Assessing Teaching Methods For A Course In Numerical Methods

Effectiveness of four instructional delivery modalities – 1) Traditional lecture, 2) Webenhanced lecture, 3) Web-based self-study, and 4) Combined web-based self-study & classroom discussion, was investigated for a single instructional unit (Nonlinear Equations) over separate administrations of an undergraduate course in Numerical Methods. Two assessment instruments – 1) student performance on a multiple-choice examination, and 2) a student satisfaction survey were used to gather relevant data to compare the delivery modalities. Statistical analysis of the assessment data indicates that the second modality where web-based modules for instruction were used in conjunction with a face-to-face lecture delivery mode resulted in higher levels of student performance and satisfaction. Background and Rationale Web-based modules have been developed for a junior-level Numerical Methods course delivered in the College of Engineering at University of South Florida, Tampa. The features of the web-based modules are addressed indirectly since the complete details are readily available in Ref 1, 2 . Stating in brief, the unique features of the web-based modules are that they are both holistic and customized. Holistically, the web-based modules review essential course background information; present numerical methods through several options textbook notes, lecture videos, PowerPoint presentations, simulations and assessments; show how course content covered is applied in real life; tell stories to illustrate special topics and pitfalls; and give historical perspectives to the material 1,2 . Faculty and students are able to choose a customized view based on their preferred computational system Maple 3 , Mathcad 4 , Mathematica 5 , Matlab 6 , and choice of engineering major Chemical, Civil, Computer, Electrical, General, Industrial, and Mechanical. Figure 1: Home page of the Holistic Numerical Methods Institute Committed to Bringing Customized Numerical Methods Holistically to Undergraduates. The focus of this research is to compare four different modes of instructional delivery, namely P ge 11242.2 1) Traditional lecture, 2) Web-enhanced lecture, 3) Web-based self-study, and 4) Web-based self-study/discussion The present study is a follow-up of findings reported in a previous paper 7 where we addressed only the first two modalities. Since the previous study was completed, the course has been delivered twice more, once with a web-based self-study and another with combined webbased self-study followed by a classroom discussion. In recent years, there has been a substantial amount of research exploring how to enhance student learning across disciplines, including science, mathematics, engineering, and technology (SMET) courses. Research in this area spans academic disciplines and professional preparation, from medicine 8 to education 9 and computing to business 10 . Furthermore, the research base is exploring how e-learning, as internet-based education is often referred to, has different benefits based on characteristics of the individual student. The British Journal of International Technology devoted an entire edition to this issue alone 11 addressing, among other things, the need to be cognizant that distance learning has a unique ability to provide students with different learning modalities with varied resources and strategies. Techniques and tools to be used to enhance learning using the web include effective and adaptive navigation as well as addressing multiple and diverse needs and interests of the student 12 . The text, How People Learn 13 provides a foundation for many of the issues facing current educators who are encountering an increasingly diverse and multi-faceted student population. This literature was foundational to the exploration of various modalities of course delivery considered in this study. According to How People Learn, experts (in this case, faculty) “often forget what is easy and what is difficult for students 13, p. 32 .” Relative to this issue, the modules and instructional materials developed through this study offer both students and faculty a comprehensive instructional package for simplifying and enhancing the teaching of numerical methods across the engineering curriculum. Further, research has demonstrated that it is beneficial to provide “instruction that enables students to see models of how experts organize and solve problems” and that “the level of complexity of the models must be tailored to the learners’ current levels of knowledge and skills 13, p. 37 .” The design and format of the web-based modules helps students see how experts apply fundamental numerical methods to solve real world engineering problems both within and across different engineering disciplines. And finally, citing again from this same synthesis of research findings, we know that “A major goal of schooling is to prepare students for flexible adaptation to new problems and settings 13, p. 65 ” and that “knowledge that is taught in only a single context is less likely to support flexible knowledge transfer than is knowledge that is taught in multiple contexts 13, p. 66 .” Our effort was to provide instruction opportunity to suit different learning styles 14 . By enabling students to select both a preferred computational system as well as to select one or more illustrative examples drawn from seven popular engineering majors within each topic area, these Page 11242.3 interactive instructional modules maximize the likelihood of lasting and flexible learning transfer of essential numerical methods course content. Implementation & Assessment Instruments The previous study 7 compared the first two modalities 1) Traditional lecture, and 2) Webenhanced lecture for the two topics of Nonlinear Equations and Interpolation. In this paper, the focus is narrowed to the topic of Nonlinear Equation, but the scope of data is broadened by looking at four modes of delivering the content. The four modalities were implemented in four separate semesters Summer 2002, Summer 2003, Summer 2004 and Spring 2005 1 semesters, respectively. In Summer 2002 semester, students in the Numerical Methods course were instructed on Nonlinear Equations using the traditional, face-to-face lecture method without the use of the web-based modules, hereafter referred to as the Traditional Lecture mode of delivery. We used a popular engineering numerical methods textbook 15 for reading assignments and problem sets. In Summer 2003 semester, students were instructed on the same topic of Nonlinear Equations using both lecture and the web-based resources that were developed for the course, hereafter referred to as the Web Enhanced Lecture. Before discussing numerical methods for a mathematical procedure, we conducted an in-class and informal diagnostic test on the background information via several multiple-choice questions. This allowed us to review specific material that most students struggle with. We used PowerPoint presentations to present the topics. These presentations were continually supplemented with discussions based on spontaneous instructor and student questions. Several times during the presentation, students were also paired in class to work out an iteration or two for a numerical problem. We also met during the weekly computer laboratory session where each student had access to a computer. Simulations for various numerical methods were conducted. Reading assignments were based on textbook notes written by the first author, and problem sets included questions based on Bloom’s taxonomy 16 . In Summer 2004 semester, students received instruction through a distance format without a classroom lecture component, hereafter called the Web-Based Self Study mode. Same resources were available to students as they were in Summer 2003. In addition, lecture videos that were video recorded in a studio were available online. Since the students were learning the material themselves, regular class periods and the weekly lab session that were devoted to the topic of Nonlinear Equations as in Summer 2003 were cancelled. At the end of the week, as part of their graded homework assignment, students were asked to submit answers to 18 short questions (6 on each of the 3 subtopics of Background, Bisection Method, and Newton-Raphson Method) that were based on six levels of Bloom’s taxonomy. The reading assignments and problem sets were the same as in Summer 2003. 1 We were planning to implement the fourth modality in Summer 2005. However, due to certain circumstances, it was co-taught by two instructors and hence assessments were not conducted like in previous semesters. The fourth modality will be implemented again in Summer 2006. P ge 11242.4 In Spring 2005 semester, students used the same self-study methods as those in Summer 2004 but were required to meet in the weekly lab session to discuss the lesson. This mode hereafter is called Web-based Self Study/Class Discussion. Although attending the weekly lab session was mandatory, they were not required to ask questions. Before the weekly lab session, as part of their graded homework assignment, students were asked to submit answers to 9 short questions (3 on each of the 3 subtopics) based on first three levels of Bloom’s taxonomy. After the weekly lab session, they were asked to submit answers to 9 more short questions (3 on each of the 3 subtopics) based on last three levels of Bloom’s taxonomy. The reading assignments and problem sets were the same as in Summer 2003. To measure the student performance, four 2 questions were asked in the Nonlinear Equations portion of the final examination. Two of the four questions were selected at the lower levels of Bloom’s taxonomy, while the other two were chosen from the upper levels of Bloom’s taxonomy. Student performance on these four questions was examined as a function of the four course delivery modes. To measure student satisfaction, a survey that gathered information on students’