State Mathematics Standards: An Appraisal of Math Standards in 46 States, the District of Columbia, and Japan
Abstract"The Thomas B. Fordham Foundation is pleased to present this appraisal of state mathematics standards by Ralph A. Raimi of the University of Rochester and Lawrence S. Braden of St. Paul's School. ...The important thing to know about the present document is that we did not ask its authors--a distinguished university mathematician and a deeply experienced school math teacher--to grade the states on how faithfully their standards incorporate the NCTM's model for math education. Rather, we asked them to appraise state standards in terms of their own criteria for what excellent math standards should contain.
Advised by two other nationally respected scholars, the authors did precisely that. They developed nine criteria (under four headings) and then applied them with great care to the math standards of 46 states and the District of Columbia. (The remaining four states either do not have published standards or would not make their current drafts available for review.) For comparison purposes, the authors also describe Japan's math standards and apply their criteria to these."
Published by the Thomas B. Fordham Foundation, March, 1998.
Alabama Course of Study, MATHEMATICS, Mathematical Power K-12
(Alabama State Department of Education Bulletin 1997, No.4)
50 North Ripley St., P.O. Box 302102
Montgomery, AL 36130-2101
(1) Math/Science Framework (1996)
(2) Mathematics Performance Standards (1997)
Department of Education
801 W. Tenth Street
Juneau, AK 99801-1894
Mathematics Performance Objectives (March 11, 1997; adopted August 26, 1996)
Arizona Department of Education
1535 West Jefferson
Phoenix, AZ 85007
General Education Division
Arkansas Department of Education
Four State Capitol Mall, Room 304A
Little Rock, AR 77201-1071
(From http://www.arkansased.gov/ July 22, 1997)
The California MATHEMATICS Academic Content Standards (Prepublication Edition, February 2, 1998) for Grades K-12
California State Board of Education
Model Content Standards (June 8, 1995)
Colorado Department of Education
Denver, CO, 80203
"Mathematics Curriculum Framework," Second Draft,
August 7, 1997
Connecticut Department of Education
165 Capitol Avenue
Room 305, State Office Building
Hartford, CT 06106-1630
Mathematics Curriculum Framework
Vol. 1 Content Standards (1995, revised March 1, 1996)
Delaware Dept. of Education
Dover, DE 19903-1402
District of Columbia
Mathematics-Science-Technology Curriculum Framework, Grades K-12, Revised Edition (undated, but post-1989)
District of Columbia Public Schools
415 12th Street, N.W., Suite 1209
Washington, D.C. 20004-1994
(1) Sunshine State Standards and Instructional Practices, Mathematics (May 29, 1996)
(2) Florida Course Descriptions, Grades 6-12, pp151-263 (1997) Florida Department of Education
Capitol Building, Room PL 08
Tallahassee, FL 32301
"Mathematics Quality Core Curriculum," Draft Revision, Edition 2 ("provided by the Georgia School Improvement Panel, February, 1997")
CD ROM available from the Georgia Department of Education
Telephone (404) 657-7411
(1) State Commission on Performance Standards (Final Report, June 1994)
(2) Essential Content (December, 1992) Department of Education
641 18th Avenue, Room V201
Honolulu, HI 96816-4444
Hawaii Department of Education
1390 Miller Street, #307
Honolulu, HI 96813
K-12 Mathematics Content Guide and Framework (1994)
(in three parts: K-4, 5-6, and 7-12)
Illinois Learning Standards (July 25, 1997)
Illinois State Board of Education
100 North First Street
Springfield, IL 62777
Mathematics Proficiency Guide (Spring 1997)
Indiana Department of Education
State House, Room 229
Indianapolis, IN 46204-2798
(Iowa apparently does not intend to publish a Standards or Framework of the sort that is under review in this report.)
