Exploring High-achieving Eighth Grade Students’ Solution Strategies and Performance on the Arithmetic Mean Problems

Abstract

Arithmetic mean is a concept that has many uses in daily life (such as; meteorology, medicine, and agriculture). Arithmetic mean is a concept that has mathematical and statistical aspects, so both aspects must be known in depth in order to understand the arithmetic mean conceptually. A conceptual understanding of the arithmetic averaging algorithm can enable students to solve arithmetic averaging problems effectively and is the first step beyond understanding the statistical aspects of the concept. The aim of this research was to investigate high achievers’ solution strategies and performance on the arithmetic mean problems. The participants consisted of 103 grade eighth students drawn from eight classes in five elementary schools of Yozgat, Turkey. All the participants were considered to be current achievers in mathematics, graded 4 or 5 out of 5, and selected via a purposive sampling method. Eighth-grade middle school students with high levels of achievement were given problem scenarios requiring flexible use of the arithmetic mean algorithm, and they were asked to solve the problems using all the strategies they knew. In addition, one student from each school was interviewed and the interview and written exam findings were compared and interpreted. It was found that nearly all high-achieving eighth grade students used the add-divide algorithm strategy. The number of students using multiple solution strategies is quite low. It was revealed that students' performance was lower in problems that required more than one term in a data set. The findings were supported by interviews with students.