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

Effect of different storage conditions on analytical and sensory quality of thermally processed milk based germinated Foxtail millet porridge

Foxtail millet porridge was prepared using germinated grains and milk and was evaluated for its storage stability after thermal processing at Ultra High Temperatures (UHT) of 142 oC for 5 s and Retort processing temperatures of 121.5 oC for 15 min. Various physical, chemical and microbial changes of the porridge were studied for a storage period of 180 days at 25 ± 1 oC. Using consumer perception and survival analysis, the predicted shelf life of the UHT treated and retort processed foxtail millet porridge samples stored at 25 ± 1 oC was found to be 186 ± 9 days and 245 ± 15 days, respectively. Also, data from consumer liking, profiling, physical, chemical and microbial parameters showed significant changes (p < 0.05) in the thermally treated packaged porridge samples over time. As the consumer overall acceptability decreased, the detection of positive attributes (Thick and uniformly coloured texture and appearance; grainy mouth texture; caramel taste and aroma) in the porridge decreased, while the detection of negative attributes (Uneven, decoloured, and curdled texture and appearance; sticky mouth texture; cooked, sour and off smell; cooked, sour and off taste) increased. The present study could establish a significant difference (p < 0.05) in the storage induced properties of UHT and retort processed porridge samples. The analytical evaluation of foxtail millet porridge found that UHT treated porridge was better in quality, but consumers preferred retort processed porridge

Quantitative imaging of concentrated suspensions under flow

We review recent advances in imaging the flow of concentrated suspensions, focussing on the use of confocal microscopy to obtain time-resolved information on the single-particle level in these systems. After motivating the need for quantitative (confocal) imaging in suspension rheology, we briefly describe the particles, sample environments, microscopy tools and analysis algorithms needed to perform this kind of experiments. The second part of the review focusses on microscopic aspects of the flow of concentrated model hard-sphere-like suspensions, and the relation to non-linear rheological phenomena such as yielding, shear localization, wall slip and shear-induced ordering. Both Brownian and non-Brownian systems will be described. We show how quantitative imaging can improve our understanding of the connection between microscopic dynamics and bulk flow.Comment: Review on imaging hard-sphere suspensions, incl summary of methodology. Submitted for special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); 22 pages, 16 fig

Relationships between students' conceptions of constructivist learning and their regulation and processing strategies

The present study investigated relationships between students' conceptions of constructivist learning on the one hand, and their regulation and processing strategies on the other hand. Students in a constructivist, problem-based learning curriculum were questioned about their conceptions of knowledge construction and self-regulated learning, as well as their beliefs regarding their own (in)ability to learn and motivation to learn. Two hypothesized models were tested within 98 psychology students, using a structural equation modelling approach: The first model implemented regulation and processing variables of the Inventory of Learning Styles [ILS, Vermunt (Learning styles and regulation of learning in higher education - towards process-oriented instruction in autonomous thinking, 1992)], the second model of the Motivated Strategies for Learning Questionnaire [MSLQ, Pintrich and de Groot (Journal of Educational Psychology, 82, 33-40, 1990)]. Results showed that structural relations exist between conceptions of constructivist learning and regulation and processing strategies. Furthermore, students who express doubt with regard to their own learning capacities are at risk for adopting an inadequate regulation strategy. A three-tiered structure of conceptual, controlling, and operational level appeared valid for the MSLQ variables, but not entirely for those of the ILS

Sucrose in the concentrated solution or the supercooled “state” : a review of caramelisation reactions and physical behaviour

Sucrose is probably one of the most studied molecules by food scientists, since it plays an important role as an ingredient or preserving agent in many formulations and technological processes. When sucrose is present in a product with a concentration near or greater than the saturation point—i.e. in the supercooled state—it possesses high potentialities for the food industry in areas as different as pastry industry, dairy and frozen desserts or films and coatings production. This paper presents a review on critical issues and research on highly concentrated sucrose solutions—mainly, on sucrose thermal degradation and relaxation behaviour in such solutions. The reviewed works allow identifying several issues with great potential for contributing to significant advances in Food Science and Technology.Authors are grateful for the valuable discussions with Teresa S. Brandao and Rosiane Lopes da Cunha during this research. Author M. A. C. Quintas acknowledges the financial support of her research by FCT grant SFRH/BPD/41715/2007

Mathematical talent in Braille code pattern finding and invention

The recognition of patterns and creativity are two characteristics associated with mathematical talent. In this study, we analyzed these characteristics in a group of 37 mathematically talented students. The students were asked to find the pattern the Braille code had been built upon and reinvent it with the aim of making its mathematical language become more functional. Initially, the students were unable to identify the formation pattern of Braille, but after experiencing the difficulties that blind people face when reading it, they recognized the generating element and the regularity. The results were in contrast with those of a control group, and it is noted that the students with mathematical talent were more effective in using visualization to identify the regularity of the pattern and their invention proposals were more sophisticated and used less conventional mathematical content.This research is part of the R+D+I project EDU2015- 69,731-R (Spanish Government/MinEco and ERDF)

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

Empowering Qualitative Research Methods in Education with Artificial Intelligence

Artificial Intelligence is one of the fastest growing disciplines, disrupting many sectors. Originally mainly for computer scientists and engineers, it has been expanding its horizons and empowering many other disciplines contributing to the development of many novel applications in many sectors. These include medicine and health care, business and finance, psychology and neuroscience, physics and biology to mention a few. However, one of the disciplines in which artificial intelligence has not been fully explored and exploited yet is education. In this discipline, many research methods are employed by scholars, lecturers and practitioners to investigate the impact of different instructional approaches on learning and to understand the ways skills and knowledge are acquired by learners. One of these is qualitative research, a scientific method grounded in observations that manipulates and analyses non-numerical data. It focuses on seeking answers to why and how a particular observed phenomenon occurs rather than on its occurrences. This study aims to explore and discuss the impact of artificial intelligence on qualitative research methods. In particular, it focuses on how artificial intelligence have empowered qualitative research methods so far, and how it can be used in education for enhancing teaching and learning