Journal Articles

Journal Publications

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Benefits of adaptive lessons for pre-class preparation in a flipped numerical methods course (2019)
International Journal of Mathematical Education in Science and Technology

A challenge with flipped instruction is the pre-class preparation, where students independently learn fundamental content outside the classroom. For this pre-class learning, instructors typically assign videos with quizzes. However, this approach is the same for all and does not address differential needs. In a prior National Science Foundation (NSF) study with three schools, differences in the outcomes for blended versus flipped instruction in a numerical method course were not statistically significant, and the effect sizes were small. To diversify pre-class preparation and potentially improve outcomes in the flipped classroom, the instructor developed lessons using an adaptive platform via a new NSF grant. The adaptive platform provides personalized, flexible learning with multiple resources, including videos, text, quizzes, and simulations, with different paths depending on a student’s progress. Adaptive lessons were implemented during two semesters in a flipped classroom, and the results were compared to (1) flipped instruction without adaptive lessons and (2) blended instruction. The comparisons consisted of direct assessments (i.e. exams) and student evaluations via survey. Analysis was done collectively for students and for several demographic groups. Based on direct and indirect measures, the flipped classroom with adaptive learning may be the preferred method for this and other STEM courses.

Analyzing the Use of Adaptive Learning in a Flipped Classroom for Pre-Class Learning (2019)
Computer Applications in Engineering Education
Vol. 27, pp. 663‐ 678, 2019.

Preclass learning, an obstacle in the success of a flipped classroom, is addressed via placing lessons on an online adaptive platform. The lessons combine the power of video lectures, textbook content, simulations, and assessments while using personalized paths for each student. This article describes the development of the adaptive lessons for a course in Numerical Methods, and the interpretation of the analytic data collected via the adaptive lesson platform and student focus groups over a two‐semester period with 146 students. Analytical data includes student metrics, such as the lesson scores and the time spent and lesson metrics, such as the percentage of students who completed the lesson and the percentage of possible adaptive paths used by students. The focus groups were conducted for two different demographic groups—students who are “white males” (comprise the majority of students in public engineering schools in the USA) and “other than white males”—to compare their perspectives on adaptive learning. Students in the focus group of the “other than white male” pupils demonstrated more favorable and positive perspectives towards the adaptive learning compared with the “white males”, although both groups identified benefits with the adaptive platform. Final examination scores were found to be correlated with the raw score of the adaptive lessons.

Evaluating Blended and Flipped Instruction in Numerical Methods at Multiple Engineering Schools, (2018)(Free)
International Journal for the Scholarship of Teaching and Learning
Vol.12 (1), 2018.

With the literature calling for comparisons among technology-enhanced or active-learning pedagogies, a blended versus flipped instructional comparison was made for numerical methods coursework using three engineering schools with diverse student demographics. This study contributes to needed comparisons of enhanced instructional approaches in STEM and presents a rigorous and adaptable methodology for doing so. Our flipped classroom consisted mostly of in-class active learning, with micro-lectures as needed, and technology used both in and out of class, including for expected pre-class review of new content. Our blended classroom consisted mostly of lecture with some in-class active learning, and technology utilized both in and out of class. However, students were not expected to review new content before class. We compared blended vs. flipped instruction based upon multiple-choice and free-response questions on the final exam as well as the perceived classroom environment. This was done for students as a whole as well as for under-represented minorities (URMs), females, community college transfers, and Pell Grant recipients. Students provided feedback via focus groups and surveys. Upon combining data from the schools, the blended instruction was associated with slightly greater achievement on the multiple-choice questions across various demographics, but the differences were not statistically significant, and the effects were small. Our free-response final exam and classroom environment data aligned, with blended instruction showing more promise at two schools. The students identified demanding expectations with flipped instruction but pointed to benefits, such as enhanced learning or learning processes, preparation, and engagement. These results aligned with our focus group and instructor interview data. Thus, in general, it may be possible to use either instructional approach with the expectation of similar outcomes in final exam scores or the perceived classroom environment, keeping in mind the students qualitatively identified benefits with flipped instruction. Nonetheless, there were some large differences for the schools individually, suggesting further research with different demographics.

Comparing the Effectiveness of Blended, Semi-Flipped, and Flipped Formats in an Engineering Numerical Methods Course (2016) (Free)
ASEE Advances in Engineering Education
Vol 5(3), 2016.

Blended, flipped, and semi-flipped instructional approaches were used in various sections of a numerical methods course for undergraduate mechanical engineers. During the spring of 2014, a blended approach was used; in the summer of 2014, a combination of blended and flipped instruction was used to deliver a semi-flipped course; and in the fall of 2014, a fully-flipped approach was taken. Blended instruction aims to integrate technology-driven instruction with face-to-face learning and is often used to enhance the traditional lecture. With “flipped” instruction, students practice skills during class after viewing or/and reading lecture content beforehand. To directly assess these instructional methods, we compared multiple-choice and free response results from identical final exams. We did this for all students as well as demographic segments of interest to our research, including underrepresented minorities and transfer students. We uncovered several differences having medium to large effect sizes, suggesting that some degree of flipped instruction may have been more beneficial than blended learning for both lower and higher-order skills development. The students rated the classroom environment using Fraser’s College and University Classroom Environment Inventory (CUCEI). The three classroom environments were statistically similar with small effect sizes. However, there was a trend in lower ratings for the flipped and semi-flipped classrooms versus the blended classroom across the various environmental dimensions. This may indicate that blended instruction had the most desirable classroom environment. Based on an evaluation survey, only 38% of respondents preferred flipped instruction to usual methods, although 54% preferred active learning to lecture. In an open-ended question, the most frequently-stated benefits of flipped instruction involved enhanced learning or learning processes, and engagement and professional behaviors. These results aligned with our focus group results. This study is believed to be one of the first to compare these three modalities in a STEM course.

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 similar 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 ( 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, the 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 were 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 was 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 a 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.