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Modernizing Curriculum and Instruction: The Case of Mathematics in the United States

Modernizing Curriculum and Instruction: The Case of Mathematics in the United States



by Joan Ferrini-Mundy

by Joan Ferrini-Mundy



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Modernizing Curriculum and Instruction: The Case of Mathematics in the United States Modernizing Curriculum and Instruction: The Case of Mathematics in the United States Presentation Transcript

  • Modernizing Curriculum and Instruction: The Case of Mathematics in the United States Joan Ferrini-Mundy Director, Division of Research on Learning in Formal and Informal Settings US National Science Foundation Panel presentation, New Skills for a Global Innovation Society: Asia-Pacific Forum on Secondary Education, March 25, 2007
  • US National Science Foundation
    • Imagining the future, working at the frontier, realizing the full potential of people, furthering promising ideas wherever and whenever they arise, and encouraging creativity and initiative.
    • A US federal agency that makes
    • grants to universities and other
    • organizations, based on merit
    • review of proposals, for research
    • in science and education.
  • Overview
    • Context and recent history of US K-12 mathematics curriculum
    • Key findings from National Mathematics Advisory Panel
    • Continuing issues in secondary mathematics education in the US
  • Mathematics Curriculum in the US:
    • Curriculum is the responsibility of the states
    • No central or national curriculum or high-stakes assessment
    • All states required by federal law (No Child Left Behind) to assess students in mathematics each year, grades 3-8, and in at least one grade 10-12
    • All states have grade-level curriculum standards in mathematics
    • Professional societies (e.g., National Council of Teachers of Mathematics) provide standards documents periodically to express what students should know and be able to do
  • A Compressed Chronology of US Mathematics Education in the Past Two Decades
    • 1989: NCTM produced Curriculum and Evaluation Standards for School Mathematics
      • Response to concerns about focus on “shopkeeper arithmetic”, emphasis on rote procedures, paper-and-pencil drill, and lack of application, together with research about learning pointing to need for student engagement and activity
  • Compressed Chronology, 1989 - 2000 :
    • Some state standards, textbooks, and teachers began to incorporate ideas of NCTM standards: more small group work, active learning, “real world” problems, student discovery and exploration
    • National Science Foundation funded curriculum development projects that followed NCTM standards
    • TIMSS 1995 results characterized US mathematics and science curriculum as “mile wide, inch deep”
  • Compressed Chronology, 2000-2008:
    • 2000: NCTM produces Principles and Standards for School Mathematics
    • emphasis on coherence across the grades
    • focus on developing mathematical content by grade band (preK-2, 3-5, 6-8, 9-12)
    • detailed examples for teachers about mathematics and teaching practice
    • references to research as a basis for the recommendations
    • 2002: No Child Left Behind legislation signed
    • states develop grade-by-grade standards in mathematics and related assessments
    • 2006: NCTM produces Curriculum Focal Points
    • most significant concepts and skills at each grade level
  • Foundations for Success National Mathematics Advisory Panel Final Report, March 2008
  • Presidential Executive Order April 2006
    • The Panel will advise the President and the Secretary of Education on the best use of scientifically based research to advance the teaching and learning of mathematics, with a specific focus on preparation for and success in algebra.
  • What Concerns Led to the President’s Order?
    • National prosperity and safety in international context
      • - Role of mathematics for national well-being
      • - Rising Above the Gathering Storm (NRC report)
      • Workforce of the future
    • Options for individuals and families
      • - College admission and graduation
      • - Candidacy for technical workforce
      • - Earning power
      • - Adaptability
  • Math Proficiency of U.S. Students
    • International comparisons
    • Low proficiency on National Assessment of Educational Progress
    • Falling proficiency at higher grades
    • Heavy remedial demand upon entry into college
    • Achievement gap
    • Algebra as a gateway
  • Overview
    • The Panel
    • Reviewed 16,000 research studies and related documents
    • Gathered public testimony from 110 individuals
    • Reviewed written commentary from 160 organizations and individuals
    • Held 12 public meetings around the country
    • Analyzed survey results from 743 Algebra I teachers
  • Curricular Content: Streamline the Mathematics Curriculum in Grades PreK-8
      • Follow a coherent progression, with emphasis on mastery of key topics
      • Focus on the Critical Foundations for Algebra
        • - Proficiency with Whole Numbers
        • - Proficiency with Fractions
        • Particular Aspects of Geometry and Measurement
      • Avoid any approach that continually revisits topics without closure
  • Curricular Content
      • Benchmarks Should Guide:
      • Classroom Curricula
      • Mathematics Instruction
      • Textbook Development
      • State Assessment
  • Curricular Content
