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

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

Petition signers from the Johns Hopkins University

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

Petition signers from

Baltimore City Community College

Scott Saunders

Associate Professor of Mathematics and Mathematics Department
Chair

Tracy Leshan

Professor of Mathematics

Gisele Icore

Professor of Mathematics

Jeffrey Grell

Assistant Professor of Mathematics

Frederick Chapple,
Assistant Professor

Department of Mathematics

Non-Academic Signers,

Allen Hirsh PhD (plant
physiology)

Senior Scientist

Transfusion &
Cryopreservation Program

Combat Casualty Care

Naval Medical Research
Center

Gerald S. Garfinkel, Ph.D.
(Math)

Senior Operations Research
Analyst

US Army Test and Evaluation
Command/Army Evaluation Center