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#### Date of Award

4-22-2015

#### Document Type

Thesis and Dissertation-ISU Access Only

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Department of Mathematics

#### First Advisor

Craig Cullen

#### Abstract

My original purpose in undertaking this dissertation research was to investigate if learning mathematics could be made meaningful for chronically ill children through robotics play. This focus evolved into three distinct stages. First, I set out to identify a central issue that is contributing to the debasement of chronically ill children that is, the ways in which chronically ill children are being conceptualized as not capable in mathematics education practice. Second, I set out to create a model that would serve as an operational definition of a mathematical environment. Finally using my new model, I addressed the question: Are robotics capable of producing a mathematical environment for chronically ill children and if so in what ways does the environment develop over time?

These objectives are address in three articles. In the first article, I present data from the pre and post interviews with 16 chronically ill children. I conducted semi-structured qualitative interviews with 16 chronically ill children to learn about their experiences learning mathematics. Through discussion of the data, I identify the ways in which chronically ill children are being conceptualized as not capable in mathematics education practice. I conclude this article with a call to action.

In article two, I report on how I adapted Garrison et al.'s CoI model to create a model appropriate for technological mathematical environments. First, through my presentation of the CoI literature I argue that the conceptualization of critical thinking both implicit and explicit in the CoI model make it valid for use in defining and describing a mathematical environment. Next, I describe my efforts to use the CoI model to determine the existence of a mathematical environment in Michala's first six robotics tasks, and how this effort resulted in my adaptations to the model. I conclude the article with the presentation of my adapted model, the technological mathematical environment (TME) model.

In article three, I present three of Michala's robotics tasks from weeks one, 27, and 46 along with an overview of her robotics work over the complete 52 weeks. I then compare the data from the tasks to the TME model to answer my research question, Are robotics capable of producing a mathematical environment for chronically ill children and if so in what ways does the environment develop over time? I found evidence for the robotics creating a mathematical environment in each of Michala's example tasks and throughout weeks 1-52 of her work. Although the mathematical environment was present beginning in week one, changes in the environment were observed over time, with the most significant change seen in the decline and eventual absence of didactic interventions (teaching in the traditional sense).

#### Recommended Citation

Nickels, Megan L., "Mathematics in the Charmed World: Creating a Mathematical Environment Through Robotics Play" (2015). *Theses and Dissertations*. 401.

http://ir.library.illinoisstate.edu/etd/401

#### Page Count

229

## Comments

Imported from ProQuest Nickels_ilstu_0092E_10534.pdf