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# K-12 Math Initiatives

This section on Math Initiatives will link you to projects around the country that seek to improve mathematics instruction by addressing standards and technology issues.

## Call for a Coherent Math Curriculum

In A Coherent Curriculum: The Case for Mathematics, William Schmidt, Richard Houang, and Leland Cogan (2002) defined "content standards and curricula to be coherent if they are articulated over time as a sequence of topics and performances that are logical and reflect, where appropriate, the sequential and hierarchical nature of the disciplinary content from which the subject matter derives" (p. 9).  In looking at the A+ composite for mathematics by topic and grade, data suggested three tiers (p. 6):

• Grades 1-4 includes emphasis on arithmetic, including common and decimal fractions, rounding, and estimation;
• Grades 5-6 are transitional, with continued emphasis on a few arithmetic topics, but also an introduction to topics such as percentages, negative numbers, integers and their properties, proportional concepts and problems, two-dimensional coordinate geometry, and geometric transformations;
• Grades 7-8 consists of topics such as number theory (including primes and factorization, exponents, roots, radicals, orders of magnitude, and rational numbers and their properties), algebra (including functions and slope), and geometry (including congruence and similarity, and 3-dimensional geometry).
• Continuity across all three tiers is provided by such continuing topics as measurement units (grades 1-7), and equations and formulas (grades 3-8).

On February 6, 2003, the U.S. Department of Education launched its Mathematics and Science Initiative, whose goals included to develop a major academic research base of what boosts student learning in mathematics and science, further engage the public, and enhance teacher knowledge.  Papers and Power Point presentations are archived from this Math Summit.  Of particular interest were presentations by W. Schmidt of Michigan State University, and G. Whitehurst, then Director of Institute of Education Sciences:

• Schmidt discussed the need for a coherent mathematics curriculum and pointed out the lack of consistency among U.S. states regarding when and how many concepts are introduced at grade levels in the U.S.  His Power Point slide #3 shows a "Coherent Curriculum in A+ Countries" for mathematics, which lists mathematics curriculum topics and when concepts are introduced in K-8; then slides 4 and 5 illustrate the varied introduction of concepts in different states.
• Whitehurst presented research on the effectiveness of practices and policies in mathematics education with respect to tracking, assessment, structured peer feedback, the Math Wars (constructivist approaches to learning mathematics vs. traditional direct instruction), the role of conceptual understanding, effectiveness of constructivist curricula vs. skills-based curricula, and alignment of the components of policy and practice.

### HOT NEWS!

HOT: September 12, 2006:  In response to the call for a more coherent curriculum, the National Council of Teachers of Mathematics released Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM, 2006a).  In its press release on September 12, 2006, NCTM indicated that this document identifies three important topics for mathematics at each grade level preK-8 and presents "a vision for the design of the next generation of state curriculum standards and state tests" (NCTM, 2006b, para. 3).

HOT:  March 13, 2008: The National Mathematics Advisory Panel, created by President George W. Bush in April 2006, released the results of its study to the President and U.S. Secretary of Education Margaret Spellings on the best use of scientifically based research to advance the teaching and learning of mathematics.  The report, Foundations for Success: Report of the National Mathematics Advisory Panel, contains 45 findings and recommendations for improving mathematics achievement for all U.S. students.  Its numerous topics include curricular content, learning processes, teachers and teacher education, instructional practices, instructional materials, assessments, and research policies and mechanisms.

Of particular relevance was the development of a list of major topics in school algebra (see p. 16) and the critical foundations in K-8 math education for algebra: whole numbers, fractions (including decimals, percents, and negative fractions), and aspects of geometry and measurement (see p. 17). "School algebra is a term chosen to encompass the full body of algebraic material that the Panel expects to be covered through high school, regardless of its organization into courses and levels. The Panel expects students to be able to proceed successfully at least through the content of Algebra II" (Executive Summary, p. xvii).

