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Algebra

Overall in the algebra strand, students should "understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various contexts." (NCTM, 2000, p. 37)
Algebra is a fundamental content strand in a world-class high school mathematics curriculum. There are several different conceptions of school algebra.

Conceptions of School Algebra

Algebra is (about):

Focus on:

Solving equations

Techniques for solving equations

Structure (re: abstract algebra)

Algebraic systems and properties

Generalized arithmetic

Algebraic expressionsùsimplify, expand, factor

Problem solving

Using algebra to model and solve problems

Functions (re: real analysis)

Patterns of change, quantitative relationships

A world-class mathematics curriculum must take a balanced approach to algebra, which includes the appropriate synthesis of all the above conceptions. The essential topics listed and described below should be emphasized.

Technology should be used appropriately to enhance and support the teaching and learning of algebra. This may include the judicious use of graphing calculators, spreadsheet software, resources on the Internet, and computer algebra systems (CAS). Such technology can be used, for example, to highlight, connect, and apply graphic, numeric, and symbolic approaches to teaching and learning algebra.

Essentail Topics in Algebra

  • Functions
  • Equations and inequalities
  • Algebraic expressions
  • Rate of change
  • Recursion and iteration

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