Abstract
This study investigated the mathematical behavior of graduate students and the experiences that contributed to their mathematical development and success. Their problem-solving behavior was observed while completing complex mathematical tasks, and their beliefs were assessed by administering a written survey. These graduate students report that a mentor, most frequently a high school teacher, facilitated the development of their problem solving abilities and continued mathematical study. The mentors were described as individuals who provided challenging problems, encouragement, and assistance in learning how to approach complex problems. When confronted with an unfamiliar task, these graduate students exhibited exceptional persistence and high confidence. Their initial problem solving attempts were frequently to classify the problem as one of a familiar type, and they were not always effective in accessing recently taught information or monitoring their solution attempts, but were careful to offer only solutions that had a logical foundation. These results provide numerous insights into the complexities of using and extending one's mathematical knowledge and suggest that non-cognitive factors play a prominent role in a student's mathematical success.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carlson, M., Buskirk, T. and Halloun, I.: 1999, ‘Assessing college students' views about mathematics with the Views About Mathematics Survey’, in press.
Carlson, M: 1998, ‘A cross-sectional investigation of the development of the function concept’, Research in Collegiate Mathematics Education, Conference Board of the Mathematical Sciences-Issues in Mathematics Education, AMS/MAA 7, 114–162.
Carlson, M.: 1997, ‘Views about mathematics survey: Design and results’, Proceedings of the Eighteenth Annual Meeting/North American Chapter of the International Group for the Psychology of Mathematics Education 2, 395–402.
Dossey, J. A., Lindquist, M.M., and Chambers, D. L.: 1988, ‘The mathematics report card: trends and achievement based on the 1986 National Assessment’, Educational Testing Service, Princeton, NJ.
Fennema, E. and Peterson, P.: 1985, ‘Autonomous learning behavior: A possible explanation of gender-related differences in mathematics’, in L. C. Wilkinson and C. Marrett (eds.), Gender Influences in Classroom Interaction, Academic Press, Orlando, FL, pp. 17–35.
Garofalo, J.: 1989, ‘Beliefs, responses, and mathematics education: Observations from the back of the classroom’, School Science and Mathematics 89, 451–455.
Halloun, I.: 1997, ‘Views about science and physics achievement. The VASS story’, Proceedings of ICUPE, College Park, MD: American Institute of Physics Press, College Park, MD, pp. 605–614.
Kroll, D. L.: 1989, ‘Connections between psychological learning theories and the elementary mathematics curriculum’, National Council of Teachers of Mathematics Yearbook, pp. 199–211.
Lester, F. K., Garofalo, J. and Kroll, D. L.: 1989, ‘Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior’, in D. B. McLeod and V. M. Adams (eds.), Affect and Mathematical Problem Solving: A New Perspective, Springer-Verlag, NY, pp. 75–88.
Mandler, G.: 1989, ‘Affect and learning: Causes and consequences of emotional interactions’, in D. B. McLeod and V. M. Adams (eds.), Affect and Mathematical Problem Solving: A New Perspective, Springer-Verlag, New York, pp. 192–201.
McLeod, Douglas B.: 1992, ‘Research on Affect in Mathematics Education: A Reconceptualization’, in D. A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, MacMillian Publishing, New York, pp. 575–596.
Monk, Steve: 1992, ‘A study of Calculus Students' Constructions of Functional Situations: The Case of the Shadow Problem’. Paper presented at the American Educational Research Association, San Francisco, CA.
Mura, Roberta, 1995, ‘Images of mathematics held by university teachers of mathematics education’, Educational Studies in Mathematics 28, 385–399.
Philippou, G. N. and Christou, C.: 1998, ‘The effects of a preparatory mathematics program in changing prospective teachers' attitudes towards mathematics’, Educational Studies in Mathematics 35, 189–206.
Schoenfeld, A. H.: 1989a, ‘Explorations of students' mathematical beliefs and behavior’, Journal of Research in Mathematics Education 20, 338–355.
Schoenfeld, A. H.: 1989b, ‘A framework for the analysis of mathematical behavior’, in D. B. McLeod and V.M. Adams (eds.), Aspects of Mathematical Thinking: A Theoretical Overview, pp. 11–45.
Strauss, Anselm and Juliet Corbin: 1990, Basics of Qualitative Research: Grounded Theory, Procedures and Techniques, Sage Publications, California
Thompson, A. G. and Thompson, P. W.: 1989, ‘Affect and problem solving in an elementary school mathematics classroom’, in D. B. McLeod and V. M. Adams (eds.), Affect and Mathematical Problem Solving: A New Perspective, Springer-Verlag, New York, pp. 162–176.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Carlson, M.P. The Mathematical Behavior of Six Successful Mathematics Graduate Students: Influences Leading to Mathematical Success. Educational Studies in Mathematics 40, 237–258 (1999). https://doi.org/10.1023/A:1003819513961
Issue Date:
DOI: https://doi.org/10.1023/A:1003819513961