Statistics plays an important role in daily life (Jacobbe & Carvalho, 2011). Hence, developing knowledge and skills to do statistics is one major goals of mathematics curriculum. In grades 5-8, students in Turkey are expected to formulate questions, collect and analyze data, and interpret results (MoNE, 2013). In this scope, students are expected to understand measures of central tendency (i.e., mean, median, and mode) as tools to represent data sets. Average, as a tool for summarizing and describing a data set, is a useful concept that is constructed within the given context in data handling (Watson & Moritz, 1999, 2000). Sometimes it refers to the mean or arithmetic average, sometimes it refers to the value the most frequently observed, that is mode. That is, measures of central tendency are specific types of averages (Van De Walle, Karp, & Bay-Williams, 2010).
Research on the concept of “average” mostly focused on students’ understandings and cognitive development (Mokros & Russel, 1995; Watson & Moritz, 1999, 2000). For instance, Mokros and Russel (1995) asked open-ended problems to fourth, sixth, and eight graders and examined how they construct and interpret the notion of average. Findings indicate that young students refer to typical, usual or middle, whereas older students also use mean, median, or mode in order to represent average of a data set. Watson and Moritz (1999) focused on students’ ideas of average in different real life contexts. They interviewed with 94 students from grades 3 to 9. Answers were analyzed by means of the levels described by The Structure of Observed Learning Outcomes (SOLO) as, prestructural, unistructured, multistructural, and relational. Also students’ answers were categorized in terms of which measures of central tendency they refer as the average of a data set. They determined six levels, namely preaverage, single colloquial usage for average, multiple structures for average, representation with average, and application of average to one complex and two complex tasks (Watson and Moritz, 2000). These studies revealed that students’ understanding of average are mostly procedural and restricted to the mean, even though median and mode could also be used to represent the average of a data set.
Research also focused on pre-service and in-service teachers’ understanding of “average.” Some studies focused on only the concept of mean (arithmetic average) (Gfeller, Niess, & Lederman, 1999), whereas others examined all measures of central tendency but not relating with average (Groth & Bergner, 2006; Jacobbe, 2007; 2008). On the other hand, some focused on the concept of average (Begg & Edwards, 1999; Callingham, 1997; Russell & Mokros, 1991). For instance, Begg and Edwards (1999) worked with in-service and pre-service elementary school teachers and found that their definition about average prone to answer “was in the middle.” Also they tended to use mean (arithmetic average) rather than median or mode and applied algorithm for computing mean when they were asked to interpret measures of central tendency (Callingham, 1997; Russell & Mokros, 1991). Research also showed that teachers didn’t think data set as a whole when they made interpretation about average and lack of conceptual knowledge (Jacobbe & Carvalho, 2011). These findings, however, are based on limited research, in accessible literature. Hence, this study aims to examine how pre-service middle school mathematics teachers interpret the concept of average in real life situations. In this way, it aims to contribute literature by analyzing pre-service teachers’ understanding of average. This study seeks to answer the following research question: “In what ways do pre-service middle school mathematics teachers interpret the concept of average?”
