Learning to ‘deal’: A microgenetic case study of a struggling student’s representational strategies for partitive division

International audienceThis paper focuses on the arithmetical understandings and behaviours of one fifteen-year old student with very low attainment in mathematics, as she worked on a sequence of scenario-based partitive division (sharing) tasks with individually-tailored verbal and visuospatial support. The student’s independent and co-created visuospatial representations of arithmetical structures, along with her verbal comments, were analysed qualitatively using a multimodal microgenetic approach. This paper focuses on three particular excerpts which illustrate the fundamentally componential nature of the concept and practice of division, some difficulties that may be experienced when modelling ‘sharing’ tasks, and the pedagogical importance of spatial structuring when a learner is moving between different kinds of representation

Service-learning and reflection in dental hygiene education

Service-Learning (SL) is widely used in education today. Little is known about the use of SL pedagogy on dental hygiene students. SL in dental hygiene is an ideal teaching medium and use frequently; however, few studies have specifically studied if it is being done effectively. This study aimed to increase the knowledge available about SL in dental hygiene educational facilities and to discover if SL was being used appropriately in dental hygiene education. In order to accomplish this, the researcher first identified current definitions that educators have for SL classes and projects. Then, the SL programs/projects were evaluated for best practices. The goal was to create an environment in which positive growth and change can occur in dental hygiene education. The research was conducted by sending out a survey questionnaire to all dental hygiene program directors in the United States. The questionnaires were then sent to appropriate full-time faculty with experience in service-learning. This study generated a total of 94 responses. Email and SurveyMonkey® were the primary modes of communication and administration of the questionnaire. Results indicate that dental hygiene programs are performing better than average in conducting service-learning courses and reflection in dental hygiene education --Document

ERME column

In this contribution we introduce three classical theoretical stances within the field of mathematics education regarding representations. Our aim is to highlight what we consider to be an interesting shift in how representations are conceived and studied in the field of mathematics education, and how this could impact both the practice of teaching and learning mathematics, and on further theorizing mathematical representation. We also indicate potential directions in which to develop ways to talk about newer forms of dynamic interactive representation

Drawing division : emerging and developing multiplicative structure in low-attaining students representational strategies

This thesis examines the particular difficulties with multiplicative thinking experienced by students with very low attainment in school mathematics, and the representational strategies they use for multiplication and division-based tasks.\ud Selected students in two mainstream secondary schools, all performing significantly below age-related expectations in mathematics, placed in ‘bottom sets’, and described by their teachers as having particularly weak numeracy, received a series of tuition sessions (individual or paired). These involved ongoing qualitative diagnosis of their arithmetical strengths and weaknesses, and personalised, flexible learning support, delivered by the author. Students engaged mainly in division-based scenario tasks designed to encourage their engagement in multiplicative thinking, and explored various visuospatial representational strategies tailored to their specific areas of conceptual and procedural difficulty.\ud Multimodal audiovisual data collected from tuition sessions was analysed qualitatively across multiple analytic dimensions using a microgenetic approach. This led to the development of an adaptable framework for the analysis of nonstandard visuospatial representations of arithmetical structures and relationships. Analysis of changes in individual students’ strategies provided insight into some possible learning trajectories for multiplicative thinking. Parallel comparison of students’ varied representational strategies resulted in evidence for the psychological power of certain fundamental representation types, such as unit arrays and containers.\ud The main findings of this thesis concern: the fundamentally componential nature of the concept and practice of division, the potential difficulties this causes in understanding, and the importance of modelling and manipulating unitary multiplicative structures; and the relationship between representational strategies, economy and efficiency in carrying out multiplication and division-based tasks.\ud Conclusions are drawn on the relationship between the development of representational strategies and multiplicative thinking. Recommendations are given regarding learning and teaching practice for students with severe and milder difficulties in mathematics, and particularly the nature of 1:1 support provision for those considered to have Special Educational Needs

Context Matters: An Analysis of assessments of XML Documents

The paper analyses searchers’ assessments of usefulness and specificity on different levels of granularity in XML-coded documents. Documents are assessed on 10 usefulness/specificity combinations and on the granularity levels of article, section, and subsection. Overlapping judgements show a remarkable lack of consistency between searchers. There is an inverse relationship between articles and sections both in the assessment of specificity and of usefulness, indicating that retrieval on different granularity levels are a useful feature of a retrieval system. Searchers find the full article more useful when they assess the same document both on the article and section level indicating that there is a need to provide context to the sections and subsections when presenting result list of XML-documents