Graduate Writings


Thirty Years of Problem Solving in Mathematics Education: Policy and Promise
(Comprehensive Exam - Fall 2010). The first of two papers written in response to a breadth test option for DSME. [


Research in Education: Rigor and Relevance
(Comprehensive Exam - Fall 2010). The second of two papers written in response to a breadth test option for DSME. [


Algebra Students’ Simplification of Rational Expression
(SME 927 - Spring 2008). “Research” report written with Hanna Figueras and Lorraine Males. [
APA manuscript version  | Appendix]


Research and Practice: Problem Solving in Secondary Classrooms
(SME 927 - Spring 2008). Literature review. [


Research and Practice: Proof in the Geometry Classroom
(SME 842 - Spring 2008). Literature review.  [


Explorations in Hyperbolic Geometry
(SME 842 - Spring 2008). A discovery-oriented investigation into a non-Euclidean geometry.  [


Explorations in Spherical Geometry
(SME 842 - Spring 2008). A class-generated documentation of investigations into a non-Euclidean geometry.


Reflections on Two Pieces by Dewey
(CEP 911 - Fall 2008). A synthesis of John Dewey's
The Child & the Curriculum and Experience and Education. [PDF]


Reflections on Edward L. Thorndike
(CEP 911 - Fall 2008). Some thoughts based on Thorndike's
Education: A First Book and Elementary Principles of Education. [PDF]


Reflections on Some Work of Jean Piaget
(CEP 911 - Fall 2008). A summary of Piaget's theory of development and brief thoughts about its implications for mathematics classrooms.


Discourse Analysis in the Classroom: Summary of a Mini-Reading Course
(SME 954 - Fall 2008). Brief sketches of chapters from Gee, Halliday, and Christie. [


Down and to the Left: Student Movement Toward Negative Numbers
(SME 840 - Spring 2009). A brief literature review that looks at a few research and a few practioner articles dealing with negative numbers in elementary school. [


Grounding Negative Numbers: A Third Grade Student Plays Two Mathematical Games
(SME 840 - Spring 2009). A mini-study that builds upon "Down and to the Left," using the framework of Lakoff and Nunez to investigate a third grader's encounters with negative numbers. [


Kupilikula by Harry G. West: A Brief Review
(TE 931 - Spring 2009). A book review focusing on the qualitative method employed by West in his remarkable ethnography. [


A Mathematician Reads the Newspaper by John A. Paulos
(EDUC 782 - Fall 2009). A book review. [


Essay on Mathematical Understanding
(EDUC 782 - Fall 2009). A brief essay on aspects of mathematical understanding present in NCTM's
Principles and Standards. [PDF]


David Hume: His Method and Theory of Knowledge
(TE 924 - Spring 2010). An overview of Hume's approach to philosophy and his epistemology, with modest connections to education.


Good Teaching: Can you know it when you see it?
In this essay, Sam discusses why he believes that good teaching cannot be recognized by merely seeing someone teach. In making this argument, some of Sam's own values about teaching come to light.


Characterizing Disciplines from Within and Without
Do popular perceptions of academic disciplines align with expert's perceptions of their own disciplines? In this outreach project, Sam responds to this question with respect to mathematics but also discusses it with friends from other disciplines.


On Authority: The bible, mathematics textbooks, and reform
Mathematics is often seen as an authoritative discipline with mathematics textbooks being the ultimate authority in mathematics classrooms. Sam explores this issue by drawing analogies between mathematics textbooks and the bible -- one of the most important authoritative texts in history.