Home

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

Communication:

• 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

Representation:

• 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