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

Identification of di- and triterpenoid lipid tracers confirms the significant role of autoxidation in the degradation of terrestrial vascular plant material in the Canadian Arctic

publisher: Elsevier articletitle: Identification of di- and triterpenoid lipid tracers confirms the significant role of autoxidation in the degradation of terrestrial vascular plant material in the Canadian Arctic journaltitle: Organic Geochemistry articlelink: http://dx.doi.org/10.1016/j.orggeochem.2017.03.011 content_type: article copyright: © 2017 Elsevier Ltd. All rights reserved

The French Didactic Tradition in Mathematics

This chapter presents the French didactic tradition. It first describes theemergence and development of this tradition according to four key features (role ofmathematics and mathematicians, role of theories, role of design of teaching andlearning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this traditionon algebra and on line symmetry-reflection. It then questions the influence of thistradition through the contributions of four researchers from Germany, Italy, Mexicoand Tunisia, before ending with a short epilogue

Where form and substance meet: using the narrative approach of re-storying to generate research findings and community rapprochement in (university) mathematics education

Storytelling is an engaging way through which lived experience can be shared and reflected upon, and a tool through which difference, diversity—and even conflict—can be acknowledged and elaborated upon. Narrative approaches to research bring the richness and vibrancy of storytelling into how data is collected and interpretations of it shared. In this paper, I demonstrate the potency of the narrative approach of re-storying for a certain type of university mathematics education research (non-deficit, non-prescriptive, context-specific, example-centred and mathematically focused) conducted at the interface of two communities: mathematics education and mathematics. I do so through reference to Amongst Mathematicians (Nardi, 2008), a study carried out in collaboration with 20 university mathematicians from six UK mathematics departments. The study deployed re-storying to present data and analyses in the form of a dialogue between two fictional, yet entirely data-grounded, characters—M, mathematician, and RME, researcher in mathematics education. In the dialogues, the typically conflicting epistemologies—and mutual perceptions of such epistemologies—of the two communities come to the fore as do the feasibility-of, benefits-from, obstacles-in and conditions-for collaboration between these communities. First, I outline the use of narrative approaches in mathematics education research. Then, I introduce the study and its use of re-storying, illustrating this with an example: the construction of a dialogue from interview data in which the participating mathematicians discuss the potentialities and pitfalls of visualisation in university mathematics teaching. I conclude by outlining re-storying as a vehicle for community rapprochement achieved through generating and sharing research findings—the substance of research—in forms that reflect the fundamental principles and aims that underpin this research. My conclusions resonate with sociocultural constructs that view mathematics teacher education as contemporary praxis and the aforementioned inter-community discussion as taking place within a third space

Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Notes for a history of the teaching of algebra

Abundant literature is available on the history of algebra. However, the history of the teaching of algebra is largely unwritten, and as such, this chapter essentially constitutes some notes that are intended to be useful for future research on this subject. As well as the scarcity of the works published on the topic, there is the added difficulty of drawing the line between the teaching of algebra and the teaching of arithmetic—two branches of knowledge whose borders have varied over time (today one can consider the arithmetic with the four operations and their algorithms and properties taught in schools as nothing more than a small chapter of algebra). As such, we will be very brief in talking about the more distant epochs, from which we have some mathematics documents but little information on how they were used in teaching. We aim to be more explicit as we travel forwards into the different epochs until modern times. We finish, naturally, with some reflections on the present-day and future situation regarding the teaching of algebra.info:eu-repo/semantics/publishedVersio

The Large Observatory For X-ray Timing: LOFT

LOFT, the Large Observatory for X-ray Timing, is a new space mission concept devoted to observations of Galactic and extra-Galactic sources in the X-ray domain with the main goals of probing gravity theory in the very strong field environment of black holes and other compact objects, and investigating the state of matter at supra-nuclear densities in neutron stars. The instruments on-board LOFT, the Large area detector and the Wide Field Monitor combine for the first time an unprecedented large effective area (~10 m2 at 8 keV) sensitive to X-ray photons mainly in the 2-30 keV energy range and a spectral resolution approaching that of CCD-based telescopes (down to 200 eV at 6 keV). LOFT is currently competing for a launch of opportunity in 2022 together with the other M3 mission candidates of the ESA Cosmic Vision Progra