Equivalent Structures on Sets: Equivalence Classes, Partitions and Fiber Structures of Functions

This study reports on how students can be led to make meaningful connections between such structures on a set as a partition, the set of equivalence classes determined by an equivalence relation and the fiber structure of a function on that set (i.e., the set of preimages of all sets {b} for b in the range of the function). In this paper, I first present an initial genetic decomposition, in the sense of APOS theory, for the concepts of equivalence relation and function in the context of the structures that they determine on a set. This genetic decomposition is primarily based on my own mathematical knowledge as well as on my observations of students’ learning processes. Based on this analysis, I then suggest instructional procedures that motivate the mental activities described in the genetic decomposition. I finally present empirical data from informal interviews with students at different stages of learning. My goal was to guide students to become aware of the close conceptual correspondence and connections among the aforementioned structures. One theorem that captures such connections is the following: a relation R on a set A is an equivalence relation if and only if there exists a function f defined on A such that elements related via R (and only those) have the same image under f.     

The contribution of non-formal learning in higher education to student teachers’ professional competence

This article reports a mixed methods study on the contribution of various aspects of pre-service student teachers’ learning in initial teacher education (ITE) to their professional competence in a Five-year Bachelor of Education Programme in Hong Kong. Special attention is given to how student teachers’ non-formal learning in higher education contributes to their professional competence, an under-researched area in teacher education. A total of 282 student teachers participated in the quantitative survey, 18 of whom were interviewed. Although  Undergraduate Learning Experience: Formal Learning and Non-formal Learning was not the most highly rated factor, multiple regression indicated that it was the only ITE professional learning factor that significantly predicted all dimensions of professional competence. This supports the hypothesis that non-formal learning as a part of learning in higher education makes a significant contribution to student teachers’ professional competence. The qualitative findings showed that non-formal learning provided opportunities for service learning, co-curricular activities, and student exchange programmes with different objects of engagement. Student teachers constructed pedagogical content knowledge, general pedagogical knowledge, and knowledge of context through hands-on experiences, professional dialogue with practitioners, and observations of others’ practice. Such knowledge contributed to their competence in classroom teaching and to work in schools. Implications for ITE are discussed.     

Faculty-student engagement in teaching observation and assessment: a Hong Kong initiative

There is now a worldwide focus on the quality of university teaching and yet there is general dissatisfaction in universities with the student evaluation of teaching system. Peer observation of teaching seems to hold much promise in the assessment of teaching quality, but such observation pays little attention to the quality of teaching as perceived by students. One approach to overcome this deficiency is for faculty and students to also partner in the assessment of a faculty member’s teaching, with a student trained in observation and feedback techniques acting as a peer in the observation process. This paper describes and evaluates an ongoing student consultant initiative at Lingnan University in Hong Kong. It presents faculty and student observations in terms of the benefits to faculty regarding potential enhancement of university teaching, and the benefits to students especially in terms of close collaboration with faculty and training in consultation techniques. The paper notes that the student consultant initiative has been more popular with students than faculty, and recommends further investigation of the potential of such programmes in Hong Kong higher education.     

The start-up phase in a research and development work project: A foundation for development

The article is based on a research and development work project (R&D project) conducted in a Norwegian lower secondary school. The purpose of the text is to describe the researchers’ and teachers’ roles during the initial phase of such a project, and what this phase and the close cooperation between the researcher and teachers mean for the progress of the project. The reader will see how the participating teachers modify their attitudes to the project throughout the start-up phase. This phase is outlined by means of empirical data. The study shows how such a project challenges the researchers’ communicative, social and knowledge competence. Furthermore, teachers have to see the need for development and willingly participate in developmental processes, listening to and using researchers as resource persons, if a start-up phase is to be successful for subsequent development in the project.     

Addressing underutilization of consumer health information resource centers: a formative study

Problem: Four consumer health information centers in Richmond, Virginia, provide one-on-one assistance in accessing health information. Because they may not be fully utilized at present, an exploratory marketing study of factors affecting usage of the centers was conducted.Method: Observers counted center passers-by and tracked their paths. Also, brief intercept interviews were conducted with people who had just used a center, people nearby who could have used one but did not, and people on the street. Finally, in-depth individual interviews were conducted with key informants.Results: There was a high degree of satisfaction with the centers among users. Nonusers universally endorsed the center concept. However, most passers-by did not even glance at the centers, and intercept interviewees suggested better signage and promoting the resource centers through various media channels. Key informants added suggestions about interpersonal strategies (e.g., physician referrals) for center usage promotion but cautioned that a large increase in traffic could not be accommodated without increasing staff size or shifting from a model of individualized service.Conclusions: Triangulating findings from multiple data collection methods can provide useful guidance for efforts to promote center utilization. At minimum, steps should be taken to make the largest centers more noticeable. Because center utilization is not only associated with consumer satisfaction with hospitals, but may also foster health literacy, both hospital-based and community-based usage promotion strategies may be warranted. All such promotional strategies should be audience-tested before they are adopted.

