# The Role of Sampling Variability in Developing K-8 Preservice Teachers’ Informal Inferential Reasoning

4-2019

## Degree Name

Doctor of Philosophy

## Department

Mathematics

Dr. Mariana Levin

Dr. Christine Browning

Dr. Steven Ziebarth

Dr. Stephanie Casey

## Keywords

statistics education, sampling variability, informal inferential reasoning

## Abstract

Recent influential policy reports, such as the Common Core State Standards (CCSS-M, 2010) and Guidelines for Assessment and Instruction in Statistics Education Report, (GAISE, 2007), have called for dramatic changes in the statistics content included in the K-8 curriculum. In particular, students in these grades are now expected to develop Informal Inferential Reasoning (IIR) as a way of preparing them for formal concepts of inferential statistics such as confidence intervals and testing hypotheses. Ben-Zvi, Gil, & Apel, (2007) describe IIR as the cognitive activities involved in informally making statistical inferences. Over this path from informal to formal inference, many important concepts will be integrated into students’ understanding and therefore underpin their IIR ability. One of these fundamental concepts is sampling variability which has been explicitly emphasized in both of the above policy documents. Given this emphasis on sampling variability in the K-8 curriculum, future teachers need support to acquire sufficient content knowledge of this concept. While previous research had outlined general frameworks for what constitutes an understanding of sampling variability (Pfannkuch, 2008; De Vetten, Schoonenboom, Keijzer, & van Oers, 2018), pilot data indicated that a fine-grained analysis of pre-service teachers’ (PSTs) reasoning about sampling variability revealed some facets of reasoning and understanding that were not accounted for in previous frameworks.

This dissertation study investigated a range of non-normative ideas that PSTs employ in reasoning about sampling variability and whether their reasoning processes were sensitive to context. These issues were studied in the context of a content course on statistics and probability for pre-service elementary and middle grades teachers at a midwestern university. Analysis of seven PSTs’ video and screen records of task-based interviews was guided by techniques of Knowledge Analysis (diSessa, Sherin, & Levin, 2016) and identified patterns of non-normative reasoning about four different facets of sampling variability. Identified patterns of reasoning were used to adapt and elaborate Pfannkuch’s (2008) framework for the ways of thinking about sampling variability. More significantly, data analysis also revealed consequential contextualities in how PSTs reasoned about sampling variability in different situations. Implications of this study for teacher education include highlighting the need for using purposefully designed curricula that explicitly emphasize detailed facets of sampling variability across multiple data-contexts.

## Access Setting

Dissertation-Open Access

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