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 “the first contemporary set of subject matter
standards in the United States” (Ferrini-Mundy, p. 869). From these three
documents arose the Standards which was written to “build upon the foundation”
and “integrate the classroom-related portions” 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
“Students discover relationships and develop
spatial sense by constructing, drawing, measuring, visualizing, comparing,
transforming, and classifying geometric figures.” NCTM, p. 112
“Geometry also has a vocabulary of its own,
including terms like rhombus, trapezoid, and dodecahedron, and students need
ample time to develop confidence in their use of this new and unique language.
Definitions should evolve from experiences in constructing, visualizing,
drawing, and measuring two- and three-dimensional figures, relating properties
to figures, and contrasting and classifying figures according to their
properties.” NCTM, p. 113
“Computer software allows students to construct
two- and three-dimensional shapes on a screen and then flip, turn, or slide
them to view them from a new perspective. Observing and learning to represent
two- and three-dimensional figures in various positions by drawing and
construction also helps students develop spatial sense.” NCTM, p. 114
“Investigations of two- and three-dimensional
models foster an understanding of the different growth rates for linear
measures, areas, and volumes of similar figures. These ideas are fundamental to
measurement and critical to scientific applications . . .
Symmetry in two and three dimensions provides
rich opportunities for students to see geometry in the world of art, nature,
construction, and so on.” NCTM,
p. 115
9
– 12