      • A major goal for K-8 mathematics education should be proficiency with fractions (including decimals, percents, and negative fractions), as foundation for algebra.
  • Curricular Content: The Major Topics of School Algebra
      • Covering all of school algebra traditionally extending over two courses, Algebra I and Algebra II
        • Symbols and Expressions
        • Linear Equations
        • Quadratic Equations
        • Functions
        • Algebra of Polynomials
        • Combinatorics and Finite Probability
  • Curricular Content
      • An Authentic Algebra Course
      • All school districts:
      • Should ensure that all prepared students have access to an authentic algebra course, and
      • Should prepare more students than at present to enroll in such a course by Grade 8.
  • Curricular Content
      • What Mathematics Do Teachers Need to Know?
      • For middle school teachers (grades 6-8)
        • - The Critical Foundations of Algebra
        • - All of the Major Topics of School Algebra
      • To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, factual knowledge and problem solving skills .
    Learning Processes
      • Limitations in the ability to keep many things in mind (working-memory) can hinder mathematics performance.
        • Practice can offset this through automatic recall, which results in less information to keep in mind and frees attention for problem solving.
        • Learning is most effective when practice is combined with instruction on related concepts.
        • Conceptual understanding promotes transfer of learning to new problems and better long-term retention.
    Learning Processes
  • Learning Processes
      • Children’s goals and beliefs about learning are related to their mathematics performance.
        • Children’s beliefs about the relative importance of effort and ability can be changed.
        • Experiential studies have demonstrated that changing children’s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes.
        • Engagement and sense of efficacy for Black and Hispanic students can be increased in mathematical learning contexts.
        • Teachers and other educational leaders should consistently help students and parents understand that an increased emphasis on the importance of effort is related to improved mathematics grades.
    Learning Processes
  • Instructional Practices
    • All-encompassing recommendations that instruction should be student-centered or teacher-directed are not supported by research.
    Instructional practice should be informed by high quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers.
  • Instructional Practices
    • The use of “real-world” contexts to introduce mathematical ideas leads to improved performance on assessments using similar kinds of “real world” problems. Performance on other kinds of assessments (computation, equation solving) is not improved.
  • Instructional Practices
    • Research on cooperative learning strategies is inconclusive, except for one very structured strategy (Team Assisted Individualization, TAI). TAI can lead to improved computational performance, but non significant effects on conceptual understanding or problem solving.
    • Research on students who are low achievers, have difficulties in mathematics, or have learning disabilities related to mathematics tells us that the effective practices include:
      • Explicit methods of instruction available on a regular basis
      • Clear problem solving models
      • Carefully orchestrated examples/ sequences of examples
      • Concrete objects to understand abstract representations and notation.
      • Participatory thinking aloud by students and teachers.
    Instructional Practices
    • Use of technology shows promise when: 
      • Computer-assisted instruction supports drill and practice
      • Well designed tutorials are delivered through computer-assisted instruction
      • Learning is supported by the careful, targeted application of computer programming
      • More research is needed!
    Instructional Practices
  • Instructional Practices
    • A review of 11 studies that met the Panel’s rigorous criteria (only one study less than 20 years old) found limited or no impact of calculators on calculation skills, problem solving, or conceptual development over periods of up to one year.
    • This finding is limited to the effect of calculators as used in the 11 studies and the Panel recommends more research.
  • Instructional Materials
    • U. S. mathematics textbooks are far too long -- often 700-1000 pages. Mathematics textbooks are much smaller in many nations with higher mathematics achievement than the U.S. Excessive length makes our books unnecessarily expensive and tends to undermine coherence and focus.
    • Publishers must ensure the mathematical accuracy of their materials.
  • Issues in Secondary Mathematics Curriculum in the US
    • The same mathematics for all? Tracking?
    • Aiming for calculus, or aiming for quantitative literacy and application (statistics, discrete mathematics)?
    • Preparation for workforce and preparation for higher education, same curriculum?
    • Appropriate role of technology? (graphing calculators, dynamic geometry software, computer algebra systems)
    • “ Core” content vs. application and real-world problems?
  • Lessons
    • Standards
    • Assessment
    • Teachers
    • Instructional materials
    • For more information:
    • Joan Ferrini-Mundy
    • [email_address]
    • National Math Panel
      • http://www.ed.gov/MathPanel