Professional Background and Research Interests (1984-1999)

This link provides information on my involvement during the past fifteen years in the development of intelligent tutoring systems and microworlds for teaching geometry. It also highlights my work with secondary teachers on creating teaching scenarios t hat integrate this microworld technology into classroom practice.

Since the mid-eighties my research interests have focused on the design and implementation of computer software systems to provide intelligent computer tools to aid in teaching and learning secondary and post-secondary school geometry. Currently, such systems fall into one of four categories: (1) automatic geometry theorem provers; (2) intelligent geometry tutors; (3) dynamic geometry microworlds; and (4) declarative dynamic geometry systems. Of the four categories, my work with Laurent Trilling has in volved systems in categories two and four. Our work places heavy emphasis on student learning through construction and exploration of geometric figures and uses open-ended, direct manipulation interfaces for both the teachers and students using the system s. The most notable examples today of systems in category three are the dynamic geometry microworlds, Cabri Geometry and Geometer's Sketchpad. The only two systems in category four of which I am aware are GéoSpécif and GDRev, two systems dev eloped by Laurent Trilling's research group in Grenoble, where I have spent two sabbatical leaves.

During the period 1984-86, I was on leave from St. Olaf as a member of the artificial intelligence team of Laurent Trilling at IRISA, a large French government computer science research lab in Rennes, France. I was one of two assigned full-time to work on the intelligent geometry tutoring project (category two above), MENTONIEZH (Breton for geometry). This tutor has four components: figure construction; figure appropriation; geometric property exploration; and proof organization. To this day intelligen t geometry tutors are expected to be equipped with these four components. During my stay at IRISA and during the period 1987-90, Laurent Trilling, Pierrick Nicolas, and I focused on the design and implementation of an interface for the figure construction component of MENTONIEZH.

It was also during my stay at IRISA that I became involved with the work of a mathematics education research group at IREM in Rennes. This group was involved in designing and carrying out teaching experiments in secondary French school geometry classro oms using two computer geometry systems, one of which was MENTONIEZH. My own involvement in this group led to my interest in research into the effects of classroom use of such systems and to my collaboration here at St. Olaf with Judy Cederberg and Martha Wallace of the Mathematics Department in two multi-year NSF funded projects during the period 1990-98. The first three-year project focused on integration of computer technology in the U.S. high school geometry classroom. The second three-year project ex panded on the first to include middle school curriculum and teaching strategies incorporating exploratory, experiential, and visual approaches, computer based or not, across the entire mathematics curriculum. Both projects used the creation and use of tea ching scenarios as the principal cognitive vehicle through which teachers changed classroom practice. These NSF projects made significant use of both dynamic geometry microworlds, Cabri Geometry and Geometer's Sketchpad.

In 1987 Laurent Trilling moved his research activity to IMAG in Grenoble where he is currently the head of the PLIAGE group, a group in which a major research effort is placed into designing intelligent systems for doing geometry. Moreover, the emphasis is on building systems with interfaces that implement a declarative approach to pro blem solving. During 1991-92 I was on leave from St. Olaf as a full-time member of PLIAGE. During this period, Laurent and I programmed the first prototype of GéoSpécif, a declarative dynamic geometry programming system. A paper written for the non-expert and describing this system and presenting declarative dynamic geometry, in general, is contained in a publication of the MAA, Mathematical Association of America Notes, volume 41. This volume is devoted to dynamic geometry in learning, teac hing, and research and is considered to be a defining document for the field of dynamic geometry. The design of GéoSpécif has provided the dynamic geometry community with a new paradigm for doing dynamic geometry and provided the computer sc ience community with a new type of geometric programming.

It was a happy coincidence that the laboratory where Cabri Geometry was designed and developed is also in Grenoble at IMAG. This laboratory is the center of a large research project on the teaching of geometry in French schools using computers as teaching tools. During my 1991-92 leave, I was invited to participate in the weekly working meetings of two of the research groups of this lab, one devoted to basic research for extending the Cabri interface itself and another devoted to designing teachin g situations appropriate for the use of dynamic geometry microworlds. In addition, during this leave year, I was one of two foreigners invited to participat e as a member of the Mandrin Working Group on Computerized Learning Environments and Formalization of Teaching Processes, a group organized and supported by the Centre National de la Recherche Scientifique (the French equivalent of NSF) that held seminars monthly in Geneva, Lyon, and Grenoble. Direct outcomes of this leave include several papers on declarative dynamic geometry system design plus several others on integrating the use of dynamic geometry software into classroom teaching.

During my latest leave in Grenoble, 1998-99, I worked with the dynamic geometry microworld, GDRev. This system is an outgrowth of development efforts surrounding the GéoSpécif system; it possesses a graphical direct manipulation interface . It also provides direct access to the underlying logical specifications for geometric objects and properties, thus making it a prime candidate for implementing a geometry programming language.