Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.
Enhance your knowledge of standards and their implementation in your instructional program. This section on state and national standards contains:
Opposition to Standards and Mathematics Education Reform - materials to keep you informed
Research Corner with selected articles about standards and making them work, raising achievement, assessment, and technology integration. The pages also address No Child Left Behind and scientifically based research, reading and conducting research, including action research, and research resources on the Web.
No Child Left Behind legislation requires that states report test data in terms of their state academic standards. Educators must be knowledgeable of their state's standards so that they can plan instruction accordingly and then use the results of testing to inform their planning.
However, the problem educators face with standards is that there are so many of them, making it nearly impossible to address all within a school year, and not all are tested on accountability tests. Popham (2006a) addresses the need for measuring fewer curricular targets on state accountability tests, and notes that Kansas and Wyoming are examples of states making "courageous efforts to reduce state-assessed curricular aims to a manageable number" (p. 88).
Educators might monitor state-level tests in an attempt to determine what standards a test has actually been addressing over the past few years, and select content for instruction based on that decision. This latter may or may not work, as the next test might include questions on standards not taught.
Using such accountability results as a diagnostic of student strengths and weaknesses to inform instruction is also problematic. Reports accompanying test results often include breakdowns of student performance within identified subcategories. While these might be indicators for instructional planning, they should be used cautiously. According to Popham (2006b), the limited number of questions used on tests that fall within particular categories cannot truly indicate if a student "(1) possesses a key cognitive skill, or (2) has mastered a particular body of knowledge" (p. 90).
These databases provide benchmarks, information about school performance, and No Child Left Behind:
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Need to revisit your math standards?
HOT: June 2, 2010. The National Governors Association Center for Best Practices and the Council of Chief State School Officers released the final form for a set of state-led education standards for K-12 English-language arts and mathematics, the Common Core State Standards. Read the key points for mathematics at http://corestandards.org/about-the-standards/key-points-in-mathematics and the full set of standards for mathematics at http://www.corestandards.org/Math.
HOT! In response to the call for a more coherent curriculum, the National Council of Teachers of Mathematics developed Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. This document identifies three important topics for mathematics at each grade level preK-8 and has been integral in the revision of many state math standards (NCTM, 2006). Focus in High School Mathematics: Reasoning and Sense Making (NCTM, 2009) addresses mathematics education in high school.
Learn about standards for the National Assessment of Educational Progress (NAEP) at the U.S. Department of Education Institute of Education Sciences. Readers should consider, however, that the NAEP is not considered a high stakes test. Gerald Bracey (2009) reported on characteristics that make it a poor accountability tool. For example, no student ever takes the entire test, nor do districts, schools, or individual students find out how they performed. Thus, students might not take NAEP as seriously as they would the ACT or SAT or their state high stakes tests (p. 33).
Programme for International Student Assessment (PISA) from the Organisation for Economic Co-Operation and Development surveys "15-year-olds in the principal industrialised countries. Every three years, it assesses how far students near the end of compulsory education have acquired some of the knowledge and skills essential for full participation in society." The U.S. is among participating countries. PISA assesses reading, mathematics, and science. Gerald Bracey (2009) also noted that PISA is not a high stakes test and points out flaws in using results as a measure of the quality of U.S. schools. Chief among those is comparing results of a nation with a diverse population of over 300-million people to results of small "homogeneous city-states like Hong Kong and Singapore." Formal schooling differs among nations as to when students start school, policies differ in relation to repeating grades, and schools might not be serving the entire population, particularly those from low-income families. The design of test items also fall into question when one considers difficulty in translating questions into several languages, and keeping those questions free of culture bias (p. 34).
Conclusions on the state of state standards differ, as the following reports from the Fordham Foundation and Education Week illustrate.
The Thomas B. Fordham Foundation, based in Washington, DC, supports research, publications, and action projects of national significance in elementary and secondary education reform, as well as significant education reform projects in Dayton, Ohio and vicinity. It is associated with the Manhattan Institute for Policy Research. In The State of State Math Standards 2005, David Klein reports that only three states received "A" and five states "B" grades on their state math standards. Nine problem areas for which states come up short are addressed. Major findings:
There is an overemphasis on calculator use. Klein, while acknowledging the positive role that calculators can play in school mathematics with proper guidance and restrictions, states for elementary students, "the main goal of math education is to get them to think about numbers and to learn arithmetic. Calculators defeat that purpose" (p. 10).
There is decreased emphasis on memorization of "basic facts" in many states. According to Klein, "Students who do not memorize the basic number facts will founder as more complex operations are required, and their progress will likely grind to a halt by the end of elementary school" (p. 10).
