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Conceptual Knowledge and Skills Task Group

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Conceptual Knowledge and Skills Task Group. Miami Meeting Progress Report June 6, 2007. Conceptual Knowledge and Skills Task Group. Task Group Members: Francis (Skip) Fennell, chair Larry Faulkner Liping Ma Wilfried Schmid Sandra Stotsky Hung Hsi Wu, ex-officio

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Presentation Transcript
slide1

Conceptual Knowledge

and Skills

Task Group

Miami Meeting

Progress Report

June 6, 2007

slide2

Conceptual Knowledge

and Skills

Task Group

Task Group Members:

Francis (Skip) Fennell, chair

Larry Faulkner

Liping Ma

Wilfried Schmid

Sandra Stotsky

Hung Hsi Wu, ex-officio

Tyrrell Flawn, staff associate

slide3

Conceptual Knowledge

and Skills

Task Group

  • Methodology
  • Literature Review
  • Analysis of State Curriculum Frameworks, Standards, and Textbooks
  • Survey of Algebra Teachers
  • Analysis of Math Content in Respected Sources
  • Synthesis of Algebra Topics and Math Skills and Concepts
slide4

Conceptual Knowledge

and Skills

Task Group

  • What are the major topics of school algebra?
  • Symbols and Expressions
  • Polynomial expressions
  • Rational expressions
  • Arithmetic and finite geometric series
  • Linear Relations
  • Real numbers as points on the number line
  • Linear equations and their graphs
  • Solving problems with linear equations
  • Linear inequalities and their graphs
  • Graphing and solving systems of simultaneous linear equations
slide5

Conceptual Knowledge

and Skills

Task Group

  • What are the major topics of school algebra? (cont.)
  • Quadratic Relations
  • Factors and factoring of quadratic polynomials with integer coefficients.
  • Completing the square in quadratic expressions
  • Quadratic formula and factoring of general quadratic polynomials
  • Using the quadratic formula to solve equations
slide6

Conceptual Knowledge

and Skills

Task Group

  • What are the major topics of school algebra? (cont.)
  • Functions
  • Linear functions
  • Quadratic functions – word problems involving quadratic functions
  • Graphs of quadratic functions and completing the square
  • Polynomial functions (including graphs of basic functions)
  • Simple nonlinear functions (e.g.. square and cube root functions; absolute value; rational functions; step functions)
  • Rational exponents, radical expressions, and exponential functions
  • Logarithmic functions
  • Trigonometric functions
  • Fitting simple mathematical models to data
slide7

Conceptual Knowledge

and Skills

Task Group

  • What are the major topics of school algebra? (cont.)
  • Algebra of Polynomials
  • Roots and factorization of polynomial forms
  • Complex numbers and operations
  • Fundamental theorem of algebra
  • Binomial coefficients (and Pascal’s triangle)
  • Mathematical induction and the binomial theorem
  • Combinatorics and Finite Probability
slide8

Conceptual Knowledge

and Skills

Task Group

  • What are the essential mathematics concepts and skills that lead to success in algebra and that should be learned as preparation for formal algebra coursework?
  • Fluency with whole numbers
  • Fluency with fractions
  • Geometry
slide9

Conceptual Knowledge

and Skills

Task Group

  • Does the sequence of topics taught at grade levels prior to algebra coursework affect achievement in algebra?
  • Response considerations:
  • Issues of coherence
  • Placement of algebra coursework
  • Other issues under investigation and further analysis
slide10

Conceptual Knowledge

and Skills

Task Group

  • Additional Questions and Issues for Consideration:
  • Mathematics background of middle school teachers
  • Role/use of the graphing calculator in teaching algebra
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