Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate




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Comparison of Final Examination Formats in a Numerical Methods Course (2015)

International Journal of Engineering Education

Vol. 31, No. 1(A), pp. 72–82, 2015


With decreasing budgets for teaching assistants, large class sizes, and increased teaching loads, it is becoming ever more important to effectively utilize resources without sacrificing best practices of assessment. In the authors' collective teaching experience of 41 years, students very rarely approach the final examinations as a learning mechanism. Therefore, the final examination serves only for demonstration of sufficient topic mastery. In this study, a hybrid multiple-choice final examination with optional partial credit (MC+PC) was evaluated as a replacement for the same examination in constructed response (CR) or strict multiple-choice (MC) formats. In the hybrid MC+PC format, students were given multiple-choice options but were also allowed to submit constructed responses that would be graded for partial credit. The three examination formats were utilized once each in three offerings of a Numerical Methods course at the University of South Florida. Multiple linear regression and item analysis of student responses demonstrate that students approach the MC+PC format similarly to a CR exam, and the administrative requirements of the test were significantly reduced. This study finds the hybrid MC+PC format to be equally reliable and appropriate for a comprehensive final examination.


A Holistic View on History, Development, Assessment, and Future of an Open Courseware in Numerical Methods (2012)

ASEE Computers in Education Journal

 Vol 3(4), pp. 57-71, 2012


Funded since 2001 by National Science Foundation, an innovative open courseware (http://nm.mathforcollege.com) has been developed for a comprehensive undergraduate course in Numerical Methods. The open courseware resources enhance instructor preparation and development as well as the student educational experience by facilitating a hybrid educational approach to the teaching of Numerical Methods, a pivotal STEM course, via customized textbooks, adapted course websites, social networking, digital audiovisual lectures, concept tests, self-assessment of the level of learning via online multiple-choice question tests and algorithm-based unlimited attempt quizzes, worksheets in a computational system of choice, and real-life applications based on the choice of one’s STEM major. The resources have been implemented successfully at the University of South Florida, Arizona State University, Old Dominion University, Milwaukee School of Engineering, and Mississippi Valley State University. With philosophies of open dissemination and pedagogical neutrality, more than 30 institutions and thousands of individual users have adopted the resources in an a la carte fashion. In this paper, we discuss the history, philosophy, development, refinement, assessment process, and future of the open courseware. The summarized assessment results include those of comparing several instructional modalities, measuring student learning, effect of collecting homework for a grade, using online quizzes as a substitute for grading homework, interpreting summative ratings of the courseware, student satisfaction, and Google Analytics.


Assessing Online Resources for an Engineering Course in Numerical Methods (2012)

Corina Owens, Autar Kaw, Melinda Hess

Computer Applications in Engineering Education

Vol. 20, No. 3, pp. 426-433, 2012.


To determine, improve, and refine the quality of the online resources for an engineering course in Numerical Methods, three assessment instruments were used to gather feedback from 1) the independent instructors of the numerical methods course, 2) the students who use the majority of the resources, and 3) the general students worldwide who use resources on an as-per-need basis. The findings of this study provide strong evidence that the use of the website modules is a valued aide to most students. The availability of information in multiple modes and formats, at any time, for the students provides them with accessible and convenient learning material that enhances traditional methods. In addition, the analyses of the open-ended items by both faculty reviewers and students provided insights into how a website used in a technical course such as Numerical Methods can be effectively organized and implemented to enhance student learning. Using the multiple and innovative approaches described in the paper, the instruments and methods illustrated in this study can be used in any other course to help instructors assess their own online initiatives.


Does Grading Homework Improve Student Examination Performance? (2011)

Ali Yalcin, Autar Kaw

International Journal of Engineering Education

Vol. 27, No. 6, pp. 1333-1342, 2011.


Our goal is to examine the impact different homework grading policies have on students’ final examination performance. We are interested in not only the overall student performance, but also in the performance of specific student subgroups with varying backgrounds as well as the impact of homework on the type of learning that takes place in the course. The study was conducted in a Numerical Methods course at a large university in the southeast of USA over a period of three years encompassing data from over 300 hundred Mechanical Engineering students. Statistical analysis of data regarding the impact of homework grading policies on student subgroups based on several factors is presented. Our results indicate that there is no statistically significant difference in student examination performance when homework is collected and graded versus when homework is assigned and not graded. However, certain grading policies did seem to put some subgroups of students at a disadvantage. While grading homework may not be critical in improving student examination performance, it is important to ensure that students practice the concepts.


Measuring Student Learning Using Initial and Final Concept Test in a STEM Course  (2011)

Autar Kaw, Ali Yalcin

International Journal of Mathematics Education in Science and Technology

Vol. 43, No. 4, pp. 435-448, 2012.


Effective assessment is a cornerstone in measuring student learning in higher education. For a course in Numerical Methods, a concept test was used as an assessment tool to measure student learning and its improvement during the course. The concept test comprised of 16-multiple-choice questions and was given in the beginning and end of the class for three semesters. Hake’s gain index, a measure of learning gains from pre-test to post-test, of 0.36 to 0.41 were recorded. The validity and reliability of the concept test was checked via standard measures such as Cronbach alpha, content and criterion related validity, item characteristic curves, and difficulty and discrimination indices. The performance of various subgroups such as pre-requisite grades, transfer students, gender, and age were also studied.


Development And Assessment Of Digital Audiovisual YouTube Lectures For An Engineering Course In Numerical Methods (2011)

Autar Kaw, Sri Garapati

ASEE Computers in Education Journal

Vol. XIX (2), 2011, pp. 89-97.


