Abstract
The aim of this study is to identify high school student's 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 student's 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 student's 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 student's prior mathematics knowledge hinders both their understanding of the average and their reasoning skills.
Highlights
In today‘s world, students need to have reasoning skills to meet their future needs which will prepare them for future success as citizens and in the workplace, as well as enable them to pursue careers in mathematics and science (National Council of Teachers of Mathematics [NCTM], 2009)
Findings related to students‘ understanding of average and their reasoning types on problem solving are presented below two headings
It was observed that students mostly considered average as mathematical point of balance
Summary
In today‘s world, students need to have reasoning skills to meet their future needs which will prepare them for future success as citizens and in the workplace, as well as enable them to pursue careers in mathematics and science (National Council of Teachers of Mathematics [NCTM], 2009). The increasing importance of statistical skills has been demonstrated by the emphasis on statistics in various mathematics education reform movements around the world. This leads a change in understanding of average concept in the curriculum of various countries (Australian Education Council, 1991; NCTM, 2000). Thereafter, in parallel with the developments in the world, mathematics curriculums have been changed to be related to real-life situations and to be conceptual rather than operational (MoNE, 2009, 2013, 2015, 2018a). According to the mathematics curriculum, 6th grade students are expected to use average to interpret and compare data related to the two data groups. In 9th grade, they are expected to associate the concepts average, midpoint and mode to the real-life situations (MoNE, 2018b)
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