In the past many years, significant innovations have been introduced in the introductory Physics and Calculus sequences required of College of Engineering undergraduates. Increasingly, these rely on a substantial emphasis on active and collaborative learning paradigms, context-driven instruction, and appropriate use of in-class or internet-based technology. These innovations enhance the student experience and leave no student unsure of the purpose of the introductory classes in preparing for their subsequent education.
In my role as University of Illinois at Urbana-Champaign, College of Engineering Calculus Project Coordinator between 2009 and 2011, I strived to make sure that when the students come to the end of the long and demanding Calculus II class, they leave with a charge to demand and expect of their subsequent instructors that the material they have been taught will be used and reinforced. I found the students both receptive and appreciative of this advocacy on behalf of their education and on behalf of the topic that they have just worked so hard to command.
An article about the College of Engineering Calculus Project appeared in Creating Engineers for the 21st Century in Spring 2011.
With support from Grants for the Advancement of Education Engineering awarded by the Academy for Excellence in Engineering Education in the College of Engineering, I initiated a curricular development effort called "Student Teaching Scholars – a model for just-in-time recertification of core engineering knowledge and skills," whose objectives were to instill a practice of life-long learning and skills recertification in our undergraduate student population, and to also provide meritorious opportunities for qualified undergraduates to receive education training and experience in leading recertification sessions as part of an Engineering Student Teaching Scholars program. During the 2012/13 and 2013/14 academic-years, this effort sought to:
- identify critical core concepts from the introductory calculus and linear algebra sequence that are targets of opportunity for recertification;
- develop pedagogically sound learning material for an accelerated recertification schedule;
- identify and develop a student-focused learning environment conducive to active and engaged recertification; and
- identify and invite potential Student Teaching Scholars and institute a recognized mechanism for rewarding their participation.
Project team: Harry Dankowicz and four undergraduate research assistants.
One of the insights of innovative teaching paradigms is that the pace of learning is defined by the individual student, not by the instructor. This becomes all the more evident in a flipped classroom environment, where most of the instruction occurs outside of the classroom, and the in-class experience is one of guided discovery. To be effective as an instructor in such a context requires careful articulation, analysis, and dissemination of learning objectives, significant opportunities for practice of rote skills in addition to exposure to concepts, and a humble willingness to prioritize when choosing content.
During the Spring, Summer, and Fall semesters in 2015, I implemented a flipped classroom learning environment in ME 340, Dynamics of Mechanical Systems, a junior-level required course on models of dynamical systems and tools for their analysis, including initial-value-problems, block diagrams, Laplace transforms, mode shapes and natural frequencies, frequency-response curves, and Newtonian and Lagrangian dynamics. I developed a 200+ page textbook consisting of narrative material and extensive collections of solved exercises. For each of the 10 chapters, the initial narrative material was produced into a total of 14 online prelectures (~5 min each) and associated multiple-choice questions that were to be completed by the students in advance of class on designated days during the semester. Additional narrative material was worked into 29 worksheets, to be completed in class in lieu of regular lectures.
Formative assessment of student progress was implemented using seven, multiple-choice in-class tests throughout the semester. Summative assessment was accomplished using a final exam with work-out problems, including seven optional questions, two of which could be used to replace the two lowest test scores. Additional learning opportunities included homework assignments with primary and secondary due dates and experimental labs with pre- and post-lab assignments.
Project team: Harry Dankowicz with feedback from close to 100 undergraduate students.
Undergraduate instruction into the subject of classical mechanics constitutes a first attempt at incorporating the mathematics taught in the undergraduate linear-algebra and calculus sequences with real-world applications, developing ideas of physical and mathematical modeling, assessing the relevance of physical phenomena, the appreciation of modeling assumptions, and the formulation of scientific inquiry. The field of multibody mechanics offers a natural environment in which to develop students’ skills in abstraction and model reduction. It allows the instructor to disassociate modeling assumptions regarding the purely geometric characteristics of a mechanism from assumptions regarding mass distribution and, the more challenging, assumptions regarding physical interactions with the environment.
These observations have served as the impetus for the continuous development of course material and instructional resources for instruction in "Multibody Mechanics and Visualization." Various versions of this course were successfully implemented in the undergraduate curriculum for computer engineering and computer science sophomores at KTH Royal Institute of Technology in Sweden between 1999 and 2003; as an undergraduate engineering-science elective for electrical and computer-engineering juniors and seniors and as a graduate-level class at Virginia Polytechnic Institute and State University between 2000 and 2004; and as a technical elective for mechanical-engineering seniors and as a graduate-level dynamics class since 2006 at the University of Illinois at Urbana-Champaign.
Examples of innovative courseware developed for this course are MAMBO and the MAMBO toolbox, described on the MAMBO website as well as the textbook Multibody Mechanics and Visualization, published by Springer-Verlag, UK, in 2004.
The responsible conduct of research (RCR) relies on a careful assessment of standards of good practice and ethics that serve to maintain broad-based trust and reliance on the scientific method in the search for testable explanations of natural phenomena, in the application to design and problem solving, and in the service of formulating policy recommendations.
Model development is that act of scientific authorship in which salient features of an observable phenomenon are reduced to an accessible formulation that enables the testing of scientific hypotheses in a rigorous and effective manner. The classical engineering sciences have used mathematical models, e.g., systems of differential equations, that reflect essential properties of a physical system and whose solution describes the system behavior. In the past thirty years, a new class of model development has become feasible, namely, the synthesis of computational models that produce quantitative information about the behavior of complex systems. Computation extends the analyst's ability to understand he behavior of simple mathematical models for which closed-form solutions are not available. More importantly, computational modeling and research is now a sub-discipline of existing engineering and science fields. In many cases, researchers can bypass the formulation of a mathematical model and instead reduce system behavior directly to computational algorithms.
With support from the National Science Foundation program for Ethics Education in Science and Engineering, I am currently engaged in a curricular development and research effort called "The Responsible Conduct of Computational Modeling and Research," whose objectives are to
- identify and examine the ethical issues and accepted professional standards for responsible conduct of computational modeling and research, particularly those not shared with experimental research.
- identify and examine standards of good practice in evaluating model integrity, model robustness, model representations, data and code integrity, and intellectual property rights.
- develop graduate-level instructional materials to engage students in domain-generic, disciplined reasoning about ethical problems and standards specific to computational modeling and research, e.g., through case studies and associated commentaries.
- assess the quality and educational effectiveness of the instructional materials with graduate students and instructors at two or more universities.
- disseminate the instructional materials through demonstrations at conferences, publications in journals, and archiving at the Online Ethics Center of the National Academy of Engineering.
The project objectives constitute an integrated effort aimed at empirically establishing accepted standards of practice in computational modeling and research, and enabling the deployment of education modules on related issues of responsible conduct of research throughout graduate programs in engineering and science.
The package "Responsible Conduct in Computational Modeling and Research" (.pdf, 1.86 Mb) contains resources for academic instruction and professional training in the responsible conduct of computational modeling and research, providing the reader with a framework within which to establish the integrity and trustworthiness of computational representations and their predictions. The package discusses learning objectives and pedagogical approaches, and provides tools appropriate for use in instruction, for example, fictional case studies, scoring guides, and check lists.
For additional information, see the project website.