DEVELOPING STATISTICAL PERSPECTIVES IN THE ELEMENTARY GRADES

Clifford Konold

University of Massachusetts, Amherst

konold@srri.umass.edu

Traci Higgins

TERC

Susan Jo Russell,

TERC

An idea that has emerged as one around which we might organize an introductory sequence in data analysis is that of data as an aggregate (Cobb, 1999). Many studies have pointed to the importance in statistical reasoning of this construct (e.g., Hancock, Kaput & Goldsmith, 1992; Mokros & Russell, 1995), but we still know little about how this perspective develops or of student ideas that might serve as precursors to it. We analyze 34 case studies written by teachers about their experiences and reflection in teaching data analysis in grades K-5. Analyses suggest three perspectives students use in their approach to data. Used as (1) pointers, data serve as shorthand records of more complex events. When they have observed the events, very young students use recorded data to help them recall other information about the observed event. The most prevalent idea among elementary students is that of data as (2) classifiers. As classifiers, data provide ways to compare individual data values or types, to easily locate a value with respect to others, and especially to determine who is the most and least. We see a few students in upper elementary grades beginning to focus on data as (3) distribution, attending to emergent features of distributions such as centers and spreads. However, when they first begin focusing on these distributional characteristics, students often disconnect plot features from the situations and questions of interest. These orientations towards data are closely tied to the questions students have when they collect and analyze data. This being the case, instruction should stress reasons for collecting data and for looking at data with those questions in mind.

References

Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5-43.

Mokros, J. & Russell, S. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20-39.

Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Psychologist 27(3), 337–364.