Mathematics Program in Japan (Kindergarten to Upper Secondary School)
Japan Society of Mathematical Education (JSME), January, 1990
(Excerpt from the National Courses of Study, Revised by the Ministry of Education)
Published by: Japan Society of Mathematical Education
Private Postbox No.18, Koishikawa Post Office
Mathematics Curriculum Standards (Revised July 1993, Reprinted October 1996)
Kansas State Department of Education
120 SE 10th Avenue
Topeka, KS 66612
Core Content for Mathematics Assessment
Kentucky Department of Education
500 Mero Street
Frankfort, KY 40601
Content Standards Foundation Skills (May 22, 1997)
Curriculum Framework for Mathematics and Science (undated, but post-1995)
Maine Department of Education
23 State House Station
Augusta, ME 04333-0023
(1) Mathematics--A Maryland Curriculum Framework (1985)
(2) High School Core Learning Goals, Mathematics (September 1996)
Maryland State Department of Education
200 West Baltimore Street
Baltimore, MD 21701-7595
Mathematics Curriculum Framework (December 1995)
Commonwealth of Massachusetts
Department of Education
350 Main Street
Malden, MA 02148-5023
Model Content Standards for Curriculum, including Academic Core Curriculum Content Standards (July 25, 1996)
"K-12 Mathematics Framework" (Draft chapters, 1997)
"Please do not quote, copy, or cite." Our copy was mailed to us from:
638 Capitol Square
550 Cedar Street
St. Paul, MN 55101
Mathematics Curriculum Structure (1995)
Mississippi Department of Education
550 High Street, Room 501
Jackson, MS 39201
Missouri's Framework for Curriculum Development in Mathematics, K-12 (1996)
Missouri Department of Elementary and Secondary Education
205 Jefferson Street
Jefferson City, MO 65102
Framework for Improving Mathematics and Science Education (1996)
Montana Office of Public Instruction
PO Box 202501
Helena, MT 59620-2501
Mathematics and Science Frameworks for Nebraska Schools (March 6, 1994)
Nebraska Department of Education
301 Centennial Mall South
P.O. Box 94987
Lincoln, NE 68509
"We are in the process of developing new math standards during the 1997-1998 school year."
K-12 Mathematics Curriculum Framework (February 1995)
New Hampshire Department of Education
101 Pleasant Street
Concord, NH 03301
(1) Core Curriculum Content Standards for Mathematics (1995, revised 1996)
(2) New Jersey Mathematics Curriculum Framework (1996)
New Jersey Mathematics Coalition
Content Standards with Benchmarks for Kindergarten Through 12th Grade (Fall 1996)
New Mexico Department of Education
300 Don Gaspar
Santa Fe, NM 87501-2786
Learning Standards for Mathematics, Science and Technology (March 1996)
New York Education Department
111 Washington Avenue
Albany NY 12234
Standard Course of Study and Grade Level Competencies, Mathematics K-12 (1992, 1993)
North Carolina Department of Public Instruction
301 N. Wilmington St.
Raleigh, NC 27601-2825
Mathematics Curriculum Framework Standards and Benchmarks (Revised 1996-1996; Draft in progress March 24, 1997)
North Dakota Department of Public Instruction
State Capitol Building, 11th Floor
Bismarck, ND 58505-0440
Model Competency-Based Mathematics Program (November 1990)
Ohio Department of Education
65 South Front Street, Room 810
Columbus, OH 43215-4183
Priority Academic Student Skills--Mathematics (March 1997)
Oklahoma State Department of Education
2500 N. Lincoln Boulevard
Oklahoma City, OK 73105-4599
(1) Standards (January 1997)
(Mathematics pages are 9-12 and 29,30)
(2) Oregon Statewide Mathematics Assessment, Test Specifications
Grade 3, Grade 5, Grade 8, Grade 10 (1997)
(3) Sample Tests for (2)
(4) Mathematics Teacher Support Package (October, 1996)
Oregon Department of Education
255 Capitol St. NE
Salem, OR 97310-0203
"Proposed Academic Standards for Mathematics' for the Governor's Advisory Commission on Academic Standards'"
Pennsylvania Department of Education
333 Market Street
Harrisburg, PA 17126-0333
Mathematics Framework K-12 (October 1995)
Department of Education
225 Westminster Street
Providence, RI 02903
(1) Mathematics Framework (November 1993)
(2) Mathematics and Academic Achievement Standards (November 1995)
Curriculum Framework Office
1429 Senate Street
Columbia, SC 29201
Mathematics Content Standards (Approved June 17, 1996)
Division of Education Services and Resources
700 Governors Drive
Pierre, SD 57501-2291
(Note: A letter of August 18, 1997 states that "South Dakota is in
the process of rewriting the Content Standards.")
