[pic]

Volker Ecke

Assistant Professor
Office: Wilson Hall 411M (formerly known as 420)
vecke @ wsc.ma.edu
Phone: (413)-572-5348
Dept. Phone: (413)-572-5349
Fax: (413)-572-5617


Currently Teaching

Calculus II: MATH 106
Modern Geometries I: MATH 306/506
Explorations in Mathematics: MATH 110

Office Hours

Monday, 1:40-2:30 pm
Tuesday, 12:35-1:25pm
Thursday, 12:45-2:00pm
Or just stop by (you're welcome whenever my door is open)
or make arrangements to meet.

Previously Taught

Foundations of Geometry: MATH 251
Discrete Structures: MATH 220
Calculus I: MATH 105
Elementary Statistics: MATH 108
Applications of Mathematics: MATH 111

Academic Interests

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

Discovering the Art of Mathematics is a proposal for a Phase I National Science Foundation grant in support of a project whose focus is the creation of learning materials and teaching strategies. The goal of this three-year project is to develop, test, refine, and distribute a library of ten inquiry-based learning guides and supplemental teacher resources entitled Discovering the Art of Mathematics. The material's primary audience is college-level Mathematics for Liberal Arts (MLA) students, but also includes several secondary audiences (e.g. gifted or home schooled secondary students, independent study students, and adult non-specialists). As completed texts, each guide in the library will be approximately 100 pages in length. Any two of these guides will provide an appropriate body of curriculum materials for a typical semester-long MLA course. The guides will be largely independent of one another so teachers may choose any combination of the texts to use with a particular class. (Proposal)

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

Westfield State College and the Westfield Public Schools propose to implement a three-year partnership project (A Partnership Linking Understanding and Standards - A PLUS). Focused on mathematics in elementary and middle school, this partnership is aimed at improving achievement for all students in mathematics through intensive, high-quality professional development activities aligned to district STEM improvement goals.

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.

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.

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: