Before the Standards . . .

 

 

 

Before there was the Principles and Standards for School Mathematics (the Standards), there was a set of three documents whose sole purpose were to provide a set of national standards in the areas of curriculum, assessment, and the profession of mathematics education. The first of these standards, Curriculum and Evaluation Standards for School Mathematics, was Òthe first contemporary set of subject matter standards in the United StatesÓ (Ferrini-Mundy, p. 869). From these three documents arose the Standards which was written to Òbuild upon the foundationÓ and Òintegrate the classroom-related portionsÓ of the original standards (Ferrini-Mundy, p. 869). This is evident especially in the Geometry Standard where ideas such as understanding two- and three-dimensional geometry are prevalent. The Curriculum and Evaluation Standards for School Mathematics stresses many geometric skills, including spatial reasoning and ability that school age children should acquire in the course of their learning that are still important ideas resonating throughout the Standards. 

 

 

K – 4

 

 

 

5 – 8

 

 

 

9 – 12

The overarching theme for this grade band is the increased attention given to three-dimensional geometry.

 

ÒStudents should have opportunities to visualize and work with three-dimensional figures in order to develop spatial skills fundamental to everyday life and to many careers. Physical models and other real-world objects should be used to provide a strong base for the development of studentsÕ geometric intuition so that they can draw on these experiences in their work with abstract ideas.Ó NCTM, p. 157

 

ÒInstruction should focus increased attention on the analysis of three-dimensional figures. Such work is especially important to students who may pursue careers in art, architecture, drafting, and engineering. Appropriate use of three-dimensional representation and CAD (computer-assisted design) software is of particular value in such exercises.Ó NCTM, p. 158

 

ÒCollege-intending students also should gain an appreciation of Euclidean geometry as one of many axiomatic systems. This goal may be achieved by directing students to investigate properties of other geometries to see how the basic axioms and definitions lead to quite different – and often contradictory – results.Ó NCTM, p. 160

 

ÒAlthough students will continue to work with two dimensions, every opportunity should be taken to explore the third dimension as well. Algebraic formulations in three-dimensional coordinate geometry should focus on figures that are simple to represent, such as points, planes perpendicular to an axis, and spheres. The coordinate representation of general planes and lines is more difficult and would best be treated as an enrichment project.Ó NCTM, p. 162

 

 

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