Math Initiatives

Call for a Coherent Math Curriculum

On February 6, 2003, the U.S. Department of Education launched its new Mathematics and Science Initiative, whose goals include 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 available at http://www.ed.gov/inits/mathscience/summit.html Of particular interest were presentations by W. Schmidt of the University of Michigan, and G. Whitehurst, 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. Readers will be interested in his Power Point slide #3 which shows a "Coherent Curriculum in A+ Countries" for mathematics (excellent visual listing mathematics curriculum strands and when concepts are introduced) and then slides 4 and 5 regarding 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. Readers short on time should at least read his summary, "Putting It all Together." There is an extensive reference list on research in mathematics education, which was used to prepare the presentation.

• 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).

HOT NEWS:  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).

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Initiatives

Achieve's Preparing Students for Success in High School Math: http://www.achieve.org/node/300.  "To help states work toward the rigorous high school math goals set forth by the American Diploma Project, Achieve has created a set of expectations that comprise the mathematical skills and knowledge that students will need to learn from kindergarten through 8th grade."  The American Diploma Project involves a network of 22 states.   Foundations for Success (Consultation draft) , 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.  The consultation draft of Foundations for Success also notes topics for grades 1-5, and 9-11 in the appendices.

IMAGES: Improving Measurement and Geometry in Elementary Schools: http://images.rbs.org/   is an initiative of the Pennsylvania State Team of the Mid-Atlantic Eisenhower Consortium for Mathematics and Science Education at Research for Better Schools.  This web site contains information and resources that are designed to help teachers develop a deeper understanding of geometry and measurement concepts and to assist in designing meaningful instruction for elementary students.

Middle School Mathematics through Applications Project (MMAP): http://mmap.wested.org/  is an technology-rich, standards-based, comprehensive curriculum developed with funding from the NSF. It has been designated "promising" as a mathematics program and as a technology program by the US Department of Education.  Read more about this project-based approach to teaching mathematics and its effectiveness at http://www.ed.gov/pubs/edtechprograms/mmap.html . This curriculum, modified for commercial publication, has been published as Pathways to Algebra and Geometry.  Typically, students solve open-ended design problems. 

National Math and Science Initiative: http://www.nationalmathandscience.org/ This initiative is sponsored by ExxonMobile and will begin with two phases: Uteach (http://www.uteach.utexas.edu/) to recruit and prepare more math, science and computer science majors for careers in secondary teaching and Advanced Placement (AP) Strategies (http://www.apstrategies.org/).

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

• The K-12 Mathematics Curriculum Center: http://www2.edc.org/mcc/  has summarized 12 NSF-sponsored curricula approaches to standards-based mathematics instruction, updated in an eighth edition in September, 2005 (See Curriculum Summaries).  The 12 curricula are listed below.

• The ARC Center: http://www.comap.com/elementary/projects/arc/  is a collaboration between the Consortium for Mathematics and Its Applications (COMAP) and the three National Science Foundation supported elementary mathematics curriculum projects:

  • Investigations in Number, Data, and Space (K-5)

  • Everyday Mathematics (K-6)

  • Math Trailblazers (K-5)

• The Show-Me Center: http://showmecenter.missouri.edu/ supports standards-based middle grades mathematics curricula, including:

  • Connected Math (6-8) [see Michigan State University: http://connectedmath.msu.edu/]

  • Math in Context (5-8)

  • MathScape (6-8) [see http://www2.edc.org/mathscape/]

  • MathThematics (6-8)

• COMPASS (Curricular Options in Mathematics Programs for all Secondary Students): http://www.ithaca.edu/compass/  and its satellite sites provides information and assistance for implementation of five secondary curriculum projects that support NCTM standards:

  • Mathematics: Modeling Our World, Application Reform in Secondary Education (ARISE) (9-12)

  • Contemporary Mathematics in Context, Core-Plus Mathematics Project (CPMP) (9-12)

  • Interactive Mathematics Program (IMP) (9-12)

  • MATH Connections: A Secondary Mathematics Core Curriculum, MATHConx, LLC (9-11)

  • Integrated Mathematics: A Modeling Approach Using Technology: Systemic Initiative for Montana Mathematics and Science Project (SIMMS) (9-12)

Project 2061 is the long-term initiative of the American Association for the Advancement of Science to reform K-12 science, mathematics, and technology education nationwide. School districts will be most interested in the evaluation of middle school mathematics and science textbooks from leading publishers, which is available online.  The analysis is based on project standards and reveals the best texts for learning mathematics.  Read Benchmarks Online and associated research, and Blueprints for Reform, an examination of 12 aspects of a K-12 system.  These aspects are grouped into three parts: Foundation, School Context, and Support Structure.  Join the dialogue.

SIMMS Integrated Mathematics curriculum is a complete NCTM Standards-based mathematics curriculum for all students which incorporates a modeling approach using technology and involves real world contexts.  The SIMMS Project from the University of Montana at Bozeman: http://www.montana.edu/wwwsimms/ has been discussed in NCTM's Mathematics Teacher and ENC's Focus Magazine, and is one of the NSF funded projects.

Success for All Foundation (SFAF): http://www.successforall.net/  SFAF is a comprehensive school restructuring program for elementary schools in reading, writing, mathematics, and social studies.  It's mission is to raise achievement of students in those areas.  The curriculum can be found in about 1800 elementary schools in 48 states.  A middle school pilot project is also underway.

TERC: http://www.terc.edu/index.html 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."

University of Massachusetts-Dartmouth's James J. Kaput Center for Research and Innovation in Mathematics Education: http://www.kaputcenter.umassd.edu/ has an ongoing math initiative called SimCalc MathWorlds for TI-graphing calculators, computers, and the TI-Navigator.  The center also researches foundational issues in math education.

References:

National Council of Teachers of Mathematics (2006a). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence.  Reston, VA: Author.  Available: http://www.nctm.org/standards/content.aspx?id=270 

National Council of Teachers of Mathematics (2006b, September 12). NCTM Releases Curriculum Focal Points to Focus Math Curricula. Reston, VA: NCTM News Release.  Available: http://www.nctm.org/news/content.aspx?id=686

National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel.  Washington, DC: U.S. Department of Education. Available: http://www.ed.gov/about/bdscomm/list/mathpanel/index.html

Schmidt, W., Houang, R., & Cogan, L. (2002, Summer).  A coherent curriculum: The case for mathematics. American Educator, 1-17.  Available: http://www.aft.org/pubs-reports/american_educator/summer2002/curriculum.pdf 

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Deubel, P. (fill in year from last revised). Math initiatives [Online]. Retrieved [fill in date] from Computing Technology for Math Excellence at http://www.ct4me.net/math_initiatives.htm