Abstract
The results shown in the following chapter come from a research that shows some of the transformations of the concept of linear function observed from its definition in mathematics when facing the written, intended and enacted curriculum. This study was developed in technological high school level, with the participation of three teachers of mathematics, who were teaching the course called Functions and Algebraic Thinking. A case study was considered as a practical research method to carry out the investigation, adopting various processes to gather evidence to describe, verify or create theory. Different sources of evidence were used to gather and analyze information, such as: the official program of the course, three textbooks, class recordings and the application of a questionnaire. The results show transformations in both, the concept of function and the concept of linear function, pointing out, in this way, an educational problem that should be solved by modifying not only the concept, but also the teaching and learning of it.
TopProblem Statement
The study of the concept of function in the teaching of mathematics in high schools plays an important role in students’ learning, not only for the fact of being related to topics of different subjects, but also for the fact that it allows to represent real situations (Hitt, 2002). The different difficulties that arise when there are new studies related to the concept of function or to a type of function must also be emphasized.
Diaz (2008) notes that the curricular aspect of the concept of function is a kind of strand that goes from the basic education to university. He also warns about the difficulties the students face to understand this concept, as well as how this concept has generated a growing body of researches, like the ones that study the problem of teaching, the difficulties of learning, those that propose theoretical frameworks or even those that are focused on the diversity of interpretations of the concept of function.
There are several authors that have been devoted to work on the concept of function. During the 1980s, Leinhardt, Zaslavsky and Stein (1990) made a bibliographic revision, in which they showed the difficulties that students face when they try to conceptualize the idea of function, emphasizing issues related to the function such as rule of correspondence as well as its different representations, its reading and interpretation. On the other side, in the research done by Birgin (2012), linear functions are seen as a complex idea of multiple faces whose power and richness cover almost all of the mathematical areas. It is important to add that due to its several applications in the real world some topics of more advanced level, like those that come from calculus, can be reinforced.
Key Terms in this Chapter
Transformations: These refer to a change or modification of an idea, concept, figure or image.
Linear Function: Linear functions have the following form: , where is the slope of the line and is the length of the intersection with the y axis to the origin.
Teaching: It involves the interaction of three elements: the teacher, student and the object of knowledge.
Mathematics Teacher: A professional that must have a thoughtful attitude regarding his own performance as a teacher.
Function: It is a rule that assigns each element of a first group a unique element of a second group. A function relates an independent variable to a dependent variable, so that to each value of the first, corresponds one single value of the second.
Lesson Recording: A tool used in research and the observation of facts, phenomena, processes and individuals, so as to demonstrate what was observed within a specific time and space.
Technological High School: An educational subsystem that corresponds to high school and offers a bivalent academic training.
Curriculum: The group of organized elements, with teaching purposes, that systematize the academic career of students.
Representation: Any way or form in which an object, an idea or a concept is shown.