2001 ANNUAL
COLLOQUIUM
on
Research in Mathematics and Science Education
Editorial
During the past years our graduate students addressing the
problems associated with mathematics and science education have followed a
variety of perspectives in carrying out their investigations. Because school is
complex, as Shulman (1988) suggested, there is a need for multiple perspectives
and procedures in mathematics and science education as a field of study. Search
for the interrelationship of the components in the schooling process leads to
the development of the broad research trends, problems and questions each of
them deserves to be investigated. Individual
researchers might utilize different methods to study each question, but must be
aware that each method produces its own set of concepts, techniques, and
procedures. To understand the current trends in research in mathematics and
science education, one must be cognizant of these perspectives and the
principles upon which they are based. This is important because differences in
methods do not merely comprise alternative ways of investigating the same
questions. What distinguishes one method from another is not only the way in
which information is gathered, analyzed, and reported, but also the very types
of questions typically asked and the principles or paradigms upon which the
methods to investigate such question are based.
After
identifying a phenomenon of interest, researchers speculate about certain
important aspects as variables of the phenomenon and surmise about how those
aspects are related. It is very important to relate the phenomenon and model to
others’ ideas by examining whether their ideas can be use to clarify, amplify,
or modify the proposed model. To built the argument,
the researchers would have read and reflected on the writings and studies of
other scholars in the field. It is imperative to see the importance of
situating a study within the work of others. It helps to make the results of
the study open to a variety of interpretations and to appreciate the
differences in perspectives of divergent authors.
Asking specific questions or making reasoned
conjectures is a key step in the research process because a number of potential
questions inevitably arise. When the “critical” questions are asked, then
“strong’ inferences can be made. The decision about what methods to use follows
directly from the selected questions, from the model the researchers have built
in order to explain the phenomenon, and from the conjecture that has been made
about needed evidence. Selection of specific procedures, and collection and
interpretation of the information are very important steps to build an argument
regarding the question being asked.
When
educational research has been adequately supported, it has benefited many
dimensions of practice and clarified the language of practice in many ways.
This has been most apparent when discoveries and conclusions have been
effectively disseminated to practitioners and when practitioners have been
enabled to play collaborative roles.
The above
is merely a brief overview of the set of activities almost every researcher
follows. But research cannot be regarded as a mechanical performance or as a
set of rules that individual follows in a prescribed or predetermined fashion.
Rather, it should be viewed as an inquiry and as an art.
This issue
of the Colloquium Journal contains articles that describe quite different areas
of research in mathematics and science education.
The Journal in general and this
volume in particular is designed for people who would benefit from a critical
synthesis and careful interpretation of research, while improving their own
practice. Readers who carefully examine this volume will find a kaleidoscope of
significant information to process that will contribute to their own knowledge
based about mathematics and science education.
I hope you will find this volume useful.
Producing the journal requires
quality work from the authors and the editorial panel. Reviewers played an important
part in the development of each manuscript. I thank all for their devotion,
perseverance and commitment
Articles
Using Written Representations to Analyze
Cognitive and Social Aspects of Non-Routine Problem Solving
Jeff Todd, UML
Tracking the Development of Students’ Written
Explanations in Mathematics: Why Roses are Not Necessarily Red
Susannah M. Givens and S.
Catherine Howell,
The Impact of High-Stakes,
State-Mandated Student Performance Assessment on 10th Grade English,
Mathematics, and Science Teachers’ Instructional Practices
Kenneth E. Vogler,
Personal Knowledge of Rational Number: A Review
of the Literature on Theories of Fraction Learning
Walter E. Stone, Jr, UML
Educational Resources
The New Medium for
Mathematics