on Research in Mathematics and Science Education



Regina M. Panasuk


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






Table of Contents


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, Boston University 

 The Impact of High-Stakes, State-Mandated Student Performance Assessment on 10th Grade English, Mathematics, and Science Teachers’ Instructional Practices

Kenneth E. Vogler, Littleton High School 

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                              

Bradford D. Allen, Florida Institute of Technology