# Facilitating Learning Events Through Example Generation

- 301 Downloads
- 47 Citations

## Abstract

This study deals with the initial understanding that advanced undergraduate mathematics students exhibit when presented with a new concept in an environment requiring self-generation and self-validation of instances of the concept. Data were collected in spring of 1995 through interviews with 11 third and fourth year undergraduate mathematics students. We discuss the data from the perspective of the student's concept image and introduce the notion of learning event to indicate when a student communicates and applies a new understanding of a concept. We infer that the students in our study who employed an example generation learning strategy were more effective in attaining an initial understanding of the new concept than those who primarily employed other learning strategies such as definition reformulation or memorization.

## Keywords

Learning Strategy Learn Event Generation Learning Concept Image Mathematics Student## Preview

Unable to display preview. Download preview PDF.

## REFERENCES

- Breidenbach, D., Dubinsky, E., Hawks, J. and Nichols, D.: 1992, ‘Development of the process conception of function’,
*Educational Studies in Mathematics***23**, 247–285.Google Scholar - Davis, R.B. and Vinner, S.: 1986, ‘The notion of limit: Some seemingly unavoidable misconception stages’,
*Journal of Mathematical Behaviour***5(3)**, 281–303.Google Scholar - Eisenberg, T. and Dreyfus, T.: 1991, ‘On the reluctance to visualize in mathematics’, in W. Zimmermann and S. Cunningham (eds.),
*Visualization in Teaching and Learning Mathematics*, MAA Notes Series**19**, 25–37.Google Scholar - Ernest, Paul: 1991,
*The Philosophy of Mathematics Education*, The Falmer Press, Taylor & Francis, Inc., Bristol, PA USA.Google Scholar - Hitt, Fernando: 1994, ‘Teachers' difficulties with the construction of continuous and discontinuous functions’,
*Focus on Learning Problems in Mathematics***16**,n4, 10–20.Google Scholar - Leinhardt, G., Zaslavsky, O. and Stein, M.: 1990, ‘Functions, graphs, and graphing: Tasks, learning and teaching’,
*Review of Educational Research***60(1)**, 1–64.Google Scholar - Moore, R.C.: 1994, ‘Making the transition to formal proof’,
*Educational Studies in Mathematics***27**, 249–266.CrossRefGoogle Scholar - Selden, J. and Selden, A.: 1995, ‘Unpacking the logic of mathematical statements’,
*Educational Studies in Mathematics***29**, 123–151.CrossRefGoogle Scholar - Spangler, D.A.: 1992, ‘Assessing student beliefs about mathematics’,
*Arithmetic Teacher***40**,n3, 148–152.Google Scholar - Tall, D.O.: 1992, ‘The transition to advanced mathematical thinking: functions, limits, infinity, and proof’,
*Handbook of Research on Mathematics Teaching and Learning*, NCTM, p. 495–511.Google Scholar - Tall, D.O. and Vinner, S.: 1981, ‘Concept image and concept definition in mathematics, with particular reference to limits and continuity’,
*Educational Studies in Mathematics***12**, 151–169.CrossRefGoogle Scholar - Vinner, S.: 1989, ‘The avoidance of visual considerations in calculus students’,
*FOCUS: On Learning Problems in Mathematics***11**, 149–156.Google Scholar - Vinner, S. and Hershkowitz, R.: 1980, ‘Concept images and common cognitive paths in the development of some simple geometrical concepts’,
*Proceedings of the Fourth International Conference for the Psychology of Mathematics Education*, Berkeley CA, p. 177–184.Google Scholar - von Glasersfeld, E.: 1984, ‘An introduction to radical constructivism’, in P. Watzlawick (ed.),
*The Invented Reality*, Norton, New York, p. 17–40.Google Scholar - Zimmermann, W. and Cunningham, S.: 1991, ‘Editors' introduction: What is Mathematical Visualization’, in W. Zimmermann and S. Cunningham (eds.),
*Visualization in Teaching and Learning Mathematics*, MAA Notes Series**19**, 1–7.Google Scholar