Technological Discourse on CAS-based Operative Knowledge

Giora Mann, Thierry Dana-Picard, and Nurit Zehavi

Weizmann Institute of Science, Israel 2 Department of Applied Mathematics, Jerusalem College of Technology, Israel
gioramann@013.netmail dana@jct.ac.il nurit.zehavi@weizmann.ac.il

This article begins with a comparison of two groups of teachers, working on the same tasks in Analytic Geometry. One group has only basic experience in CAS-assisted problem solving, and the other group has extensive experience. The comparison is discussed in terms of the interplay between reflection, operative knowledge and execution. The findings indicate that because of the different levels of their respective CAS-based operative knowledge, the first group outsourced traditional techniques and the more experienced teachers developed new instrumented techniques. By doing so, the second group uncovered routes to a lateral exploration of the problem. Following Chevallard's anthropological approach, we propose initial elements of a new praxeology, comprising tasks in the specific topic, instrumented techniques, technological discourse, and new mathematical perspectives.

Factors Influencing the Integration of Computer Algebra Systems into University-Level Mathematics Education

Zsolt Lavicza

Faculty of Education, University of Cambridge, United Kingdom
zl221@cam.ac.uk

Computer Algebra Systems (CAS) are increasing components of university-level mathematics education. However, little is known about the extent of CAS use and the factors influencing its integration into university curricula. Pre-university level studies suggest that beyond the availability of technology, teachers’ conceptions and cultural elements are key factors in technology integration into mathematics teaching and learning. This article reports on interviews, examining mathematicians’ conceptions of CAS and its pedagogic uses, conducted with 22 mathematicians’ in three countries, Hungary, United Kingdom, and United States. The findings showed some similarities, but numerous differences, with school-level studies. In the article, I shall outline the methodological approach of the study, discuss some preliminary results from my data analysis, and compare my results with findings of school-level studies.

Experiences in the Integration of CAS into Engineering Education at the University of Pécs

Csaba Sárvári

University of Pécs, Department of Mathematics, Hungary
sarvari@witch.pmmf.hu

This paper provides some examples of how lecturers in our department have attempted to tackle the didactical challenges posed by CAS. In addition, it outlines the research approaches we took to better understand these issues.

Technologies for Teaching and Learning about Box Plots and Statistical Analysis

Patricia A. Forster

Edith Cowan University, 100 Joondalup Drive, Joondalup 6027, Western Australia, Australia
p.forster@ecu.edu.au

This paper analyses technology-based instruction on data-analysis with box plots. Examples of instruction taken from the research literature inform a study of two classes of 17 year-old students (upper secondary) in which the mathematical relationships that their teachers targeted are distinguished as being, or not being, relevant to statistical analysis. In analysing the features of technologies, the paper identifies the potential of displaying dot plots and corresponding box plots on the same screen display as being a particularly powerful way of motivating new interpretations of data structures for learners.

Projects Using a Computer Algebra System in First-year Undergraduate Mathematics

Martin Rosenzweig

Department of Mathematics, Bryant University, USA
mrosenzw@bryant.edu

This paper illustrates the use of computer-based projects in two one-semester first-year undergraduate mathematics classes. Developed over a period of years, the approach is one in which the classes are organised into work-groups, with computer-based projects being undertaken periodically to illustrate the class material. These projects are undertaken in computer labs using the Maple software package and have proved beneficial on two counts. First, in leading students to an understanding of mutual enterprise and encouraging them to participate in team activities, and, secondly, students have gained an enriched understanding of the classroom material. Nevertheless, student response remains variable with some students saying that they enjoy the additional exposure to mathematical ideas, while others dislike the additional work

A Case Study of the Issues Arising When Teachers Adopt the Use of a New Form of Technology in their Teaching for the First Time

John S. Berry, Ted Graham, Suki Honey and Carrie Headlam

University of Plymouth, School of Mathematics and Statistics, Drake Circus, Plymouth, PL4 8AA
jberry@plymouth.ac.uk, egraham@plymouth.ac.uk, shoney@plymouth.ac.uk, cheadlam@plymouth.ac.uk

Introducing any new initiative into teaching involves professional development and training. This paper investigates the reactions of three teachers to the introduction of graphics calculators into their department. Each teacher was followed through one academic year. They were interviewed formally on two occasions and also met informally with the researchers to discuss how they were using the calculators. The interviews were used to develop profiles of the three teachers. From these profiles a set of recommendations was developed that could guide other schools who were introducing graphics calculators for the first time. These recommendations were (i) that the department should have an action plan which describes where and why the calculators are to be used (ii) both initial and on-going training is necessary (iii) appropriate support in the form of both teaching resources and hardware should be readily available.

 

 

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