Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

The effects of different knowledge-dissemination interventions on the mastitis knowledge of Tanzanian smallholder dairy farmers

We developed three different knowledge-dissemination methods for educating Tanzanian smallholder farmers about mastitis in their dairy cattle. The effectiveness of these methods (and their combinations) was evaluated and quantified using a randomised controlled trial and multilevel statistical modelling. To our knowledge, this is the first study that has used such techniques to evaluate the effectiveness of different knowledge-dissemination interventions for adult learning in developing countries. Five different combinations of knowledge-dissemination method were compared: 'diagrammatic handout' ('HO'), 'village meeting' ('VM'), 'village meeting and video' ('VM + V), 'village meeting and diagrammatic handout' ('VM + HO') and 'village meeting, video and diagrammatic handout' ('VM + V + HO'). Smallholder dairy farmers were exposed to only one of these interventions, and the effectiveness of each was compared to a control ('C') group, who received no intervention. The mastitis knowledge of each farmer (n = 256) was evaluated by questionnaire both pre- and post-dissemination. Generalised linear mixed models were used to evaluate the effectiveness of the different interventions. The outcome variable considered was the probability of volunteering correct responses to mastitis questions post-dissemination, with 'village' and 'farmer' considered as random effects in the model. Results showed that all five interventions, 'HO' (odds ratio (OR) = 3.50, 95% confidence intervals (CI) = 3.10, 3.96), 'VM + V + HO' (OR = 3.34, 95% CI = 2.94, 3.78), 'VM + HO, (OR=3.28, 95% CI=2.90, 3.71), WM+V (OR=3.22, 95% CI=2.84, 3.64) and 'VM' (OR = 2.61, 95% CI = 2.31, 2.95), were significantly (p < 0.0001) more effective at disseminating mastitis knowledge than no intervention. In addition, the 'VM' method was less effective at disseminating mastitis knowledge than other interventions. Combinations of methods showed no advantage over the diagrammatic handout alone. Other explanatory variables with significant positive associations on mastitis knowledge included education to secondary school level or higher, and having previously learned about mastitis by reading pamphlets or attendance at an animal-health course. (c) 2005 Elsevier B.V. All rights reserved.

Does SMS text messaging help or harm adults’ knowledge of standard spelling?

The recent increase in short messaging system (SMS) text messaging, often using abbreviated, non-conventional ‘textisms’ (e.g. ‘2nite’), in school-aged children has raised fears of negative consequences of such technology for literacy. The current research used a paradigm developed by Dixon and Kaminska, who showed that exposure to phonetically plausible misspellings (e.g. ‘recieve’) negatively affected subsequent spelling performance, though this was true only with adults, not children. The current research extends this work to directly investigate the effects of exposure to textisms, misspellings and correctly spelledwords on adults’ spelling. Spelling of a set of key words was assessed both before and after an exposure phase where participants read the same key words, presented either as textisms (e.g. ‘2nite’), correctly spelled (e.g. ‘tonight’) or misspelled (e.g. 'tonite’)words. Analysis showed that scores decreased from pre- to post-test following exposure to misspellings, whereas performance improved following exposure to correctly spelled words and, interestingly, to textisms. Data suggest that exposure to textisms, unlike misspellings, had a positive effect on adults’ spelling. These findings are interpreted in light of other recent research suggesting a positive relationship between texting and some literacy measures in school-aged children.

Investigating orthographic and semantic aspects of word learning in poor comprehenders

This study compared orthographic and semantic aspects of word learning in children who differed in reading comprehension skill. Poor comprehenders and controls matched for age (9-10 years), nonverbal ability and decoding skill were trained to pronounce 20 visually presented nonwords, 10 in a consistent way and 10 in an inconsistent way. They then had an opportunity to infer the meanings of the new words from story context. Orthographic learning was measured in three ways: the number of trials taken to learn to pronounce nonwords correctly, orthographic choice and spelling. Across all measures, consistent items were easier than inconsistent items and poor comprehenders did not differ from control children. Semantic learning was assessed on three occasions, using a nonword-picture matching task. While poor comprehenders showed equivalent semantic learning to controls immediately after exposure to nonword meaning, this knowledge was not well retained over time. Results are discussed in terms of the language and reading skills of poor comprehenders and in relation to current models of reading development.

