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.

The effectiveness of assessment learning objects produced using pair programming

Pair Programming is a technique from the software development method eXtreme Programming (XP) whereby two programmers work closely together to develop a piece of software. A similar approach has been used to develop a set of Assessment Learning Objects (ALO). Three members of academic staff have developed a set of ALOs for a total of three different modules (two with overlapping content). In each case a pair programming approach was taken to the development of the ALO. In addition to demonstrating the efficiency of this approach in terms of staff time spent developing the ALOs, a statistical analysis of the outcomes for students who made use of the ALOs is used to demonstrate the effectiveness of the ALOs produced via this method.

Can knowledge of the state of the stratosphere be used to improve statistical forecasts of the troposphere?

Recent analysis of the Arctic Oscillation (AO) in the stratosphere and troposphere has suggested that predictability of the state of the tropospheric AO may be obtained from the state of the stratospheric AO. However, much of this research has been of a purely qualitative nature. We present a more thorough statistical analysis of a long AO amplitude dataset which seeks to establish the magnitude of such a link. A relationship between the AO in the lower stratosphere and on the 1000 hPa surface on a 10-45 day time-scale is revealed. The relationship accounts for 5% of the variance of the 1000 hPa time series at its peak value and is significant at the 5% level. Over a similar time-scale the 1000 hPa time series accounts for 1% of itself and is not significant at the 5% level. Further investigation of the relationship reveals that it is only present during the winter season and in particular during February and March. It is also demonstrated that using stratospheric AO amplitude data as a predictor in a simple statistical model results in a gain of skill of 5% over a troposphere-only statistical model. This gain in skill is not repeated if an unrelated time series is included as a predictor in the model. Copyright © 2003 Royal Meteorological Society

Exploring teachers' knowledge of children's literature

In the context of the current debate about teaching reading, research to ascertain primary teachers' personal and professional reading practices was undertaken. The study explored teachers' reading habits and preferences, investigated their knowledge of children's literature, and documented their reported use of such texts and involvement with library services. Questionnaire responses were gathered from 1200 teachers. The data were analysed and connections made between the teachers' own reading habits and preferences, their knowledge of children's literature, their accessing practices and pedagogic use of literature in school. This paper reports on part of the dataset and focuses on teachers' knowledge of children's literature; it reveals that primary professionals lean on a narrow repertoire of authors, poets and picture fiction creators. It also discusses teachers' personal reading preferences and considers divergences and connections between these as well as the implications of the teachers' limited repertoires on the reading development of young learners.

Changing Standards? Children's awareness and knowledge of features of written standard English at ages 10-11

This paper reports the findings of a small-scale research project, which investigated the levels of awareness and knowledge of written standard English of 10- and 11-year-old children in two English primary schools over a six-year period, coinciding with the implementation in the schools of the National Literacy Strategy (NLS). A questionnaire was used to provide quantitative and qualitative data relating to: features of writing which were recognised as standard or non-standard; children's understanding of technical terminology; variations between boys' and girls' performance; and the impact of the NLS over time. The findings reveal variations in levels of recognition of different non-standard features, differences between girls' and boys' recognition, possible examples of language change, but no evidence of a positive impact of the NLS. The implications of these findings are discussed both in terms of changes in educational standards and changes to standard English.

Example uses of a learning object

A self study course for learning to program using the C programming language has been developed. A Learning Object approach was used in the design of the course. One of the benefits of the Learning Object approach is that the learning material can be reused for different purposes. 'Me course developed is designed so that learners can choose the pedagogical approach most suited to their personal learning requirements. For all learning approaches a set of common Assessment Learning Objects (ALOs or tests) have been created. The design of formative assessments with ALOs can be carried out by the Instructional Designer grouping ALOs to correspond to a specific assessment intention. The course is non-credit earning, so there is no summative assessment, all assessment is formative. In this paper examples of ALOs and their uses is presented together with their uses as decided by the Instructional Designer and learner. Personalisation of the formative assessment of skills can be decided by the Instructional Designer or the learner using a repository of pre-designed ALOs. The process of combining ALOs can be carried out manually or in a semi-automated way using metadata that describes the ALO and the skill it is designed to assess.