The California state school board last week approved a slate of mathematics textbooks that heavily favors a skills-based approach to instruction and, for the first time, meets the state's 3-year-old math standards and the frameworks that guide curriculum in the subject.
But the adoption jarred many teachers and administrators, including the state schools superintendent, who maintain that the board's rejection of an acclaimed instructional program undermined the recommendations of an advisory panel and created a roadblock for more innovative approaches to teaching math.
The adoption "is a disappointment, to say the least, because we view it as a setback ... for quality math instruction for students," said Elizabeth Sullivan, the president-elect of the California Mathematics Council, which represents 10,000 math teachers.
Some officials, however, defended the list, saying the selected texts meet a complex and comprehensive set of criteria, and the rejected books do not.
"In the [adopted] texts, we felt the standards were covered ... so that students would have mastery of the subject for future learning," said Susan Stickel, an assistant superintendent in Elk Grove, Calif., and a member of the state curriculum commission, which advises the board on textbooks.
"While we applaud those districts and teachers who say they are getting results from other programs, effectiveness was not one of our criteria [for selecting the texts]," she added...
The California board selected texts that are seen as likely to hold the greatest potential for improving students' scores on standardized tests and for being used effectively by teachers with a wide range of skills in teaching math.
That meant a thumbs- up for 12 texts, including two series by Saxon Publishers, a Norman, Okla., company specializing in skill-building through repetitive practice. The Saxon books are considered "teacher proof," and include prepared daily lessons and tests that eliminate the need for teachers to create their own.
In contrast, Everyday Mathematics, seen as a "progressive" program, was rejected as too difficult for teachers to use.
The state board, in essence, rejected the recommendations of two review panels, which gave high ratings to Everyday Mathematics, K-3. The program, developed by the University of Chicago's School Mathematics Project, was one of six deemed "exemplary" in 1999 by a panel sponsored by the U.S. Department of Education. ("'Exemplary' Texts Withdrawn From Calif. Adoption Process," Oct. 18, 2000: http://www.ca4cs.org/CometData/001023COMET.html#anchor31137.)
The textbook-adoption list reflects the standards California adopted in 1998, which veer away from conceptual understanding of mathematics and real-life problem-solving skills in favor of an instructional approach that reinforces basic skills and repeated practice of math functions.
In letters to the board last week, a group of 15 district superintendents and Superintendent of Public Instruction Delaine Eastin urged the members to approve Everyday Math, citing evidence that it improves student performance...The board instead established a waiver process that will allow districts already using Everyday Mathematics to continue, but only if they can prove it has contributed to higher student achievement. Districts that have not used the series will be ineligible to apply for waivers.
California lawmakers allocated $415 million for instructional materials in all subjects this year. Of that, $250 million is specifically for textbooks and other materials that meet state standards in the core content areas, including math. Districts must spend 70 percent of the remaining funds on state-approved texts. The new adoption list is valid for six years.
California's massive standardized testing program is having some unintended effects, both in and outside the classroom, results that have little to do with lawmakers' goals of improving education and boosting accountability.
At some schools, teachers have students read short passages instead of entire books because that's what's on the test. At other schools, lessons on science and social studies have been abandoned to make more time for drilling on test-related material...
"There's less and less teaching happening, and more and more test preparation," said Lorna Karagiozov, president of the Santa Ana Educators Assn. "It's administrative anxiety coming down on the teachers: 'You must do this; otherwise our school looks bad' "...
As the state this week releases a new round of school rankings based on the test, it's easy to understand the anxiety that accompanies the Stanford 9 exam, given each spring to most students in second through 11th grades. Money and careers are on the line.
The Stanford 9 scores are, for now, the only measurement used to create the state's Academic Performance Index, which publicly ranks schools. Low-ranking campuses can be taken over by the district or the state and their principals and teachers reassigned. But schools that do well, or improve substantially, are eligible for huge bonuses, including as much as $25,000 for individual teachers...
Most state officials and lawmakers are thrilled with the results of their new accountability program. They cheer about the rising scores across California. For the first time, the API has made schools accountable to the public, they say, and schools have responded by working harder.
But better scores don't equal better education, said Wayne Johnson, president of the 300,000-member California Teachers Assn. "And serious damage is being done to the quality of public education"...
More often, the Stanford 9's power is altering what goes on behind the classroom door. For teachers, high scores equal money and prestige; declining ones spell shame and occasionally reassignment. For students, low scores can mean stints in summer school or even repeating grades.