"Only a minority of states explicitly require knowledge of the standard algorithms of arithmetic for addition, subtraction, multiplication, and division" (p. 10). Being able to use the standard algorithms and understand how and why they work is a foundational skill for elementary students.
Too little attention is paid to fraction development "in the late elementary and early middle grades; and there is not enough emphasis on paper-and-pencil calculations." At the high school level "much more attention is needed in the arithmetic of rational functions. Many state standards would also benefit from greater emphasis on completing the square of quadratic polynomials, including a derivation of the quadratic formula, and applications to graphs of conic sections" (p. 11).
There is too great an emphasis on patterns across K-12 standards. "[A]ttention given to patterns is far out of balance with the actual importance of patterns in K-12 mathematics" (p. 11).
There was concern for an overuse of manipulatives in that students might come to depend on them and focus on the manipulatives more than on the math. "[M]any state standards recommend and even require the use of a dizzying array of manipulatives in counterproductive ways" (p. 11). Klein states that manipulatives are useful for introducing new concepts to elementary students, but, "In the higher grades, manipulatives can undermine important educational goals" (p. 11).
There is a tendency to overemphasize estimation at the expense of exact arithmetic calculations.
Concern was raised about probability and statistics study beginning in Kindergarten, and excessive data collection standards. "Statistics and probability requirements often crowd out important topics in algebra and geometry" (p. 11).
"[F]ew states offer standards that guide the development of problem-solving in a useful way. Likewise, mathematical reasoning should be an integral part of the content at all grade levels. Too many states fail to develop important prerequisites before introducing advanced topics such as calculus" (p. 11).
The report includes four suggestions for improvement in state math standards. Of most value, perhaps, is the suggestion that states borrow a complete set of high-quality math standards from a top-scoring state, such as California, Indiana, and Massachusetts. These latter were the three states that received an "A" grade for their "standards' clarity, content, and sound mathematical reasoning, and the absence of negative features" (p. 9), which were the criteria used to judge the math standards in states. Also states should use authors of standards documents who thoroughly understand mathematics. States should develop coherent arithmetic standards emphasizing both computational fluency (How about good ol' paper and pencil as your manipulative?) and conceptual understanding. Finally, states should avoid problems in mathematical development resulting from overuse of calculators and manipulatives, overemphasis of patterns and probability and statistics, and insufficient development of standard algorithms and fraction arithmetic (p. 25).
Fordham's review of state math standards is only one perspective and caution should be exercised in completely accepting or completing ignoring the results of their study. However, results give states relevant feedback to consider when policymakers, practitioners, and mathematicians meet to examine and revise standards, hopefully on a regular basis.
Readers might get an entirely different view of their state standards by examining reports from Education Week. For example, in its State Report Card, part of Quality Counts 2005, which takes a broader look at standards, Ohio was one of 12 states that earned A's in the category of standards and accountability for its "clear and specific standards in English, mathematics, and science for elementary, middle, and high schools" (sec: Ohio Report Card, par. 1). Compare this to Fordham's rating of "D" for Ohio's math standards, and Klein's statement in their report (2005) that "Ohio’s 2001 revision of its math standards turned out to be a dreadful mistake. There are serious deficiencies in these standards, including coverage of arithmetic and the algebra indicators" (p. 92).
Likewise, Education Week (2006) reports in its Quality Counts at 10: A Decade of Standards-Based Education that Ohio again earned a high mark (A-) "for policies related to standards and accountability. Ohio scores particularly well in the area of academic standards. Its standards for the four core subjects at nearly every grade span have been rated as clear, specific, and grounded in content by the American Federation of Teachers" (sec: Ohio's State Highlights, par. 2).
Concerned about assessment and accountability?
Read what the National Education Association has to say about Assessment and Accountability for Improving Schools and Learning: http://www.nea.org/home/12627.htm
Web sites listed below provide additional information on professional math standards, teaching standards, implementing standards, and standards-based instructional materials.
Achieve, Inc.: http://www.achieve.org One of the missions of Achieve, Inc. is to serve as a national clearinghouse of state standards and school improvements. See Achieve's State Profiles for what your state is doing to improve achievement. Achieve also has benchmarks for math in their K-12 Expectations. Achieve's American Diploma Project Assessment Consortium posted practice tests and released test items from recent end of course exams for Algebra I and Algebra II.
AOL@SCHOOL: http://www.aolatschool.com/message AOL has made its content available on other sites:
Awesome Library: http://www.awesomelibrary.org/ has organized the Web with 17,000 carefully reviewed resources, including the top 5 percent in education.
Blue Web'N: http://www.kn.pacbell.com/wired/bluewebn/ Pacific Bell's library of blue ribbon learning sites on the web.