Tapping into Floor Staff: Using the knowledge of floor staff to conduct formative evaluations of exhibits in a Canadian science centre

Most science centres in Canada employ science-educated floor staff to motivate visitorsto have fun while enhancing the educational reach of the exhibits. Although bright andsensitive to visitors’ needs, floor staff are rarely consulted in the planning,implementation, and modification phases of an exhibit. Instead, many developmentteams rely on costly third-party evaluations or skip the front-end and formativeevaluations all together, leading to costly errors that could have been avoided. This studywill seek to reveal a correlation between floor staff’s perception of visitors’ interactionswith an exhibit and visitors’ actual experiences. If a correlation exists, a recommendationcould be made to encourage planning teams to include floor staff in the formative andsummative evaluations of an exhibit. This is especially relevant to science centres withlimited budgets and for whom a divide exists between floor staff and management.In this study, a formative evaluation of one exhibit was conducted, measuring both floorstaff’s perceptions of the visitor experience and visitors’ own perceptions of the exhibit.Floor staff were then trained on visitor evaluation methods. A week later, floor staff andvisitors were surveyed a second time on a different exhibit to determine whether anincrease in accuracy existed.The training session increased the specificity of the motivation and comprehensionresponses and the enthusiasm of the staff, but not their ability to predict observedbehaviours with respect to ergonomics, learning indicators, holding power, and successrates. The results revealed that although floor staff underestimated visitors’ success ratesat the exhibits, staff accurately predicted visitors’ behaviours with respect to holdingpower, ergonomics, learning indicators, motivation and comprehension, both before andafter the staff training.

Teaching Mathematics in English to Swedish Speaking Students : The Use of Second Language Teaching Practices in the Teaching of Mathematics in English to Swedish Speaking Students in Lower Secondary School

Over 20,000 Swedish lower high school students are currently learning mathematics in English but little research has been conducted in this area. This study looks into the question of how much second language learner training teachers teaching mathematics in English to Swedish speaking students have acquired and how many of those teachers are using effective teaching practices for second language learners. The study confirms earlier findings that report few teachers receive training in second language learning but indicates that some of the teaching practices shown to be effective with second language learners are being used in some Swedish schools

Prediction Of Hydrological Models’ Uncertainty By A Committee Of Machine Learning-Models

This study presents an approach to combine uncertainties of the hydrological model outputs predicted from a number of machine learning models. The machine learning based uncertainty prediction approach is very useful for estimation of hydrological models' uncertainty in particular hydro-metrological situation in real-time application [1]. In this approach the hydrological model realizations from Monte Carlo simulations are used to build different machine learning uncertainty models to predict uncertainty (quantiles of pdf) of the a deterministic output from hydrological model . Uncertainty models are trained using antecedent precipitation and streamflows as inputs. The trained models are then employed to predict the model output uncertainty which is specific for the new input data. We used three machine learning models namely artificial neural networks, model tree, locally weighted regression to predict output uncertainties. These three models produce similar verification results, which can be improved by merging their outputs dynamically. We propose an approach to form a committee of the three models to combine their outputs. The approach is applied to estimate uncertainty of streamflows simulation from a conceptual hydrological model in the Brue catchment in UK and the Bagmati catchment in Nepal. The verification results show that merged output is better than an individual model output. [1] D. L. Shrestha, N. Kayastha, and D. P. Solomatine, and R. Price. Encapsulation of parameteric uncertainty statistics by various predictive machine learning models: MLUE method, Journal of Hydroinformatic, in press, 2013.

Dental students' knowledge of ergonomic postural requirements and their application during clinical care

Aim:To examine how much final-year undergraduate dental students know about postural dental ergonomic requirements, and how well they apply these requirements clinically.Background:Dentists are vulnerable to diverse mechanical (e.g. postural) and non-mechanical occupational risks.Materials and Methods:Eight postural requirements found in normalising documents were identified, reproduced, photographed, and analysed to develop a test of visual perception (TVP). Photographs of the 69 participating students were taken during their clinical care to ascertain ergonomics compliance, after which the students were administered the TVP. Pearson's test was used to correlate the level of knowledge (TVP) and its clinical application (photographic analysis) among the 552 observations made for each test (total of 1104 observations).Results:65.7% of the TVP questions were answered correctly and 35% of the photographic cases were in compliance with ergonomic requirements (+ 0.67, P < 0.0001).Conclusion:The knowledge of ergonomics postural requirements and their clinical application among the dental students surveyed were not satisfactory. The reasons for the learning difficulties encountered by the students should be identified to improve the learning process. The didactic use of digital images in this study may help in this endeavour.

