Bridging Transformational Geometry and Matrix Algebra with a Spreadsheet-based Tool Kit (Word 98 doc)
Co-authored by Sergei Abramovich (SUNY Potsdam), this paper suggests a link between transformational geometry and linear algebra through use of a dynamic spreadsheet tool kit. We discuss the concept of a tool kit and its usefulness in connecting mathematical ideas, specifically in students' understanding of matrices. The full paper will be presented at SITE 2001 and published in the procedings, on CD-ROM and on-line. The Excel file comprising the prescribed tool kit is linked here: Fractal.xls
Fractals, Matrices and Spreadsheets (Word 98 doc)
Here, the topic is the same as above, but we focus upon the mathematical ideas. These ideas were presented as a contributing paper for ICTCM 2000 . The paper will be published electronically at http://archives.math.utk.edu/ICTCM/
Student Conjectures in Geometry (Word 98 doc).
This is my first independently written paper, with roots in my master's thesis (below). The paper focusses on the nature of students' conjectures, particularly those of high school geometry students. It uses von Glasersfeld's scheme theory and Peirce' theory of abduction as a framework. I will present this paper in Tuscon, AZ at PME 2000. And, here is the presentation PME.ppt.
Plausible Reasoning in Geometry (Work 98 doc)
This is it -- my thesis required for completion of an MA in Mathematics Education. I worked with 3 high school geometry students, using Geometer's Sketchpad as a medium for learning about their conjectures and plausible reasoning.
Technology-Enabled Pedagogy as an Informal Link Between Finite and Infinite Concepts in Secondary Mathematics (Word 98 doc)
I wrote this paper with Sergei Abramovich. The paper explores the concept of limits with extensive use of bisector-bounded staircases in Excel and GSP. I presented this paper at North Carolina's Conference of Teachers of Mathematics (NCCTM 99) and at the Asian Technology Conference in Mathematics (ATCM 99). It is being published in Summer 2000 issue of The Mathematics Educator (Excel file).
Exploring Quadratic-Like Sequences with Spreadsheets Through a Toolkit Approach (Word 98 doc)
This paper was written by Sergei Abramovich, Andrew Brantlinger and myself. It addresses the use of spreadsheet-based toolkits in exploring the bifurcation model, leading to chaos. A prototype of such a spreadsheet (written in Excel) is linked below. I presented this paper at the 1998 International Conference for the Use of Technology in Collegiate Mathematics (ICTCM 98).
Bifurcation Spreadsheet (Excel)