The Effects of the Geometer\u27s Sketchpad Software on Achievement of Geometric Knowledge of High School Geometry Students

Digitized thesi

Transitioning from "It Looks Like" to "It Has To Be" in Geometrical Workspaces: affect and near-to-me attention

Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner’s perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person’s deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason’s teaching-practice-based ‘noticing’; qualitative data analysed in this report include individual interviews with school teachers on in-service courses and reflective notes from teaching. Basic Euclidean geometry is used as the medium for investigating transition from ‘it looks like’ to a reasoned ‘it has to be’

How the activity of proving is constituted in a Cypriot classroom for 12 year old students

The aim of this study is to identify how the activity of proving is constituted in a Cypriot primary classroom for 12 year old students. Through Cultural-Historical Activity Theory (CHAT), the influence of research literature, curriculum prescriptions, the students and critically the teacher is documented. The evolution of objects, in particular the aims of the teacher, and other components in the activity systems is traced. Within the qualitative enquiry, this study employs CHAT alongside a collaborative design approach to explore the way the teacher is working with the students to foreground mathematical argumentation. The research is situated in a Cypriot primary school classroom with the researcher having the role of teacher researcher. The usual class teacher and researcher co-developed Dynamic Geometry Environment (DGE)-based tasks to be used with the children. As a result it was possible to track how the nature of the teacher’s objects changed and how contradictions emerged. Evidence from the curriculum documentation and from classroom observations was used to develop the activity systems of exploring and explaining. One important finding lies in how exploring and explaining were key sub-systems within the central activity system of proving as they provided a key pathway, which often included defining. Processes of explaining, defining and exploring appeared to create a fertile ground for the development of proving. I refer to these developments as pre-proving. However, it turns out that there are inherent contradictions within explaining and exploring that hinder the constitution of proving in the classroom. An emerging primary contradiction was apparent in the multifaceted nature of the object of both exploring and explaining to both facilitate mathematical argumentation and address a prescribed curriculum. Due to the tension between these objects, the teacher was often faced with dilemmas such as whether to open up playful activity or close it down to focus on the curriculum specifics. These led to a constant struggle in the teacher’s everyday practice. I report also on how primary contradictions led inevitably to higher-level contradictions between other components of the activity systems

Instructional strategies in explicating the discovery function of proof for lower secondary school students

In this paper, we report on the analysis of teaching episodes selected from our pedagogical and cognitive research on geometry teaching that illustrate how carefully-chosen instructional strategies can guide Grade 8 students to see and appreciate the discovery function of proof in geometr

Hybrid-dynamic objects: DGS environments and conceptual transformations

A few theoretical perspectives have been taken under consideration the meaning of an object as the result of a process in mathematical thinking. Building on their work, I shall investigate the meaning of ‘object’ in a dynamic geometry environment. Using the recently introduced notions of dynamic-hybrid objects, diagrams and sections which complement our understanding of geometric processes and concepts as we perform actions in the dynamic software, I shall explain what could be considered to be a ‘procept-in-action’. Finally, a few examples will be analyzed through the lenses of hybrid and dynamic objects in terms of how I designed them. A few snapshots of the research process will be presented to reinforce the theoretical considerations. My aim is to contribute to the field of the Didactics of Mathematics using ICT in relation to students’ cognitive developmen

Iowa Core: Mathematics, December 2012

Iowa Core Mathematics includes recommendations for curriculum, instruction, and assessment, as well as standards for mathematical content and mathematical practices

Proceedings of the 12th International Conference on Technology in Mathematics Teaching ICTMT 12

Innovation, inclusion, sharing and diversity are some of the words that briefly and suitably characterize the ICTMT series of biennial international conferences – the International Conference on Technology in Mathematics Teaching. Being the twelfth of a series which began in Birmingham, UK, in 1993, under the influential enterprise of Professor Bert Waits from Ohio State University, this conference was held in Portugal for the first time. The 12th International Conference on Technology in Mathematics Teaching was hosted by the Faculty of Sciences and Technology of the University of Algarve, in the city of Faro, from 24 to 27 June 2015, and was guided by the original spirit of its foundation. The integration of digital technologies in mathematics education across school levels and countries, from primary to tertiary education, together with the understanding of the phenomena involved in the teaching and learning of mathematics in technological environments have always been driving forces in the transformation of pedagogical practices. The possibility of joining at an international conference a wide diversity of participants, including school mathematics teachers, lecturers, mathematicians, mathematics educators and researchers, software designers, and curriculum developers, is one facet that makes this conference rather unique. At the same time, it seeks to foster the sharing of ideas, experiences, projects and studies while providing opportunities to try-out and assess tools or didactical proposals during times of hands-on work. The ICTMT 12 had this same ambition, when embracing and welcoming just over 120 delegates who actively and enthusiastically contributed to a very packed program of scientific proposals and sessions on various topics