## Smertelig enkelt : Studie med fokus på elevenes utfordringer som manifesterer seg gjennom rasjonelle feil ved konvertering mellom ulike semiotiske representasjoner av lineære funksjoner

##### Abstract

“... a person often meets the challenge of solving a new mathematical problem state by creating rule-based but erroneous algorithms that lead to rational errors. These erroneous algorithms are the problem solver's attempt to create a reasonable solution in a relatively short period of time with minimal computational cost. In essence, the person's efforts are directed toward interpreting and adapting to the mathematical environment in much the same way that he or she would adapt to a social or physical environment.” (Ben-Zeev, 1998, s.378-379)Coordination between different representations in mathematics, as in this study referred to as conversion, is considered an important and essential skill through which pupilswill develop reasoning and understanding of mathematical ideas.The only way to represent mathematical ideas or objects is by using the mathematical language,seen from the perspective of the complexity of the mathematical language, this is by no means a trivial process.With this as a basis, this study examines the conversion between different semiotic representations of linear functions as a mathematical object. Semiotic representations in mathematics are important communists and are the only entrance to the mastery and conceptualization of mathematical ideas, and are thus a foundation of understanding, whether it is conceptual or preserved or both. These are again essential for the construction of mathematical competences and thus the depth of learning in mathematics.This leads tothree questions that underlie and to be illuminated in this study. The main question concerns challenges that pupils face in conversion between different semiotic representations.The complexity of processes that lie in conversion between semiotic representations of the same mathematical object bottoms in the syntax and semantics of the mathematical language. Representations of linear functions as a mathematical object have different origins depending on the type of representation that is manipulated and rules that determine how this representation can be manipulated. Therefore, in order to answer this question, it becomes necessary to look at the errors produced by different conversions. Considering the fact that only by looking at errors and providing these labels is not enough to say anything about the challenges of students and with regard to it, this study seeks for possible explanations of or precursors to the failures that occur, and therefore takes the aim to E for possible sources of error. For as it stands in the opening quotation errors produced in mathematics often appear to be rule-based but erroneous algorithms, and the rationality of it is that humans adapt to themathematical environment in the same way they would do so socially. By analyzing students ' written work and interviews based on their answers to the conversion between different representations of linear functions and focusing on challenges that are being proved by mistake, this study should provide possible explanations of where these Problems come from and the challenges students have.Triangulation as a method used in the study gives it a design that can be considered a hybrid between comparative and partly experimental study, with a theoretical basis that has its weight in cognitive theory and focusing on individual learning and how it can be understood.The study's findings should be seen as didactic implications of this understanding from challenges that students face and distinctive mistakes, they manifest themselves through.

##### Description

Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2019