Analysis of high school students’ errors in mathematical proving: the case of mathematical induction

Abstract

The ability in proving mathematical statements is a pivotal skill to own. Mathematical induction as a tool for proving mathematical statements related to natural numbers requires three steps to conduct, namely the basic step, the hypothetical step and the induction step. Meanwhile, errors and mistakes can occur during the process of proving. The purpose of this study is to describe mistakes made by students when they use mathematical induction, based on Newman’s Error Analysis (NEA) stages model. The research was a qualitative descriptive study with the type of a case study. The subjects of this study were 25 eleventh grader students in a senior high school. The data were collected by giving tests and conducting interviews. The results of the research, viewed from the stages of NEA, show that the students can reach the first stage (Reading and Recoding) and the second stage (Comprehension) in doing the proving properly. Most of them, however, made errors beginning from the third stage and afterwards (Transformation, Process Skills and Encoding). It is also found that their errors are due to their poor understanding in using hypothetical step in mathematical induction.