The use of mathematical symbolism in problem solving: An empirical study carried out in grade one in the French community of Belgium

This article relates to an empirical study based on the use of mathematical symbolism in problem solving. Twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a “top-down” approach (an approach that is still applied within the French Community of Belgium): conventional symbols are presented to the pupils immediately with an explanation of what they represent and how they should be used. Teaching then focuses on calculation techniques (considered as a pre-requisite for solving problems). The results presented here show the abilities (and difficulties) demonstrated by the children in making connections between the conventional symbolism taught in class and the informal approaches they develop when faced with the problems that are put to them. The limits of the “top-down” approach are then discussed as opposed to the more innovative “bottom-up” type approaches, such as those developed by supporters of Realistic Mathematics Educations in particular.     

A change in legal status: an overlooked dimension in the transition to higher education

The transition from high school to college entails a change in legal status for individuals with learning disabilities. As students leave high school and the dominion of P.L. 94-142, they enter a setting structured by Section 504 of the Rehabilitation Act of 1973. How does this change in legal status affect student rights and responsibilities? Do students with learning disabilities need specific skills to facilitate their legal transition into higher education? Is current transition programming addressing To investigate these questions, basic provisions of P.L. 94-142 and Section 504 were reviewed. Implications of the change in legal status were discussed, and existing transition programs were examined. Guidelines are proposed for incorporating legal transition skills in future transition programming.     

The ability to understand and use conceptual change pedagogy as a function of prior content learning experience

This research examined the relationship between content instruction and the development of elementary teacher candidates' understanding of conceptual change pedagogy. Undergraduate students (n = 27) enrolled in two sections of a science methods course received content instruction through either traditional or conceptual change methods, followed by instruction about conceptual change pedagogy. Candidates were interviewed pre- and postinstruction about their content and pedagogical knowledge and also wrote conceptual change lessons. Twelve of the 27 subjects were videotaped teaching in the field. Results indicate that prior to instruction, most candidates had weak content knowledge and held traditional pedagogical conceptions. After instruction, students in the conceptual change group had significantly larger gains in their content knowledge than those in the traditional group, gave qualitatively stronger pedagogical responses, and used conceptual change strategies more consistently in practice. These results indicate that personal experience of learning science content through conceptual change methods facilitated the development of understanding and use of conceptual change pedagogy in teaching practice. Thus if conceptual change methods are to be incorporated into teacher candidates' repertoire, science content courses that students take prior to teacher education should be taught using conceptual change pedagogy. In addition, courses in science education should use pedagogy more in line with that taught in methods courses.     

Oliver Twist: an exploration of interactive storytelling and object use in communication

Keith Park invites practitioners to respond to his detailed plans for integrating communication skills, and the use of real object 'props', with the teaching of literature to pupils with severe and profound and multiple learning difficulties. This article builds on work described in two previous contributions to the pages of the British Journal of Special Education . In the first (Park, 1997), Keith Park reviewed the theory and practice of communicating using 'objects of reference'. In the second article (Park, 1998), he described an approach to teaching Dickens which used interactive storytelling as a context for promoting communication skills. Keith Park combines these themes in this article, which provides both a theoretical commentary and ideas for a series of practical sessions.     

高职数学教学中数学文化的融入探索与实践

文章借鉴了一些本科院校开设数学文化课的经验,结合高职院校的实际情况,提出了在开设高职数学课的同时进行数学文化的融入,以及如何在高职数学教学中寻找数学文化的融入点,结合具体实例探索如何挖掘若干数学题材中的文化意义,并将其融入到高职数学教学中去,把传授数学知识和揭示数学文化相结合,从而提升学生的人文素养和创新精神。     

Continuity and change in intrafamilial agreement in beliefs concerning the adolescent: a follow-up study

In a 2-year follow-up investigation of parent-child agreement in beliefs concerning the child and of the child's awareness of parental beliefs in families with children in transition to early (ages 10-11 to 12-13) and mid-adolescence (ages 15-16 to 17-18), 42 families were reinterviewed with the Family Belief Interview Schedule. Major results indicated that over the follow-up interval: (1) accuracy of the child's prediction of parental beliefs increased sharply between 10-11 and 12-13 but not between 15-16 and 17-18 years; (2) congruence of both mothers' and fathers' beliefs with the child's self-beliefs increased; and (3) between families, overall levels of intrafamilial agreement in belief concerning the child remained remarkably stable. Findings support the notion that changes in adolescents' understanding of their own development and of their changing relationships to parents occur within a framework of overall consistency in level of intrafamilial agreement in belief.     