(1) Mathematics Framework/ Grades Kindergarten Through Grade Eight (October 11, 1996)
(2) Mathematics Curriculum Framework, Grades 9-12 (November 15, 1991)
Tennessee Department of Education
Andrew Johnson Tower
Nashville, TN 37243-0375
Texas Essential Knowledge and Skills for Mathematics ("Chapter 111," to be implemented by September 1, 1998, with Chapter C, 9-12, "effective September 1, 1996")
Texas Education Agency
1701 North Congress Avenue
Austin, TX 78701-1494
Core Curriculum/Mathematics Units (September 19, 1996)
Vermont's Framework of Standards and Learning Opportunities--Science, Mathematics and Technology Standards (1996)
Vermont State Board of Education
120 State Street
Montpelier, VT 05620-2501
Standards of Learning for Virginia Public Schools (June 1995)
Commonwealth of Virginia Department of Education
101 N. 14th Street
Richmond, VA 23219
An Entry from the Diaries of John Adams (1735-1826)
June 1, 1756.
Drank Tea at the Majors. The Reasoning of Mathematics is founded on certain and infallible Principles. Every Word they Use, conveys a determinate Idea, and by accurate Definitions they excite the same Ideas in the mind of the Reader that were in the mind of the Writer. When they have defined the Terms they intend to make use of, they premise a few Axioms, or Self evident Principles, that every man must assent to as soon as proposed. They then take for granted certain Postulates, that no one can deny them, such as, that a right Line may be drawn from one given Point to another, and from these plain simple Principles, they have raised most astonishing Speculations, and proved the Extent of the human mind to be more spacious and capable than any other Science.
State Mathematics StandardsAn Appraisal of Math Standards in 46 States, the District of Columbia, and Japan
Ralph A. Raimi and Lawrence S. Braden
EXPERT ADVISORY COMMITTEE
Henry Alder, Ph.D., Professor Emeritus of Mathematics, University of California, Davis, California
Harold Stevenson, Ph.D., Professor of Psychology, University of Michigan, Ann Arbor, Michigan
TABLE OF CONTENTS
District of Columbia
National Report Card
Numerical Ratings for the States
The Thomas B. Fordham Foundation is pleased to present this appraisal of state mathematics standards by Ralph A. Raimi of the University of Rochester and Lawrence S. Braden of St. Paul's School.
This is the fourth such publication by the Foundation. In July 1997, we issued Sandra Stotsky's evaluation of state English standards. In February 1998, we published examinations of state standards in history and geography. Science follows.
Thus, we will have gauged the states' success in setting standards for the five core subjects designated by the governors and President Bush at their 1989 education "summit" in Charlottesville. The national education goals adopted there included the statement that, "By the year 2000, American students will leave grades four, eight, and twelve having demonstrated competency in challenging subject matter including English, mathematics, science, history and geography." Although other subjects have value, too, these five remain at the heart of the academic curriculum of U.S. schools.
All are critically important, to be sure, but mathematics has special significance in today's debates about boosting the performance of U.S. students by setting ambitious standards for their academic achievement.
Mathematics is, of course, the third of the "three R's." Practically nobody doubts its central place in any serious education, its intellectual significance, or its practical value. Math is ordinarily the second subject (after reading) that young children encounter in primary school. "Math aptitude" constitutes half of one's S.A.T. score. And it was in no small part the weak math performance of American youngsters on domestic and international assessments that led us to understand that the nation was at risk. (Because it is universal, because it is sequential and cumulative, and because its test questions are easy to translate, mathematics has long been the subject most amenable to illuminating cross-national comparisons of student performance.)
Math also blazed a trail into the maze of national standards. Even as the Charlottesville summit was convening, the National Council of Teachers of Mathematics (NCTM) was putting the finishing touches on its report entitled Curriculum and Evaluation Standards for School Mathematics. In the ensuing decade, that publication and its progeny have had considerable impact on U.S. education, not least on the state math standards reviewed in the following pages. I have no doubt that, of all the "national standards" set in the various academic subjects, these have been the most influential. Indeed, I have heard policy makers declare that what America needs in other academic subjects are counterparts to the "NCTM math standards."
