GeoGebra in mathematics teacher education: the case of quadratic relations

GeoGebra affords a variety of representational resources and computational utilities that have the potential to engage prospective mathematics teachers in insightful investigations of fundamental ideas of mathematics. Given that many prospective mathematics teachers have a fragmented view of mathematics, GeoGebra, as an integrated system of algebra, geometry, and calculus, stands as a mathematically enriched environment where prospective teachers could explore and/or construct mathematical objects and further develop a connected view of mathematics. In this article, we share our experience in using GeoGebra with prospective middle and secondary mathematics teachers, highlighting the need for reconceptualization and remediation for both the instructor and the prospective teachers.

Initial Experience with GeoGebra

We initially introduced GeoGebra to our middle and secondary prospective teachers in Spring 2007, when we were teaching a methods course on the use of technology in mathematics education at a large public university in southeast US. The primary objective of the course is to engage prospective teachers in exploring and reflecting on the multiple uses of instructional technologies in the middle and secondary grades in order to foster their awareness and subsequent development of technological pedagogical content knowledge (TPCK) for mathematics teaching [5, 6]. The entire course was implemented in a computer lab where all the computers were preloaded with the Geometer’s Sketchpad™ (GSP) at that time. Of their own choices, the nstructor and the prospective teachers quickly switched to the open source GeoGebra. While both the instructor and the prospective teachers were learning about the features of GeoGebra, the class tackled a variety of “bite-size” problems [7], including triangle area, curve-fitting, and a few geometric construction problems. The reality was that our prospective teachers did not learn their mathematics in a technology-supported environment at schools, and thus they had no prior experience in connecting the different fields of mathematics such as arithmetic, algebra, geometry, and calculus with technology. Although many of them could recognize the significance of technology in the teaching and learning of mathematics, they tended to believe that mathematics should be first taught with traditional methods and then be explored using technology, revealing challenges associated with all dimensions of TPCK….