The result is test obsession that has stolen the joy and creativity from their work, many teachers say. Long-trusted lesson plans that excite students have been ripped up and new ones frantically created to meet the demands of the multiple-choice exam. Some worry that they are transforming students into a generation of nervous, test-obsessed drones.
"I've been here 30 years, and I've never before felt this kind of terror," said Margaret DeArmond, a math resource teacher in the Kern High School District. "There's a sense of feeling threatened, but not knowing what they should do."
In her job, DeArmond talks to many of the district's teachers, and they are not happy. "Quite honestly, a lot of them are wondering if teaching is the profession for them," she said...
This problem is compounded, teachers say, because the Stanford 9 test is not fully aligned with California's curriculum standards.
Architects of the plan acknowledge that the system has kinks, but promise that it will get better.
Just last week, legislative leaders on education announced that they plan to reevaluate the state's testing system because they fear it doesn't measure what students are actually learning. This spring, an additional language arts test will start counting toward the API. The extra test matches California's curriculum standards.
And the API is going to be expanded to include attendance and graduation rates, writing samples and perhaps even proof of good citizenship...
[Jerry] Hayward, the education specialist who helped craft the API, said he sympathizes with teachers who say it's unfair to judge what their students learn on the basis of a single test. But the idea of holding teachers and principals responsible for student achievement is sound, he said. "The public has a right to know what students know and are able to do," he said...
State officials also maintain that they have never wanted educators to "teach to the test." But teachers scoff at such assertions.
"When the state rewards and punishes schools based on test scores, you've created...an environment that is going to push people to raise scores at the expense of real learning," said Josh Pechthalt, a teacher at Manual Arts High School in Los Angeles.
The pressure has driven a handful of teachers to cheat. Seven schools across California have admitted to the state that cheating occurred on their campuses, said Doug Stone, spokesman for the California Department of Education. Thirty more are under investigation.
But one of the state's most honored teachers said she refuses to change what she does because of a standardized test. "I teach my kids to think," said Cynthia Stern. The second-grade teacher at Peterson Elementary School in Huntington Beach recently became one of 786 teachers in California to achieve national board certification. The current test preparation mania is "nuts," she said. "I think sometimes . . . we as teachers should say: 'I'm here with these kids every day, and I'm the expert and this is not the way it needs to be done.'
A public briefing for the release of "Adding it All Up: Helping Children Learn Mathematics" will be held at the National Academy of Sciences building in Washington, DC, from 10:30-noon on 24 January 2001 (contact: Brian McQuillan, 202-334-3012). This book "explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.
"The Committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning:
(a) Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction.
(b) Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics.
"The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics."
* Related Press Release (23 January 2001): "Overhaul of School Mathematics Needed To Boost Achievement for All"
FOR IMMEDIATE RELEASE
NEW STUDY BY NATIONAL RESEARCH COUNCIL
WASHINGTON -- American students' progress toward proficiency in mathematics requires major changes in instruction, curricula, and assessment in the nation's schools, says a new report from the National Research Council of the National Academies. To help schoolchildren successfully develop all aspects of mathematics learning, a coordinated and systematic approach to mathematics education from pre-kindergarten through eighth grade is critical.
"Too few students leave elementary or middle school with adequate mathematical knowledge, skill, and confidence for the nation to be satisfied with the condition of school mathematics," said Jeremy Kilpatrick, chair of the committee that wrote the report and Regents Professor of Mathematics Education at the University of Georgia, Athens. "Simply developing speed in pencil-and-paper arithmetic may have been sufficient when their parents and grandparents were in school, but today's students need a deeper understanding of mathematics to thrive in an increasingly technical economy. Improvement requires a comprehensive and sustained effort among policy-makers, administrators, teachers, university faculty, parents, and others to enhance both instruction and achievement."
Knowledge of mathematics is important for making sense of a high-tech world, yet the nation's approach to mathematics in pre-kindergarten through eighth grade has been inconsistent and marked by an emphasis on routine arithmetic -- with a heavy dose of memorization and repetition, the committee said. Furthermore, recent studies have shown that many elementary and middle school teachers have only a shaky grasp of mathematics themselves, and often are unable to clarify key concepts for students or solve problems that involve more than basic calculations.
Such failure to more fully explore mathematics limits an individual's potential and hampers national progress by insufficiently preparing future workers and citizens, the report points out. Results from state, national, and international assessments conducted over the past 30 years indicate that U.S. students can adequately perform straightforward computational procedures, but they tend to have a more limited understanding of fundamental mathematical ideas. They also have trouble applying mathematical skills to solve even simple problems. And these trends may further impede the academic advancement of at-risk students.
