The Teaching and Learning of Probability, with Special Reference to South Australian Schools from 1959-1994
Date
2001
Authors
Truran, John Maxwell
Editors
Advisors
Brice, Mr Ian
Scott, Paul
Scott, Paul
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Thesis
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Abstract
The teaching of probability in schools provides
a good opportunity for examining how a new topic
is integrated into a school curriculum. Furthermore,
because probabilistic thinking is quite different
from the deterministic thinking traditionally found
in mathematics classrooms, such an examination is
particularly able to highlight significant forces
operating within educational practice.
After six chapters which describe relevant aspects
of the philosophical, cultural, and intellectual
environment within which probability has been
taught, a 'Broad-Spectrum Ecological Model' is
developed to examine the forces which operate on
a school system. The Model sees school systems and
their various participants as operating according
to general ecological principles, where and
interprets actions as responses to situations in
ways which minimise energy expenditure and
maximise chances of survival. The Model posits
three principal forces-Physical, Social and
Intellectual-as providing an adequate structure.
The value of the Model as an interpretative
framework is then assessed by examining three
separate aspects of the teaching of probability.
The first is a general survey of the history of
the teaching of the topic from 1959 to 1994,
paying particular attention to South Australia,
but making some comparisons with other countries
and other states of Australia. The second examines
in detail attempts which have been made throughout
the world to assess the understanding of probabilistic
ideas. The third addresses the influence on
classroom practice of research into the teaching
and learning of probabilistic ideas.
In all three situations the Model is shown to be
a helpful way of interpreting the data, but to
need some refinements. This involves the uniting
of the Social and Physical forces, the division of
the Intellectual force into Mathematics and
Mathematics Education forces, and the addition of
Pedagogical and Charismatic forces. A diagrammatic
form of the Model is constructed which provides a
way of indicating the relative strengths of these
forces.
The initial form is used throughout the thesis
for interpreting the events described. The revised
form is then defined and assessed, particularly
against alternative explanations of the events
described, and also used for drawing some
comparisons with medical education. The Model
appears to be effective in highlighting uneven
forces and in predicting outcomes which are
likely to arise from such asymmetries, and this
potential predictive power is assessed for one
small case study. All Models have limitations,
but this one seems to explain far more than the
other models used for mathematics curriculum
development in Australia which have tended to
see our practice as an imitation of that in other
countries.
School/Discipline
Graduate School of Education and Department of Pure Mathematics
Dissertation Note
Thesis (Ph.D.)--Graduate School of Education and Department of Pure Mathematics, 2001.