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.     

Exploring who we are in the context of global reforms in education: the Second Level Support Service in conversation

How will the Second Level Support Service (SLSS), established to support curriculum reform and the professional development of teachers, sustain its own professional development and identity in a climate of change and uncertainty? How will the SLSS maintain its vision of continuous professional development in the midst of educational reform? This article reports on a research project undertaken jointly by the SLSS and the Department of Education and Professional Studies, University of Limerick, designed to support the professional development of the SLSS, as it addressed, in a reflexive way, the questions posed above. The article outlines: the context, including the public policy context, in which the research was undertaken; the research design which incorporates narrative enquiry and collegial conversation; and some of the main themes which emerge from the three focus groups, whose conversations provided the research data. Chief among these themes is the degree to which the vision and practice of the SLSS supports or challenges the view of teachers and teaching which underlies the reform of education. The article offers some concluding remarks which relate the project to critical theory and organisational development.     

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.     

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.     

The Influence of Teacher Expectations about Twice-Exceptional Students on the Use of High Quality Gifted Curriculum: A Case Study Approach

Twice-exceptional students show evidence of high academic performance or potential and also have a disability that impedes their ability to learn. Twice-exceptional students remain under-represented in gifted programs, and some researchers attribute such under-representation to the negative beliefs and low expectations about twice-exceptional students held by teachers. While researchers have begun to investigate the curricular models and instructional strategies that are effective for twice-exceptional students, little research addresses how teacher beliefs and expectations about student ability are reflected in the ways teachers implement such models and strategies for twice-exceptional students in gifted classrooms. Even less research addresses gifted students with emotional and behavioral disabilities. We used a case study of a third-grade teacher using a structured, model-based language arts curriculum to better understand how her expectations about a gifted student with an emotional disability influenced her instructional choices. Using observational and interview data, the case study approach allowed the researchers to personalize the experiences of this teacher and provided a context in which to examine the subtleties of teacher expectations when teaching a gifted student with an emotional disability. Implications for educational practice, particularly the need for comprehensive school-based support systems for students with emotional disabilities, are discussed.     

Selection of School Counselor Candidates: Future Directions at Two Universities

A new vision of school counseling asserts that counselors must address all children and must orient counseling services toward the primary mission of schools: to educate young people and to support their healthy development. Two universities that are working to prepare new vision school counselors have changed their recruitment and selection procedures to attract increased numbers of candidates who can be optimally trained to fulfill the requirements of this vision. The authors describe criteria and procedures used to select graduate students who have the greatest promise of becoming leaders, advocates, and change agents in schools to promote student learning and achievement.     

The Organization of Reactivated Memory in Infancy

The specificity of memory retrieval by 3-month-old infants was examined in 3 experiments. All infants were trained in the mobile conjugate reinforcement paradigm to kick their feet to produce movement in an overhead crib mobile and were tested 2 weeks later. 24 hours prior to the test, subjects received a 3-min reminder treatment. The results of Experiment 1 demonstrated that only the moving training mobile alleviated forgetting after the 2-week retention interval; forgetting was not alleviated by exposure to the stationary training mobile or to the mobile stands and ribbon alone. The results of Experiments 2 and 3 demonstrated that, once retrieved, the reactivated memory was highly specific to the conditions of original training. Furthermore, the memory attributes that were the last to be forgotten (e.g., the general or global features) were the first to be retrieved following the reminder treatment. Conversely, those memory attributes that were forgotten first (e.g., the specific or local details) were the last to be retrieved. These findings have important implications for infant memory retrieval, reminiscence, and infantile amnesia.     

Conflict in the family: A continuing education course produced by the open university

This course, first presented by the Open University in 1980, is designed for independent study by people who, in the course of their working lives, come into contact with families suffering serious internal conflicts which place any members—adult or child—in danger of physical or emotional abuse in their own home. The course has been developed at a level which should make it a serious contribution to in-service training for a wide variety of professionals and experienced voluntary workers. It is unique in that it not only examines constructive and destructive aspects of conflict but also integrates written material (16 units) with an audiovisual component (8 TV programmes and 7 cassette tapes) on prevention, diagnosis and intervention relating to the whole spectrum of family conflict and violence including child abuse, sexual abuse, adolescent abuse, spouse abuse, abuse of and by the elderly and abuse of parents by their children. This paper provides a brief outline of the course aims, objectives and content together with information on its usage in the UK and the availability of certain components for international usage.     

The Impact of Disordered Eating Behavior on College Relationships: A Qualitative Study

The authors explored how college students’ disordered eating behaviors affect their peers. Participants were 8 undergraduate students from a northeastern university with a peer who currently or previously engaged in eating disorder (ED) behaviors. Results from a consensual qualitative analysis provided preliminary evidence that students’ EDs negatively affect peers. Outreach and interventions such as cognitive behavior therapy could be used to assist peers of students with EDs. Researchers should investigate the impact of students’ ED behaviors on peers’ health and academic performance.