ENC Learning (formerly Eisenhower National Clearinghouse) (K-12 math and science): http://www.goenc.com/ Now subscription based, including individual memberships.
The K-12 Mathematics Curriculum Center: http://www2.edc.org/mcc/ is funded by the National Science Foundation to inform and assist schools and districts as they select and implement standards based mathematics curricula. They have also summarized 12 NSF-funded elementary, middle, and high school curricula approaches to standards-based mathematics instruction.
Michigan eLibrary:: http://www.mel.org/SPT--BrowseResourcesNewMeL.php The section called Michigan Online Resources for Educators contains over 500 Web sites of interest to math educators. Note that CT4ME is one of those math resources. Sites are organized by content subcategories and also include clearinghouses for math, math journals, math organizations, math history, and math curriculum and assessment resources.
Mid-continent Research for Education and Learning (McREL) Content Knowledge (4th ed.): http://www.mcrel.org/standards-benchmarks/ is a compendium of content standards and benchmarks for K-12 education in searchable and browsable formats. Activities, lesson plans, and other resources are included. McREL has organized the database from different subject areas into categories containing that essential content and includes grade-level intervals for when that content might be taught. Recommendations are research-based.
Note how McREL's compendium is valuable for mathematics: Robert Marzano of McREL (2003, p. 27) found that the 241 benchmark statements in the 2000 NCTM K-12 standards document (Principles and Standards for School Mathematics, pp. 392-402) actually contain 741 instructional concepts. Therefore, a sequence and organization of standards into essential content is necessary to ensure that students have adequate time to learn it, which is key to achievement.
See: Marzano, R. (2003). What works in schools: Translating research into action. Alexandria, VA: ASCD. ISBN: 0-87120-717-6.
MiddleWeb: http://www.middleweb.com/ receives support from the Clark Foundation's Program for Student Achievement and Office of Communication and provides links, resources, and original reporting to individuals interested in urban middle school reform and raising student achievement. It offers a focus on classroom assessment, academic standards, and performance-based teaching. Subject matter resources, including mathematics, are provided. Of particular value is access to the complete online book by A.C. Lewis, Figuring It Out: Standards-based Reforms in Urban Middle Grades.
National Board for Professional Teaching Standards: http://www.nbpts.org includes five core propositions that outline what the National Board values and believes should be honored in teaching. The NBPTS Standards detail what constitutes accomplished teaching in every subject and for students at all stages of their development. National Board Certification® is addressed.
National Center for Research on Evaluation, Standards, and Student Testing (CRESST): http://www.cse.ucla.edu/ conducts research on K-12 educational testing. Site contains reports, policy briefs, newsletters, assessments, rubrics, and products, for example. There is a section where users can "ask the expert" any questions regarding assessment and educational reform.
National Council for Accreditation of Teacher Education (NCATE): http://www.ncate.org/ NCATE has program standards in 20 different disciplines and includes relevant documents and links to the discipline's Web site.
National Educational Technology Standards Project (NETS): http://www.iste.org/AM/Template.cfm?Section=NETS has identified technology standards for students and teachers. This ongoing initiative of the International Society for Technology in Education and its partners and co-sponsors links technology with curriculum and standards. A searchable database of lessons and activities is included for major content areas in grades preK-12.
Ohio Resource Center for Mathematics, Science, and Reading: http://www.ohiorc.org/ improves teaching and learning by promoting best practices based upon the national and state standards in mathematics, science, and reading for Ohio schools and universities. Math resources, for example, can be browsed by topic or grade level. Professional development resources address instruction, content, assessment, general education, and acquisition of professional knowledge. Although geared toward Ohio educators, this site has peer-reviewed resources of value to educators nationwide.
Pacific Research.Org: http://www.pacificresearch.org/ conducts research in five areas: business and economics, education, environment, health care, and technology. In terms of its education studies, "Through research and grassroots outreach, EDS advances parental choice in education, high academic standards and accountability, charter schools, teacher quality, and school finance reform." Several of its publications are available online.
PBS Teachers: http://www.pbs.org/teachers/ "provide thousands of lesson plans, teaching activities, on-demand video assets, and interactive games and simulations. These resources are correlated to state and national educational standards and are tied to PBS' award-winning on-air and online programming like NOVA, Nature, Cyberchase, Between the Lions and more." Subject areas include arts and literature, health and fitness, mathematics, social studies, science and technology. Grade levels include prek-12.
Principles and Standards for School Mathematics: http://standards.nctm.org/ by the National Council of Teachers of Mathematics is online along with a host of e-resources and interactive activities that support standards. An overview of preK-12 principles and standards is available. Curriculum Focal Points (NCTM, 2006) expands on the document with the most important math topics for each grade level preK-8. Focus in High School Mathematics: Reasoning and Sense Making (NCTM, 2009) addresses mathematics education in high school.
