Explanations and Context in the Emergence of Students' Informal Inferential Reasoning

Abstract

Explanations are considered to be key aids to understanding the study of mathematics, science, and other complex disciplines. This paper discusses the role of students' explanations in making sense of data and learning to reason informally about statistical inference. We closely follow students' explanations in which they utilize their experiences and knowledge of the context, statistical tools, and ideas to support their emerging informal inferential reasoning (IIR). This case study focuses on two independent inquiry episodes of sixth-grade students (age 12) within an unstructured, inquiry-based, technology-rich learning environment that was designed to promote students' IIR. We discuss research and practical issues related to the role of explanations and context in developing students' IIR.

Acknowledgments

We thank our colleagues from the International Collaboration for Research on Statistical Reasoning, Thinking, and Literacy (SRTL) for stimulating discussions on the topic of explanations and context. We would also like to thank our anonymous reviewers and Katie Makar, co-editor of this issue. Their thoughtful and constructive comments urged us to better clarify and connect the ideas presented.

Notes

¹The decision to start from a relatively small sample size (N = 20) was taken from pedagogic and instructional design considerations to highlight and discuss sampling variability, the influence of sample size in reducing sampling variability, and confidence in drawing informal inferences.

²For the purpose of presentation in this paper, the original transcripts were sometimes abridged maintaining the original meaning in the Hebrew dialogue.

FIGURE 1 Yoram and Gilad's first random sample (N = 20), comparing Time with friends by Gender. The mean for each distribution is marked with a triangle under each axis.

³Some Episode 3 excerpts have been reported in Ben-Zvi, Gil & Apel (2007) and Makar, Bakker, & Ben-Zvi (this issue) but not in the context of a study about explanations and context.

FIGURE 3 Long jump results by grade and gender in TinkerPlots. The means are marked by triangles. Note that there is one girl only in the sixth grade group.

⁴See Footnote 2 regarding shortened transcripts.

⁵See also Ben-Zvi et al. (2007).