Exploring variation in measurement as a foundation for statistical thinking in the elementary school

This study was based on the premise that variation is the foundation of statistics and statistical investigations. The study followed the development of fourth-grade students' understanding of variation through participation in a sequence of two lessons based on measurement. In the first lesson all students measured the arm span of one student, revealing pathways students follow in developing understanding of variation and linear measurement (related to research question 1). In the second lesson each student's arm span was measured once, introducing a different aspect of variation for students to observe and contrast. From this second lesson, students' development of the ability to compare their representations for the two scenarios and explain differences in terms of variation was explored (research question 2). Students' documentation, in both workbook and software formats, enabled us to monitor their engagement and identify their increasing appreciation of the need to observe, represent, and contrast the variation in the data. Following the lessons, a written student assessment was used for judging retention of understanding of variation developed through the lessons and the degree of transfer of understanding to a different scenario (research question 3).