Professional Standards for Teaching Mathematics by the National Council of Teacher of Mathematics: http://standards.nctm.org/ [access with your membership].
For example, Standard 4: Tools for Enhancing Discourse
The teacher of mathematics, in order to enhance discourse, should encourage and accept the use of:
computers, calculators, and other technology
concrete materials used as models
pictures, diagrams, tables, and graphs
invented and conventional terms and symbols
metaphors, analogies, and stories
written hypotheses, explanations and arguments
oral presentations and dramatizations
Thinkfinity: http://thinkfinity.org/ This is "the Verizon Foundation’s free online professional learning community, providing access to over 50,000 educators and experts in curriculum enhancement, along with thousands of award-winning digital resources for K-12 — aligned to state standards and the common core."
In Getting Our NETS Worth: The Role of ISTE's National Educational Technology Standards, M.D. Roblyer (2003) noted that the dissent of those who oppose student standards stems from three different perspectives:
Standards as Beginnings vs. Endings. Standards should be viewed as guidelines or benchmarks for performance. The problem is when standards turn into standardization, forcing educators to put children into a "one size fits all curriculum," which is unrealistic and self-defeating.
Authentic Standards vs. the Evil Twin: High Stakes Testing. High stakes testing has caused curriculum to become test-driven in many states.
Testing vs. Accountability Systems. There is a difference between standards-based testing and the use of test results to inform decisions regarding students, teachers, policies, and funding. The problem might not be testing, but rather the accountability system that upsets people. Such systems should have positive, formative effects and not negative, punitive ones.
AlfieKohn: http://www.alfiekohn.org/index.html Kohn is one of the most vocal opponents of the standards movement. The site contains strategies for coping with standards, and ways to develop organized opposition to standards. Numerous articles are included.
Mathematically Correct: http://www.mathematicallycorrect.com is devoted to concerns raised by parents and scientists around the country about reforms in mathematics education and the need to restore a focus on basic skills. Several articles are provided, along with a host of webs of interest.
National Center for Fair & Open Testing (FairTest): http://www.fairtest.org/k-12.htm is an advocacy organization working to end the abuses, misuses and flaws of standardized testing and ensure that evaluation of students is fair, open, and educationally sound. Broad concerns at K-12 include:
Standardized testing is harmful to children and to education;
Basing high stakes decisions on standardized tests is bad practice; and
There is need for implementation of authentic assessment as an alternative to standardized tests.
Pencils Down: http://www.pencilsdown.org T.H.E. Newsletter (September 13, 2001) reports that Gary Stager, an adjunct professor of education at Pepperdine University at the time, started this site in an effort to organize opposition to President Bush's drive for standardized testing. The site is promoted as "the meeting place for parents, educators and citizens concerned with the miseducation of children in the name of higher standardized test scores." Resources include web sites, articles, books, and more about standardized testing.
Bracey, G. (2009, November). The big tests: What ends do they serve? Educational Leadership, 67(3), 32-37.
Education Week. (2005, January). Quality counts 2005: No small change, Targeting money toward student performance. Education Week, 24(17). Retrieved from http://www.edweek.org/ew/toc/2005/01/06/index.html
Education Week. (2006, January). Quality counts at 10: A decade of standards-based education. Education Week, 25(17). Available: http://www.edweek.org/ew/toc/2006/01/05/index.html
Gayler, K., Chudowsky, N., Kober, N., Hamilton, M., & Yeager, M. (2004, August). State high school exit exams: A maturing reform. Washington, D.C.: Center on Education Policy. Available under section High School Exit Exams: http://www.cep-dc.org/
Klein, D. (2005, January). The state of state math standards 2005. Washington, D.C.: Thomas B. Fordham Foundation. Retrieved from http://www.edexcellence.net/publications/sosmath05.html
National Council of Teachers of Mathematics (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Reston, VA: Author. Retrieved from http://www.nctm.org/standards/content.aspx?id=270
National Council of Teachers of Mathematics (2009). Focus in High School Mathematics: Reasoning and Sense Making. Reston, VA: Author. Retrieved from http://www.nctm.org/standards/content.aspx?id=23749
Popham, J. (2006a, September). Content standards: The unindicted co-conspirator. Educational Leadership, 64(1), 87-88.
Popham, J. (2006b, October). Diagnostic assessment: A measurement mirage? Educational Leadership, 64(2), 90-91.
Roblyer, M. D. (2003, May). Getting Our NETS Worth: The Role of ISTE's National Educational Technology Standards. Learning & Leading with Technology, 30(8), 6-13.
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