# Images of the limit of function formed in the course of mathematical studies at the university

@article{Przenioso2004ImagesOT, title={Images of the limit of function formed in the course of mathematical studies at the university}, author={Małgorzata Przeniosło}, journal={Educational Studies in Mathematics}, year={2004}, volume={55}, pages={103-132} }

The paper is based on extensive research carried out on students of mathematics who had completed a university course of calculus. The basic purpose of the research was to determine the students' images of the concept of limit, that is to find out their associations, conceptions and intuitions connected with limits and to determine the degree of their efficiency and the sources of their formation. To achieve the objectives an expanded set of selected problems — simple but not quite standard…

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## References

SHOWING 1-10 OF 18 REFERENCES

### Some Remarks on Understanding in Mathematics.

- Philosophy
- 1990

ing and epistemological obstacle are found; it is argued that understanding as an act and the act of overcoming an obstacle can be regarded as complementary images of the same mental reality.…

### Models of Limit Held by College Calculus Students.

- Education
- 1991

This study documents 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Common informal models of limit were identified among the 10…

### Concept image and concept definition in mathematics with particular reference to limits and continuity

- Education
- 1981

The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept. This may not be globally coherent and may have aspects which are quite…

### Higher Mathematics Education

- Education
- 1996

This chapter pertains to higher mathematics education in various countries of the world. We try to present a review of significant and interesting research investigations and teaching experiences.…

### Conflicts in the Learning of Real Numbers and Limits.

- Education
- 1978

The majority of students thought that 0.999 . . . was less than one. It may be that a few students had been taught using infinitesimal concepts, or that the phrase “just less than one” had…

### The Psychology of Advanced Mathematical Thinking

- Psychology
- 2002

Exponents of the two disciplines are likely to view the subject in different ways the psychologist to extend psychological theories to thinking processes in a more complex knowledge domain the…

### Understanding in Mathematics

- Education, Philosophy
- 1994

Chapter 1 Understanding and Meaning: Understanding Meaning. Chapter 2 Components and Conditions of an Act of Understanding: What could be an act of understanding? Components of an act of…

### Thought and language

- Philosophy
- 1962

Since it was introduced to the English-speaking world in 1962, Lev Vygotsky's highly original exploration of human mental development has become recognized as a classic foundational work of cognitive…