Paramount in the report's recommendations is the finding that the nation can and should groom all students to be "mathematically proficient," mastering much more than disconnected facts and procedures. Moreover, this target should drive school-improvement efforts, the committee emphasized after its exhaustive review and synthesis of scientific literature on mathematics education in pre-kindergarten through eighth grade.
Five intertwined and equally important strands comprise the committee's definition of mathematical proficiency. First, capable students should be able to understand and apply important concepts. They also should be able to compute with ease, formulate and solve problems, and explain their reasoning. Finally, they should have confidence in their abilities and view mathematics as a sensible and worthwhile subject. Each strand requires constant attention, the report says.
The committee concentrated on how students learn about numbers and operations. Relevant research was abundant in those areas, and debates over mathematics curricula and instruction in elementary and middle schools often center on arithmetic. Nonetheless, the goal of proficiency also applies to other important areas of mathematics, including algebra, geometry, and statistics, the report says.
Mathematical proficiency develops over time, building on a knowledge base that begins to take shape in infancy. The committee did not endorse any single approach to effective instruction, but recommended that teachers use students' informal understanding of mathematics as a steppingstone toward mastery of more challenging skills and concepts in the subject.
Beginning in preschool, educators should offer students opportunities to extend their rudimentary comprehension of numbers. In subsequent years, the curriculum should link calculation to everyday situations to help students make such connections. And it should illustrate numbers and operations in various ways, the report adds. For example, one-half could be shown as a fraction, decimal, or percentage; a point between zero and one on a number line; or as a shaded portion of a figure.
In addition, educators should teach important concepts in depth, instead of covering a multitude of topics superficially, the committee said. Significant time also should be devoted to daily mathematics instruction in every grade of elementary and middle school. Exams should test students' progress in all five strands of mathematical proficiency.
To better prepare teachers for elementary or middle school math instruction, colleges and universities should create programs or courses that emphasize thorough knowledge of mathematics and of processes through which schoolchildren come to understand the subject, the committee said. On the job, schools should give teachers more time and other resources -- such as continuous and high-quality training, as well as useful instructional materials -- to acquire a solid understanding of mathematics and improve their techniques. Teachers who have special training in the subject also should be available in all elementary schools to assist colleagues.
Proficiency is an ambitious goal, and the United States will never reach it by continuing to tinker with the controls of education policy, pushing one button at a time, the report says. In recent years, many states and school districts have raised academic standards in mathematics, introduced new assessments, and offered teachers new professional-development opportunities. But these efforts have been fragmented.
While a solid base of scientific evidence supports the committee's call for immediate action to help all students become mathematically proficient, additional research is needed to shed more light on the elements of successful mathematics teaching and learning, as well as obstacles that block progress. The fruits of such investigation, coupled with data from systematic evaluation of programs and initiatives, should routinely inform improvement efforts, the report says.
The study was sponsored by the U.S. Department of Education and the National Science Foundation. The National Research Council is the principal operating agency of the National Academy of Sciences and the National Academy of Engineering. It is a private, nonprofit institution that provides science advice under a congressional charter. [Committee members included Jeremy Kilpatrick (chair), Deborah Loewenberg Ball, Hyman Bass, Jere Brophy, Felix Browder, Thomas Carpenter, Carolyn Day, Karen Fuson, James Hiebert, Roger Howe, Carolyn Kieran, Richard Mayer, Kevin Miller, Casilda Pardo, Edgar Robinson, and Hung-Hsi Wu; NRC staff member and study director: Jane Swafford]
A coalition of nearly a dozen national education groups called last week for a set of "midcourse corrections" that it believes are necessary for the promise of standards-based education to be fulfilled for all students.
The statement by the Washington-based Learning First Alliance emphasizes the group's continuing support for high academic standards and public accountability in education. But it also raises "serious concerns" about how states and districts are implementing their standards-based initiatives.
"In too many places," the group argues, "essentials for student success are lacking. In too many places, the emphasis is on testing rather than on learning."
Alliance members identify five areas that "require urgent attention." In particular, the group recommends:
* The use of rich instructional programs and curricula that support state and district standards, as well as high-quality testing systems that adequately gauge achievement of the standards and use a variety of measurement techniques;
* An assurance that every child is taught by well- prepared teachers, who must receive professional development to help them teach to the standards;
* A commitment to provide extra help for children who need it and sufficient resources for schools to meet the standards;
* Better communication about the content, purposes, and consequences of standards and accountability systems, including how they will affect students; and
* Responsible accountability systems that couple high-quality, aligned assessments with incentives for students and schools that meet standards, and supports for students and schools that do not.