It is vital to understand, however, that the NCTM's mission was not--and today is not--the codification of traditional school mathematics into clear content and performance standards. Rather, NCTM's main project was to transform the teaching and learning of mathematics in U.S. schools.
The effects of that hoped-for transformation on state math standards are abundantly clear in this appraisal. Some readers may judge that the states should go further still to transform their expectations for students and teachers in the direction set forth by NCTM. Others will judge that they have gone much too far already. In any case, it's noteworthy that today, nine years after it was unveiled, "NCTM math" no longer commands the public consensus that it once appeared to have. California, for example, recently adopted new statewide standards that could fairly be termed a repudiation of the NCTM approach.
The important thing to know about the present document is that we did not ask its authors--a distinguished university mathematician and a deeply experienced school math teacher--to grade the states on how faithfully their standards incorporate the NCTM's model for math education. Rather, we asked them to appraise state standards in terms of their own criteria for what excellent math standards should contain.
Advised by two other nationally respected scholars, the authors did precisely that. They developed nine criteria (under four headings) and then applied them with great care to the math standards of 46 states and the District of Columbia. (The remaining four states either do not have published standards or would not make their current drafts available for review.) For comparison purposes, the authors also describe Japan's math standards and apply their criteria to these.
The results are sobering. Only three states (California, North Carolina, and Ohio) earn "A" grades, and just nine get "B's." Those 12 "honor" grades must be set alongside 16 failing marks (and seven "C's" and 12 "D's").
The results differ markedly from those of the recent Council for Basic Education (CBE) appraisal of the "rigor" of state math standards at grades 8 and 12. The CBE study begins with a list of performance standards expressed in 51 clauses (or "benchmarks") for the 8th grade and 30 for the 12th. These clauses are largely drawn from the NCTM standards of 1989. The state documents under study were then scanned for those 81 demands, which, when present (and weighted by their closeness to the template clauses), were counted up for a total score.
The present document does not begin with a list of this kind, and similarity to the NCTM standards was not a desideratum. The criteria used by Braden and Raimi are well described within the report itself, and include not only analyses of the "academic content" expressed or implied, but also qualities of exposition and taste affecting the standards' usefulness.
In view of the ferment in American math education and the continuing lackluster performance of U.S. youngsters in this key discipline, we must take notice of the findings reported herein. While state math standards are in many cases too new for them fairly to be held responsible for pupil attainment in this discipline, it appears that these documents, which were supposed to improve the situation, in most cases will not help and in many instances appear to be symptoms of the very failure they were intended to rectify.
To be sure, excellent math education continues in some classrooms and schools. State standards are not supposed to place a ceiling on how much is taught and learned. But they are meant to serve as a floor below which schools and teachers and children may not sink. As we learn from Messrs. Raimi and Braden, in many states today that floor seems to have been confused with the muddy excavation that ordinarily precedes construction.
We are grateful indeed to both authors for the rare energy, thoroughness, and mathematical insight that they brought to this arduous project. Raimi is professor emeritus of mathematics at the University of Rochester and former chairman of the math department (and graduate dean) at that institution. His scholarly specialty is functional analysis, and he has had a lifelong interest in effective mathematics teaching. Braden has taught mathematics and science in elementary, middle, and high schools for many years in Hawaii, in Russia, and now in New Hampshire. He is a recipient of the Presidential Award for Excellence in Science and Mathematics Teaching. He holds a bachelor's degree in mathematics from the University of California and an M.A.T. in mathematics from Harvard.
We also thank the two distinguished scholars who advised the authors throughout. Henry Alder is professor emeritus of mathematics at the University of California and a former president of the Mathematical Association of America. He has been a member of the California State Board of Education and recently served on the committee to rewrite that state's mathematics framework. Harold Stevenson is professor of psychology at the University of Michigan, a 1997 recipient of the American Psychological Association's Distinguished Scientific Award, and can fairly be termed America's foremost authority on Asian primary/secondary education and its comparison with U.S. schools and students. Among many publications, he co-authored The Learning Gap, a pathbreaking analysis of elementary education in Asia and the United States. He has a particular interest in the standards, curricula, and pedagogy of mathematics, which discipline has been the focus of many of his comparative studies, and has been deeply involved with the Third International Mathematics and Science Study (TIMSS).
