An Analysis of High School Students’ Understanding and Reasoning of Average Concept

Abstract

The aim of this study is to identify high school students' understanding of average concept and the reasoning types they appeal to solve average problems. The case study approach was used in this study and the participants were selected by purposeful sampling. The participants consisted of five 9th grade and four 10th grade students, studying at a high school in Istanbul. In order to identify students' understanding of average, a test consisting of 5 open-ended problems were used and semi-structured interviews were held with each of the students. The data were analyzed by thematic analysis approach. For data analysis, framework proposed by Mokros and Russel (1995) was used to determine students' understanding of average and Lithner's (2008) framework was used to reveal their reasoning types. Results showed that students mostly understood average as mathematical point of balance. Creative mathematically founded reasoning and algorithmic reasoning was used the most. Creative reasoning is effective in reaching the right answer. In solutions where creative reasoning is used, students generally also have the idea of representativeness. The type of problem influences the reasoning process. Inadequacy of students' prior mathematics knowledge hinders both their understanding of the average and their reasoning skills.