HOT:  June 1, 2009: Common Core State Standards Initiative: In its June 1 press release, the National Governors Association Center for Best Practices and the Council of Chief State School Officers (2009) announced that 49 states and territories joined the Common Core State Standards Initiative.  This initiative is "a state-led process to develop a common core of state standards in English-language arts and mathematics for grades K-12. These standards will be research and evidence-based, internationally benchmarked, aligned with college and work expectations and include rigorous content and skills" (para. 3).  See the standards at https://www.thecorestandards.org

HOT: October 6, 2009:  As a follow-up to its 2006 Curriculum Focal Points, NCTM released Focus in High School Mathematics: Reasoning and Sense Making, a "conceptual framework to guide the development of future publications and tools related to 9–12 mathematics curriculum and instruction."  It highlights reasoning opportunities in numbers and measurements, algebraic symbols, functions, geometry, statistics and probability (NCTM, 2009a).  In its press release NCTM stated that this book "suggests practical changes to the high school mathematics curriculum to refocus learning on reasoning and sense making. This shift is not a minor refinement but constitutes a substantial rethinking of the high school math curriculum" (NCTM, 2009b, para. 1).  Reasoning habits are organized into four broad categories: analyzing a problem, implementing a strategy, seeking and using connections, and reflecting on a solution (NCTM, 2009a, FAQs, p. 4).

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 shifts for mathematics.

HOT: November 9, 2011: The Partnership for Assessment of Readiness for College and Careers (PARCC) released its October 2011 Model Content Frameworks for Mathematics, Grades 3-11 to the public.

HOT: May 2012: From an announcement by Achieve.org, Common Core Math Standards Implementation Can Lead to Improved Student Achievement, we learn that "Dr. William Schmidt released key conclusions from his research detailing how the Common Core State Standards (CCSS) for mathematics can potentially improve the performance of U.S. students if implemented appropriately" (para. 1).  Dr. Schmidt's work was entitled: Common Core State Standards Math: The Relationship Between High Standards, Systemic Implementation and Student Achievement.  "Unlike previous research, Schmidt analyzed the link between states with standards that were similar to the CCSS and their NAEP [National Assessment of Educational Progress] math scores. He used cut scores aligned to NAEP as a proxy to determine if states were serious about high expectations and implementation of standards. The preliminary results showed states with standards in line with CCSS combined with higher cut scores also had higher NAEP scores" (para. 7).  A PowerPoint Presentation and video are available related to this research.

See the map showing the educational standards in your state.

## Math Initiatives

Achieve: Foundations for Success is also found on Issuu.com, as follows:

"To help states work toward the rigorous high school math goals set forth by the American Diploma Project, Achieve created a set of expectations that comprise the mathematical skills and knowledge that students will need to learn from kindergarten through 8th grade."  Foundations for Success, published in 2002, contains math expectations for the end of grade 8, which incorporates fundamentals that students are learning in top-performing countries.  It contains illustrative problems and sample solutions that focus on concepts, which are difficult to teach and need clarification.  Foundations for Success also notes topics for grades 1-5, and 9-11 in the appendices.

Alabama Math, Science, and Technology Initiative is the Alabama Department of Education’s initiative that began in 2002 to improve math and science teaching statewide.  Math is listed by K-8 grade level, and for algebra, geometry, and advanced math.  Read the results: Evaluation of the Effectiveness of the Alabama Math, Science, and Technology Initiative, released February 2012.  The study was conducted by the Institute of Education Sciences Regional Education Laboratory Southwest and focused on grades 4-8.

Assessment for Learning Project is valuable for all educators.  It is a "grant program and field-building initiative" of the Center for Innovation in Education, Next Generation Learning Challenges at Educause and design partner 2Revolutions.  Its goal is to invite educators to rethink the role of assessment in advancing student learning and improving K-12 education.  Learn more about performance assessment, formative assessment, capstone projects, portfolios, and exhibitions of learning, and community engaged success definitions.

Charles A. Dana Center at The University of Texas at Austin: Launch Years is a math initiative that is designed to support students for college preparation and to guide them though pathways for degree attainment.  The focus is on the junior year of high school through the junior year in college.  The developers "believe it is time to better align the mathematics courses and expectations from high school to post secondary education" (Creating a New Paridigm for Mathematics section).  Open access resources developed are made available to schools.

Common Core State Standards Initiative, as described in its FAQ was a joint effort by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) in partnership with Achieve, ACT and the College Board. Governors and state commissioners of education from across the country committed to joining a state-led process to develop a common core of state standards in English-language arts and mathematics for grades K-12. These standards are research and evidence-based, internationally benchmarked, aligned with college and work expectations and include rigorous content and skills. Read the full set of standards for K-12 mathematics at https://www.thecorestandards.org/Math/, which were released in their final form on June 2, 2010.  Educators might also appreciate the Common Core Toolkit, which includes resources for implementing the standards and the Common Core Video Series.

