Mathematical Flexibility: Aspects of a Continuum and the Role of Prior Knowledge

Abstract

Psychologists and mathematics educators have long viewed flexibility as critical to students’ mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified research-based aspects of flexibility with algebra and assessed students on them following a two-step equations unit. Results indicated that certain aspects of flexibility develop prior to others and that prior knowledge of algebra plays a significant role in that development. Study 2 confirmed and elaborated on these results using a larger sample size. Implications for theory and for supporting flexibility in classrooms are discussed.     

Social cohesion and integration: learning active citizenship

This article starts from a conceptual clarification of the notions social integration and social cohesion as a prerequisite for the reorientation of citizenship education. Turning away from uncritically reproduced assumptions represented in mainstream ‘deficiency discourse’, the article first focuses on sociological conditions for the rise of active citizenship and its role in the revitalization of the public sphere. Next a number of educational objectives are deduced from competencies needed and learning processes taking place in practices of active citizenship. Finally, the article argues for the adoption of a lifelong learning perspective, relating formal citizenship education to informal and non‐formal experiences of active citizenship.     

Education and assessment in Sweden

Education and assessment in Swedish schools have been affected by several reforms during the last two decades. The educational system has moved from centralization to decentralization and a goal‐oriented approach has been introduced on all educational levels. This paper provides an historical overview of the Swedish educational system, educational and assessment policies and principles, to explain why and how the reforms have been carried out. This is followed by a discussion on the effects and consequences of recent reforms, based on findings in recent education and assessment research.     

Continuity in Parent-Child Relationships from Infancy to Middle Childhood and Relations with Friendship Competence

This cross-cultural study examined continuity in parent-child relationships from infancy to middle childhood in a sample of German families. Connections were traced between individual differences in a composite of markers of the parent-child attachment relationship system (including classification of the infant via the Strange Situation and parent via the Adult Attachment Interview and for mothers' ratings of sensitivity) and later parent-child communications. Fundings within the mother-child relationship revealed modest links between the composite and communications and were taken to suggest that the divergent fields of attachment and family communication research are addressing similar underlying relationship processes involving the interplay between relatedness and autonomy. Further findings revealed that the composite modestly predicted variability in children's competence in forming friendships and that differences in concurrent child-mother communications significantly added to and possibly mediated these effects. Results were interpreted as supporting a process model of development, whereby adaptation is influenced by both current and past relationship status.     

Exploration De La Résilience éducationnelle Chez Des Enseignants

AN EXPLORATION OF THE EDUCATIONAL RESILIENCE OF TEACHING STAFF – This study focuses on the degree of resilience displayed by teaching staff with the aim of promoting their professional development and preventing job-related exhaustion. Seven underprivileged schools in Montreal were selected, and 24 teaching staff with contrasting personal profiles were interviewed on the subject of their work. The Alceste software was used to analyse the conversations, which revolved around techniques applied when dealing with critical incidents. The main analysis identified five different discourses among the respondents. Three of these were associated with the more resilient of the teachers and two were associated with the more vulnerable ones. Resilient teaching staff characteristically discussed dealing with aggressive behaviour, the teaching-learning relationship and the subject of social relationships, whereas vulnerable teaching staff focused on work beyond the classroom, people in positions of higher authority and the community. The authors note that teachers who are just embarking on their careers appear more vulnerable than more experienced teaching staff, which suggests that more resources should be provided to support teachers in their profession.     

WOMBAT A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood （REML）

WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http://agbu. une.edu.au/~kmeyer/wombat.html     

Together I Can! Joint Attention Boosts 3- to 4-Year-Olds’ Performance in a Verbal False-Belief Test

Effects of joint attention were addressed on 3- to 4-year-olds’ performance in a verbal false-Belief Test (FBT), featuring the experimenter as co-watcher rather than narrator. In two experiments, children (N = 183) watched a filmed-FBT jointly with a test leader, disjointed from a test leader, or alone. Children attending jointly with a test leader were more likely to pass the FBT compared with normative data and to spontaneously recall information indicating false-belief understanding, suggesting that joint attention strengthens the plausibility of the FBT and renders plot-critical information more salient. In a third experiment (N = 59), results were replicated using a typical, image-based FBT. Overall findings highlight the profound impact of experimenter as social context in verbal FBTs, and link recall of specific story features to false-belief understanding.     

Literacy,languages and development in Africa: a policy perspective

International Review of Education - In the multilingual environments of Africa, national literacy policies vary in terms of the attention they give to the roles and purposes of local, national and...