A Ph.D. Program in Mathematics
Education in a Dept. of Mathematics:
Arizona State University as an Example
Marilyn Carlson
Arizona State University
marilyn.carlson@asu.edu
Thursday January 8, 2004,
1:00 p.m.-2:20 p.m.
Overview of Programs
 Degree Options



Ph.D. in Mathematics
Ph.D. in Curriculum and Instruction
M.N.S. in Mathematics with concentration in
Math Ed.
 Mathematics Education Faculty


Department of Mathematics and Statistics (3)
College of Education (3)
What Makes It Work?
 Support from Mathematics Department
administrators and faculty
 Active participation of interested mathematicians
 Strong program with high standards
 Leadership of mathematics education faculty
 Strong collaborations between the College of
Education and Department of Mathematics math
education faculty
What Are the Benefits?
 Mathematicians and Mathematics Educators
collaborate in:

Supervising Ph.D. students in mathematics education

Developing and implementing mathematics education
courses and projects

Writing proposals
 Mathematicians and Mathematics Educators
engage in regular information exchange about
issues of knowing and learning mathematics.
Required Courses
Ph.D. in Mathematics
 Sequence of Four 500-level Math Education Courses (12 hrs)
 Two 400-level Qualifier Sequences
(12 hrs)
 Three - Six Courses in College of Education
(9-18 hrs)
 Remaining Courses in Mathematics or Statistics (18-27 hrs)
 Research and Dissertation
(24 hrs)
Other Requirements
Ph.D. in Mathematics
 2 mathematics qualifying exams
Algebra, Differential Equations, Discrete, Numerical Analysis,
Real Analysis, Statistics
 1 written comprehensive exam
 Dissertation prospective defense
 Dissertation defense
Required Courses
Ph.D. in C & I
 Core Requirements
 Inquiry and Analysis
(6 hours)
(15 hours)
Quantitative and Qualitative Research
 Major Area of Concentration
(30 hours)
Mathematics and Mathematics Education
 Internships
(6 hours)
Teaching and Research
 Cognate Study
(12 hours)
Mathematics Courses
 Dissertation Research
(24 hours)
Other Research Experiences
 Participation in faculty research projects
 Conference presentations
 Participation in proposal writing
 Participation in paper presentation
Faculty
 Dept. of Mathematics





Marilyn Carlson
Michelle Zandieh
Michael Oehrtman
Phil Leonard
Dennis Young
 College of Education



Alfinio Flores
Jim Middleton
Jae Baek
Ph.D. Students in Mathematics
Education
 8 students, Math Dept – full time TA’s and RA’s
 9 students, C & I program, but mentored by Dept.
of Mathematics Faculty
 10 (Approx) students, C & I, mentored by C & I
Student Research Topics
Sean Larsen
Supporting the Guided Reinvention of the Concepts of
Group and Group Isomorphism: An Evolving Local
Instruction Theory
Nicole Engelke
An Investigation of Cognitive Aspects of Learning Related
Rate Problem
Sally Jacobs
Advanced Placement BC Calculus Students’ Ways of
Thinking About Variable
Jessica Knapp
Complexities of Learning to Prove
Student Research Projects
C&I
 Irene (Apple) Bloom
The Development of Secondary Preservice Mathematics
Teachers’ Mathematical Behaviors: An Evaluation of the
Effectiveness of Extended Analyses Problems
 Marguerite George
An Examination of questioning patterns in mathematics
instructors
 Mark Burtch
Student Conjecturing in a Differential Equations Course
Dissertation Project: Sean Larsen
Mathematics
TITLE: Supporting the Guided Reinvention of the Concepts of Group and Group
Isomorphism: An Evolving Local Instruction Theory
ABSTRACT: In this talk I will describe a local instruction theory that emerged over
the course of a sequence of three teaching experiments in elementary group theory.
Each of the experimental "classrooms" consisted of two university students and the
teacher/ researcher. These teaching experiments were guided by the instructional design
theory of Realistic Mathematics Education (RME). The goal was to promote the guided
reinvention of the concepts of group and group isomorphism. The local instruction
theory consists of a sequence of instructional activities and a justification (theoretical
and empirical) for the sequence. The concepts of group and group isomorphism are
seen as first emerging as models of students’ informal mathematical activity and then
evolving into models for more formal mathematical reasoning. This process was driven
by the students’ participation in classroom mathematical practices. The individual
students’ mathematical development is seen as reflexively related to their participation
in these mathematical practices.
Dissertation Project: Sally Jacobs
C&I
TITLE: Advanced Placement BC Calculus Students’ Ways of Thinking
About Variable
ABSTRACT: The dissertation was an exploratory study investigating
calculus students’ notions about the concept of variable in the contexts of
function, limit and derivative. The findings indicate that students think
about variable in qualitatively different ways, depending on whether they
have a calculational versus conceptual orientation to the mathematical task
at hand. Also, in the context of limit and derivative, their conceptions of
variable are somewhat less flexible. Finally, a Variable Conceptions
Framework for analyzing student conceptions of variable is proposed.