Civil and Environmental

Engineering

Martin Peckerar

Professor of Electrical and Computer Engineering, (Part time), UMCP

Also Head, Surface and Interface Sciences Branch at Naval Research Labs (NRL)

Oscar W. Greenberg

Professor of Physics

Tom Cohen

Professor of Physics, (whose children attend Montgomery County Public Schools, added:

"The inclusion of data analysis and statistics is useful. In the modern world citizens must understand statistics and not be swindled by the abuse of statistical methods.

However, the way data analysis is taught and tested troubles me. In particular, the use of linear regressions (done by a calculator) to fit lines is not appropriate for Algebra I students, in my view. The students are NOT taught what a "best fit" line means mathematically, how to judge whether the model fits the data well (i.e. chi square or other statistical measure) nor even given any clear way to understand whether the data ought to fit a line. If you ask the calculator for a line which will fit points which lie on a parabola the calculator will spit back a line and the students will dutifully write it down. The issues are subtle and Algebra I students are not prepared to deal with them. Thus, the students are being miseducated in data analysis and statistics.

In my view this treatment is worse than useless; it is positively destructive. Students are told in essence to plug things in which they don't understand and then to trust the answers. This is diametrically opposed to the critical reasoning about data analysis that we need to instill in students.

Finally, significant time is spent on this activity in algebra one classes which thus comes at the expense of learning algebra. My daughter's class spent more than two weeks on this activity.")

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Non-signers, who have not signed the petition, but have made a personal statement that the state should either put algebra on the Maryland State Algebra Exam or change the name to the MD State Mathematics Exam.

Jim Yorke,

Professor of Mathematics and Distinguished University Professor and past director of the Institute for Physical Sciences and Technology at UMCP,

And Robert Ellis,

Professor of Mathematics, UMCP

Steve Zelditch, Professor and Chair

Department of Mathematics

Jack Morava, Professor

Department of Mathematics

Vyacheslav Shokurov, Professor

Department of Mathematics

(With the written comment:

This is one of the main reasons for me to keep my boys in Russia.)

Chris Sogge, Professor

Department of Mathematics

W. Stephen Wilson, Professor

Department of Mathematics

Steven Zucker, Professor

Department of Mathematics

Jean-Pierre Meyer, Professor Emeritus

Department of Mathematics

Kristine Bauer, Assistant Professor

Department of Mathematics

Gregory S. Chirikjian, Professor

Department of Mechanical Engineering

(joint appointment in Computer Science)

Doris R. Entwisle, Professor Emerita

Department of Sociology

(A career of doing research on schools.)

Jerry Prince, Professor and William B. Kouwenhoven Chair

Electrical and Computer Engineering

Andrew S Douglas, Professor

Department of Mechanical Engineering

Associate Dean for Academic Affairs

Whiting School of Engineering

Pablo A. Iglesias, Professor

Department of Electrical and Computer Engineering

Gerard G. L. Meyer, Professor and Chair

Department of Electrical and Computer Engineering

Moise H. Goldstein, Jr., Professor Emeritus

Department of Electrical and Computer Engineering

Wilson J. Rugh, Professor

Department of Electrical and Computer Engineering

Marc Parlange, Professor and Chair

Department of Geography and Environmental Engineering