Initiating a Programmatic Assessment Report

Abstract

In the context of a department of applied mathematics, a program assessment was conducted to assess the departmental goal of enabling undergraduate students to recognize, appreciate, and apply the power of computational tools in solving mathematical problems that cannot be solved by hand, or would require extensive and tedious hand computation. A test was designed and administered in order to discover whether students are adept at thinking computationally at various levels of mathematical maturity in the program. The results were explained by the mathematical maturation that goes hand-in-hand with the development of computational thinking.

Keywords:

• Computational thinking
• computational tools
• technology use
• conceptual understanding
• mathematical maturity
• assessment report
• program evaluation

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Corrigendum

ACKNOWLEDGEMENTS

This manuscript is dedicated to Prof. Zaur Berkaliev who took the lead position in the planning that went into the early stages of this paper. We would not have done this without him. Also, we would like to thank Prof. Chris Rasmussen, San Diego State University, for input during early phases of project planning and also during the conceptualization of the paper.

Notes

2. ¹More students either derived or discovered the simplification that follows from the lower triangular form by using the standard cofactor expansion of a determinant compared to those who apparently just “knew” this.

3. ²Such a “brute force” method was enacted by 55% of those students who obtained the correct answer (or 46% of the total population).

Additional information

Notes on contributors

Zaur Berkaliev

Zaur Berkaliev was a Professor of Mathematics and Statistics at California State University, Chico. He taught mathematics education at the Illinois Institute of Technology and served as a lecturer at Fresno State. He also taught mathematics at Karaganda State University in the former Soviet Union from 1985 to 1998. He held a doctorate in Mathematics Education from Indiana University and one in Applied Mathematics from Moscow State University. He passed away June 3, 2013 at age 53. His death was the result of a previously undetected health condition.

Shavila Devi

Shavila Devi is a full-time faculty member in the Mathematics Department at Kennedy-King College, One of the City Colleges of Chicago. She is currently pursuing a Ph.D. in Collegiate Mathematics Education (a joint degree with the Department of Applied Mathematics and Mathematics and Science Education) at the Illinois Institute of Technology. Her research and teaching interests are in undergraduate mathematics education, including community college students, developmental mathematics instruction, and teaching and learning of calculus. She is particularly interested in equity issues and successful strategies for traditionally underrepresented students.

Gregory E. Fasshauer

Gregory E. Fasshauer studied mathematics and English planning to become a high school teacher in Germany. Toward the end of his studies he fell in love with computational mathematics research, moved to the U.S. to earn his Ph.D., and has been working in the field ever since. He is still passionate about teaching and enjoys spending his time outdoors.

Fred J. Hickernell

Fred J. Hickernell was educated at Pomona College and the Massachusetts Institute of Technology. His research and teaching focuses on applied and computational mathematics and statistics. At the present he is looking for a more trustworthy algorithm for numerical integration.

Ozgul Kartal

Ozgul Kartal was a high school mathematics teacher for 5 years in the Republic of South Africa and in Turkey. She is currently a Ph.D. candidate in Mathematics Education at the Illinois Institute of Technology, and her research interests are in mathematical problem solving and modeling, and curriculum and instruction.

Xiaofan Li

Xiaofan Li was awarded his Ph.D. in Applied Mathematics from UCLA. He has taught undergraduate and graduate mathematics courses at Illinois Institute of Technology for many years. His research interests include computational mathematics with applications in fluid mechanics, materials science, and biology.

Patrick McCray

Patrick McCray was educated at the Illinois Institute of Technology. After a 30-year career in mathematical application software support in the pharmaceutical industry, he has been focusing on pedagogical issues with calculus instruction. His scholarly interests include the history of mathematics and mathematical exposition accessible to undergraduates, such as the transcendence of the base of the natural logarithms (e).

Stephanie Whitney

Stephanie Whitney is an Assistant Professor of Secondary Mathematics Education at DePaul University in the Department of Teacher Education. Her research interests are in how students make sense of mathematics and how teachers can support and elicit such thinking.

Judith S. Zawojewski

Judith S. Zawojewski is an Associate Professor Emeritus at the Illinois Institute of Technology and Senior Curriculum Developer at the University of Chicago Center for Elementary Science and Mathematics Education, both in Chicago. Her scholarly activity involves the design of mathematical modeling problems in engineering contexts and research on what and how students learn when working collaboratively in the solution of the modeling problems.