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

  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},
  • M. Przeniosło
  • Published 1 March 2004
  • Mathematics
  • Educational Studies in Mathematics
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… 

Three concepts or one? Students’ understanding of basic limit concepts

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of

Prospective mathematics teachers’ concept image on the limit of a function

The concept of limit is one of the prerequisite subjects in studying calculus. Previous studies indicate that the use of the limit concept in learning that is not in accordance with the limit concept

Students’ images and their understanding of definitions of the limit of a sequence

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students’ understanding of the rigorous definition of

The Abstraction Process of Limit Knowledge.

Limits are a basic and important concept in mathematics. They can be assumed as one of the most fundamental concepts and influential instruments of general mathematics because they lead especially to

Using Menelaus' Theorem and Dynamic Mathematics Software to Convey the Meanings of Indeterminate Forms to Students.

This study investigates the effectiveness of a teaching activity that aimed to convey the meaning of indeterminate forms to a group of undergraduate students who were enrolled in an elementary

Conceptions of a sequence formed in secondary schools

The paper is based on research carried out on secondary school students and students commencing their university studies in mathematics. The basic purpose of the research was to investigate the

Math majors' visual proofs in a dynamic environment: the case of limit of a function and the ϵ–δ approach

Despite few limitations, GeoGebra as a dynamic geometry software stood as a powerful instrument in helping university math majors understand, explore, and gain experiences in visualizing the limits

Mathematics Teacher Candidates’ Conceptual Knowledges of the Concept of Limit in Single-Variable Functions

The aim of this study is to investigate teacher candidates’ conceptual understanding of the concept of limit in single-variable functions. The study sample consisted of 30 students who were studying

The notion of motion: covariational reasoning and the limit concept

ABSTRACT This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit

Coordination of aproximations in secondary school students’ understanding of limit concept

Analysis of the answers of 64 post-secondary school students to 7 problems considering the dynamic and metric conception of limit of a function indicates that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.



Some Remarks on Understanding in Mathematics.

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.

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

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

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.

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

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

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

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