The Learning Opportunities Presented by Mathematics Coursebooks Used in Middle Schools in Turkey on the Concept of Arithmetic Mean

Abstract

In this study, it was investigated how the concept of arithmetic mean (an essential concept in the learning domain of data) was presented in middle school coursebooks in Turkey, what type of problems related to the arithmetic mean was covered, the type of representation form through which the problems were presented, and the type of representation forms and solving strategies used for solving problems. For this study, the coursebooks used in the 2019–2020 academic year were analyzed. A 2D framework (horizontal and vertical analysis) was used to answer research questions, and the analyses were conducted by two researchers. Although balance and fair-share models are strong analogies for conceptually understanding arithmetic mean, the two coursebooks of grade 6 did not sufficiently cover these models. Furthermore, the relationship between the arithmetic mean and elements in a data set and the discussions related to arithmetic mean as a value that represents the data set were not covered in coursebooks. Most problems in the coursebooks were verbally developed, and the problems were solved only via the add–divide algorithm. Note that, for solving these problems, different representation forms were not used, and the solutions were only presented in the arithmetic form. In the coursebooks, the content might cause students to superficially learn the concept of arithmetic mean and have difficulties with questions at the evaluation level. Thus, for teaching the concept of arithmetic mean, fair share and balance point should be used via coursebooks, and they should be enriched in terms of problems in various types. Furthermore, different strategies and multiple representation forms should be used for solving arithmetic mean problems in coursebooks.