Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

the italian didactic tradition

Starting with a historic overview highlighting the increasing interest and involvement of the community of mathematicians in educational issues, the chapter outlines some of the crucial features that shaped Italian didactics and, more specifically, the emergence of research studies on mathematics education. Some of these features are related to local conditions, for instance, the high degree of freedom left to the teacher in the design and realization of didactic interventions. The specificity of the Italian case can also be highlighted through a comparison with the reality of other countries. The fruitfulness of this comparison is presented by reporting on collective and personal collaboration experiences between the French and Italian research communities. A final contribution, coming from East Asia, puts the Italian tradition under the lens of a completely new eye, and invites reflection upon historical and institutional aspects of the Italian tradition

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM-The International Journal on Mathematics Education-by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers' and didacticians' engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. © 2014 FIZ Karlsruhe

Mathematics teaching development as a human practice: identifying and drawing the threads

This article was published in the journal, ZDM Mathematics Education [© FIZ Karlsruhe] and the definitive version is available at: http://dx.doi.org/10.1007/s11858-012-0437-7The didactic triangle links mathematics, teachers and students in a consideration of teaching– learning interactions in mathematics classrooms. This paper focuses on teachers and teaching in the development of fruitful learning experiences for students with mathematics. It recognises primarily that teachers are humans with personal characteristics, subject to a range of influences through the communities of which they are a part, and considers aspects of teachers’ personhood, identity and agency in designing teaching for the benefit of their students. Teaching is seen as a developmental process in which inquiry plays a central role, both in doing mathematics in the classroom and in exploring teaching practice. The teacher-as-inquirer in collaboration with outsider researchers leads to growth of knowledge in teaching through development of identity and agency for both groups. The inclusion of the outsider researcher brings an additional node into the didactic triangle

Signifying “students”, “teachers” and “mathematics”: a reading of a special issue

This paper examines a Special Issue of Educational Studies in Mathematics comprising research reports centred on Peircian semiotics in mathematics education, written by some of the major authors in the area. The paper is targeted at inspecting how subjectivity is understood, or implied, in those reports. It seeks to delineate how the conceptions of subjectivity suggested are defined as a result of their being a function of the domain within which the authors reflexively situate themselves. The paper first considers how such understandings shape concepts of mathematics, students and teachers. It then explores how the research domain is understood by the authors as suggested through their implied positioning in relation to teachers, teacher educators, researchers and other potential readers

The Story Format and the Cycle of Meaning Construction for Physics Education in Primary Schools

The story format may provide a stimulating environment, including tasks, questions or problems, giving space for scientific experimentation and group discussions guided by the teacher. In this contribution we present the main advantages of the story format for physics teaching and learning and the features that a story should have in order to implement what we call the \u201ccycle of meaning construction\u201d, which constitutes an attempt to integrate the attributes already accredited to the story format in science teaching with pedagogical, methodological and didactic approaches. Lastly, a story will be presented in brief as a possible example for primary school physics education