Ecological footprinting: its potential as a tool for change in preservice teacher education

Environmental and sustainability issues pose challenges for society. Although education is seen as being a contributor to addressing sustainability, teacher education has been slow to act in preparing future teachers to teach sustainability. Recent Australian curriculum documents nominate sustainability as one of three cross-curriculum priorities. In one Australian university course, an Ecological Footprint Calculator tool has been employed to challenge preservice early childhood teachers to consider the sustainability of their lifestyles as a means for engaging them in learning and teaching for sustainability. Students enrolled in an integrated arts and humanities subject voluntarily engaged with the online calculator and shared their findings on an electronic discussion forum. These postings then became the basis of qualitative analysis and discussion. Data categories included reactions and reflections on reasons for the ‘heaviness’ of their footprints, student reactions leading to actions to reduce their footprints, reflections on the implications of the footprint results for future teaching, reactions that considered the need for societal change, and reflections on the integration of sustainability with the visual arts. The power of the tool’s application to stimulate interest in sustainability and education for sustainability more broadly in teacher education is explored.     

The mediation of tools in the development of formal mathematical concepts: The compass and the circle as an example

This study focuses on the process by which children develop a formal mathematical concept of the circle by using various instruments to draw circles within the context of a goal-directed drawing task. Particular attention was given to the transition from using tracers and templates to using a compass for drawing circles and to the extent to which the use of different drawing instruments may contribute to the formation of a formally defined mathematical concept of the circle. The critical difference considered in the study is that the compass, in contrast to circle-drawing tracers or templates, induces by its physical structure and its functional use the generative features of formal mathematical concepts of the circle, that is, the centre and the radius. Analysis of the empirical data indicates that the use of the compass in circle drawing structures the circle-drawing operation in a radically different fashion than circle tracers and templates, and brings into play an action-bound practical thinking. Such thinking has an overall positive influence on the construction of analytical concepts by children that are analogous to the formally defined mathematical concepts of the circle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Making a difference: an exploration of leadership roles within sixth form colleges in maintaining ethos within a context of change

In 2001–02, the Nuffield Foundation funded research into the impact of government policy upon the management of sixth form colleges since 1992. National and regional questionnaire surveys were carried out among senior managers at sixth form colleges, further education colleges and schools. Case studies were undertaken at five sixth form colleges in the North‐West and South‐East of England, and in the East Midlands. This article reports on the findings in relation to the following factors: the prevailing ethos of sixth form colleges, the changing context within which that ethos is maintained, and the role of leaders at all levels of the colleges in maintaining it.     

Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study

This article reports results of a four-year longitudinal study that investigated the impact of specific and non-specific precursors on mathematical school achievement. Preschool quantity-number competencies (QNC) predicted mathematical achievement in primary school. Furthermore, basic arithmetic fact retrieval in Grade 1 had an impact on early mathematics school achievement. The influence of socioeconomic status and number naming speed, assessed in kindergarten, became especially important at the end of Grade 4. Particularly, a subgroup of mathematically low-achieving children in Grade 4 had already performed more poorly than normal children in tasks assessing preschool QNC, number naming speed, and basic arithmetic fact retrieval, as well as nonverbal intelligence and socioeconomic status.     

Locomotor activity and exploration: The use of traditional manipulators to dissociate these two behaviors in the rat

An apparatus designed by Berlyne was used to dissociate locomotor activity and inspective exploratory responses with the aid of traditional manipulators. In this apparatus, novel and complex stimulation increased exploration but did not affect locomotor activity (LA), d-amphetamine (1.5 mg/kg) increased LA but decreased exploration. These findings provide a double dissociation of the behavioral components. In addition, low intrasubject correlations for the two behaviors were demonstrated. Results are discussed with reference to the need for simultaneous separate measures to obtain valid indices of exploratory behavior and LA.     

Teenagers in cyberspace: an investigation of language use and language change in internet chatrooms

This article reports on a small‐scale investigation into the use of Internet chatrooms by teenage girls. Based on interview and observational data, it illustrates how the use of popular electronic communication is resulting in linguistic innovation within new, virtual social networks in a way that reflects more wide‐reaching changes in the communication landscape. The paper suggests that teenagers and young people are in the vanguard of these processes of change as they fluently exploit the possibilities of digital technology, radically changing the face of literacy. The study looks at teenagers’ perceptions of chatroom encounters and their learning about new ways of social and linguistic interaction. Observations of teenagers online show how rapid written conversations which combine features of face‐to‐face talk with explorations in interactive writing and the exchange of additional digital information, such as image files and web addresses, are enabling these young people to develop sophisticated and marketable skills. These innovations are contrasted with recent media and educational criticism of the language use associated with new technology. This tension between change and conservatism is explored by applying Bourdieu’s concept of ‘linguistic capital’.