For a letter to the editor of the Daily Breeze (a newspaper in Torrance, Ca) from Richard Wagoner about the final outcome of the LAUSD Algebra I Pacing Plan, along with an earlier letter and reply from District K administrator Howard M. Vogel, click here.

An Open Letter to the LAUSD School Board and Superintendent Romer

September 25, 2002

Dear Superintendent Romer and LAUSD Board Members;

We are writing to draw your attention to the potentially negative impact of the Los Angeles Unified School District Pacing Plan for Algebra I students. It is our opinion, as LAUSD high school math teachers, scientists, and university mathematicians, that the LAUSD Pacing Plan for Algebra I should be dropped.

The LAUSD Pacing Plan for Algebra I prescribes the order in which topics, sections, and chapters of Algebra I textbooks are to be presented to LAUSD students, in the 8th and 9th grades. LAUSD has two individualized pacing plans for each of the three textbooks for Algebra I used in LAUSD. One of the pacing plans for each textbook is designed for the two year Algebra I course based on that book, and the other pacing plan is for a one year course based on that textbook. Both plans cover approximately the same topics in algebra.

One of the textbooks used for Algebra I in LAUSD is "Algebra I: Structure and Method" by Brown, Dolciani, et al. This textbook has been approved by the California State Board of Education. In contrast to the most widely used Algebra I textbook in LAUSD, "Concepts and Skills," the textbook "Algebra I: Structure and Method" received a positive review from mathematicians appointed by the State Board of Education to evaluate the Algebra I textbooks for statewide adoption. The official Content Review Panel Report for all three Algebra I textbooks used in LAUSD, written by four university mathematics professors, is available at:

http://www.csun.edu/~vcmth00m/mmath.html

According to the summary of the Content Review Panel Report for "Algebra
I: Structure and Method":

"We recommend this book highly. The book is well-organized, and topics are clearly and precisely explained. We found no inaccuracies, terminological or otherwise. Where possible, facts are proved/explained, not just asserted or concluded from a few examples. There are many problems, including word problems, of a range of difficulty."

A copy of the LAUSD pacing plan for "Algebra I: Structure and Method"
is included at the end of this letter. It undermines the organization
of ideas in this textbook, and it undermines the California Mathematics
Framework and Standards. We illustrate with some examples.

The two year pacing plan for "Structure and Method" calls for the quadratic
formula together with completing the square of quadratic polynomials (in
Chapter 12 of the textbook) to be explained to students before basic factoring
techniques for polynomials (in Chapter 5), and before an introduction to
radicals, including techniques for simplifying radicals (in Chapter 11).
This choice of ordering of topics is so mathematically unsound that it
will most likely seriously undermine the ability of LAUSD math teachers
to teach algebra in a coherent and meaningful way. It will reduce the learning
of algebra to memorizing meaningless formulas without understanding.
In the words of the chairman of the Math Department of San Pedro High School
(in LAUSD), Richard Wagoner:

"First and foremost among the problems with the Pacing Plan is that

it renders the textbook and all support materials useless and obsolete.

The sequence is so seemingly random that students must jump back and

forth between sections of chapters through most of the course.

Therefore, all review materials, diagnostic tests, supplementary

materials and enriched materials -- all of which are tied to the

sequence as designed by the authors -- can no longer be used."

Unfortunately, this pacing plan is being forced on high school math
teachers in District K of LAUSD, according to Richard Wagoner.

Here is another example of ordering of topics by the two-year algebra plan:

Solving Systems of Linear Equations, in Chapter 9, is to be presented in the third quarter of the first year. The material in Chapter 9 requires that students have a clear understanding of Section 7-3, "Equations With Fractional Coefficients." But Section 7.3 is postponed by the pacing plan until the fourth quarter of the first year. Chapter 9 also relies on prerequisites in Chapter 4 that are not presented until the first quarter of the second year. For example, the addition method of solving systems of linear equations requires an understanding of adding and subtracting polynomials, a topic in Chapter 4 presented long after it is needed.

The examples described here are not exhaustive, and the one-year Algebra course topics are also poorly ordered. Among the serious defects of the pacing plan for the one-year course is the complete omission of Chapter 11. Students are thus expected to use the quadratic formula without a complete understanding of square roots, and practice in simplifying radicals.

