Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis

The complex process of scaling the integration of technology enhanced learning in mainstream classrooms

The early optimism for how technology might transform teaching and learning practices in mainstream school classrooms has long faded in many countries around the world. Whilst early research findings suggested that this was due to obvious barriers such as access to the technology itself, more recent attempts to scale student-access have illuminated other factors and provided a more sound theoretical foundation for us to understanding the processes and products of scaling educational technology innovations. This keynote will use findings from key projects and initiatives to highlight what is being learned – and how this might inform future endeavours to realise a more 21st century curriculum

Collaboration between Mathematics and Mathematics Education

Abstract Our chapter is in four sections. Michèle Artigue tells the story of her transition from mathematical logic to mathematics education and of collaborations at a wide variety of institutional levels. Günter Törner gives a history of collaboration between mathematics and mathematics education in Germany along with a list of recommendations to foster collaboration. Ehud de Shalit shares lessons learned from personal experiences collaborating in the production of a math fair and in the design of a mathematics education major. Pat Thompson tells of several collaborative efforts at his home institution and examines ways that mathematics education contributed mathematically to them. A concluding section provides a reflection on our charge -structural and cultural issues involved in collaborations between mathematics and mathematics education

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

Development of a methodology for extreme flood estimation

The development of a methodology for extreme flood estimation is the aim of the project CRUEX++. This project follows the CRUEX project which aimed at the development of a PMP-PMF methodology (PMP=Probable Maximum precipitation, PMF=Probable Maximum Flood). Numerous tools, models and methods have been developed during the last years. The goal of the CRUEX++ project is to combine and enrich these elements leading to a methodology for extreme flood estimations in order to verify dam safety. A PhD thesis has been initiated in 2012 to lead this project and to conclude on a final methodology

The influence of technology on the mathematical modelling of physical phenomena

A study is presented in which students are asked to model two physical phenomena using applications on electronic tablets : a bounce of a ball and the extension of a spring. The analysis focusses on (a) the influence of characteristics of the applications on the tablets on the decisions that groups of 16-year-old students made during the modelling phases in which reality and mathematics are related, (b) mathematisation of the phenomena and (c) interpretation of the models. The phenomena were recorded using an app that requests users establish a set of references during the mathematisation process, which makes students focus on the way the references have been set to interpret the model properly. Our findings indicated inconsistences between student decisions made during mathematisation and their considerations during interpretation of the model. To conclude we suggest reasons students experience problems in working without a pre-defined reference syste