Further discussion also occured at the recent International Congress on Mathematics Education 10, in Copenhagen, where I co-chaired a Topic Study Group 16 on Visualisation in the teaching and learning of mathematics TSG 16
My own paper, distributed at ICME10, was about Claims and Questions towards a Research Program in Visualization. Download a PDF file of this paper.
I am working with Margaret Sinclair, Faculty of Education, on an SSHRC funded project developing activities for pre-service and in-service elementary teachers developing visual and spatial reasoning. The hypothesis is that: these are important for younger children; the children can do a lot more of this that the curriculum currently provides; teachers are a key resource in supporting this critical development for school children.
I have a series of PowerPoint presentations (with companion GSP sketches, web pages, etc.) on this and related topics. I plan to post some of them but will share them, informally, with interested folk who contact me. I have local support, including a small SSHRC grant, for this ongoing work.
Earlier presentations were partially supported by a SCOTL grant and an SSHRC conference travel grant to attend the International Congress of Mathematical Education in Tokyo, where I gave an invited one hour regular lecture. Copies of some related papers are below, in PDF format.
I also served as the York University representative on the Council of Ontario Universities (COU) Mathematics Curriculum Review Task Force. We provided input to the ministry (and the minister) and are working to coordinate the responses, including university admissions requirements for the new curriculum. Feel free to contact me for information.
This May, Bernd Schulze completed his Ph.D. Thesis on Combinatorial and Geometric Rigidity with Symmetry Constraints. It is available for download
Recent work, available only in preprint form, includes:
I am also a senior researcher on a team four year National Institute of Health grant through Arizona State University and Michigan State University on New algorithms for protein flexibility. My collaborators there are Professor Michael Thorpe and Professor Leslie Kuhn . Some of the materials from the work are now available for downloading or for use from the web, at flexweb.asu.edu
Recently, we organized a workshop at BIRS (Banff) on this topic. From the workshop, there is a Web Comptes Rendus site with a number of papers which are freely available for downloading by the public. The site also includes some 'problems' (and solutions) from the discussions around the workshop.
I am working with a Masters Student in Computer Science, two Ph.D students in mathematics, and several undergraduate students in mathematics and computer science on problems in bioinformatics, molecular flexibility and rigidity, etc..
We are now informally gathering researchers at York who are interested in bioinformatics, including protein structure and classification. If you share this interest, get in touch with me. There is a graduate course in bioinformatics COSC 5290 which is taught in the Computer Science Graduate Program. More information is available from the web pages of Mariana Kant, the course director.
For several years I have been collaborating with a group centered in computer science at Yale. Two of the senior researchers are Professor Stephen Morse and Professor Yang (Richard) Yang . Working in particular with a recent Ph.D. student (now a post-doc at Columbia) Tolga Eren, we have a number of conference papers published, and some journal articles being submitted.
A specific project, with Ileana Streinu, applied the analysis of convexifying simple polygons in the plane to one-vertex origami: when can a folded paper with one vertex (a folded cone) be flattened, or made into a convex cone, without any new folds?