A Model for Combining Allegorical Mental Imagery with Intuitive Thinking in Understanding the Limit of a Function

Abstract

The main purpose of this article is to use a combination of mental imagery and puppet allegory to intuition the concept of limit for learners. Usually to start teaching, teaching the limit of functions, there are several methods, but most instructors use the Epsilon and Delta formula. Obviously, starting with teaching with formulas, it is not easy to explain the concept of limit. Because, learners achieve a deep understanding of the limit, when the concepts become intuitive for them. Intuition of the limit of functions, with proper mental imagery and allegory, can make understanding the limit easy and enjoyable. Obviously, following the optimal understanding of the limit, understanding, Neighborhood. Derivation and integrals, for learners It becomes easier. The use of a combination of mental imagery with puppet allegorical patterns to intuitive or sensory thinking that is the result of three decades of experience and teaching of the author, to be available to learners and educators. In this way, very soon, learners (especially non-mathematics learners), especially in high school classes, or the first years of university, they manage to have a deep understanding of the limit, Because one of the ways to teach mathematics is to use the properties of mental imagery to be objective or sensory through allegory, which has a high effectiveness and feedback in understanding the limit. In this article functions limit education is considered by combining mental and sensory imagery through allegory or simile with six puppet images. The experiences in this research can be used by teachers of teacher training centers, teachers and high schools and universities and designers of educational materials.