Abstract
The purpose of this study was to investigate the flow of thought of the pre-service mathematics teachers through the answers of a function limit evaluation by formal definition. This study used a qualitative approach with descriptive method. The research subjects were the students of mathematics education department of Universitas Serang Raya, Indonesia. After analyzing the students’ written answers, we interviewed the subjects to get further explanation on their strategies and common mistakes. This study found that based on the students’ results in the function limit evaluation by formal definition, there were common strategies, i.e. (1) preparing the proof and (2) proving. The stage of preparing the proof consisted of (1) determining delta value by the final statement of formal definition, (2) substituting the given f(x) and L process, (3) simplifying value in the absolute sign, (4) solving the inequality, and (5) finding the delta value. The stage of proving consisted of (1) stating positive epsilon, (2) defining delta, (3) stating positive delta, (4) substituting the constants and delta values in the initial statement of formal definition, and (5) solving the inequality to create the final inequality statement of the formal definition.
Highlights
Abstrak Tujuan penelitian ini adalah untuk menginvestigasi alur pikir mahasiswa calon guru matematika melalui jawaban soal mengevaluasi limit suatu fungsi dengan menggunakan definisi formal
Calculus is the early course towards advanced mathematics which is taken by undergraduate students in most exact science and engineering department
The result of a preliminary study found that the difficulty of most students in evaluating limit by formal form is related to the understanding of the concept of the formal definition of limit
Summary
Abstrak Tujuan penelitian ini adalah untuk menginvestigasi alur pikir mahasiswa calon guru matematika melalui jawaban soal mengevaluasi limit suatu fungsi dengan menggunakan definisi formal. It was found that definition and theorem had been fragmented in the students’ minds as something absolute and do not need to be proven again This fact showed that they were not used to thinking that they needed to prove it as the basis of a generalization of a proposition and checking evidence, so it was difficult for them to see the central idea of a formal definition. This result was closely related to the students’ habit to not pay attention to the theoretical aspect. Selden & Selden (2003) state that students cannot determine whether the particular proof is valid or not
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