Computation, Exploration, Visualisation: Reaction to MATLAB in First-Year Mathematics

This paper describes a model for effective incorporation of technology into the learning experience of a large and diverse group of students in first-semester first-year tertiary mathematics. It describes the introduction of elementary use of MATLAB, in a course offered both on-campus and at a distance. The diversity of the student group is outlined, types of tasks employing MATLAB are listed, progressive class reaction is traced, and retrospective views expressed in interviews and focus discussion groups are reported. In conclusion, it is argued that careful introduction to MATLAB on attitudes to technology in the learning of mathematics. Recommendations are made for using scientific packages, for learning mathematics, for developing concepts, and for raising levels of involvement and appreciation in large classes. (Author) Reproductions supplied by EDRS are the best that can be made from the original document. Computation, Exploration, Visualisation: Reaction to MATLAB in First-Year Mathematics Patricia Cretchley, Chris Harman, Nerida Ellerton and Gerard Fogarty University of Southern Queensland [email protected] ; [email protected] ; [email protected] ; [email protected] This paper describes a model for effective incorporation of technology into the learning experience of a large and diverse group of students in first-semester first-year tertiary mathematics. It describes the introduction of elementary use of MATLAB, in a course offered both on-campus and at a distance. The diversity of the student group is outlined, types of tasks employing MATLAB are listed, progressive class reaction is traced, and retrospective views expressed in interviews and focus discussion groups are reported. In conclusion, it is argued that careful introduction to MATLAB leads to the effective use of a powerful software tool, and has a positive effect on attitudes to technology in the learning of mathematics. Recommendations are made for using scientific packages, for learning mathematics, for developing concepts, and for raising levels of involvement and appreciation in large classes. Introduction and Background Many mathematicians and mathematics educators believe that the use of technology can enliven and revitalise the learning of mathematics. However, those who design early undergraduate mathematics programs face constraints imposed by large classes and limited resources, as well as two further major issues. One is the challenge of coping with the diversity of background, mathematical skills, interests, needs and aspirations that students have on entry. The other is the declining commitment to, and enjoyment of, the study of mathematics. Taylor and Morgan [1] reported on declining skills and uneven preparedness on entry to Australian tertiary mathematics, and drew attention to similar reports in the UK2Forgasz-and Leder [2] reported “a general decline in the enjoyment of mathematics between schdol and university”, in a study of five Australian universities. Enrolment patterns are changing. Course design has become a delicate balance: under conditions of diminishing resources we try to support and encourage under-prepared students, while trying to stimulate and maintain the interest of talented students. And we do this in the face of stiff competition from other subject areas, which offer favourable career prospects. The University of Southern Queensland is a growing dual-mode university, balancing its commitment to supportive on-campus teaching with the strength and experience it has developed in distance education. The university attracts many mature-age and international students alongside Australian school-leavers. Algebra & Calculus I is the primary first-semester mathematics unit for students entering Engineering, Mathematics, Science, and Business, covering topics in calculus, vectors, linear equations, and matrix algebra. Well over 300 students register, but many of the external students deregister without penalty, finding themselves unable to make the time commitment necessary to pass. Against this background, the decision was made to employ technology in the unit, in an attempt to assist students to develop concepts and skills. Existing reports have often supported the view that effective use of computers in the learning of mathematics can motivate students at both ends of the spectrum of skills and ability, even those quite indifferent to mathematics. USQ experience included trials of computer-based learning over several years, using Mathematica, and the programming language APL. Many believe that the use of available and accessible scientific software empowers students in ongoing courses, and it was felt that introduction to elementary use of such a package would be more appropriate for the needs and aspirations of this large and very diverse group, than currently available teaching-specific software and materials. EST COPY AVAHA PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY 1 TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvernt EDUCATIONAL RESOURCES INFORMAT CENTER (ERIC) This document has been reproduced a received from the person or organizati, originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represen official OERI position cr MATLAB, which is used in a number of higher level undergraduate units, is the software package most favoured by Engineering and Applied Mathematics at USQ. In 1997, pilot trials in a few Algebra & Calculus I tutorials which support the four lectures per week, revealed its strong potential as a supplement. In 1998 it was decided to support MATLAB in the unit for on-campus students. Positive experience in that trial led to extension of support for its use to distance students in 1999. A range of elementary tasks employing MATLAB to support the learning of the parallel Calculus and Linear Algebra components of the unit, was integrated into five assignments and the weekly tutorials. Basic use of MATLAB was demonstrated in lectures, and a brief guide supplied, covering the commands and syntax needed. Many students in this early mathematics unit have little or no experience of programming and file-management, so no work of that kind was expected. Students were offered access to the Classroom Version of MATLAB for the duration of the semester, but were encouraged to buy the Student Version. On-campus students were supported by their tutors in computer laboratories during the second hour of their weekly tutorial. During the first hour students were assisted in a classroom, doing standard mathematical tasks. Distance students had to rely on prearranged telephone tutorials, and assistance by telephone, email, newsgroup, or fax, on request. It was made clear to students that they would not be examined on MATLAB usage, and that they were free to use alternative software or graphics calculators. They were told that notebook computers and graphic calculators would be permitted in their open book examination, but were warned that for equity reasons, questions would be designed so that they did not need the support of technology. They were also told that no computers would be allowed into their other examination. Searches reveal very few published reports on such early tertiary use of MATLAB. Use in more focused Linear Algebra courses is better documented. Trials of DERIVE, MAPLE, and Mathematica are reported quite widely, but MATLAB has different strengths and potential syntax problems for students not yet familiar with matrix algebra. Because of the extra effort and cost of supporting such an add-on, and the paucity of such studies of software in the current literature, it was felt that appropriate research into the effects of introducing the use of powerful scientific software would be valuable. A research project was therefore undertaken to investigate the effect of the use of MATLAB on early undergraduate students’ attitudes to mathematics and learning, invoking the skills of a team of specialists in the appropriate disciplines of mathematics, education, and psychology. Analysis reported here constitutes some preliminary findings from this in-depth study. The project is supported by a USQ Project Team Research Grant. Research Design and Methodology A broad range of instruments was used to gather information and monitor the effects of this trial on students’ skills, views, and approaches to mathematics and learning. Breadth of information was sought via pre-and posttests given to all students, and a broad range of assignment tasks. Depth was established via focus discussion groups and case studies which included interviews. A survey instrument was developed to assess students’ views on learning mathematics, their experience using computer software for learning mathematics, and their self-efficacy in mathematics and the use of computers. It comprised 68 self-report items that employed a Likert-style response format, with options ranging from 1 (strongly agree) to 5 (strongly disagree). It was administered at the commencement of the unit, and with the last assignment. 447 students responded to the presurvey, reflecting much higher enrolment than usual but numbers dropped back to around average when well over a hundred de-registered without penalty within the first month. 172 responded to the post-survey. Views were also established by means of feedback questions on assignments, selfselection of some assessment tasks, interviews, and focus discussion groups. A number of reasons are postulated for the sharp increase in enrolment and subsequent quick drop in numbers, and these need further investigation, but the unexpected increase in enrolment resulted in delays in students accessing their study materials and textbooks.