Radu C. Cascaval
Assistant Professor of Mathematics
University of Colorado Colorado Springs
Letters, Arts and Sciences
Mathematics
Applied Mathematics
1420 Austin Bluffs Parkway
Colorado Springs, CO 80918
719.255.3759
a. What is the central question, issue, or problem you plan to explore in your proposed work?
The central question is: “What is the most effective method for introducing computational tools early
in the math curriculum for undergraduates in STEM disciplines?”
b. Why is your central question, issue, or problem important, to you and to others who might benefit from or build on your findings?
Finding an answer to our central question would be crucial in the
next step of designing and implementing optimal courses and labs (or other instruments, traditional
or online), intended to match the rest of the common Math curriculum. If done properly, it could
benefit all science and engineering majors taking Math courses at UCCS. Other universities of similar size, academic mission, and structure could benefit equally from these findings in adapting
these practices to their own academic environment.
High-level computational platforms, such as Matlab, Mathematica and Maple, have evolved tremendously over the past decade and many, if not most, STEM fields have found regular use of one such platform. In Mathematics, a good undergraduate training now assumes several senior level applied courses, such as Mathematical Modeling or Stochastic Modeling. In recent years, it has become increasingly clear that students often reached these advanced (even senior level) courses without any formal exposure to basic computational tools. In this unfortunate situation, some of students were able to rectify the deficiency on the fly, but many were not, thus negatively impacting their course performance and diminishing their prospects for a technical career. The Department of Mathematics at UCCS has experimented with offering a course (Math 265 – Intro to Computational Mathematics) in the past two years, which has received very positive reviews from the students who actually enrolled. (See attached the Math 265 survey, Spring 2009). The overwhelming obstacle, which resides in front of such initiatives, has been that vast majority of students see no immediate incentives for them in place to have this class, so they do not even consider enrolling. In our opinion, making such a course mandatory is not seen as the solution to this problem. Instead, making it relevant to more majors and communicating it with the interested departments is a better alternative. In addition, advising could play a major role in overcoming the lack of incentives or other enforcements.
c. How do you plan to conduct your investigation? What sources of evidence do you plan to examine? What methods might you employ to gather and make sense of this evidence?
An extensive literature and web research, performed with the help of a student assistant, will help us develop a database of different practices that already exists at other universities, in specific fields(such as engineering, etc.) and across disciplines. We will then design instruments that quantify the outcomes of each method/experiment. These can be measurables such as: short term and medium term impact, course specific, relevance to the study towards a specific major, perceived relevance of the method for students who already graduated. A special emphasis will be give to the in-house practices of incorporating computational tools in different curricula. We intend to conduct several focus groups and subsequently build and administer a more extensive survey. We also plan to interview faculty and students at other regional universities (certainly all from within the CU system and beyond). A web survey of other programs and universities will also be conducted, and if necessary, selected faculty will be contacted at those institutions as well.
d. How might you make your work available to others in ways that facilitate scholarly critique and review, and that contribute to thought and practice beyond the local?
We intend to publish our findings in a relevant, peer-reviewed journal and also distribute them to
participating faculty directly. We also plan to attend and present our results to regional and national
meetings.
e. Include a literature review of the theory and effective teaching practice of the subject of your inquiry in order to locate your research in the literature preceding it.
A preliminary search already indicated the proposed inquiry belongs to a significant and active area
of research ([1], [2]). In particular, specific questions addressing the effective use of simulations in
the learning environment are already available ([3],[4]) and could be readily modified to address the
specifics of the STEM majors. We note the extensive literature present in the recent thesis [4] as the
starting point for our investigations.
References:
1. “STEM-Based Computational Modeling for Technology Education”, by Aaron C. Clark
and Jeremy V. Ernst, in Journal of Technology Studies, Vol 34, No. 1, Spring 2008
http://scholar.lib.vt.edu/ejournals/JOTS/v34/v34n1/clark.html
2. “Undergraduate Computational Science and Engineering Education”, SIAM Working
Group on CSE Undergraduate Education, by Peter Turner & Co-chairs, 2009,
http://www.siam.org/about/pdf/CSE_Report.pdf
3. Hargrave, C., & Kenton, J. (2000). Preinstructional Simulations: Implications for Science
Classroom Teaching. Journal of Computers in Mathematics and Science Teaching, 19(1),
47""58.
4. Magan de Leon, A. (2009): “Professor's and Student's Perceptions and Experiences of
Computational Simulations as Learning Tools”, PhD Thesis, Purdue University.
f. What is your record of innovation in teaching and/or the assessment of learning?
I was part of the 2006-2007 PTLC cohort, with a project related to the video archiving of math
lectures, which are then made accessible to asynchronous learners. A research paper detailing our
findings has appeared in the Journal of Asynchronous Learners Network in 2008 and the actual
video archiving has been extremely popular both among faculty and students.
g. Are you able to attend the required meetings as specified in Section 5, What are the Benefits?
Yes, as long as it does not conflict with my teaching assignments during AY 2010/2011.
h. Can you suggest an appropriate coach/mentor for your project? Please also provide the email address for your proposed coach/mentor.
I have not identified a coach/mentor at this time, but I am confident that I can find a good fit from the available coaches, either from UCCS or from the other campuses.
i. If your project is selected, are you willing to serve as a coach in PTLC in a future year?
I definitely plan to be a coach in future years, if selected.
