Thesis (Ph. D.) -- Columbia University. / Vita. Published also without thesis note. Bibliography: p. 335-361.

Thesis (Ph.D.)--Indiana University, Dept. of Educational Leadership and Policy Studies, 2005. / Source: Dissertation Abstracts International, Volume: 66-04, Section: A, page: 1289. Adviser: Thomas A. Schwandt. "Title from dissertation home page (viewed Nov. 9, 2006)."

Thesis (Ph.D.)--Indiana University, School of Education, 2006. / "Title from dissertation home page (viewed July 12, 2007)." Source: Dissertation Abstracts International, Volume: 67-10, Section: A, page: 3705. Adviser: David J. Flinders.

Thesis (Ed.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 67-07, Section: A, page: 2399. Adviser: Paul Thurston. Includes bibliographical references (leaves 110-115) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 67-11, Section: A, page: 4077. Adviser: Walter Feinberg. Includes bibliographical references (leaves 184-194) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--Indiana University, Dept. of Instructional Systems Technology, School of Education, 2006. / "Title from dissertation home page (viewed June 26, 2007)." Source: Dissertation Abstracts International, Volume: 67-06, Section: A, page: 2125. Adviser: Thomas M. Schwen.

To understand what the future requirements of education are to be, one must examine education from a new perspective. One of the keys in understanding that the challenge facing education is recognizing that it is, in fact, a tool of the industrial world and is therefore tied to its capitalistic economic vision. The vision for the future is one in which the new world order is based on an age of ideas and information. Institutions of education have, over the years, evolved and emerged as the primary force in the transmittal of ideas. In this process of transmittal, it assigns value to those ideas which further the interest, goals, and means of western economics (capitalism). Future policy issues should address global economic concerns. Education must take into consideration the role that economics plays in the development of its curriculum. Furthermore, it must assume a position of leadership in the information age, where the validity of ideas will drive economy.

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The essays in this thesis attempt to answer the most difficult questions that I have faced as a teacher and consultant for school-based data teams. When we report statistics to our fellow educators, what do we say and what do we leave unsaid? What do averages mean when no student is average? Why do we treat our population of students as infinite when we test for statistical significance? I treat these as important philosophical questions. In the first essay, I use Paul Grice’s philosophical analysis of conversational logic to understand how data teams can accidentally mislead with true statistics, and I use Bernard Williams’s philosophical analysis of truthfulness to understand the value, for data teams, of not misleading with statistics. In short, statistical reports can be misleading when they violate the Gricean maxims of conversation (e.g., “be relevant,” “be orderly”). I argue that, for data teams, adhering to the Gricean maxims is an intrinsic value, alongside Williams’s intrinsic values of Sincerity and Accuracy. I conclude with some recommendations for school-based data teams. In the second essay, I build on Nelson Goodman and Catherine Z. Elgin’s analyses of exemplification to argue that averages (i.e., medians and means) are attenuated, moderate, and sometimes fictive exemplars. As such, medians and means lend themselves to scientific objectivity. In the third essay, I use Goodman’s theory of counterfactuals and Carl Hempel’s theory of explanation to articulate why data teams should make statistical inferences to infinite populations that include possible but not actual students. Data teams are generally concerned that their results are explainable by random chance. Random chance, as an explanation, implies lawlike generalizations, which in turn imply counterfactual claims about possible but not actual subjects. By statistically inferring to an infinite population of students, data teams can evaluate those counterfactual claims in order to assess the plausibility of random chance as an explanation for their findings.

Why do schools teach mathematics, and why do they teach the mathematics that they do? In this three-part dissertation, I argue that the justifications offered by national education systems are not convincing, and that students are tested on content whose purpose neither they nor their teachers clearly understand. In the first part of the dissertation, I propose a theoretical framework for understanding the content and pedagogy of school mathematics as a set of practices reflecting socio-political values, particularly in relation to labor and citizenship. Beginning with a critical study of history, I trace the origins of modern mathematics education, in the process unearthing common, unexamined assumptions regarding the place and form of mathematics education in contemporary society. In the second part of the dissertation I use the above theoretical framework to re-examine the literature on mathematical word problems. Word problems have interested research because they operate at the intersection between mathematics, education, and labor. I argue that scholarly discussions of word problems have so far adopted unexamined assumptions regarding the role of history, the structure of everyday life, and the relationship between mathematics and other disciplines. Through the lens of political economy I examine these assumptions and offer new categories and explanation for understanding word problems. In the final part of the dissertation, I apply my theoretical framework to practice. Using a dialogical approach, I present a group of undergraduate students and pre-service teachers with artifacts and problems that embody some of the defining tensions of mathematics education. Through twelve weeks of in-depth discussion, fieldwork and exploration, students eventually arrive at a more critical understanding of the social purpose of mathematics and the impact of this purpose on its teaching and learning in various contexts. The results for the students include an expanded vision of the possibilities of mathematics, a radical critique of its place in society, and reports of reduced math anxiety as well as increased curiosity toward mathematics. / Culture, Communities, and Education