The Role of Counterintuitive Examples in Statistics Education
Lesser,
http://www.ugr.es/~batanero/v11ab98.htm) as well as in Newsletter of the International Study
Group for Research on Learning Probability and Statistics, 9 (3).
(July 1996; http://www.ugr.es/~batanero/v9ju96.html)
---------------
The purpose of this study
was to develop a theoretical model for the use of counterintuitive examples in
the introductory non-calculus-based statistics course at the college
level. While intuition and misconceptions continue to be of great
interest to mathematics and science educators, there has been little research,
much less consensus or even internal consistency, in statistics curriculum
development concerning the role of examples with counterintuitive
results. Because the study intended to provide educators with useful
connections to content, instructional methods (e.g., cooperative learning) and
learning theory constructs that have been successfully used in mathematics or
science education, the model that emerged was organized around a typical
syllabus of topics.
The study critiqued and then
reconciled "Traditional" and "Alternative"
perspectives. The Traditional Position attempts to minimize possible
confusion and frustration by avoiding such examples, while the Alternative
Position uses them to motivate and engage students in critical thinking, active
learning, metacognition, communication of their
ideas, real-world problem solving and exploration, reflection on the nature and
process of statistics, and other types of activities encouraged by current
reform movements. The study delineated
specific criteria and conditions for selecting and using counterintuitive
examples to achieve numerous cognitive and affective objectives. Examples
explored include the Monty Hall problem, Simpson’s Paradox, the birthday
problem, de Méré’s Paradox, the Classification
Paradox, the Inspection Paradox, and required sample size.
The study connected many of
these examples (especially Simpson’s Paradox) with other counterintuitive
examples, with known probability or statistics misconceptions many students
have, with representations from other branches of mathematics, and with the
constructivist paradigm. Problematic issues addressed include difficulty in
constructing assessment instruments and a multiplicity of terminologies and
typologies. Additional directions for research were suggested, including
several empirical investigations of various facets of the model. The
connections, examples, and representations presented should be extremely useful
for teachers of statistics, but should also enrich the pedagogy of teachers of
other courses.
This file has the main
part of my dissertation (with page numbers potentially off by about a
page): http://www.math.utep.edu/Faculty/lesser/LesserDISSfrontmatter.pdf
This file has the front
matter (e.g., table of contents) of my dissertation:
http://www.math.utep.edu/Faculty/lesser/LesserDISSmainpart.pdf