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OCR for page 35

A Framework for Change
Curriculum discussions always
involve, implicitly if not explicitly,
many different curricula of progres-
siveiy diminishing scope:
· An expected curriculum, that
represents future neecis of
employers and science.
· An ideal curriculum, that establishes actual goals for
teaching and learning.
· An available curriculum, that can be taught with existing
teaching materials and currently trained teachers.
· An adopted curriculum, that a school district says should
be taught.
An implemented curriculum, that teachers actually
teach.
An assessed curriculum, that is examined by tests or other
forms of evaluation.
An achieved curriculum, that most students actually master.
A major aim of curriculum development should be to close
the gap between the expected and the achievecl curricula.
To do this, one must make the gaps between each pair of suc-
cessive steps in the hierarchy as small as possible. There are,
however, no unique curricula that will do this. We aim, there-
fore, to provide a framework within which many curricula may
bloom.

OCR for page 35

36
Reshaping School Mathematics
Principles
Pressure to reshape mathematics education comes from
many directions from technology, from society, from
research, and from mathematics itself, The broad practical
view of mathematics as a science and language of patterns
provides a strong foundation for new mathematics curricula.
Technological change and research findings suggest direc
tions for curricular change, Such change will take many forms,
but should be built on certain fundamental principles that fol-
low from our view of mathematics and our review of research,
Principle 1: Mathematics eclucation must focus on the devel-
opment of mathematical power.
Mathematical power enables students to understand
mathematical concepts and methods and to discern
mathemofical relations in a variety of contexts. It helps
students to reason logically and to solve a variety of
problems, both routine and nonroutine, To be effective,
mathematical power requires
of students that they be able
to read documents using
mathematical methods and
express quantitative and logi-
cal analyses in both oral and
written form.
Students who achieve sig-
nificant mathematical power
during their school years will
be able to use mathematics in
their careers and in everyday
lives, They will be intelligent
users of mathematical ideas,
accepting or rejecting claims
that are ostensibly based on
mathematical arguments,
They will see things mathemat-
ically, recognizing when
mathematical analyses help
to explain events. They will
have sufficient mathematical
knowledge to pursue a profes-
sion or vocation of their
choice and to undertake fur-
ther study of subjects that
require mathematical profi-
ciency.