National Council of Teachers of Mathematics

Curriculum Standards

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STANDARD 1: MATHEMATICS AS PROBLEM SOLVING

In grades 9-12, the mathematics curriculum should include the refinement and extensions of methods of mahtematical problem solving so that all students can-

  • use, with increasing confidence, problem-solving approaches to investigate and understand mathematical content;
  • apply integrated mathematical problem-solving strategies to solve problems from within and outside mathematics;
  • recognize and formulate problems from situations within and outside mathematics;
  • apply the process of mathematical modeling to real-world problem stiuations..
STANDARD 3: MATHEMATICS AS REASONING In grades 9-12, the mathematics curriculum should include numerous and varied experiences that reinforce and extend logical reasoning skills so that all students can-
  • make and test conjectures;
  • formulate counterexamples;
  • follow logical arguments
  • judge the validity of arguments;
  • construct simple valid arguments.
STANDARD 4: MATHEMATICAL CONNECTIONS

In grades 9-12, the mathematics curriculum should include investigation of the connections and interplay among various mathematical topics and their applications so that all students can--

  • recognize equivalent representations of the same concept;
  • relate procedures in one representation to procedures in an equivalent representation;
  • use and value the connections among mathematical topics;
  • use and value the connections between mathematics and other disciplines.