Salt stains from evaporating droplets

The study of the behavior of sessile droplets on solid substrates is not only associated with common everyday phenomena, such as the coffee stain effect, limescale deposits on our bathroom walls , but also very important in many applications such as purification of pharmaceuticals, de-icing of airplanes, inkjet printing and coating applications. In many of these processes, a phase change happens within the drop because of solvent evaporation, temperature changes or chemical reactions, which consequently lead to liquid to solid transitions in the droplets. Here we show that crystallization patterns of evaporating of water drops containing dissolved salts are different from the stains reported for evaporating colloidal suspensions. This happens because during the solvent evaporation, the salts crystallize and grow during the drying. Our results show that the patterns of the resulting salt crystal stains are mainly governed by wetting properties of the emerging crystal as well as the pathway of nucleation and growth, and are independent of the evaporation rate and thermal conductivity of the substrates

Inquiry in University Mathematics Teaching and Learning

The book presents developmental outcomes from an EU Erasmus+ project involving eight partner universities in seven countries in Europe. Its focus is the development of mathematics teaching and learning at university level to enhance the learning of mathematics by university students. Its theoretical focus is inquiry-based teaching and learning. It bases all activity on a three-layer model of inquiry: (1) Inquiry in mathematics and in the learning of mathematics in lecture, tutorial, seminar or workshop, involving students and teachers; (2) Inquiry in mathematics teaching involving teachers exploring and developing their own practices in teaching mathematics; (3) Inquiry as a research process, analysing data from layers (1) and (2) to advance knowledge inthe field. As required by the Erasmus+ programme, it defines Intellectual Outputs (IOs) that will develop in the project. PLATINUM has six IOs: The Inquiry-based developmental model; Inquiry communities in mathematics learning and teaching; Design of mathematics tasks and teaching units; Inquiry-based professional development activity; Modelling as an inquiry process; Evalutation of inquiry activity with students. The project has developed Inquiry Communities, in each of the partner groups, in which mathematicians and educators work together in supportive collegial ways to promote inquiry processes in mathematics learning and teaching. Through involving students in inquiry activities, PLATINUM aims to encourage students` own in-depth engagement with mathematics, so that they develop conceptual understandings which go beyond memorisation and the use of procedures. Indeed the eight partners together have formed an inquiry community, working together to achieve PLATINUM goals within the specific environments of their own institutions and cultures. Together we learn from what we are able to achieve with respect to both common goals and diverse environments, bringing a richness of experience and learning to this important area of education. Inquiry communities enable participants to address the tensions and issues that emerge in developmental processes and to recognise the critical nature of the developmental process. Through engaging in inquiry-based development, partners are enabled and motivated to design activities for their peers, and for newcomers to university teaching of mathematics, to encourage their participation in new forms of teaching, design of teaching, and activities for students. Such professional development design is an important outcome of PLATINUM. One important area of inquiry-based activity is that of “modelling” in mathematics. Partners have worked together across the project to investigate the nature of modelling activities and their use with students. Overall, the project evaluates its activity in these various parts to gain insights to the sucess of inquiry based teaching, learning and development as well as the issues and tensions that are faced in putting into practice its aims and goals

Inquiry in University Mathematics Teaching and Learning. The Platinum Project

The book presents developmental outcomes from an EU Erasmus+ project involving eight partner universities in seven countries in Europe. Its focus is the development of mathematics teaching and learning at university level to enhance the learning of mathematics by university students. Its theoretical focus is inquiry-based teaching and learning. It bases all activity on a three-layer model of inquiry: (1) Inquiry in mathematics and in the learning of mathematics in lecture, tutorial, seminar or workshop, involving students and teachers; (2) Inquiry in mathematics teaching involving teachers exploring and developing their own practices in teaching mathematics; (3) Inquiry as a research process, analysing data from layers (1) and (2) to advance knowledge inthe field. As required by the Erasmus+ programme, it defines Intellectual Outputs (IOs) that will develop in the project. PLATINUM has six IOs: The Inquiry-based developmental model; Inquiry communities in mathematics learning and teaching; Design of mathematics tasks and teaching units; Inquiry-based professional development activity; Modelling as an inquiry process; Evalutation of inquiry activity with students. The project has developed Inquiry Communities, in each of the partner groups, in which mathematicians and educators work together in supportive collegial ways to promote inquiry processes in mathematics learning and teaching. Through involving students in inquiry activities, PLATINUM aims to encourage students‘ own in-depth engagement with mathematics, so that they develop conceptual understandings which go beyond memorisation and the use of procedures. Indeed the eight partners together have formed an inquiry community, working together to achieve PLATINUM goals within the specific environments of their own institutions and cultures. Together we learn from what we are able to achieve with respect to both common goals and diverse environments, bringing a richness of experience and learning to this important area of education. Inquiry communities enable participants to address the tensions and issues that emerge in developmental processes and to recognise the critical nature of the developmental process. Through engaging in inquiry-based development, partners are enabled and motivated to design activities for their peers, and for newcomers to university teaching of mathematics, to encourage their participation in new forms of teaching, design of teaching, and activities for students. Such professional development design is an important outcome of PLATINUM. One important area of inquiry-based activity is that of „modelling“ in mathematics. Partners have worked together across the project to investigate the nature of modelling activities and their use with students. Overall, the project evaluates its activity in these various parts to gain insights to the sucess of inquiry based teaching, learning and development as well as the issues and tensions that are faced in putting into practice its aims and goals

Characterizing cassava farmer typologies and their seed sourcing practices to explore opportunities for economically sustainable seed business models in Rwanda

The overdependency on local cassava varieties and informal seed sources by farmers in Rwanda has contributed to the spread of cassava viral diseases. The use of improved planting materials made available through formal seed sources, that assure seed quality, is one way to prevent future disease outbreaks. In order to increase the availability of, and farmers access to, such materials there is increasing interest to develop seed business models. This study aims to understand seed sourcing practices of different farm typologies to inform the development of tailored seed business models. A total of 390 farmers were interviewed and the collected data was analyzed into clusters, resulting in seven farm typologies. Seed sourcing strategies, seed replacement dynamics and purchasing behavior of these typologies were explored via a seed tracing study. We find that more commercial oriented farmers have better access to formal seed sources. Nevertheless, the majority of farmers in all typologies accessed new varieties and quality cassava seed via informal channels. At both formal and informal sources, cash investments in seed were mainly made by the categories of better-off farmers, and were one-time investments to acquire a new variety. Based on farmers current seed sourcing practices, clarifications on the differences between farmers and their willingness-to-pay, the roles of seed degeneration, cost-benefit analysis, value propositions and profit formulas seem important requirements for the further development of viable cassava seed business models. We conclude that tailoring seed business models can have a high potential as it acknowledges differences among farmers, but that careful coordination is needed to ensure that one approach or intervention does not contrast with and/or undermine the others