School of Education, Brooklyn College - CUNY, Brooklyn, NY 11226
The research presented here is a group case study of students learning calculus in a Computer Algebra System (CAS) environment which examines the following research questions: What are students’ perceptions of the role of technology in their learning? What is the students’ relationship to CAS? What is the effect of learning in a CAS environment on students’ conceptions of mathematics, as a subject? The primary data for the study consists of audio and video tapes of a group of students in a college course learning calculus using CAS software. This data was supplemented by interviews with the students as well as analysis of the students’ homework and tests. Analysis of the data via the Didactic Triangle provides a lens through which to view the place of technology in the CAS classroom and through which to view the journey of each student during the course. The evidence of the study shows the importance of understanding the relationship students have to CAS in the mathematics classroom since it can act as an inhibitor of student work as well as an enhancement as it challenges them in profound ways with regard to their beliefs and attitudes about mathematics.
David L. Neumann, Michelle Hood & Michelle M. Neumann
School of Psychology, Griffith University, Australia
In a previous report, Neumann (2010) described the use of interactive computer-based simulations in the assessment of statistical concepts. This assessment approach combined declarative knowledge of statistics with experiences in interacting with computer-based simulations. The aim of the present study was to conduct a systematic evaluation of the approach. A stratified random sample of students (n = 38) was selected and participated in an interview to provide qualitative data that was coded into themes. The students reported that the assessment approach improved their understanding of statistics and its practical application, gave them a way to practice statistics, motivated them to complete it, was interesting and engaging, and gave a visual aid to learning. Students also commented on the immediate feedback, the unique nature of the assessment, and the technological requirements involved. The results suggest that the use of computer-based interactive simulations in assessment can be a positive addition to assessment practices in a university statistics course.
Generalised Assignment Matrix Methodology in Linear Programming
Park University, DeVry University,Capella University,Southern New Hampshire University, US
Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same methodology can be expanded to other linear programming software. The paper extends the assignment matrix methodology in linear programming to a wide range of Discrete Mathematics and OR problems, including knapsack problems, independent sets, matching problems, max flow problems, travelling salesman problems, and transportation time and cost problems. By relaxing the constraint that assignment matrices must be binary, this linear programming approach can be extended to a wide range of increasingly complex problems. The paper goes on to show how to apply these different assignment matrices to a variety of specific problems documented in the literature using Excel Solver and Premium Solver.