The
Development of Comprehension of Chance Language: Evaluation and Interpretation
Jane
M. Watson and Jonathan B. Moritz
University
of Tasmania
Comprehension
of chance language, such as is found in newspapers, is a fundamental aspect of
statistical literacy. In this study, studentsâ understandings of chance
language were explored through responses to two items in surveys administered
to 2,726 students from grades 5 to 11. One item involved evaluating the chance
expressed in phrases from newspaper headlines using a number line, and
responses were described in four levels of chance language evaluation. The
other item involved interpreting, in context, an expression of percent chance,
and responses were described in four levels of chance language interpretation.
Students in higher grades were more likely to demonstrate higher levels of
both evaluation and interpretation. The association between levels of
evaluation and interpretation was further explored generally and in relation
to one of the headlines involving percent. Implications for mathematics
educators in relation to chance language in the curriculum across the years of
schooling are discussed.
Fuzzy
Logic, Neural Networks, Genetic Algorithms: Views of Three Artificial
Intelligence Concepts Used in Modeling Scientific Systems
Cynthia
Szymanski Sunal, Charles L. Karr, and Dennis W. Sunal
The
University of Alabama
Studentsâ
conceptions of three major artificial intelligence concepts used in the
modeling of systems in science, fuzzy logic, neural networks, and genetic
algorithms were investigated before and after a higher education science
course. Students initially explored their prior ideas related to the three
concepts through active tasks. Then, laboratories, project work, use of
computer modeling of scientific systems, and cooperative group work were used
to help students construct key characteristics of each concept. Finally, they
applied each concept in contexts different from that in which it had been
previously studied. In postcourse interviews using a set of scenarios for each
of the major course concepts, 49% of studentsâ applications included key
characteristics of the concepts studied versus an application of 5% in
precourse interviews. Studentsâ post interview applications were
inconsistent even though they were more frequent, indicating a state of
transition in their conceptual change. Applications were most consistent when
used with scenarios deemed very familiar to the students, indicating the
effects of context in conceptual change.
Whodunit?
Exploring Proportional Reasoning Through the Footprint Problem
Karen
Koellner-Clark, Georgia State University
Richard
Lesh, Purdue University
This
paper describes a proportional reasoning problem set within a real-life
context and a complete analysis of one small group discussion of this problem
over the course of a 90-minute block. The seventh-grade studentsâ discourse
is described to provide insights into typical mathematical interpretations of
this problem, as well as some generalizations for other problems of this type.
The interpretations provided reveal the gradual development of proportional
reasoning in a local context from additive to multiplicative understandings.
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