**Math Topics**- Common Core
- Initiatives
- Methodology
- Resources
- Projects
- Manipulatives
- Software

**Learning Support**- Standardized Test Prep
- Technology Integration
- Assisting Readers

The Best Related Resources

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

Education Research 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 required 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).

American Education Reaches Out (Project AERO) has academic standards in mathematics, social studies, science, English language arts, and technology for American schools overseas. These are based on a condensed compilation of national standards identified by the Council for Basic Education.

Common Core State Standards Initiative for English language arts and Mathematics. The standards for mathematics are organized by grade level for Grades K-8. The high school math standards are organized by strand. Note: Educators might also appreciate the Common Core Toolkit, which includes resources for implementing the standards and a Common Core Video Series.

Domains within the Common Core
Math Standards |
|||||||||

K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | HS |

Counting & Cardinality | |||||||||

Number & Operations in Base 10 | Ratios & Proportional Relationships | Number & Quantity | |||||||

Number & Operations-Fractions | The Number System | Algebra | |||||||

Operations & Algebraic Thinking | Expressions & Equations | Algebra | |||||||

Operations & Algebraic Thinking | Functions | Functions | |||||||

Geometry | Geometry | ||||||||

Measurement & Data | Statistics & Probability | Statistics & Probability | |||||||

Source: Common Core State Standards. (2010). Mathematics Standards. Washington, DC: National Governors
Association Center for Best Practices, Council of Chief State School Officers.
https://learning.ccsso.org/common-core-state-standards-initiative |

These databases provide benchmarks, information about school performance:

- The Education Trust
- GreatSchools
- Council of Chief State School Officers (CCSSO)
- Education Commission of the States

**
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.

**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 dating back to 2005 from the Fordham Institute and Education Week illustrate. However, even with rise of a new era of Common Core Standards in 2010, controversy remains.

The Thomas B. Fordham Institute, 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 reported 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 included 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" (Ohio Report Card section, 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) reported 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" (Ohio's State Highlights section, para. 2).

The Common Core Standards Initiative ushered in a new era on state standards for math and English language arts in 2010. The CCSS have become controversial.

**HOT**: **September 1, 2014**:

The Education Commission of the States released its report on the Common
Core Standards,
States and the (not so) new standards — where are they now?
by Tonette Salazar and Kathy Christie. "This brief provides a sampling of
state legislative activity and executive branch action around the CCSS through Sept. 1, 2014. It is not intended to
be an exhaustive list; rather, it is narrowly focused on the single issue of
state affirmation, modification or replacement of the Common Core" (para.
2). Within the Appendix are state names for Common Core Standards.

**HOT**: **November 13, 2017**:
Achieve, Inc. released a report,
Strong
Standards: A Review of Changes to State Standards Since the Common Core.
Twenty-four of the 45 states and the District of Columbia that adopted
the CCSS in 2010 have revised their English Language Arts and Math
standards, largely due to political influences or "associated opposition
to testing and accountability policies" (p. 2). Further, "across
the country and with very few exceptions, the quality of state standards
is significantly higher now than prior to the development of the Common
Core" (p. 3). Per Achieve, "The report found that most
states kept their standards rigorous and maintained college- and
career-ready expectations for students."

**September 5, 2018**: Since 2010,
state math standards have improved in four ways per David
Griffith (2018) of the Fordham Institute with "much of that improvement
due to the Common Core math standards" (para. 1). Those ways
include:

- Stronger focus on arithmetic in grades K-5;
- More coherent treatment of proportionality and linearity in middle school;
- Appropriate balance between conceptual understanding, procedural fluency, and application;
- Better organization and teacher supports.

Keep up with NEA news on Common Core State Standards: https://www.nea.org/professional-excellence/student-engagement/tools-tips/common-core-101 NEA's position on the CCSS is: "NEA believes the Common Core State Standards have the potential to provide all childen access to a complete and challenging education" (NEA, 2013, p. 3). However, in a letter to NEA members in 2014, then NEA President, Dennis Van Roekel, voiced concerns about implementation of the standards, indicating that "in far too many states, implementation has been completely botched" (para. 6). He provided advice to policy makers on what to do to make the standards work.