Highlights

• Both users and nonusers of consumer health information centers said they would think more highly of a hospital with a center and would refer friends or family members to such a center.
• Study participants classified as nonusers of the centers were unaware of the centers or found them hard to locate.
• Suggestions for increasing center traffic ranged from improving signage to promoting routine referrals from hospital staff.
• An alternative to increasing center traffic is delivering information to places where consumers are located.

Implications

• Those responsible for making funding decisions about health information centers should be made aware that hospitals with health information centers are perceived more positively.
• The potential trade-off between intensive, personalized customer service and serving large numbers of consumers must be considered carefully.

     

Whose participation is it anyway? Examining the context of pupil participation in the UK

Helen May recently completed her doctoral studies at the University of Leeds. Her EdD thesis, written with the benefit of extensive experience of practice, focused on the engagement of children with learning difficulties in interactions in primary classrooms. In this article, Helen May draws on her familiarity with the literature to explore the topic of pupil participation. This issue has attracted considerable attention in recent years, especially since it is on the Government's agenda for education in the UK. Here, Helen May examines the political, research and pedagogical contexts in which pupil participation is currently being addressed. She notes that the adult role in bringing about pupil participation is currently emphasised in each of these contexts and expresses concern that pupil participation is therefore being portrayed as requiring professional intervention. By calling for greater exploration of pupil participation from the perspectives of pupils themselves, Helen May makes a persuasive case for seeking a more balanced recognition of the active roles that pupils and professionals can play in this area.     

The tyranny of setting (ability grouping): Challenges to inclusion in Scottish primary schools

Debate around the use of ability grouping in schools, resonates across national boundaries as concerns rise around the possible negative impact on young people, particularly those in already disadvantaged groups. In this paper, a survey focussing on primary schools in Scotland established the extent to which some form of ability grouping has emerged within classes dealing with children from 5 to 12 years of age, the rationale behind the decisions made and the issues and challenges faced by schools.     

Beyond the Given: Stretching Mathematical Thinking Through Journaling

This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one that they themselves can justify. This experiment was conducted in the Discrete Mathematical Structures course; as it contains several subtopics, each of which uses a discrete set of elements with specific conditions. The textbook does not mention how those conditions are effectively put to use, and often uses the natural numbers as the default domain. Students are required to identify in their journals the exact properties that the elements need to have, justify how they are being put to use, and in ambitious cases attempt to sharpen them if possible. This activity can be adapted to different contexts and is not specific to the topic of Discrete Mathematical Structures.     

Rethinking Equity: Preservice Teachers' Perceptions and Practice Around Policy

Despite the body of literature around practicing teachers and policy (Knapp, Ferguson, Bamberg, &; Hill, 1998; Kumar &; Scuderi, 2000; Lortie, 1975/2002), little is known about the involvement of their preservice counterparts. Preservice teachers have limited exposure to policy-related coursework in their professional training (Floden &; Meniketti, 2005) and scholarship is relatively silent regarding preservice teachers' experiences with educational policies and their sense-making process (Spillane, 2004; Weick, 1995; see Heineke, Ryan, &; Tocci, 2015, for a notable exception).

This paper examines preservice teachers negotiating and making sense of a particular policy, the Massachusetts' Rethinking Equity and Teaching for English Language Learners (RETELL). It addresses the following questions: First, what do preservice teachers know about policy in general and the RETELL language policy in particular? Second, how do preservice teachers make sense of the implementation of the RETELL policy in the various settings of their professional training? Third, in what ways do preservice teachers' experiences with the policy influence their orientations toward teaching emergent bilingual students? This analysis demonstrates that preservice teachers have limited general knowledge of educational policy process, and limited specific knowledge around the RETELL language policy. Yet, they learn important lessons about how to “do” policy from their field supervisors and play an important role in policy implementation. The impact of the RETELL policy on preservice teachers' beliefs about teaching emergent bilingual students is mediated by the lack of policy information they receive and by their experiences in the field. This paper adds to the limited literature around preservice teachers involvement in policy and offers recommendations for highlighting the importance of policy education in teacher training.