Journal of Computers in Mathematics and Science Teaching
Volume 14, Number 3 1995
Articles
Teachers' Attitudes Toward Distance Learning Technology in a Science/Society Global Issues
William J. Boone, Christine Bennett, and Carlos OvandoTechnology and Algebra Curriculum Reform: Current Issues, Potential Directions, and Research Questions
Sharon Dugdale et alThe Relationship Between Experience and Philosophical Orientation: A Comparison of Preservice and Practicing Teachers' Beliefs About Calculators
M. Jayne FleenerCollaborative Learning for Computer Science Students
Phillip Ramsey, Roy Rada, and Sharon AcquahTechnology-Motivated Teaching of Advanced Topics in Discrete Mathematics
Sergei AbramovichSpreadsheet Structures as a Model for Proving Combinatorial Identities
Erich Neuwirth
Abstracts
Teachers' Attitudes Towards Distance Learning Technology in a Science/Society Global Issues Course
WILLIAM J. BOONE, CHRISTINE BENNETT, AND CARLOS OVANDO
School of Education
Indiana University, Bloomington, IN 47405, USA
This paper presents a summary of teachers' attitudes towards an innovative science and society global issues class. This class was simultaneously provided to three urban school sites using two-way audio/two-way full motion technology. No other distance education class using this advanced technology to so many sites appears to have been conducted in other settings. The data provide insight into how distance education courses for science and mathematics education efforts can be enhanced and refined. In general, teachers of mathematics and science may be most receptive to distance education technology because of (a) its ability to provide easy access to individuals with specific curricular specialties and (b) the ease with which such a class can be attended. Survey results indicated that teachers strongly felt that fully interactive, two-way audio/video technology would be needed for any distance education class.
Technology and Algebra Curriculum Reform: Current Issues, Potential Directions, and Research Questions
SHARON DUGDALE
Division of Education
University of California, Davis, CA 95616, USA
PATRICK W. THOMPSON
Department of Mathematics and Center for Research in Mathematics and Science Education
San Diego State University, San Diego, CA 92120, USA
WAYNE HARVEY
Education Development Center
55 Chapel Street, Newton, MA 02160, USA
FRANKLIN DEMANA AND BERT K. WAITS
Department of Mathematics
Ohio State University, Columbus, OH 43210, USA
CAROLYN KIERAN
Department of Mathematics
Université du Québec à Montréal, Québec, H3C 3P8, Canada
JOHN W. MCCONNELL
Glenbrook South High School
Glenview, IL 60025, USA
PAUL CHRISTMAS
John Hersey High School
Arlington Heights, IL 60004, USA
The infusion of computers and calculators into mathematics instruction raises new possibilities for teaching and understanding algebra, as well as rethinking the nature of algebra itself. In this paper we characterize algebra as a way of reasoning involving three broad, interrelated themes: (a) variables and functional relationships, (b) generalization and modes of representation, and (c) mathematical investigation and argument. We examine curricular goals and consider the contributions of technology to reconceptualizing algebra in terms of these three themes. We suggest directions for future development of tools and implementation models, possibilities for a research agenda, and implications related to assessment and evaluation.
A Survey of Mathematics Teachers' Attitudes About Calculators: The Impact of Philosophical Orientation
M. JAYNE FLEENER
College of Education
University of Oklahoma, Norman, OK 73019, USA
This paper addresses the possible effect of technological diffusion efforts on teachers with fundamentally different beliefs about the use of technology tools for mathematics instruction. Responses of 94 middle school and secondary mathematics teachers on the Attitude Instrument for Mathematics and Applied Technology (AIM-AT) were analyzed to determine the relationship among personal philosophy, experience, and attitudes about calculator use. Teachers participating in this study had similar beliefs about the motivational effects of calculators for mathematics instruction; however, beliefs about the cognitive benefits of calculator use were not as well defined. Differences were found on several items between groups of teachers who believed calculators should not be used until students achieved conceptual mastery and those who disagreed conceptual mastery was necessary before calculators could be used. Interactions between mastery orientation and experience were suggested when analysis of responses on AIM-AT items revealed responses were divided by mastery groups and experience with calculators. Apparently, experience with calculators for instructional purposes and beliefs about whether students should have conceptual mastery before calculators are used are important for deciding other issues related to calculator use. Persons leading reform efforts encouraging the use of technology to assist teaching and learning of mathematics must consider the fundamental differences in attitudes and beliefs of teachers with contrasting philosophical perspectives and experience levels in order to be more effective.
Collaborative Learning for Computer Science Students
PHILLIP RAMSEY, ROY RADA, AND SHARON ACQUAH
Department of Computer Science
University of Liverpool, Liverpool L69 3BX, England
This paper will describe the development of a collaborative learning tool for use by second year Computer Science students at the University of Liverpool, to help them in an Algorithmics course. Part of the course textbook was placed on-line and students used this to aid their understanding of the subject. Students interacted using the tool by adding to the course text and then defending these additions to their fellow students. Working together in the classroom caused synchronization problems that were partially solved by allowing students to do the exercises anytime they wanted. As students were worried about cheating, the assignments were changed so as to reward building on the work of other students.
Technology-Motivated Teaching of Advanced Topics in Discrete Mathematics
SERGEI ABRAMOVICH
Department of Mathematics Education
University of Georgia, 105 Aderhold Hall, Athens, GA 30602-7124, USA
The reform of mathematics curricula and the revision of traditional teaching strategies deal with the task of incorporating discrete mathematics into the curriculum with a strong emphasis on technological setting. This article presents teaching ideas concerning the application of a spreadsheet in introducing discrete concepts through recursive definition. It shows how students can be involved in comparing the results of modeling integers with different combinatorial meaning, so that in both specializing and in generalizing students can unexpectedly discover the celebrated Eulerian numbers. An important aspect of the proposed teaching sequence is the possibility of using a spreadsheet as a technological tool for facilitating creativity. The spreadsheet used is Microsoft Excel 4.0 for Macintosh computers.
Spreadsheet Structures as a Model for Proving Combinatorial Identities
ERICH NEUWIRTH
Institute Of Statistics, Operations Research & Computer Science
University of Vienna, A-1010 Vienna, Austria
In this paper we want to show that spreadsheets as a model for mathematical relations can help in gaining insight into recursive relations for combinatorial formulas. The use made of spreadsheets, however, is not the standard one. The "spreadsheet metaphor" we apply works by graphically representing the relations between the objects under consideration and tries to help the basic structures without use of extensive algebraic formulas and without losing any mathematical rigor or insight.