Articulating syntactic and numeric perspectives on equivalence: the case of rational expressions

Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. The theoretical framework we adopt is the Anthropological Theory of Didactics (Chevallard 19:221–266, 1999), in combination with semiotic aspects from the instrumental approach to tool use. The analysis we present is based on interviews carried out with a 10th grade student who participated in our research. Our findings highlight the mathematical knowledge (technological discourse) constructed in the process of confronting, differentiating, and articulating the several mathematical techniques and theoretical ideas (pertaining to the numeric perspective and the syntactic perspective on algebraic equivalence) related to the designed equivalence tasks.     

EDUCATION ABOUT AGING: A RATIONALE

Based on a review of studies on children's and adolescents’ attitudes and conceptions about aging and older people and on studies analyzing media content such as children's literature, textbooks, and public television programs to determine how older persons are portrayed, a rationale is provided for systematic education about aging in the public schools of the United States.     

Measuring gifted adolescents' implicit theories of creativity

This paper examines the structure of implicit theories of creativity in a sample of gifted adolescents and describes the development and use of the Creative Self Checklist and the Creative Individual Checklist, adjective checklists designed to assess endorsement of creativity‐related personality and behavioral attributes. Findings indicate that the gifted rate aspects of risk‐taking and inquisitiveness as primary facets of their own creativity while defining artistic abilities and energy and motivation as important parts of creativity in others. This study also assessed the role that these implicit theories play in the display of creative behaviors with regard to both performance on creativity tests and participation in creative hobbies. Findings indicate that while performance on creativity measures is predictive of creative hobby participation, greater self‐endorsement of beliefs that are positively related to creativity also significantly predict creative behaviors.     

Cognitive style of gifted and average readers

Thirty gifted and 30 average readers were selected from a population of 300 eighth, tenth, and twelfth grade students in small towns or rural areas in Kansas. Students were classified as field independent or field dependent. It was found that gifted and average readers used the same reading strategies but there were significant differences in how frequently some strategies were used. There were also significant differences in how frequently some strategies were used by field independent and field dependent readers. Gifted readers scored significantly higher than average readers on the Hidden Figures Test. No significant differences in the frequency of reading strategy use were found between field independent gifted readers and field dependent gifted readers or between field independent and field dependent average readers.     

Examining primary schools' physical education coordinators' pedagogical content knowledge of games: are we just playing as this?

A detailed insight into how the current educational climate influences the pedagogical decisions made by primary school teachers when teaching games is limited. Studies examining the pedagogical content knowledge (PCK) of teachers within physical education have revealed its close relationship with specific forms of subject knowledge. In recognition of this, Veal and MaKinster's framework of general, domain and topic-specific PCK was employed to examine 12 primary school teachers' PCK of games. It was concluded that when personal experiences of pedagogy and content knowledge are unchallenged and reinforced by teachers' training and continuing professional development (CPD) programmes, very narrow topic-specific PCK results. This PCK was characterised bythe inseparable paring of constricted pedagogical strategies and limited content knowledge. When teachers do not integrate this very narrow topic-specific PCK with other types of PCK, it has significant repercussions upon the planned curriculum and learning experiences offered to pupils.     

Principles of Play: a proposed framework towards a holistic overview of games in primary physical education

The playing of games has been a long standing tradition in physical education. Yet despite its history, the teaching of games within primary physical education lessons remains something of a weakness. This is most evident through a continued focus upon skill acquisition and a lack of fostering of a real ‘tactical understanding’ of game play. Despite attempts to rectify this issue through the development of instructional models, a lack of conceptual clarity remains. This paper proposes a framework that goes some way to rectify this ambiguity by proposing to focus upon what are referred to as ‘Principles of Play’. It is recommended that this approach should become the focus when conceptualising what constitutes primary games lessons.     

Reducing Student Bias Against Older Adults Through the Use of Literature

Human services educators must address the issue of students’ bias toward older adults to encourage interest and meet the growing need for professionals in the field. The use of literature can challenge students’ preconceptions of older adults while innovative teaching methods can guide their development of more tolerant views and introduce them to a field that they may have previously given little consideration. Based on a model of cultural competence development, teaching strategies, learning objectives, literature, and an evaluation are suggested.     

Avoiding the Perils of “Teacher-Proof” Online Design: A Content Analysis

This content analysis explored how previously validated Web-based inquiries (WBIs) for science instruction are designed and to what extent they match the proposed teacher-support guidelines of the American Association for the Advancement of Science. Examined WBIs implemented few recommended teacher-support mechanisms. This article explores the reasons why so few mechanisms were supported and proposes ways to enhance the curricular usefulness of WBIs by incorporating more recommended mechanisms.