Value and Relevance of an Engineering Statistics Course

1. Value and Relevance of an Engineering Statistics Course By KumerPial Das, PhDAssociate Professor of Statistics Department of MathematicsLamar University, Beaumont, TX

2. Objectives: • To discuss the ‘health’ of engineering statistics courses taught nationwide. • To evaluate the importance of identifying students’ attitudes towards this course. • To discuss different approaches taken in this course. • To evaluate the effect of Moore method on students’ final exam scores.

3. Engineering students perceive statistics as a ‘nuisance to endure’. Why? There are many reasons. Most importantly, • Lacking space (most of the engineering curricula include few or no • statistics courses, and often these courses are very packed and • highly theoretical). • They (engineering students) don’t perceive statistics as a part of their engineering toolkit. Rather students often view statistics courses as overwhelming learning and survival tasks that cause a great deal of stress (Onwuegbuzie and Daley, 1999) • Teaching statistics is an extremely complex and challenging task. The complexity goes even deeper when this is taught by teachers who are not experts in statistics.

4. Students’ Attitudes: • Instructors and students alike believe that students’ attitudes toward statistics impact their statistics achievement and even their willingness to try to complete these courses. • Attitudes toward statistics affect a large number of students in their college (and eventually professional careers . • There are many studies exploring attitudes towards statistics. Moreover, most of these studies have explored the relationships between attitudes and achievement scores and most studies report small to moderate correlations between these two variables. • Wisenbaker and colleagues created, tested, and modified structural models of statistics achievement. Their models included achievement and four components of students’ attitudes towards statistics.

5. A general overview of the course: • Course Purpose: The intent of this course is to resent a solid undergraduate foundation in statistical theory and, at the same time, to provide an indication of the relevance and importance of the theory in solving practical problems in the real world. • Student Learning Outcomes: Students who successfully complete the course will be able to: • Calculate the probability of an event; • Recognize and use the discrete and continuous type of distribution; • Make inference about a population based on information contained in a sample taken from that population; • Understand the central limit theorem; and • Know the test of hypothesis.

6. What we have tried: An interview at the beginning of the semester: • During the first or second week of class I distribute a simple questionnaire among the students. • Instead of collecting it in class I ask them to come to my office with the questionnaire ( I usually offer a couple of bonus points for that). • For every student I usually spend about 10 minutes. • Even though I ask them to bring their first quiz and/or Homework I try not to talk about any ‘statistical’ topic directly.

7. Problem based teaching: The Problem-Based Learning (PBL) approach integrated in the traditional curriculum seemed particularly well adapted to teaching basic statistics to students in higher education. • PBL first appeared in the medical school of McMaster University in Canada and in Maastricht University in the Netherlands. An extensive literature about this particular field is available. For example, • Teaching statistics through concrete real-life cases. • Active learning with experiments. • Teaching statistics with computer programs. • Cooperative learning with group work.

8. Characteristics and steps of PBL: • PBL is a way of organizing instruction by focusing on a problem as a motivation for the student activities. The problem should be professionally relevant and as close as possible to real-life situations. • Students usually solve problems in small groups (4-7 students), where cooperative learning is encouraged. • In this model the teacher is more like a facilitator rather than a lecturer. The teacher assists the students in the skills acquisition process and develops the students’ independent-learning capacities. PBL according to the 7 Steps Model • 1 Clarification of unclear terminology and concepts • 2 Definition of the problem • 3 Analysis of the problem (brainstorming) • 4 List of possible explanations • 5 Formulation of learning aims and key tasks • 6 Independent search for additional information outside the group • 7 Report, synthesis and testing of the new information

9. Moore Method: Robert L. Moore (1882-1974) was a towering figure in 20th century mathematics. • Moore-method teaching has been associated with pedagogies including discovery-based, inquiry-based, student-centered and constructivist, yet it is not encompassed by these (Mahavier, 2009). • The majority of a Moore-method mathematics course consists of students’ presentations of solutions they produce independently from material provided by the instructor. • Moore summed up his method in just eleven words “That student is taught the best who is told the least.” • The Moore method is appropriate for a class like topology or real analysis.

10. Structure of the course: • In a modified Moore method class, instructors usually provide course notes and they serve as mentors. They provide minimal information during the class time. In fact, they don’t “lecture” in class. However, I didn’t practice exactly the Moore method. Rather I have tried what people call “Modified Moore Method”. • Even though in a purely Moore method course instructor usually don’t use a text book, I use both a text book and my notes for the class. • On Mondays and Wednesdays I presented definition, theory, concepts and one or two examples in class. And at the end of the class I assigned 4 to 5 problems and call them “Friday Problems”. • On each Friday, students were asked to present their work and solution to those “Friday Problems” in board.

11. Statistical Significance: • This instructor has taught two different sections of this course in Fall 2011. We have used the identical syllabus, textbook etc. in those two sections. The only difference is that the section taught by the traditional method met twice a week (MW) whereas the Moore method section met three days in a week (MWF). Identical final exam has been administered. • To test the significance of the difference between the means of these two independent samples a two-sample t-test has been performed. • Our null and alternative hypothesis is: Ho: µ_Moore = µ_Traditional Ha: µ_Moore ≠ µ_Traditional

12. Descriptive Statistics: Inferential Statistics: Difference=µ_M-µ_T Estimate for difference:  6.86000 95% CI for difference:  (-0.17926, 13.89926) T-Test of difference = 0 (vs not =): T-Value = 1.95  P-Value = 0.056  DF = 59