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