Exploring variation in measurement as a foundation for statistical thinking in the elementary school
English, LD and Watson, J, Exploring variation in measurement as a foundation for statistical thinking in the elementary school, International Journal of STEM education, 2, (3) pp. 1-20. ISSN 2196-7822 (2015) [Refereed Article]
Background: 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
Results: The results were based either on the application of the hierarchical SOLO model or on non-hierarchical
clustering of responses to individual questions in the student workbooks. Students' progress throughout the lessons
displayed a wide range of explanations for the estimate of a single student's arm span, general surprise at the variation in
measurements, and a large variety of hand-drawn representations based on the values or frequencies of measurements.
Many different representations were also created in the software for the single student measurements and for
the comparison of measurements for the two scenarios. Although the students' interpretations of their plots were
generally more basic than sophisticated, the results of the assessment indicated that many students had developed the
ability to transfer their appreciation of variation to another context and could clearly explain the meaning of variation.
Conclusions: The findings highlight the importance of an early focus on variation and distribution, with meaningful
activities that motivate students to conduct and observe measurements, together with creating both hand-drawn and
software representations to relate their experiences