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

Objects, actions, and images: a perspective on early number development

It is the purpose of this article to present a review of research evidence that indicates the existence of qualitatively different thinking in elementary number development. In doing so, the article summarizes empirical evidence obtained over a period of 10 years. This evidence first signaled qualitative differences in numerical processing, and was seminal in the development of the notion of procept. More recently, it examines the role of imagery in elementary number processing. Its conclusions indicate that in the abstraction of numerical concepts from numerical processes qualitatively different outcomes may arise because children concentrate on different objects or different aspects of the objects, which are components of numerical processing

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

Protection and Prevention: The Shortcomings of U.S. Copyright Law in Combatting Cultural Appropriation in the Fashion Industry

American fashion represents an eclectic patchwork of diverse experiences and ideas; however, drawing upon Indigenous communities’ cultural identities and sacred traditions can easily cross the line between inspiration and appropriation. In reality, designs derived from culturally significant symbols, which have been stolen from Indigenous communities and stripped of their meaning, flood the American market. From runway shows to sports teams’ mascots to undergarment designs, these manifestations of cultural appropriation occur legally under the existing U.S. copyright regime, and adaptations to the current, Westernized system of intellectual property (IP) rights must integrate Indigenous perceptions of communal ownership with respect to their intellectual property. Copyright protection empowers native communities with both a sword and a shield, allowing for the protection and enforcement of their sacred art forms. By expanding current notions of authorship, copyright protection can extend to traditional designs and protect them from constant appropriation, and quite frankly, stealing by fashion labels. Moreover, granting a valid copyright to Indigenous designs in fashion must be accompanied by the explicit recognition of moral rights to provide comprehensive protection. In the United States, a suit for copyright infringement relies on the existence of a valid copyright; thus, the current law denying these protections to Native American and Alaskan Native communities leaves them without legal remedy when faced with the appropriation of their intellectual property. This Note proceeds in three Parts. Part One discusses Indigenous designs in fashion as a classification of Traditional Cultural Expressions (TCEs). Part Two analyzes the legal framework of U.S. copyright law as it stands and offers insight into the discrepancies between Western and Indigenous notions of intellectual property rights. Finally, Part Three suggests two legislative adaptations to account for these discrepancies and provide for the protection of Indigenous fashion designs, and all classes of TCEs, drawing upon international solutions to this issue

Integrating constructive feedback in personalised e-learning

When using e-learning material some students progress readily, others have difficulties. In a traditional classroom the teacher would identify those with difficulties and direct them to additional resources. This support is not easily available within e-learning. A new approach to providing constructive feedback is developed that will enable an e-learning system to identify areas of weakness and provide guidance on further study. The approach is based on the tagging of learning material with appropriate keywords that indicate the contents. Thus if a student performs poorly on an assessment on topic X, there is a need to suggest further study of X and participation in activities related to X such as forums. As well as supporting the learner this type of constructive feedback can also inform other stakeholders. For example a tutor can monitor the progress of a cohort; an instructional designer can monitor the quality of learning objects in facilitating the appropriate knowledge across many learners

The challenges in the transition to adulthood for foster care youth: a literature review

The years of emerging adulthood are oftentimes filled with both happiness and anxiety while youth move toward adult roles and responsibilities. According to Courtney and Dworsky (2006), a subset of American emerging adults, those who are transitioning out of foster care face greater vulnerability than do their peers in the general population in a number of issues. As a result, this paper reviewed the literature on the challenges faced by these former foster youth, namely relationships, well-being, substance use, education, employment and finances. Limitations of this extant research are noted along with directions in future research on programs designed to facilitate these former foster youth\u27s transition. Lastly, real-world implications of the findings are discussed

A Rheological Model for Cupuassu (Theobroma grandiflorum) Pulp at Different Concentrations and Temperatures

This work was made aiming at studying the best model for the rheological properties of Cupuassu (Theobroma grandiflorum, Schum) pulps with 14 (in nature), 17, 19, 23 and 25°Brix of total soluble solids (TSS) which were me asured at 20, 30, 40, 50 and 60°C temperature using a conc entric cylinder rheometer. The results were adjusted to the following nine models: Ostwald-de-Waele (power law), Bingham, Casson, Generalized Casson, Heinz–Casson, Herschel–Bulkley, Mizrahi–Berk, Schulmann–Haroske–Reher and Windhab. The parameters of the best model were correlated with pulp temperature and TSS by polynomial regression analysis and were kept in the regression equation only those parameters that contributed more than 1% to the variation of the independent variable. The results indicate that the rheological behavior of Cupuassu pulp in different concentrations and temperatures can be modeled by the Windhab model, although other models can be used in a narrower band of shear stress

The effect of polymer/plasticiser ratio in film forming solutions on the properties of chitosan films

In this work physical-chemical properties of chitosan/ glycerol film forming solutions (FFS) and the resulting films were analysed. Solutions were prepared using different concentrations of plasticising agent (glycerol) and chitosan. Films were produced by solvent casting and equilibrated in a controlled atmosphere. FFS water activity and rheological behaviour were determined. Films water content, solubility, water vapour and oxygen permeabilities, thickness, and mechanical and thermal properties were determined. Fourier transform infrared (FTIR) spectroscopy was also used to study the chitosan/glycerol interactions. Results demonstrate that FFS chitosan concentration influenced solutions consistency coefficient and this was related with differences in films water retention and structure. Plasticiser addition led to an increase in films moisture content, solubility and water vapour permeability, water affinity and structural changes. Films thermo-mechanical properties are significantly affected by both chitosan and glycerol addition. FTIR experiments confirm these results. This work highlights the importance of glycerol and water plasticisation in films properties.This work was supported by National Funds from FCT - Fundacao para a Ciencia e a Tecnologia, through project PEst-OE/EQB/LA0016/2011.Authors Joana F. Fundo, Andrea C. Galvis-Sanchez and Mafalda A. C. Quintas acknowledge FCT for research grants SFRH/ BD / 62176 / 2009, SFRH/BPD/37890/2007 and SFRH / BPD / 41715 / 2007, respectively