"In designing these accountability systems," the group urges, "states and districts should examine carefully the use of a single standardized-test score as the sole basis for important decisions about students or schools." Standardized-test scores should be considered along with other information in making such decisions, the group says...
The Learning First Alliance was founded in 1997 as a permanent partnership of national education organizations working to improve student learning...
Judy Wurtzel, the executive director of the alliance, said each of the member organizations has a "slightly different take on the issues," given their constituencies.
"We thought it was really important to make it completely clear that these organizations agree that standards-based reform is the best road for improvement," she said. "But it's a long road, and we've been learning some lessons as we go along."
The statement was drafted, in part, to address concerns about a potential backlash against states' standards-based initiatives. "We very much wanted to be on the record saying, yes, there are legitimate concerns that need to be addressed," Ms. Wurtzel said, "but there should not be a backlash against the whole movement."
At its board meeting later this month, the coalition plans to consider the next steps that its membership might take collectively. In addition, Ms. Wurtzel noted, each of the groups will communicate the statement to its own members, who together number about 10 million.
The organizations supporting the statement are: the American Association of Colleges for Teacher Education, the American Association of School Administrators, the American Federation of Teachers, the Association for Supervision and Curriculum Development, the Council of Chief State School Officers, the National Association of Elementary School Principals, the National Association of Secondary School Principals, the National Association of State Boards of Education, the National Education Association, the National PTA, and the National School Boards Association.
One thing the standards movement will never be accused of is a lack of critical opposition. But for all the fiery rhetoric that critics direct against this powerful, nationwide movement, there is perhaps no greater threat to standards-based reform than much of what is being perpetrated in the name of standards-based reform. The so-called movement -- so-called, because it is not truly a single movement but twin movements bearing the same name -- has become its own worst enemy.
If giving twins the same name is a recipe for confusion, consider the havoc that gets unleashed when one of them proves to be an "evil twin." In the case of the standards movement, the evil twin is the more visible and powerful of the siblings, and so its authentic namesake is in an increasingly perilous situation. In fact, the problem is even worse: the two are essentially joined at the hip.
So what are these twin movements? First, let's distinguish them by name. I would rename the evil twin "test-based reform" or more specifically "high-stakes, standardized, test-based reform." The sibling, then, is "authentic, standards-based reform." The defining distinction between them is their respective influence on the instructional core of schooling and on equity issues.
When academic progress is judged by a single indicator and when high stakes -- such as whether a student is promoted from one grade to the next or is eligible for a diploma -- are attached to that single indicator, the common effect is to narrow curriculum and reduce instruction to test "prepping." What gets lost when teachers and students are pressured to make students better test-takers is precisely the rich, high-level teaching and learning that authentic, standards-based reform aims to promote in all classrooms and for all students...
In its influence on both the instructional core of schooling and on equity, the evil twin constitutes an inversion of the "real thing." It is a politically warped variation on what is arguably among this nation's most powerful and promising education reforms. Although the evil twin purports to be standards-based, it actually flies in the face of research-based standards on the appropriate use of testing...
Another problem is that tests are frequently misused. Standardized tests designed for national comparisons between students, without reference to a particular school's curriculum or content standards, are, for example, too often used to evaluate teachers and schools...
High-stakes, test-based reform is an approach that is most often driven by state-level mandate, and it suits the political appetite for rapid, quantifiable (hence readily digestible by the public) results. Test-based reform represents a potentially lethal threat to its authentic twin. Whether by design or happenstance, it is effectively sabotaging the authentic standards movement. And not surprisingly, it is unleashing a swelling and intensifying backlash against standards and testing that is taking form legally and politically, as well as through mobilized grassroots opposition.
It is the combination of test-based reform, in the name of standards, and the wholesale backlash that such practice provokes that is placing the authentic standards movement in peril. Not only in the general media, but also in specialized education media, one can see that the war between proponents and opponents of high-stakes testing tends to define the entire standards movement in such a way that its actual nature and potential, which some school districts are beginning to demonstrate, gets buried under an avalanche of rhetoric...
Identical twins can be difficult to distinguish solely by surface characteristics. But if one is evil and the other virtuous, their character traits or essential natures will stand in stark contrast. So it is with test-based reform and standards-based reform. On the face of it, they are both about moving from an approach to education that values inputs to an approach that values outputs or results. But a deeper look into the essential natures of these twins reveals that test-based reform is nothing less than a 180-degree inversion of its authentic counterpart. This, I believe, becomes readily apparent when their essential characteristics are considered side by side.
