NCTM (National Council of Teachers of Mathematics) write the following concerning the activity of mathematics:

Guide to Mathematical Norms: From NCTM Standards for grades 6-8

Problem Solving:

  • Share varied solutions

Reasoning and Proof:

  • Examine patterns and structures and note regularities (possible generalizations)
  • Make conjectures about possible generalizations
  • Evaluate conjectures
  • Use inductive and deductive reasoning to construct (formulate) and evaluate mathematical arguments


  • Express thinking orally and in writing
  • Present/explain strategies used to solve problems
  • Analyze, compare, contrast the meaningfulness, efficiency, and elegance of a variety of strategies (explanations should include mathematical arguments and rationales)
  • Free to express one’s ideas honestly and openly, without fear of ridicule


  • Create, compare, and use various representations to organize and record thinking about mathematical ideas
  • Representations consist of physical objects, drawings, charts, graphs, and symbols – these representations help communicate one’s thinking

Big Ideas in Geometry: From NCTM Standards for grades 6-8

  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships (e.g., investigating perimeters, areas, and side lengths)
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems
  • Apply transformations and use symmetry to analyze mathematical situations (“transformational geometry offers another lens through which to investigate and interpret geometric objects”
  • Use visualization, spatial reasoning, and geometric modeling to solve problems

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