In addition to published copies, this report (and its companion appraisals of state standards in other subjects) is available in full on the Foundation's web site: http://www.edexcellence.net. Hard copies can be obtained by calling 1-888-TBF-7474 (single copies are free). The report is not copyrighted and readers are welcome to reproduce it, provided they acknowledge its provenance and do not distort its meaning by selective quotation.
For further information from the authors, readers can contact Ralph Raimi by writing him at the Department of Mathematics, University of Rochester, Rochester, N.Y. 14627, or e-mailing firstname.lastname@example.org. Lawrence Braden can be e-mailed at email@example.com. The Thomas B. Fordham Foundation is a private foundation that supports research, publications, and action projects in elementary/secondary education reform at the national level and in the vicinity of Dayton, Ohio. Further information can be obtained from our web site or by writing us at 1015 18th Street N.W., Suite 300, Washington, D.C. 20036. (We can also be e-mailed through our web site.) In addition to Messrs. Raimi and Braden and their advisors, I would like to take this opportunity to thank the Foundation's program manager, Gregg Vanourek, as well as staff members Irmela Vontillius and Michael Petrilli, for their many services in the course of this project, and Robert Champ for his editorial assistance.
Chester E. Finn, Jr. President
Thomas B. Fordham Foundation
|On the whole, the nation flunks. Only three states received a grade of A, and just nine others a grade of B.|
|The failure of almost every State to delineate even that which is to be desired in the way of mathematics education constitutes a national disaster.|
Almost every one of the 50 States and the District of Columbia have by now published standards for school mathematics, designed to tell educators and the public officials who direct their work what ought to be the goals of mathematics education from kindergarten through high school. They are generally given as "benchmarks" of desired achievement as students progress through the grade levels to graduation, though sometimes they include guides to pedagogy as well. The present report represents a detailed analysis of all such documents as were available, 47 in all, though it has only space to offer rather abbreviated judgment of their value and a rating of their comparative worth. Grades of A, B, C, D, or F were given to each state, based on an analysis of the contents according to criteria and grade levels as described early in the report. Some comments on each State conclude the report.
On the whole, the nation flunks. Only three states received a grade of A, and just nine others a grade of B. More than half receive grades of D or F, and must be counted as having failed to accomplish their task. The grading is described below, but it should be understood that anything less than an A should be unacceptable.
A state, after all, is not a child to be graded for promise or for effort; the failure of a state to measure up to the best cannot be excused for lack of sleep the night before the exam. The failure of almost every State to delineate even that which is to be desired in the way of mathematics education constitutes a national disaster.
Even if the states' standards documents were exemplary, there would remain a problem of implementation. The public usually hears of the problems of schools as questions of funding, of discipline, and even sometimes of teacher preparation or recruitment, but it generally imagines that their intellectual goals are clear. For basketball players and musicians the goals are indeed known. But for elementary and secondary education in the United States today, there are no such agreements in place regarding its essential core: its academic program. This is especially so in mathematics, as the standards under review here illustrate.
The authors of this report believe it unconscionable that, in writing these standards--these documents of pure intent, whose success depends only on the efforts of experts already in place--so many states are so remiss in their duty.
As we have seen it, the principal failures stem from the mathematical ignorance of the writers of these standards, sometimes compounded by carelessness and sometimes by a faulty educational ideology. We are convinced that the average math teacher can be led to a better grasp of both the material that should be taught at various grade levels and the manner in which it should be presented, than the writers and editors of these documents imagine.
Our criteria for judgment were four: Clarity of the document's statements, and sufficient Content in the curriculum described or outlined in the text, were our first two demands. Third, since deductive reasoning is the backbone of mathematics, we looked to see how insistently that quality (denominated Reason) was to be found threaded through all parts of the curriculum. Finally, we assessed whether the document avoided the negative qualities that we called False Doctrine and Inflation. These four major criteria, some of them broken down into subcriteria, were individually graded and the scores combined for a single total.
