Definitions and Images for the Definite Integral Concept

Abstract

Definitions and images, as well as the relation between them of the definite integral concept, were examined in 41 English high school students. A questionnaire was designed to explore the cognitive schemes for the definite integral concept that are evoked by the students. One question aimed to check whether the students knew to define the concept of definite integral. Five others were designed to categorize how students worked with the concept of definite integral and how this related to the definition. The results show that only 7 students out of 41 of our sample knew the definition. All mathematical concepts except the primitive ones have definitions. Many of them are introduced to high school or college students. However, the students do not necessarily use the definition to decide whether a given idea is or is not an example of the concept. In most cases, they decide on the basis of their concept image, that is, all the mental pictures, properties and processes associated with the concept in their mind. (Tall & Vinner, 1981; Rasslan & Vinner, 1997). The concept of the definite integral is a central in the calculus. In many countries, including the UK, it is taught in the last two years of school to students aged

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