Types of Task related to “Tangent to a Curve” Concept for 11th Grade Students in Vietnam: A Study based on the Anthropological Theory of the Didactic

Abstract

Topic “the tangent to a curve” is one of main contents of Calculus. The problem “find the tangent to the graph of a function” was mentioned in the curriculum of Algebra and Calculus for 11ͭ ͪ Grade in Vietnam when students begin to study “derivative” concept, geometrical meanings of derivative. We approached to the Anthropological Theory of the Didactic which considered a model of school mathematical activity as a “praxeology” consisting of a practical clock (know-how) and theoretical block (knowledge) to study the types of task related to “tangent to a curve ” concept in Algebra and Calculus for 11ͭ ͪ grade students in Vietnam. The results were that all the types of task in textbooks only had only mathematical contents. It showed that Vietnamese mathematics educators paid little attention to realistic mathematics in teaching mathematics to secondary school students. In addition, another investigation indicated that 11ͭ ͪ grade students in Vietnam found it impossible to determine the tangent to the graph of a function defined implicitly.