Student teachers’ knowledge of students’ difficulties with the concept of function

Abstract

An important part of the mathematics syllabuses at the secondary school level in most countries is the concept of function. However, secondary school students often experience difficulties with this concept. These difficulties are well-known in the research literature. The study applies the mathematical knowledge for teaching (MKT) framework, including the category knowledge of content and students (KCS). Teachers’ ability to anticipate students’ difficulties is one aspect of KCS. The aim of this study is to investigate secondary mathematics student teachers’ KCS regarding the concept of function. Ten mathematics student teachers participating in a Supplementary Teacher Education Program answered a questionnaire about fictive secondary school students’ various difficulties with the concept of function. Follow-up interviews were conducted with four of the respondents. Compared to the findings of previous research on students’ difficulties with the concept of function, the respondents in the study sometimes provide reasonable suggestions about the sources of students’ difficulties. Some of the respondents demonstrate an aspect of KCS when they suggest that students can reason that a function must be defined by one algebraic expression only, and that students only know about continuous functions. However, no respondent suggests that one source of students’ difficulties with a constant function with an implicit domain is the missing domain. In addition, some respondents take for granted that students can interpret the algebraic representation of a piecewise-defined function and translate it into a graph.

Learning Difficulties with the Concept of Function in Maths: A Literature Review

“…Difficulties with the definition of a function are closely related to misconceptions and difficulties related to its meaning or interpretation. One of the most common interpretations that students hold of functions is that they are like transformative «boxes» or «automatic machines» [14,18,23,33] (M21-Table 3). Many students maintain this interpretation of functions since teachers sometimes use the analogy of the box and the transformation to explain the concept, as we mentioned in the previous section.…”

“…Another misconception that students have is that the relationship between domain and range elements must be bijective (M23-Table 3); that is, one element of the domain corresponds to one element of the range, and vice versa [14,15,26,36,37,39,41]. However, the definition only says that an element of the domain corresponds to exactly one element of the range.…”

Una experiencia para favorecer el aprendizaje profundo del concepto umbral de función en Matemáticas

“…Por otro lado, la literatura apunta a que, en el ámbito de las matemáticas, las funciones, los límites, las derivadas y las integrales se reconocen como conceptos umbrales (Petterson, 2008). Hay numerosos estudios que demuestran los problemas que tienen los estudiantes con estos conceptos (Akkoç, 2003;Bardini 2014;Borke, 2021;Cansiz, 2011;Dubinsky 2013;Sajka, 2013). Respecto al concepto de función, Harel y Dubisnky (1992) editaron un libro sobre los problemas de comprensión de los estudiantes sobre este concepto, que a día de hoy siguen vigentes (Parhizgar, 2021).…”