The apparent purpose of the Pacing Plan is to organize topics within the Algebra I curriculum so that each topic is taught at nearly the same time in all Algebra I classes at LAUSD schools (for the one year and two year courses, respectively), regardless of which textbook is used. Not only does the Pacing Plan seriously undermine the mathematical content of Algebra I by scrambling topics without regard to logical order and prerequisites, it even fails to meet the modest goal of ordering topics so that they are taught at the same time, independent of the textbook. A comparison of the Pacing Plans for "Concepts and Skills," "Structure and Method," and "Prentice Hall Algebra I" shows that the plans are not coordinated with each other. Richard Wagoner reports the following inconsistencies for the one-year algebra class plans:

a) The topic of functions is introduced in the second quarter of the year for "Structure and Method" and for "Concepts and Skills," but only in the fourth quarter for the Prentice Hall book.

b) Solving Inequalities is presented in the second quarter for "Structure and Method" and in the first quarter for the other two books.

c) Rate-Time-Distance problems are introduced in the third quarter for "Structure and Method," the second quarter for the Prentice Hall text, and not all in "Concepts and Skills."

d) Square roots are not in the pacing plan for "Structure and Method" but they are presented in the third quarter for "Concepts and Skills," and the fourth quarter for the Prentice Hall text.

e) Quadratic polynomials are studied in the third quarter for "Structure and Method" and "Concepts and Skills", but in the fourth quarter for Prentice Hall.

f) Percents are explained in the fourth quarter for "Structure and Methods" but in the first quarter for the other two texts.

The LAUSD Pacing Plan thus does not comport with the California Math Framework. According to the Framework (page 231):

"The order of presentation of mathematical topics is mathematically and pedagogically sound."

"Prerequisite skills and ideas are presented before the more complex topics that depend on them."

"Student materials ensure that students can look back in the textbook for help with understanding a topic; compilations, such as indices, tables of contents, and review summaries, also provide assistance."

The textbook, "Structure and Method" was adopted and approved for use in California schools because it is well aligned to the Framework. The effect of the Pacing Plan is to compromise and weaken this alignment to the California Framework and Standards.

It is our opinion that well written textbooks play an important role
in mathematics education generally, and the teaching of algebra specifically.
The view that a "standards driven math program" should not be "text driven"
and therefore that "jumping around" shouldn't cause too much distress is
misguided. Algebra teachers should be encouraged to take advantage
of the logical development of algebra available in the best state standards
aligned textbooks, as well as review problems in these books, and other
teaching tools. We urge you to drop the Pacing Plan and allow LAUSD
algebra teachers to teach the subject coherently and in a logical order.

Sincerely,

Richard Wagoner, Chair

Department of Mathematics

San Pedro High School (LAUSD)

David Klein

Professor of Mathematics

California State University, Northridge

Nenita Andres-Sandor

Department of Mathematics

San Pedro High School

Robert Baker

Assistant Principal

San Pedro High School

Jessica Barker

Department of Mathematics

San Pedro High School (LAUSD)

Gerrold Beer

Professor of Mathematics

California State University, Los Angeles

Wayne Bishop

Professor of Mathematics

California State University, Los Angeles

Julio Blanco, Chair

Department of Physics

California State University, Northridge

Peter Collas

Professor of Physics

California State University, Northridge

J. Crawley

Department of Mathematics

Dodson Middle School

Sandra Crosby

Department of Mathematics

San Pedro High School

Mark Denni

Special Education - Mathematics

San Pedro High School

John Dye

Professor of Mathematics

California State University, Northridge

Ron Faerber

Math Department

Birmingham High School

Debbie Ferguson

Department of Mathematics

San Pedro High School

Catherine Figuracion

AP Calculus Instrructor, Dept. of Mathematics

San Pedro High School

Anna Fox

Department of Mathematics

San Pedro High School

Don Gallaher

Department of Mathematics

San Pedro High School

Steve Grgas

Department of Mathematics

Banning High School

Jeffrey H. Holyfield

Department of Mathematics

San Pedro High School

J. Jones-Reed

RSP - Mathematics

San Pedro High School

Sheldon Kamienny

Professor of Mathematics

University of Southern California

Elizabeth Kim

Department of Mathematics

San Pedro High School

Joyce Kimura

Department of Mathematics

Dodson Middle School

Christina Kumor

Department of Mathematics

San Pedro High School

Paul Lee

Professor of Physics

California State University, Northridge

Martin Lizarraga

Department of Mathematics

San Pedro High School

Jennifer Marple

Department of Mathematics

Monroe High School (LAUSD)

