An E-Learning Innovative Approach for Mathematical Argumentative Thinking
By Giovannina Albano, Umberto Dello Iacono and Maria Alessandra Mariotti
This paper concerns the design of a specific computer-based educational environment fostering students’ shift from argumentation to proof in geometry. In particular, we focus on the language difficulties that such a shift might present and on the need for suitable interventions to overcome them. In this respect, we designed a specific device, named Digital Toolkit for Proof (DTP), based on the use of suitable digital tiles, to promote the transition from colloquial register to literate register, used in mathematical communication. We discuss the findings of the experimentation involving 14-15 years old students from high school who conjecture and prove within the designed environment. The analysis presented shows how the DTP device can promote the emergence of new formulation of justifications that make explicit references to geometric theory. However, the DTP device also shows the occurrence of new specific language issues highlighting difficulties hidden by the use of the colloquial register.
(Dis)Continuity and Feedback in Using a Duo of Artefacts for Robust Constructions: The Case of Pre-Service Mathematics Teachers Using Paper-and-Pencil and Dynamic Geometry
By Gülay Bozkurt and Candas Uygan
This paper focuses on pre-service mathematics teachers’ geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The data were collected through task-based interviews in which the participants were asked to complete angle bisector construction first with PPE and then in DGS, using together with the PPE to support the development of their construction strategies in DGS. Data analysis was carried out to examine (dis)continuities that the pre-service teachers faced while connecting the duos and the feedback received during such process. Findings indicated that the pre-service teachers had difficulties in comprehending (1) the concept of robustness of the construction and (2) the dependency relationships between the objects in DGS, which created discontinuities for them to differentiate between a static representation on paper and dynamic representation in DGS. In this, the use of duos and the feedback different artefacts generated – i.e., direct manipulation feedback, evaluation feedback and tool operation feedback from the DGS, and strategy feedback scaffolded by the interviewer –, promoted their conception of angle bisector construction.
Pre-Service Teachers’ TPACK and Attitudes Toward Integration of ICT in Mathematics Teaching
By José M. Marbán and Edgar J. Sintema
The effective integration of Information and Communication Technologies (ICT) in mathematics education has become a challenge for practitioners and researchers. In this sense, the TPACK framework has been employed in many studies associated with the use of ICT in the classrooms. However, reports on the pre-service teachers’ development of TPACK in mathematics teaching and learning environments appear to be still insufficient to provide sound understanding of such an evolution and, in particular, of their perceptions regarding the use of technology subsequent to their university training in mathematics teaching. With this purpose in mind, through a single survey design study, information from a sample of 166 pre-service primary teachers has been collected and a multiple regression analysis has been performed leading to a predictive model where contextual knowledge and technological knowledge in pre-service teachers’ TPACK contain best information to be able to predict their attitudes towards the integration of ICT in the mathematics classroom.
Incorporating Statistics Into College Algebra
By Sheldon P. Gordon and Florence S. Gordon
The authors discuss the status of college algebra and related offerings and their relationship to introductory statistics education. They also describe an innovative approach to college algebra that integrates a significant amount of statistical reasoning and concepts and statistical methods as natural applications of basic ideas that are part of a modern college algebra course. This can serve either as an introduction to a subsequent introductory statistics course or as a reminder/ reinforcement of key statistical ideas for students who have previously taken an introductory statistics course.
This issue also contain a visualisation of a proof, by Moshe Stupel, Shaanan (Academic Religious) Teachers’ College and Gordon (Teachers’ Academic) College, Haifa, Israel.