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ERIC Number: ED502315
Record Type: Non-Journal
Publication Date: 2008-Aug-7
Pages: 35
Abstractor: As Provided
A Modified Moore Approach to Teaching Mathematical Statistics: An Inquiry Based Learning Technique to Teaching Mathematical Statistics
McLoughlin, M. Padraig M. M.
Online Submission, Paper presented at the Annual Meeting of the American Statistical Association (Denver, CO, Aug 7, 2008)
The author of this paper submits the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Probability and Mathematical Statistics (PAMS) course sequence to teach students PAMS. Furthermore, the author of this paper opines that set theory should be the core of the course's pre-requisite with logic and calculus as antecedents to the set theory, an introduction to the theory of functions as subsets of the complex plane as consequents of set theory. The connections between logic, set theory, and proofs about probability, random variables and processes, & inferential mathematical statistics cannot be understated--the better the student's pre-requisite knowledge the easier it is for the student to understand probability theory and flourish in a Probability & Statistics course sequence. The author of this paper has experienced teaching such a course sequence for approximately fifteen years; mostly teaching the course at a historically black college. The paper is organised such that in the first part of the paper an explanation as to why Logic, Set Theory, and Calculus are proper pre-requisites to a Probability & Statistics course sequence and a brief overview is presented of the Moore method. The second part of the paper, presents justification for use of a modified Moore approach in teaching probability & statistics (or what is termed mathematical statistics often); both pedagogical and practical justification is submitted. In the third part of the paper, the author submits the model for the Probability & Statistics courses and focuses on what is effective for the students, what seems not useful to the students, and why. Also, explanation is presented as to why the courses were designed the way they were (content), how the courses were revised or altered over the years; hence, explaining what practices were refined, retained, modified, or deleted and how such was helpful or not for the faculty and students. The final part of the paper discusses the successes and lack thereof how the methods and materials in the PAMS courses established an atmosphere that created for some students an easier transition to graduate school, preparation for actuarial tests, to the work force in applied statistics, assisted in forging a long-term undergraduate research component in the major, and encouraged some faculty to direct undergraduates in meaningful research. So, this paper proposes a pedagogical approach to mathematical statistics education that centres on exploration, discovery, conjecture, hypothesis, thesis, and synthesis such that the experience of doing a mathematical argument, creating a statistical model, or synthesising ideas is reason enough for the exercise--and the joy of mathematics and statistics is something that needs to be instilled and encouraged in students by having them do proofs, counterexamples, examples, and counter-arguments in a Probability and Mathematical Statistics course (indeed in any course). (Contains 50 footnotes.)
Publication Type: Reports - Descriptive; Speeches/Meeting Papers
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A