The Students’ Images and Definitions of the Function Concept from Single Variable to the Two Variable Functions
Because function concept is one of the foundation stone of the mathematics, the mathematics education literature includes a lot of studies on this concept. The focus on multiple representations of the function concept has been a topic of research in mathematics education for the past twenty years. Since the 1960’s, Drichlet-Bourbaki definition of the function concept is seen in the most textbooks and the curricula. According to the Dirichlet-Bourbaki approach, functions are defined as a correspondence between two non-emty sets that assigns every element in the domain to exactly one element in the range. Tall and Vinner (1981) call the total cognitive structure which includes all the mental pictures, properties and processes associated in the student’s mind with the concept name by the concept image. According to Tall and Vinner, the definition of a concept which they call by the concept definition is a form of words used to specify the concept.
In Spite of the fact that the mathematics education literature includes several studies of single variable functions, students have various misconceptions and difficulties with this concept. When faced with the multivariable functions, understanding is getting more difficult for students. They must confront several “cognitive” shifts to understand the concept of the multivariable functions. The aim of the study is to determine the students’ developments of images and definitions of the function concept from single variable to the two variable functions. A test which is on single variable functions was prepared and conducted to 22 students at the beginning of multivariate analysis course. After concept of the two variable function was given to these students, another test on two variable was prepared in a similar manner and conducted to the students. Students’ developments of images and definitions of the function concept from single variable to the two variable functions were analyzed qualitatively.
Keywords: Function, Concept Image, Concept Definition
Assistant Proffessor, Elementary Mathematics Education Program, Anadolu University