Consortium for Mathematics and Its Applications (COMAP) "is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world" (Who We Are section).  It provides math and modeling resources, including contests.

C-STEM (Computing, Science, Technology, Engineering, Mathematics) is an initiative of UCDavis, which promotes "Transforming Math Education Through Computing."  "By working with K-14 educators, the C-STEM Center integrates computer programming and robotics into teaching STEM subjects by creating project-based computing and robotics activities, integrated curriculum, and hands-on personalized and collaborative learning strategies aligned with Common Core State Standards (CCSS) and Career and Technical Education (CTE) Standards. This integration helps students make meaningful connections between regular STEM topics and their relevance to real-life applications as well as help develop students’ critical thinking and problem-solving skills" (About Us section).  Further, the curricula for elementary, middle, and high school learners within the C-STEM Math-ICT Pathway provide "hands-on integrated learning of math and computer science with coding in Blockly and C/C++."  The C-STEM Center also developed "teaching strategies, textbooks, and courseware including lesson plans, PowerPoint lessons, video lessons, group computing activities, optional robotic activities, and assessment tools" (Curriculum section). The programs C-STEM Studio and RoboBlockly are free downloads and include video tutorials.

Development and Research in Early Mathematics Education (DREME) is an initiative of Stanford University that promotes early math development in children from birth to age 8, with an emphasis on preschool years (About section).  There are resources for family math, teachers, teacher educators, and preK-3 alignment.

EdReports.org is an independent, non-profit launched in winter 2014.  It provides free reports on K-12 instructional materials to help in the adoption process.  There are over 100 reports for math.  The reviewers rely on three "gateways" that address the questions:

1. "Are the instructional materials aligned to the standards?"
2. "Are all standards present and treated with appropriate depth and quality required to support student learning?"
3. "Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom." (Review Tools section, Advancing Through Gateways)

HOT!: Global Math Project, hosted by the American Institute of Mathematics, is a "is a worldwide movement of teachers committed to igniting and sustaining a love of mathematics in their students." Its programs include "an ever-growing collection of curriculum-aligned mathematics lessons for you to explore with your wonderful mathematics learners."  Get excited with resources in James Tanton's Exploding Dots.

Idaho Math Initiative from the Idaho Department of Education focuses on improving math education in all grades to ensure every student is prepared for higher levels of math in the middle grades, high school, post-secondary, and work-force setting. The Idaho Math Initiative offers professional development for teachers, assessment tools for all grades and research-based intervention programs for students.

Illustrative Mathematics was founded in 2011 at the University of Arizona.  Since then the project has yielded "a comprehensive suite of math curricula, designed to encourage engaging mathematical discussion, supported by tasks, lesson plans, and professional learning."  Tasks align with the Common Core State Standards for Mathematics.  Illustrative tasks are available for the K-8 and High School standards.  The project is an initiative of the Institute for Mathematics and Education at the University of Arizona and the Bill & Melinda Gates Foundation.

HOT!: Inside Mathematics at The Dana Center, University of Texas, grew out of the Noyce Foundation's Silicon Valley Mathematics Initiative.  It is exemplary as a professional resource for educators "passionate about improving students' mathematics learning and performance." This site features multiple tools for educators such as non-routine math problems organized by five levels of difficulty, formative re-engaging lessons, performance assessment tasks aligned to the Common Core standards (grades 2-8, algebra 1, geometry, and algebra 2), classroom videos of innovative teaching methods and insights into student learning, and social and emotional resources for math classrooms. Inside Mathematics also has a section devoted to Common Core Resources with videos, tasks, and problems aligned to each math standard in K-8 and high school organized by strands.

National Math and Science Initiative (NMSI): This initiative's mission is to improve student performance in the critical subjects of science, technology, engineering and math (STEM).  The NMSI approach involves "training teachers in grades 3-12 to inspire students to succeed in rigorous math and science courses and by recruiting and preparing more college students to become dedicated math and science teachers" (About NMSI section).  You'll also find free lessons and Common Core Open Resources within its Resource section.

