Date of Award

December 2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Teaching and Leadership

Advisor(s)

Helen M. Doerr

Keywords

Statistics Education

Subject Categories

Education

Abstract

Bootstrapping has become an important tool for statisticians, who assert that it is intuitive to novice statistics students. The process of collecting bootstrap resamples was once time demanding, but technology now allows data collection to be performed nearly instantaneously. This study focuses on the construction and development of secondary and tertiary introductory statistics students' (n=68) reasoning about bootstrapping and informal inference. Students engaged in a four-week instructional unit designed as two model development sequences. Through the use of hands-on manipulatives and technology, students constructed and developed reasoning of sampling, the resampling process of bootstrapping, and inference. The focus of my analysis was on the model development of four focus groups of students. Groups of students constructed models of sampling and inference that they used to collect samples, aggregate the samples to form an empirical sampling distribution, and use the aspects of this distribution of samples to make claims about the population from which the samples were drawn. I summarize and categorize groups of students’ models and trace the development of the focus groups’ models throughout the unit.

Simulation of data led some students to develop a global view of the randomness of sampling and reason with multiple aspects of empirical sampling distributions to draw inferential claims. Some students applied a multiplicative view of the sample and global view of the sampling process to construct a resampling process similar to bootstrapping, but fell short of constructing the bootstrapping process by not collecting resamples that were equal in size to the original sample. Class discussion of a follow-up activity, similar in structure to the model eliciting activity, encouraged students to consider the value of drawing resamples of equal size to the population and led students to construct the method of bootstrapping. Students then used the

bootstrapping process to drawn inferences about one population and to compare two populations of data.

The findings of this study contribute to the field of statistics education by examining student thinking while constructing and developing bootstrapping methods, as well as investigating the relationship between this thinking and the drawing of informal inferences. This study demonstrates that it is possible for model development sequences to elicit and develop students’ models of bootstrapping. With the trend in statistics education of moving from the focus on theoretical distributions towards the simulation and analysis of data, these findings have implications towards the design of future introductory statistics curricula.

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