The Evaluation of a Pre-Service Mathematics Teacher’s TPACK: A Case of 3D Shapes with GeoGebra
By İpek Saralar, Mine Işıksal-Bostan and Didem Akyüz
Abstract: This paper describes a pre-service mathematics teachers’ technological pedagogical content knowledge (TPACK) during her school experience. This study focuses on how the participant taught different views of three-dimensional objects in a private middle school. It is a descriptive case study in which the data was collected through semi-structured interviews, observations, lesson plans and corresponding GeoGebra files. The data analysis showed that there is an increase in the technological pedagogical content knowledge of the participant during the practicum. In other words, the findings of the study reveal that there was an observable development in the participant’s skills in teaching with technology during the school experience course which helped the improvement of her TPACK. It is proposed that the school experience helped her develop her knowledge of teaching in dynamic geometry-integrated mathematics classrooms. This claim and resulting implications for practice are unpacked in further detail.
Visualizing and Understanding Regression and Correlation Using Dynamic Software
By Sheldon P. Gordon and Florence S. Gordon
Abstract: This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that stress ideas on curve fitting techniques.
Using Automated Reasoning Tools in GeoGebra in the Teaching and Learning of Proving in Geometry
By Zoltán Kovács, Tomás Recio and M. Pilar Vélez
Abstract: This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some examples of the use in the classroom of such commands are provided, including one describing how intuitive handling of GeoGebra automated reasoning tools may result in unexpected outputs. In all cases the emphasis is made in the potential utility of these tools as a guiding stick to foster student activities (exploration, reasoning) in the learning of elementary geometry. Moreover, a collection of appendices describing other, more sophisticated, low-level GeoGebra tools (Prove, ProveDetails), as well as instructions on how to obtain the translation of GeoGebra commands into other languages, and details about debugging, are included.