= Authentic, standards-based reform involves teachers, parents, and others as active participants in developing and refining common learning standards. Test-based reform uses high-stakes tests, written in secret by expert psychometricians, as single indicators for deciding whether students are promoted or graduate, thereby making the tests the real standards.
= Authentic standards describe what all students should be learning at each level (not necessarily at each grade level). Test-based reform makes the scores on standardized tests for students at specific grade levels, in effect, the only meaningful standards.
= Under a system of authentic standards, the school system invests heavily in high-quality professional development for teachers and administrators in an effort to support their work in teaching to the standards. Under a system of test-based reform, teachers and principals are pressured in a variety of ways to raise test scores, and students are drilled accordingly.
= Under a system of authentic reform, student assessments are aligned with the standards, and students have numerous opportunities to demonstrate that they have met the standards. No single test is used to determine whether a standard has been met. Under test-based reform, a single state or national test is used to determine whether students are promoted to the next grade or are allowed to receive a diploma.
= High-quality, individualized support for students is a hallmark of authentic, standards-based reform. Such support is rare in test-based reform efforts. When it is present, it tends to focus on test-taking techniques rather than on teaching and learning.
= Authentic, standards-based reform has implications for every person, policy, and practice in a school system because it involves a complete abandonment of the bureaucratic, "seat time" approach to education and replaces it with a system of learning communities dedicated to helping all students reach their intellectual, social, and personal potential. By contrast, test-based reform, through its focus on high-stakes tests, narrows the curriculum to what is included on the tests and reduces instructional practice to test preparation.
A still more profound point of contrast between the two movements emerges
when we consider what educational purpose is implicit in each kind of reform. In
the case of test-based reform, the purpose of education is raising test scores.
In the case of authentic, standards-based reform, the purpose is enabling all
students to achieve as much of their creative, intellectual, and social
potential as possible. Thus the goal of authentic, standards-based reform is to
prepare students to live successfully and contribute actively in their
(1) "Teaching and Learning Mathematics: Using Research to Shift From the 'Yesterday' Mind to the 'Tomorrow' Mind" by Jerry Johnson
Jerry Johnson, Professor of Mathematics at Western Washington University, authored this summary of mathematics education research. Topics include research related to teaching a variety of mathematics topics, the use of manipulatives, ability grouping, computing technologies, constructivism, etc. Commissioned by Washington State's Superintendent of Public Instruction, the book can be downloaded at the URL above; or a free, bound print copy can be obtained by completing the order form at http://www.k12.wa.us/publications/ or by calling (888) 595-3276. The book contains an extensive reference list, and the writing style helps make the reviewed research easily accessible for teachers, administrators and parents. (Permission to copy has been granted.)
CITE is published by the Society for Information Technology and Teacher Education (SITE), and is the electronic counterpart of the "Journal of Technology and Teacher Education." The editorial review of this new cross-disciplinary journal is conducted by five professional organizations, including the Association of Mathematics Teacher Educators (AMTE). Peer-reviewed articles describing innovative approaches to integrate technology into teacher education are included; these online papers are often enhanced by the inclusion of video, animation, and audio.
The Hoover Institution has announced a new online/print publication entitled "Education Matters" (Editor-in-Chief: Paul E. Peterson; Senior Editor: Chester E. Finn Jr.). The editorial board consists of a number of President G.W. Bush's education advisors.
"'Education Matters' will steer a steady course, presenting the facts as best they can be determined, giving voice (without fear or favor) to worthy research, sound ideas, and responsible arguments...'Education Matters' is committed equally to readability and scholarly integrity...More comprehensive versions of our authors' research and essays, complete with notes and data, are available on-line in Education Matters More (www.edmattersmore.org).
"This journal has sections with distinctive missions. The Forum enables scholars and commentators to express differing views on major education issues and reform proposals... The Features section provides notable authors with a place to reflect on important concerns... In Research, the journal shifts from interpretations and commentary to the presentation of new (peer-reviewed) studies...Education Matters presents their key results in lively, readable prose; Education Matters More offers supporting documentation. Check the Facts asks whether research that is already influencing policy actually withstands close scrutiny...our Book Review section will often supply more than one commentary on the same book. And on the journal's last page, various authors speak in personal terms about how Education Matters to Me...We encourage you to send us your thoughts. The journal will benefit from your feedback. We also invite you to submit manuscripts for consideration and to contact us with your ideas."
COMET is sponsored in part by a grant from the California Mathematics Project.
COMET is produced by:
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