Constructing formulas “from scratch” for calculating geometric measurements of shapes—for example, the area of a triangle—involves reasoning deductively and drawing connections between different methods (Usnick, Lamphere, and Bright 1992). Visual and manipulative models also play a role in helping students understand the underlying mathematics implicit in measurement and make sense of the numbers and operations in formulas.
Margaret Rathouz, Christopher Novak, and John Clifford
Dustin L. Jones and Max Coleman
Many everyday objects–paper cups, muffins, and flowerpots–are examples of conical frustums. Shouldn't the volume of such figures have a central place in the geometry curriculum?
This is a description of a collaborative investigation by mathematics teachers into the numbers of dimensional boundaries for n > 2. Functions are fit to the patterns observed, and a relationship to Pascal's triangle is noted.
Carol J. Bell
Reasoning and Proof is one of the process standards set forth in NCTM's principles and standards for school mathematics (2000).