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

Workshop report: Developing a methodology to communicate climate services for farmers at scale

This report summarizes the proceedings of the workshop; “Developing a Methodology to Communicate Climate Services At Scale Through Intermediaries for Farmer Communities in Africa and South Asia,” held in Nairobi, Kenya on June 12-14, 2013. The workshop brought together experts from different countries and institutions to work together to develop tools and guidance materials to train various intermediary groups in climate service communication, including public extension services, professional communicators, media, rural radios, NGOs, CBOs, farmers’ organizations, women self help groups and other boundary organizations. Participants developed an outline of potential training modules, and committed to contributing and further developing materials for a training resource guidebook

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

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

Reducing vulnerability to hydro-meteorological extremes in Africa. A qualitative assessment of national climate disaster management policies: Accounting for heterogeneity

In Africa, hydro-meteorological disasters (HMDs) have hit with increasing frequency and magnitude in recent years, with detrimental impacts on local livelihoods. African countries display a patchwork of national policies and institutional frameworks to address these rising HMDs. This paper examines the heterogeneity that exists within Africa's institutional arrangements for climate-related disaster risk management, and introduces a three-partite policy classification that ranks each country as one of three disaster management policy types: the "Unprepared Firefighters" (whose response to disasters is late, delayed and ineffective), the "Prepared Firefighters" (for the most part effective disaster responders) and the "Disaster Averters" (who experienced a paradigm shift and moved focus away from the hazard itself towards a reduction of the underlying risk factors that cause disasters). Through extensive data mining, interviews and qualitative country assessments, we map where African countries lie on this spectrum of effective climate-related disaster risk management. We find that African countries lay at different levels on the spectrum of effective disaster risk management. Across Africa, countries display differential progress in achieving the Hyogo Framework for Action goals and great variation and heterogeneity exists from country to country, one that calls for a concomitant heterogeneity in aid programs and initiatives meant to support comprehensive disaster risk reduction and climate change adaptation (DRR-CCA) in Africa. In closing, this paper suggests ways to support African countries' efforts towards effective disaster risk management and planning. It offers a qualitative method to continually assess developing countries' progress in achieving the Hyogo Framework for Action goals, one that straddles top-down country self-reporting and bottom-up civil society assessment