National Science Foundation Standards-based Curriculum Projects are located at four centers:

HOT!: New Jersey Center for Teaching and Learning: Progressive Mathematics Initiative and Progressive Science Initiative "includes not only course materials, but also innovative and effective recommendations for curriculum, teacher methods, environment, scheduling, policies and practices" (What is PSI-PMI? section).  Its K-12 STEM resources are free.  Mathematics course materials at the elementary K-8 level are posted by grade level and also include accelerated materials for grade 7 and algebra 1 at grade 8.  High school courses include algebra I and II, geometry, pre-calculus, AP Calculus at AB and BC levels, and Integrated Math levels I, II, and III.  They are also available in Spanish.  You'll find presentations, homework assignments, lab activities, and assessments in unit resources, as appropriate for each course.  Each course is designed for use with interactive whiteboards and polling devices.

Open Up Resources began as the K-12 OER Collaborative.  It is creating comprehensive, high-quality, open educational resources (OER) supporting Mathematics and English Language Arts aligned with standards.  The Middle School Math program is problem-based and promoted as sparking student engagement.

Smarter Balanced Assessment Consortium (SBAC) is a state-led consortium working to develop assessments associated with the Common Core State Standards.

TERC is a not-for-profit education research and development organization in Cambridge (MA), whose mission is to improve mathematics, science, and technology teaching and learning.  Work includes "research, curriculum and technology development, and implementation support in the form of professional development and assistance to districts and schools."

Understanding Language: Supporting ELLs in Mathematics is an initiative at Stanford University to develop materials that illustrate how Common Core aligned math tasks can be used to support math instruction and language development for English language learners in elementary, middle, and high school. You'll find adapted tasks from the publicly accessible curriculum projects Inside Mathematics and the Mathematics Assessment Project, principles for teaching mathematics to ELLs, and "Language of Math" Task Templates that can be used by teachers to design and write their own language-focused activities, and more.

University of Massachusetts-Dartmouth's James J. Kaput Center for Research and Innovation in STEM Education researches fundamental issues in STEM education.  Among its completed projects is SimCalc MathWorlds software for TI-graphing calculators, computers, and the TI-Navigator.

U.S. Department of Education's Raise the Bar: STEM Excellence for All Students is a Biden-Harris administration initiative.  It is "designed to strengthen Science, Technology, Engineering and Mathematics (STEM) education nationwide" for learners in preK through higher education regardless of background.  Numerous STEM resources are provided, including grant opportunities.

WestEd Early Math Initiative (EMI) per its description is a "national initiative to help federal and state-funded preschool programs enhance mathematical development and learning in young children."  Primary goals of the EMI include "1) to scale the implementation of the Pre-K Mathematics Curriculum nationally and 2) to develop regional training networks to assist programs with their implementation through a sustainable continuous improvement plan."

#### References

National Council of Teachers of Mathematics. (2006a). 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. (2006b, September 12). NCTM Releases Curriculum Focal Points to Focus Math Curricula. Reston, VA: NCTM News Release.  https://web.archive.org/web/20170224130843/https://www.nctm.org/News-and-Calendar/News/NCTM-News-Releases/NCTM-Releases-Curriculum-Focal-Points-to-Focus-Math-Curricula/

National Council of Teachers of Mathematics. (2009a). Focus in high school mathematics: Reasoning and sense making.  Reston, VA: Author.  https://www.nctm.org/Standards-and-Positions/Focus-in-High-School-Mathematics/

National Council of Teachers of Mathematics. (2009b, October 6). NCTM Releases new landmark publication: Focus in High School Mathematics: Reasoning and Sense Making. Reston, VA: NCTM News Release.  https://web.archive.org/web/20230320133153/https://www.nctm.org/News-and-Calendar/News/NCTM-News-Releases/NCTM-Releases-New-Landmark-Publication_-Focus-in-High-School-Mathematics/

National Governors Association and Council of Chief State School Officers. (2009, June 1). Forty-nine states and territories join common core state standards initiative.  Washington, DC: NGA Press Release.  https://web.archive.org/web/20160801130149/http://www.nga.org:80/cms/home/news-room/news-releases/page_2009/col2-content/main-content-list/forty-nine-states-and-territorie.html

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel.  Washington, DC: U.S. Department of Education. https://files.eric.ed.gov/fulltext/ED500486.pdf

Schmidt, W., Houang, R., & Cogan, L. (2002, Summer).  A coherent curriculum: The case for mathematics. American Educator, 1-17. Reprint available at https://www.nifdi.org/research/journal-of-di/volume-4-no-1-winter-2004/454-a-coherent-curriculum-the-case-of-mathematics/file.html