The most serious failure was found in the domain of Reason. There is visible in these documents a currently fashionable ideology concerning the nature of mathematics that is destructive of its proper teaching. That is, mathematics is today widely regarded (in the schools) as something that must be presented as usable, "practical," and applicable to "real-world" problems at every stage of schooling, rather than as an intellectual adventure.
Mathematics does indeed model reality, and is miraculously successful in so doing, but this success has been accomplished by the development of mathematics itself into a structure that goes far beyond obvious daily application. Mathematics is a deductive system, or a number of such systems related to one another and to the world, as geometry and algebra are related to each other as well as to statistics and physics; to neglect the systematic features of mathematics is to condemn the student to a futile exercise in unrelated rule memorization. Most of the standards documents we have read, for all that they claim to foster "understanding" above rote learning, lack the qualities that would lead their readers, America's teachers, in the desired direction.
This lack of logical progression, seen especially in what passes for geometry and algebra in the grades from middle school upward, is visible in the lack of clarity of the documents. It is also visible in their advocacy of the use of calculators and computers in the early grades, where arithmetic and measurement as ideas should rather be made part of the student's outlook, by his learning through much experience and practice the nature of the number system. Learning to calculate, especially with fractions and decimals, is more than "getting the answer"; it is an exercise in reason and in the nature of our number system, and it underlies much that follows later in life. Only a person ignorant of all but the most trivial uses of calculation will believe that a calculator replaces--during the years of education-- mental and verbal and written calculation. Adults have need of calculators, and indeed computer programs, for computing their income taxes and doing their jobs. But the educational needs of children are quite different.
Content was the most successful part of these documents. This country has a traditional curriculum from the point of view of content, and many states at least mention most of it, including such recent additions as statistics and probability. However, much has been lost, especially from the Euclidean geometry that was so large a part of a high school program 50 years ago; and the fragmentation of the curriculum into too many different "threads" has also diluted the traditional curriculum.
The enterprise of writing standards goes hand-in-hand with the improvement of classroom practice, and there is no doubt that teachers of the next few years, seeing the inadequacy of most of what we have surveyed, will themselves offer suggestions for improvement. Members of the public, too, are often dissatisfied with vague education, led by vague standards, and they, too, will be heard. We believe the exercise of writing these documents is worthwhile, and we wish more states took it seriously enough to put their best talent to work on them.
In particular, the "best talent" must include not only members of the school establishment and state departments of education, but also persons knowledgeable in the uses of mathematics and the creation of new mathematics. That is to say, scientists (including statisticians, engineers, and applied mathematicians) and research mathematicians from the mathematics departments of the universities. These two communities have been most noticeably absent from the first rounds of standards construction, and future improvement is not possible without them. There is visible in these documents a currently fashionable ideology concerning the nature of mathematics that is destructive of its proper teaching.NATIONAL REPORT CARD
State Math Standards
< td>Arizona< tr>< td>4.7</ tr>< td>B< td>West Virginia
|State (in alphabetical order)||Score||Grade|
|District of Columbia||4.7||D|
< tr>< td>C< td>Oregon< td>D< td>F< /tr>
|State (by rank)||Score||Grade|
|District of Columbia||4.7||D|
Grading Scale: A=13-16, B=10-12.9, C=7-9.9, D=4-6.9, F=0-3.9, N=Not Evaluated *Partial Grades
Essential Academic Learning Requirements/Mathematics (February 26, 1997)
Commission on Student Learning
Room 222, Old Capitol Building
Olympia, WA 98504-7220
Instructional Goals and Objectives for West Virginia Schools (September, 1996)
West Virginia Board of Education
1900 Kanawaha Blvd. E.
Charleston, WV 25305-0330
"Model Academic Standards for Mathematics" (Draft, 1997)
Wisconsin Department of Public Instruction
P.O. Box 7841
Madison, WI 53707
Standards are in progress and were not available for review at
The Thomas B. Fordham Foundation
1015 18th Street, N.W.
Washington, D.C. 20036
Telephone: (202) 223- 5452
FAX: (202) 223- 9226
To order publications: 1-888-TBF-7474 (single copies are free)
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