Steven Schlicker

Numbers Simultaneously Polygonal and Centered Polygonal

Summary The study of polygonal numbers (triangular, square, etc.) has a long and rich history. Similar, but lesser known, are the centered polygonal numbers which have not been as extensively studied. These sequences of figurate numbers contain a wealth of interesting and fun mathematics. As an example, we make connections between the polygonal and centered polygonal numbers to find a previously unknown family of integer sequences that describe those numbers that are simultaneously polygonal and centered polygonal for the same number of sides.

A “model” multivariable calculus course

ABSTRACT This article describes a rich, investigative approach to multivariable calculus. A major focus of the approach is a project in which students construct physical models of surfaces that represent real-life applications of their choice. These models, along with student-selected data sets, serve as vehicles to study most of the concepts of the course, from both continuous and discrete perspectives.

ENHANCING CORE MATHEMATICS COURSES

ABSTRACT The Departments of Mathematics and Statistics at Grand Valley State University are engaged in a project to address the mathematical preparation of all its majors, including prospective elementary and secondary mathematics teachers. In this article, we describe how the mathematics and mathematics education faculty in our mathematics department formed a partnership and worked together to change two (Modern Algebra and Discrete Structures) of the six core mathematics courses that all mathematics majors take in order to make them more relevant for prospective teachers while at the same time maintaining core content and rigor for all majors. In particular, we have used the NSF-supported K-12 curricula projects and NCTM Standards-based materials as a foundation to create college-level mathematics activities. By using activities that incorporate and expand upon these K-12 materials, all majors are reminded of where they have encountered core mathematical concepts in previous courses, concepts are made more relevant as they are set in real-world or concrete settings, and prospective teachers are more motivated to learn the mathematics as they see how their coursework relates to the mathematics they will teach.