Investigation of the conception of third-grade female high school students of the concept of limit and continuity

One of the most important concepts in mathematics, which has always been difficult for students to understand, is the concept of limit. Due to the connection of this concept to many other concepts such as infinitely large and infinitesimally small, continuity, derivative and integral, its correct understanding and comprehension is of particular importance and this has led to its teaching and learning by math educators. Although this concept has been explored many times in educational research by researchers, it is still difficult for students to understand. There are several ways to identify problems in understanding concepts, including the concept of limit. One of these methods is to study how concepts and structures are formed that students create to learn concepts in their minds. The aim of this study is to assess students, understanding of the concept of limit in the third year of secondary school based on the APOS theory. APOS theory is a theory of learning that is used in academic mathematics. The theory categories students’ understanding of concept across the levels, and is able to models mental structures that person to understand of the concept.

 Method and Materials: 

This research is a descriptive study using survey. The sample of this research is 234 students in third grade from Qarchak city who have been randomly selected. The instrument is a researcher-made questionnaire with six questions. The reliability of the test was estimated by Cronbach’s alpha and is approved in the amount of 0.82.

The results show that most students do not have a good understanding of the concept of limit and they mostly can do the limit problems correctly, if they have a routine way to solve them. The weak structures affect not only their understanding of the concept, but also depend on the understanding of the concepts such as continuity.

When introducing the concept of limit, the teacher can prevent the construction of correct schemas of the concept of limit by using slang and giving the initial idea. Because the role of the teacher in constructing a concept of limit is very important, if the teacher teaches in an inappropriate way, it may prevent the student from absorbing the concept of limit. Another reason for stopping the growth and development of the concept is the continuous evaluations in educational environments that do not emphasize the need for conceptual understanding of the concepts and are limited to routine methods to achieve better results. For this reason, doing research in the field of teaching and learning any concept in mathematics, such as the concept of limit, can lead to more effective teaching strategies.