Description of Research

I have carried out problem solving research in the area of mathematics education, and also I have worked in the content area of applied mathematics. The paragraphs below will present a brief description of my research in these two areas.

In the area of mathematics education, I am engaged in the Calculus Problem Solving research work. I have published in refereed journals in this area and in the area of Microteaching, and I have presented papers in various national and international meetings.

One of my paper in the area of problem solving examines various learning theories keeping in view of psychological aspects of problem solving behaviors of students. I have analyzed further Lester’s four research variables -- Task, subject, process and instructional, and formulated research questions for future research studies.

Additionally, my Ph.D. research dissertation entitled “ An Exploration of Cognitive-Heuristic Processes and Difficulties in Solving Calculus Word Problems” was completed at University of Maryland College Park. The main thrust of my dissertation was to explore the “cognitive-heuristic” processes employed and difficulties encountered by the university students in solving calculus problems. The statistical procedure used was principal component analysis reducing the variables and transforming the data such that the new set of variables or components obtained are uncorrelated. Furthermore, regression analysis on principal components with 156 cases suggested that the evaluation processes, and misuse of calculus concepts and differentiation errors significantly ( alpha = 0.05) affect the task performance. This study was an exploratory venture designed to report data-grounded hypothesis and questions. Moreover, the hypothesis generated may not always be affirming, but the prospect of making even a small contribution to theoretical foundation and classroom instruction should be exciting and heartening to problem solving researchers.

In the second area of my research, I have worked on some problems that relates to the applied mathematics area of elastic vibrations of beams that could represent turbo-machinery blades. The paragraph below will describe the nature and importance of the research study.

The problem of determining a mathematical estimation of the natural frequencies and modes of bending vibrations is important at an early design stage of turbo-machinery blades. The failure of any one of several thousands rotating turbo-machinery blades may result in system shutdown. All of the blades possess different characteristics such as setting angle, root fixing etc., and there are many other factors (e.g., the rotating speed, disk radius, blade pre-twist, blade asymmetry etc.), which play an important role in blade design. Because of the inherent mathematical intricacies in describing mathematical models that are necessary at an early prototype design stage of turbine blades, many important engineering problems remain unsolved. 

The research papers in the area of elastic-beam vibrations problems are published in the refereed journals (national and international), and in the proceedings of the International Conference on Computational Engineering Sciences (ICES) meetings held at Hawaii, Costa Rica, and Atlanta. Also, visit my web site: http://faculty.coppin.edu/arsahu/ for more information.

Following is the list of publications in the research area of mathematics education and applied mathematics:

Research Papers Published in Refereed Journals

1. Atma Ram Sahu (1985); An Introduction of Microteaching: A Systems Approach; International Journal of Mathematics Education in Science and Technology, Vol. 16, No. 1, pp.25-31.

2. Atma Ram Sahu (1984); Microteaching: Some research Studies and Research Questions; International Journal of Mathematics Education in Science and Technology, Vol. 15, No. 6, pp.727-735.

3. Atma Ram Sahu (1983); On Some Educational and Psychological Aspects of Problem Solving. International Journal of Mathematics Education in Science and Technology, Vol. 14, No. 5, pp.555-563.

4. Atma Sahu (2001): Theoretical Frequency Equation of Bending Vibrations of an Exponentially Tapered Beam Under Rotation. Journal of Vibration and Control, Vol. 7 (in press). Also, published in ICES’97 proceedings: Advances in Computational Engineering Science, Atluri Satya, &Yagawa Genki (Editors). Tech. Science Press pp. 70-78;

ISBN: 0 96 570001 0 0.

5. Atma Sahu (2001): Effect of small change in depth on frequencies of torsional vibrations of a pre-twisted beam of rectangular cross-section. Far East Journal of Applied Mathematics (in press). ISBN 0972-0960.

6. Atma Sahu (2001): A perturbation procedure analysis to determine the change in bending frequencies of a turbine blade due to a small change in its cross-section. Far East Journal of Applied Mathematics (in press). ISBN 0972-0960. Also published in Modeling and Simulation Based Engineering, Tech Science Press, Palmdale CA pp.1176-1182, ISBN 09657001; ICES’98 October 6-9, 1998.

7. Atma Sahu (1998): Determination of the Change in Bending Frequencies of a Wedge Shape Turbine Blade Due to a Small Change in the Radius of Rotating Disc. Modeling and Simulation Based Engineering, Atluri, S.N. and O’Donoghue (Editors). Tech Science Press, Palmdale CA pp.1170-1175, ISBN 09657001; ICES’98.

8. Atma Sahu (1995): The Effects of Resisting Media and other Rotating Beam Parameter Changes on the Fundamental Frequency of Bending Vibrations. Computational Mechanics’95 Vol.1, Atluri, S.N.; Yagawa,G. and Cruse,T.A. (Editors.). Springer-Verlag Berlin Publications, NY.pp. 1274-1278, ISBN 3-540-59114-1; ICES’95.

9. J.S.Tomar and A.R.Sahu (1977): Bending Vibrations of an Exponential Beam in a Centrifugal Force Field. The Journal of the Aeronautical Society of India, February-May, Vol. 29, No.1-2.

10. Atma Sahu (1975): Conical Design of a Blade of Turbomachinery and the Effects of Various Blades Parameters on its Vibration Characteristics, Journal of Structural Engineering, April, Vol. 3, No.1, pp.37-46.

11. Atma Sahu and J.S. Tomar (1975): Torsional Vibrations of a Pre-Twisted Cantilever Beam. Indian Journal of Pure & Applied Mathematics. Vol.6, No.2, February, pp.151-157.

12. J.S.Tomar and A.R.Sahu (1975): Bending Vibrations of Wedge Shape Beam in a Centrifugal Force Field. Journal of Aeronautical Society of India, August, Vol. 27, No.3, pp.125-132.

Research Proceedings

Sahu, A.R., Bhargava, R.R., Gupta, A.P. (editors) (2001); Advances in Elastic Vibrations and Smart Structures. Phonix Publishing House Pvt.Ltd. New Delhi, pages 281, (ISBN 81-7484-043-5).

Acknowledgements for this publication: Partially funded by National Science Foundation.

Research Monograph

Sahu, A., Quinn, D.D., Sotelino, E. (2001). The Elastic Vibrations, Smart Structures and Their Solution Technologies. National Science Foundations Grant INT 0002002000 report.