The Best of Creative Computing Volume 1 (published 1976)

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Recent Trends in Mathematics Curriculum Research

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(5) "...for those who take mathematics only a few years after grade
elementary feeling for probability and statistics...[and]...a nodding
acquaintance with the calculus."

	The 1969 book [4] contains some interesting thoughts about the mathematics and
science curricula in general, which reveal a fuller development of CCSM's point
of view:  "Science and mathematics, by their inherent simplicity in comparison
to most areas of knowledge, lend themselves to the development in children of
attitudes of lifelong and general value.... They include (in no order of
priority) a conviction that through analysis and synthesis comes understanding;
a belief that quantitative measure adds dimensions to one's understanding that
are always difficult and sometimes impossible to achieve by other means; a
tolerance that permits consideration of all reasonable testable hypotheses which
are consistant with available evidence; a healthy skepticism even toward
conclusions supported by existing evidence; an optimism based on the belief that
nothing is unknowable while much remains unknown; and finally, a belief that to
understand, while indeed a means to power, is to enjoy and is therefore an end
in it elf."

	"In his school experience with science, a child can make his own observations
and organize them, then make his own predictions and check them.  Thus he can
directly appreciate the power of the scientific style of thought."  

	"We do not want these experiments to be done occasionally as a sort of special
treat,... but sufficiently often that the thought patterns that underlie the
world of science will be habitual, if rudimentary, in every school graduate.”

 	"A primary message of education should, we believe, be that thinking is
worthwhile. Unfortunately, education has often been directed away from the
imaginative and creative toward uninteresting, rote attention to details."  

	"Each child must be convinced that his thinking is worthwhile." 

	This is very exciting intellectual stuff:  it's wise and idealistic in the best
sense of that word. Reading it, one almost forgets two important things: (1) In
spite of a clear intention to the contrary, these goals put pressure on
researchers and schools to focus attention on still more new topics and new
courses and away from such perennial problems as student motivation, teacher's
job satisfaction, and the real need for students to acquire essential skills in
an acceptable length of time. (2) The mathematicians and scientists who have
come together as CCSM conferrees seem to have only a very hazy notion of what
the non-mathematics-using citizen needs:  

	"...difficult and important decisions are better made by people used to
connecting reality with rationality....through the vital process of constructing
simplified conceptual models for real world objects and interactions....There
are severe limitations on a quantitative approach in a real life situation; but
it seems better to go as far as one can with that approach than to abandon
decisions to guess or superstition."  

	"Environmental pollution, for example, is among the most critical problems of
our times. Its solution will require the active cooperation of every individual.
We will not get this cooperation until every citizen understands the problem
well enough to feel the importance of his own role in the solution."   

	In our highly organized and specialized society, I wonder whether the ability
of an individual to make "simplified conceptual models" will contribute directly
to his role in decision making.  Also, is it realistic to imply that a process
which has "severe limitations" in the hands of professionals will survive in a
classroom setting lacking any but the most primitive tools for computation and

	One curriculum project has grown directly out of CCSM's efforts --Unified
Science and Mathematics for Elementary Schools (USMES), and another has
dedicated itself to implementing CCSM's goals-- Comprehensive School Mathematics
Program (CSMP).  However, there is not the boundless enthusiasm of old, nor the
move to make swift changes in schools.  Many researchers simply do not believe
that the acceleration proposed is compatible with growth in understanding and
enjoyment, especially at the elementary level.  Burt Kaufman, Director of CSMP,
an advocate of CCSM's goals, is cautious:

	"We've simply torn down the entire curriculum and rebuilt it from scratch.  It
could have a very big impact if the public is ready for it but it is going to be
more difficult for the teacher." [12]

	The third major trend in the 1964-74 period is a very different kind of
phenomenon.  It has some, but not all, of the aspects of a new 'glamour
movement' --computers in education. (While not strictly a development in
mathematics, computing has impinged more on the mathematics curriculum than
other subject areas for complex reasons, some social, some technical.) Before
1964, pioneering research in computer-assisted instruction by Bitzer at the
University of Illinois and Suppes at Stanford gave rise to high hopes and some
inflated statements:

	"the kind of individualized instruction once possible only for a few members of
the aristocracy can be made available to all students at all levels of ability."
[Suppes, 1]

	In the period since, and at the present, a good deal of research has been
undertaken regarding not only computer-assisted instruction but a variety of
other computer uses in education. An idea of the growth of research in computing
can be gotten from Figure 1. This is a chart of some major mathematics
curriculum (and related) projects, selected mainly from [10] and [15]. It is not
exhaustive, but should encompass most projects mentioned in widely read
journals. Computer manufacturers have actively promoted their products to
schools for both educational and administrative purposes. All this would point
to a new educational panacea destined to fade or be absorbed without any deep
effect.  However, at least two features of this trend definitely set it apart
from those have come (and gone) before it.

	First, the adoption of computers in schools is taking place independently as
well as with funded research activity. The American Institutes for Research
Survey [5] * figures of secondary schools using computers for educational or
instructional (not administrative) purposes are:

1965 ------- 2%
1970 ------- 13%.

Even though these figures must be considered very approximate, this growth
cannot be accounted for by research programs.

*A new survey is scheduled for release in 1975.

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