Proposal of convergence of e-Learning systems for t-Learning

This article presents considerations about viability on reutilize existing web based e-Learning systems on Interactive Digital TV environment according to Digital TV standard adopted in Brazil. Considering the popularity of Moodle system in academic and corporative area, such system was chosen as a foundation for a survey into its properties to create a specification of an Application Programming Interface (API) for convergence to t-Learning characteristics that demands efforts in interface design area due the fact that computer and TV concepts are totally different. This work aims to present studies concerning user interface design during two stages: survey and detail of functionalities from an e-Learning system and how to adapt them for the Interactive TV regarding usability context and Information Architecture concepts.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

CLIL materials in Secondary Education: focusing on the language of instruction in the subject area of Mathematics

[EN]Applying a CLIL methodological approach marks a shift in emphasis from language learning based on linguistic form and grammatical progression to a more ‘language acquisition’ one which takes account language functions. In this article we will study the elements of the “language of instruction” of the area of Maths in Secondary Education, by focusing on the analysis of the communicative functions, and the lexical and the cultural items present in the textbook in use. Our aim is to present the CLIL teacher with the linguistic and didactic implications that he or she should take into consideration when implementing the bilingual syllabuses with their students. In order to do that, we will present our conclusions emphasizing the need for coordination in different content areas, linguistic and communicative contents, between the foreign language teacher and the CLIL subject one.

Moving from sustainable management to sustainable governance of natural resources: The role of social learning processes in rural India, Bolivia and Mali

The present paper discusses a conceptual, methodological and practical framework within which the limitations of the conventional notion of natural resource management (NRM) can be overcome. NRM is understood as the application of scientific ecological knowledge to resource management. By including a consideration of the normative imperatives that arise from scientific ecological knowledge and submitting them to public scrutiny, ‘sustainable management of natural resources’ can be recontextualised as ‘sustainable governance of natural resources’. This in turn makes it possible to place the politically neutralising discourse of ‘management’ in a space for wider societal debate, in which the different actors involved can deliberate and negotiate the norms, rules and power relations related to natural resource use and sustainable development. The transformation of sustainable management into sustainable governance of natural resources can be conceptualised as a social learning process involving scientists, experts, politicians and local actors, and their corresponding scientific and non-scientific knowledges. The social learning process is the result of what Habermas has described as ‘communicative action’, in contrast to ‘strategic action’. Sustainable governance of natural resources thus requires a new space for communicative action aiming at shared, intersubjectively validated definitions of actual situations and the goals and means required for transforming current norms, rules and power relations in order to achieve sustainable development. Case studies from rural India, Bolivia and Mali explore the potentials and limitations for broadening communicative action through an intensification of social learning processes at the interface of local and external knowledge. Key factors that enable or hinder the transformation of sustainable management into sustainable governance of natural resources through social learning processes and communicative action are discussed.

Improving sixth grade student knowledge of ecology using fish rearing and release as a real-world context

This research project measured the effects of real-world content in a science classroom by determining change (deep knowledge of life science content, including ecosystems from MDE – Grade Level Content Expectations) in a subset of students (6th Grade Science) that may result from the addition of curriculum (real-world content of rearing trout in the classroom). Data showed large gains from the pre-test to post-test in students from both the experimental and control groups. The ecology unit with the implementation of real-world content [trout] was even more successful, and improved students’ deep knowledge of ecosystem content from Michigan’s Department of Education Grade Level Content Expectations. The gains by the experimental group on the constructed response section of the test, which included higher cognitive level items, were significant. Clinical interviews after the post-test confirmed increases in deep knowledge of ecosystem concepts in the experimental group, by revealing that a sample of experimental group students had a better grasp of important ecology concepts as compared to a sample of control group students.

A Socioeconomic Approach to the Development of E-Learning

A multitude of products, systems, approaches, views and notions characterize the field of e-learning. This article attempts to disentangle the field by using economic and sociological theories, theories of marketing management and strategy as well as practical experience gained by the author while working with leading edge suppliers of e-learning. On this basis, a distinction between knowledge creation e-learning and knowledge transfer e-learning is made. The various views are divided into four different ideal-typical paradigms, each with its own characteristics and limitations. Selecting the right paradigm to use in the development of an e-learning strategy may prove crucial to success. Implications for the development of an e-learning strategy in businesses and educational institutions are outlined.