Westfield State College
Department of Mathematics

Currently Teaching

Office Hours

Previously Taught

Discovering the Art of Mathematics: Library of Inquiry-based Learning Guides to support Mathematics for the Liberal Arts courses (Proposed NSF grant)

A PLUS: A Partnership Linking Understanding and Standards, Westfield Community for Mathematics in the Elementary Schools (Proposed Title II-B grant)

The Inquiry-Based Classroom Ecosystem

Joint work with Mairead Greene (Rockhurst College) and Christine von Renesse (Westfield State College). Rich and diverse collections of classroom practices are being reported in the literature that all focus on students actively involved in problem solving activities, inquiring deeply into unknown materials, and discovering significant mathematical ideas for themselves, often in small group settings. We refer to these as inquiry-based learning.

Our project goal is to pursue in depth research into the efficacy and effects of such approaches. For example, we want to learn more about (1) programs with more than anecdotal evidence of efficacy, or the lack thereof; (2) means of assessment used to determine efficacy of discovery-based programs; (3) the operational meaning of terms such as Inquiry-based Learning, and thus on what specific aspects of programs actually are responsible for any observed differences in outcomes; and/or (4) differences in outcomes in later mathematics courses for those in discovery-based programs vs. traditional lecture-based.

We are interested in the connections between student beliefs, attitudes, interests and learning in mathematics courses and how to use this knowledge in our teaching.

• Ingredients in the inquiry-based classroom ecosystem and their effect on student learning
• Measuring student attitudes, beliefs, practices, and their effect on student learning
• Survey Instruments (CLASS)
• CRESMET: Reformed Teaching Observation Protocol (RTOP)

Mathematics and Computing Science

Most recent advances in computational power arise from networking large numbers of regular PC-like computers into a single supercomputing system. It is very hard to write correct software that splits computational problems into thousands of tasks that can be farmed out to such "massively parallel" supercomputers. Due to its parallel nature, testing such software is often not feasible. Therefore, software engineers need tools that help them gain confidence that the software is correct.

Our research program aims at developing mathematical models of software and model checkers that allow engineers to check whether certain properties (e.g. "the program will not deadlock") are true on all possible executions.

Situated at the intersection of mathematics and computer science, this project uses ideas from recent advances in computational algebra and geometry to create models and model checkers and investigate their usefulness with a variety of parallel software constructs.

• Mathematical Methods for the Analysis of Parallel and Concurrent Computer Systems
• Computational Algebraic Geometry: Creating Shapes in Space Computer Aided Geometric Design
• Discrete Mathematics: Applications to Computer and Information Science
• Algorithmic Algebra and Geometry (Mathematical Sciences Research Institute, Berkeley)

Scholarship of Teaching and Learning

Naturally growing out of my experience in the classroom, new ideas about teaching and learning are constantly arising. Here's a small collection:

• Explorations of Mathematics for Liberal Arts Majors: (Annotated Bibliography)
• Effective warm-up activities in Discrete Structures (PREP)
• Teaching and Technology: (ICTCM)
• Math Anxiety and Contemplative Practice in Higher Education
• History of Mathematics in regular mathematics courses
• Learning Styles, Modalities and Strategies