Advantages of Using the CAS Mathematica in a Study of Supplementary Chapters of Probability Theory
Author: Mezhennaya, Natalia M.
Date: 2019-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Probability,Statistics,Teaching Methods,Educational Technology,Technology Uses in Education,Visualization,Mathematical Concepts,Computation,Telecommunications,Handheld Devices,College Mathematics,Foreign Countries,Graphs,Concept Formation

Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training materials for seminar studies) supported by the CAS (computer algebra system) Mathematica, as suggested by the authors for several topics of the course 'Supplementary Chapters of Probability Theory'. These methods help to solve tasks requiring routine calculation and simplify the ability to find analytical and graphical dependencies in the tasks under consideration. Visualisation possibilities built in the CAS contribute to students' comprehension of new theoretical material and complicated probabilistic notions. The article contains examples of CAS-performed tasks including the calculation and visualisation of the notions of the conditional probability density function, conditional expectation, order statistics and running maximum. The purpose of the suggested CAS-based materials is to solve a whole class of tasks of similar types; it is possible to obtain new results by varying the input data without spending much time elaborating the solution method. The methods using innovative teaching materials yield advantages to both students and teachers. These methods simplify and individualise the process of education, shorten the time necessary for students' independent work and motivate students to achieve the results. Moreover, the preparation and renovation of the bank of tasks of varying levels of difficulty require much less time. Consequently, teachers and students have more time to devote toward discussing and analysing the results obtained. Another possible effect of using the novel teaching means is reducing the differentiation in students' training levels. In the present research, examples of teaching materials and scenarios of their usage are presented. In order to clarify possible scenarios of using the suggested methods, the authors explored the necessity of their modifications, and assessed students' attitudes toward the aforementioned education methods as well as toward traditional methods, the advantages and difficulties of their usage are also explored. For this purpose, students were asked questions, and their answers have been analysed statistically. The research demonstrates that students regard interactive templates as complicated and difficult to understand; however, they do not conclude that they are unnecessary. The most remarkable aspect for students is the convenience of work with mobile devices and the possibility of a full-text search. However, the students did not make a connection between the interactive templates and the presentations prepared with their use. One can conclude that students should begin learning CAS in the first term of their university education. Additional adaptation of the teaching materials for mobile devices is necessary as well.