Learning
involves a complex and interactive engagement with ideas, facts and
strategies within a given discipline. My own discipline of mathematics
education engages me with learning from many perspectives, and it
challenges me to address a wide range of development, from students at
the Pre-Kindergarten level up to graduate students and undergraduate
students intent on becoming teachers themselves. Regardless of the
learning situation, I look at the teaching and learning processes
through a consistent framework that highlights the engagement of a
learner with their situation and environment. *Learning trajectories*
are conceptual tools I use to frame learning as an increasingly
sophisticated process that involves passages from one level of thinking
to another, identifying a level, accounting for reasoning with mental
objects, and specifying tasks to prompt growth. Teaching
requires a vigilant engagement with learners from the standpoint of
such trajectories as instructional maps and toolsets.

- MAT 131 Geometric Reasoning (Quantitative Reasoning middle core requirement)

MAT 130 - Dimensions of Mathematical Thinking

MAT 152 - Structure of Number Systems II

MAT 201 - Teaching Mathematics in the Elementary School

MAT 202 - Math for the K-8 Specialist

MAT 204 - Geometry for K-8 Teachers

MAT 302 - Teaching Mathematics in Grades 5-8

MAT 401 - Current Research in School Mathematics

MAT 402 - Instructional Strategies for Elem. And Jr. High Mathematics

MAT 403 - Theories of Mathematical Learning

MAT 422 - Topics in Geometry for Teachers

MAT 429.09 - Enhancing Middle-School Students’ Geometric Reasoning through Computer-Based Technology

MAT 429.10 - Teaching Problem Solving in Grades K-4: Using Extended tasks in Geometry and Measurement

MAT 580 - Mathematical Thinking and Learning (Advanced cognitive accounts of learning)

MAT 585 - Topics in Mathematics Education Seminar:

• Geometry Learning, Spring, 1999,

• Design-Based Methods of Research, Summer, 2003,

• Learning Environments, Fall 2006.