Cyberlearning is transforming education by offering course content through multiple context and platforms. As part of this transformation, this paper describes the experience of preparing, recording, uploading, organizing, and assessing audiovisual lectures for an engineering course in Numerical Methods. More than 250 short modular videos are currently available that cover the syllabus of a comprehensive undergraduate course in Numerical Methods for Engineers. The motivation for the development of the audiovisual lectures was based on a pilot study that showed that the examination performance and student satisfaction increased with the availability of audiovisual lectures. A final assessment of these resources made via a video analytics tool shows increasing popularity of the videos, gives insight into the audience attention, and presents demographics by gender, age, and geography. In addition, a summative rating survey of the courseware shows significant increase in the value of the quality of content and enhancement in student learning.


Introducing and Assessing Laboratory Experience in a Numerical Methods Course for Engineers (2009)

Autar K. Kaw and Ali Yalcin

ASEE Computers in Education Journal

Vol. XVIIII (3), July-September 2009, pp. 57-65.


Several low cost, low space, low setup time experiments were developed and implemented in an undergraduate course in Numerical Methods for Engineers.  The analysis and interpretation of the collected experimental data encompassed most of the mathematical procedures covered in the course.  This paper describes these experiments and shows how they were used throughout the course.  The effect of introducing experiments in the course was quantitatively and qualitatively surveyed via student satisfaction surveys over a two-semester period.  The results of the student surveys indicate high student satisfaction, especially in the areas of applying programming concepts, problem formulation, and relevance to their engineering major.


Problem-Centered Approach in a Numerical Methods Course (2008)

Autar K. Kaw and Ali Yalcin

Journal of Professional Issues in Engineering Education and Practice

Vol. 134, No. 4, October 2008, pp. 359-364


This paper is an illustration of using a problem-centered approach in an undergraduate course in numerical methods. The problem used in the course was first encountered in a research project that related to the assembly procedure of the fulcrum of bascule bridges. It involved the study of the fulcrum assembly procedure where a trunnion cooled in a dry-ice/alcohol mixture for shrink fitting became stuck halfway in the hub before full insertion could take place. The solution of the problem and its implementation involved numerical solutions of mathematical procedures taught in a typical numerical methods course. The effect of the problem-centered approach in the classroom was quantitatively and qualitatively surveyed over a two-semester period. The results indicate very high student satisfaction in helping them: acquire basic knowledge and skills; reinforce information presented in class, reading assignments, and problem sets; learn to clearly formulate a specific problem and then work it through to completion; develop generic higher-order thinking and problem solving skills; and develop a sense of competence and confidence and see the relevance of the course material to their major.


Comparing Effectiveness of Instructional Delivery Modalities in an Engineering Course (2007)

Autar Kaw and Melinda Hess

International Journal of Engineering Education

Vol. 23, No. 3, pp. 508-516, 2007.


The effectiveness of four instructional delivery modalities, (i) traditional lecture, (ii) Web-enhanced lecture, (iii) Web-based self-study and (iv) Web-based self-study and classroom discussion, was investigated for a single instructional unit (Non-linear Equations) over separate administrations of an undergraduate engineering course in Numerical Methods. Two assessment instruments - student performance on a multiple-choice examination and 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, in which Web-based modules for instruction were used during face-to-face lecture delivery mode, resulted in higher levels of student performance and satisfaction.


Assessment of a Web-Enhanced Course in Numerical Methods (2005)

Autar Kaw, Glen Besterfield, and James Eison

International Journal of Engineering Education

Vol. 21, No. 4, pp. 712-722, 2005. 


Effectiveness of web-based modules developed for a course in Numerical Methods was measured via three mixed assessment instruments – student satisfaction survey, student performance in a multiple-choice examination based on Bloom’s taxonomy, and summative rating of the modules based on content, learning, usability and technology. The web-based modules are holistic and are customized based on a student’s engineering major and choice of computational system. Statistical analysis of the assessment data indicates that web-based modules for instruction improved both student satisfaction and performance.


Techniques Employed by Highly Effective Engineering Educators (2005)

Autar Kaw

ASCE Journal of Professional Issues and Engineering Education

Vol. 131, No 3, pp. 175-177, 2005.


Techniques include being organized, understand the importance of first day, use teaching tools effectively, being compassionate, give rapid feedback, ask questions, and having high expectations.


Holistic but Customized Resources for a Course in Numerical Methods (2004)

Autar Kaw, Nathan Collier, Michael Keteltas, Jai Paul, Glen Besterfield

Computer Applications for Engineering Education

Vol. 11, No 4, pp. 203-210, 2004


Prototype web based resources have been developed for an undergraduate course in Numerical Methods.  The web modules are holistic, that is they include pre-requisite information, real-life applications, presentations and notes, simulations, and self-assessment.  The student interest and learning are maximized by providing customization of content based on a student’s engineering major and computational system of choice.


On Comparing Computational Systems - Maple, MathCAD, MATHEMATICA & MATLAB (2004)

Nathan Collier and Autar Kaw

ASEE Computers in Education Journal

Vol. XIV, No 1, pp. 12-24, 2004. 


For developing web-based resources for an undergraduate course in Numerical Methods, four computational systems (Maple®, MathCAD®, MATHEMATICA®, and MATLAB®) were used to illustrate algorithms, convergence, and pitfalls of different numerical methods.  In this paper, we discuss the advantages and drawbacks of each mathematical package based on this experience.  Also as an example, from the four computational systems, we show the source code and output for one of the simulations.


Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.