Prospective Elementary Teachersâ Use of
Mathematical Reasoning in Solving a Lever Mechanics Problem
Carol Briscoe and David Stout
University of West Florida
This study explored how prospective elementary teachers (n = 106, 29
groups) enrolled concurrently in elementary science and elementary mathematics
methods courses used algebraic reasoning to construct and describe relationships
among and between variables in the context of solving a problem involving
the action of Class 1 levers. Group members collected data and tried to
develop a mathematical formula that would allow them to predict where a
weight of given size could be placed on one side of the lever to balance
a specified weight at a specified distance from the fulcrum on the opposite
side. Data sources for the study included journal entries, transcripts,
and documents produced by students. Four categories encompassing the most
general groupings of studentsâ representations based on both the rule and
formula were constructed. Eighteen out of the 29 groups were able to solve
the problem. Specific weaknesses characterized by the solutions presented
were (a) a confusion in the meaning of mathematical concepts connected
with ratio and proportion; (b) a lack of mathematical language skills and/or
understanding of how to symbolically represent relationships among variables
in formulae; and (c) a lack of understanding of the generalizability characteristic
of variables in mathematics and science.
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Writing, Mathematics, and Metacognition: Looking
for Connections Through Studentsâ Work in Mathematical Problem Solving
David K. Pugalee
University of North Carolina at Charlotte
This study investigated whether studentsâ writing about their mathematical
problem solving processes showed evidence of a metacognitive framework.
Twenty ninth-grade algebra students provided written descriptions of their
problem solving processes as they worked mathematics problems. A qualitative
analysis of the data indicated the presence of a metacognitive framework.
Studentsâ written descriptions demonstrated engagement of various metacognitive
behaviors during orientation, organization, execution, and verification
phases of mathematical problem solving. This article provides a description
of the more predominant metacognitive behaviors identified through the
data analysis. The findings of this study underscore the importance of
implementing writing as an integral part of the mathematics curriculum
and emphasize the need for additional research on writing in mathematics.
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Teaching Science in Higher Education: Faculty
Professional Development and Barriers to Change
Dennis W. Sunal, The University of Alabama
Jeanelle Hodges, Eastern Connecticut State University
Cynthia S. Sunal, Kevin W. Whitaker, and L. Michael Freeman, The University
of Alabama
Leo Edwards and Ronald A. Johnston, Fayetteville State University
Michael Odell, University of Idaho
The focus of this research was to better understand the change processes
necessary for university science teaching reform to be successful. The
professional development processes involved faculty cognitive perceptions
of learning, teaching skills, and pedagogical knowledge, as well as faculty
culture in teaching science courses. A series of faculty development programs
were conducted at nine U.S. locations to explore, develop strategies, and
implement changes in science classrooms. A review of research and these
professional development experiences provided a base to carry out research
activities related to understanding change in science faculty. Faculty
participants in the program from 30 institutions were selected to be involved
in the study. Ethnographic and case study approaches were used to collect
and analyze data. Many faculty members encountered in this study had conceptions
of the change process that inhibited successful action. These research
efforts provide a predictive model for assisting faculty change and help
determine which faculty professional development efforts may be successful
in overcoming barriers to change in undergraduate science classrooms.
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Reviewing Integrated Science and Mathematics:
The Search for Evidence and Definitions From New Perspectives
Marlene M. Hurley
University of Wisconsin-Superior
Based upon current research needs indicated from recent literature
reviews, this integrative review concentrates on two of the perceived major
impediments to integrating science and mathematics: The lack of evidence
to support integration and the lack of a definition for integration. Using
mixed methodology, this review found quantitative evidence favoring integration
from a meta-analysis of 31 studies of student achievement, qualitative
evidence revealing the existence of multiple forms of integration, and
historical evidence of publishing patterns from across the 20th century.
The forms of integration were identified and defined; differential effects
were identified both between forms and between science and mathematics
when the forms were analyzed by effect size. Additional research implications
and suggestions for future research were also identified.
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