See the
Frequently Asked Questions about the CCSS. In answering *Why is the sequence
of key math topics in the math standards important?,* you'll find:
"The mathematical progressions, or sequencing of topics, presented in the
Common Core State Standards are coherent and based on evidence. Part
of the problem with having many different sets of state standards
was that different states covered different topics at different
grade levels. Coming to a consensus on the standards guarantees
that, from the viewpoint of any given state, topics will move up or
down in a consistent grade level sequence. What is important
to keep in mind is that the progression in the Common Core is
mathematically coherent and leads to college and career readiness at
an internationally competitive level." (FAQ, p. 7)

Web sites listed below provide additional information on professional math standards, teaching standards, implementing standards, and standards-based instructional materials.

Awesome Library has organized the Web with 37,000 carefully reviewed resources.

International Society for Technology in Education (ISTE) Standards has identified technology standards for students, educators, administrators, coaches, and computer science educators.

The K-12 Mathematics Curriculum Center "was funded by the National Science Foundation to inform and assist schools and districts as they select and implement standards based mathematics curricula." The Center was a project at Education Development Center from 1997 to 2007. Publications and research are available.

Mid-continent Research for Education and Learning (McREL) Content Knowledge 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. Common Core is included.

Note how McREL's compendium is valuable for mathematics: Robert Marzano (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 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.

National Board for Professional Teaching Standards 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) "conducts research on assessment, evaluation, methodology, and technology to improve learning and outcomes." Multiple publications, games, and simulations are available. You can also sign-up for its newsletter.

PBS LearningMedia includes resources for preK-13+ math searchable by grade level and standards. Narrow a search with media type and subject.

Principles and Standards for School Mathematics 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 is by the National Council of Teacher of Mathematics: [access with your membership] or see https://www.nctm.org/store/Products/Professional-Standards-for-Teaching-Mathematics/

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

*
*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: 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.

National Center for Fair & Open Testing (FairTest) 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.

Bracey, G. (2009, November). The big tests: What ends do they serve?
*Educational Leadership, 67*(3), 32-37.
https://www.ascd.org/el/articles/the-big-tests-what-ends-do-they-serve

Education Week. (2005, January). Quality counts 2005: No small change,
Targeting money toward student performance. *Education Week, 24*(17).
https://www.edweek.org/policy-politics/quality-counts-2005-no-small-change

Education Week. (2006, January). Quality counts at 10: A decade of
standards-based education. *Education Week, 25*(17).
https://www.edweek.org/teaching-learning/quality-counts-2006-a-decade-of-standards-based-education

Griffith, D. (2018, September 5). Four ways state math standards have improved [Commentary]. https://fordhaminstitute.org/national/commentary/four-ways-state-math-standards-have-improved

Klein, D. (2005, January). *The state of state math standards 2005*.
Washington, DC: Thomas B. Fordham Institute.
https://fordhaminstitute.org/national/research/state-state-math-standards-2005

National Council of Teachers of Mathematics. (2006). *Curriculum focal points
for prekindergarten through grade 8 mathematics: A quest for coherence*.
Reston, VA: Author.
https://www.nctm.org/store/Products/Curriculum-Focal-Points-for-Prekindergarten-through-Grade-8-Mathematics-A-Quest-for-Coherence/

National Council of Teachers of Mathematics. (2009). *Focus in high school
mathematics: reasoning and sense making*. Reston, VA: Author.
https://www.nctm.org/store/Products/Focus-in-High-School-Mathematics--Reasoning-and-Sense-Making/

National Education Association. (2013). NEA Common Core State Standards Toolkit. http://www.smmcta.com/uploads/9/9/4/2/9942134/common_core_toolkit_nea.pdf

Popham, J. (2006a, September). All about accountability/ Content standards: The unindicted co-conspirator.
*Educational Leadership, 64*(1), 87-88.
https://www.ascd.org/el/articles/content-standards-the-unindicted-co-conspirator

Popham, J. (2006b, October). All about accountability/ Diagnostic assessment: A measurement mirage?* Educational
Leadership, 64*(2), 90-91.
https://www.ascd.org/el/articles/diagnostic-assessment-a-measurement-mirage

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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