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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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Conceptual Knowledge

and Skills

Task Group

Miami Meeting

Progress Report

June 6, 2007


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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


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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


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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


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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


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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


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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


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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


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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


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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