Michael McKeown

Professor of Medical Science, Brown University

Member, Committee to write the California Mathematics Program Advisory

Stan Metzenberg

Assistant Professor of Biology

California State University, Northridge

Cesar Michel

Department of Mathematics

San Pedro High School

R. James Milgram

Professor of Mathematics

Stanford University

Steven B. Oppenheimer, Ph.D.

Director, CSUN Center for Cancer and Developmental Biology

Trustees Outstanding Professor, the CSU system

Fellow, American Association for the Advancement of Science (AAAS)

Janette Pacitti

Department of Mathematics

El Camino Real High School

Marcus Perez

Department of Mathematics

Dodson Middle School

Yoshiko Ramirez

Department of Mathematics

San Pedro High School

Dianne Ramstead

Special Education: Mathematics

San Pedro High School

Lany Ryons

Department of Mathematics

Dodson Middle School

Daniel Sanchez

Department of Mathematics

San Pedro High School

Martha Schwartz, Geophysicist

USC Research Associate

California Mathematics Framework Committee

Co-founder of Mathematically Correct

Barry Simon

I.B.M. Professor of Mathematics and Theoretical Physics

Chair, Department of Mathematics

Caltech

Jim Stein

Professor of Mathematics

California State University, Long Beach

Ann Sullivan

Department of Mathematics

Dodson Middle School

Craig Tagler

Department of Mathematics

Dodson Middle School

Carl Winton

Department of Mathematics

San Pedro High School

ALGEBRA PACING PLAN SUMMARY 2002-2003

(Q1 means "the first quarter," Q5 means the "fifth quarter" in a two year program)

2-Year Algebra (1A1-1B2)

CLASS SECTION TOPICS

1A1 (Q1) 1.1-1.9 Intro/Variables

2.1-2.9 Real Numbers

1A1 (Q2) 3.1-3.8 Equations

10.1-10.6 Inequalities

1A2 (Q3) 9.1-9.5 Linear Systems

8.1-8.10 Intro Functions

SUPP Midpoint

1A2 (Q4) 10.7-10.8 Lin. Inequalities

9.5-9.7 WP: Linear Systems

7.3-7.4 Fractional Equations

1B1 (Q5) 4.1-4.10 Polynomials

12.1-12.8 Quadratic Functions

1B1 (Q6) 5.1-5.13 Polynomial Factoring

6.1-6.7 Fractions/Polynomials

1B2 (Q7) 12.1-12.8 Quadratic Equations
(Rep)

11.1-11.10 Rationals/Irrationals

7.1-7.6 Ratio/Proportion/Fractions

8.9-8.10 Radicals

1B2 (Q8) SUPP SAT-9 Review

7.3-7.10 Ratio/Proportion/Fractions

6.4-6.7 Fractions/Polynomials
(Rep)

11.4-11.10 Rationals/Irrationals
(Rep)

1-Year Algebra (1A-1B)

CLASS SECTION TOPICS

1A (Q1) 1.1-1.9 Intro/Variables

2.1-2.9 Real Numbers

3.1-3.8 Equations

4.1 Exponents

1A (Q2) 3.4-3.8 Equations (Repeat)

8.1-8.9 Intro Functions

9.1-9.5 Linear Systems

10.1-10.8 Inequalities

1B (Q3) 4.1-4.9 Polynomials

5.1-5.13 Polynomial Factoring

12.1-12.7 Quadratic Functions

1B (Q4) SUPP
SAT-9 Review

6.1-6.7 Fractions/Polynomials

7.1-7.10 Ratio/Proportion/Fractions