Mathematical induction: A pedagogical discussion

It is observed that many students have difficulty in producing correct proofs by the method of mathematical induction. The notion of a correct proof by this method is analysed mathematically. Subsequently, the topic is analysed into behavioural skills and subjected to a conceptual analysis. Common misconception of induction are considered, with recommendations for their remediation. Finally, criteria for the analysis and evaluation of textbook treatments of induction are evolved and applied to a selection of texts.     

The pedagogical logics of arts-rich schools: a Bourdieusian analysis

The arts are under threat in English schools. But some schools and teachers work against the trend. To understand how they continue to offer rich arts experiences to students, we bring Bourdieusian thinking to arts teacher practices that were common across the 30 secondary schools we studied for three years. In addition to a flexible approach to the curriculum which encouraged independence, intellectual challenge and risk-taking, teachers also engaged in arts brokerage – embodiment of arts engagement, ensuring students regularly visit cultural events/institutions, using local cultural resources, organising visits from artists/cultural organisations, enabling students to exhibit and perform for wider audiences, connecting students with arts workplaces and enhancing community arts participation. We approach this as a logic of practice associated with arts broker dis/positions drawn from teachers simultaneously occupying two chiasmatic fields – art and education.     

High Possibility Classrooms as a pedagogical framework for technology integration in classrooms: an inquiry in two Australian secondary schools*

Understanding how well teachers integrate digital technology in learning is the subject of considerable debate in education. High Possibility Classrooms (HPC) is a pedagogical framework drawn from research on exemplary teachers’ knowledge of technology integration in Australian school classrooms. The framework is being used to support teachers who teach various stages of schooling to take ‘pedagogical steps’ in their practice with technology. This article focuses on the use of the HPC conceptual framework in a study of seven teachers and their students at two secondary schools in New South Wales, Australia. Analysis confirms the practicality of this conceptual framework for technology integration in secondary school classrooms. This inquiry has implications for addressing the reluctance of teachers to integrate technology in curriculum. The article concludes by suggesting that more schools might consider using conceptual frameworks like HPC to support secondary school teachers to enhance student learning with technology.     

Towards a pragmatic science in schools

This paper contrasts naive beliefs about the nature of science, with science as it appears from sociological and philosophical study, feminist critique and insights from multicultural education. I draw implications from these informed views to suggest how school science might be modified to project a pragmatic view of science to its students that allows students to know science and its relationships to themselves and society in multi-faceted ways. From these perspectives, pragmatic school science is situated within a values framework that questions how we know. Pragmatic school science also requires that the naive inductivist views that permeate school science inquiry methods at present be modified to recognise that observations and inquiry are guided by prior knowledge and values; that new knowledge is tentative; that some knowledge has high status, as it has been constructed consensually over a long period; but that even high status knowledge can be challenged. For implementation of these reforms, yet still to embrace the need for some students to appropriate understanding of discipline knowledge required for advanced science education, a broad set of aims is required.     

Performance indicators: Towards a synoptic framework

This paper sets out to sketch a synoptic framework within which performance indicators may be used within higher education.The evidence to date suggests that the use of performance indicators has not adequately taken into account a number of factors - the level within the higher education system at which they are being used, their practicability, and the inter-relationship between both quantitative and qualitative data. The effective use of performance indicators is discussed in terms of exercises in which judgments have to be made upon complex sets of data rather than upon a narrow range of parameters, with significant implications for what is managerially feasible.     

The Many Identities of Pedagogics as a Challenge: Towards an ontology of pedagogical research as pedagogical practice

The history of pedagogics gives the impression that pedagogics has never had an identity of its own. Throughout history it has borrowed its identity from philosophy, theology, psychology and sociology. Against the background of this historical challenge, the article proposes pedagogical practice as an alternative identity to pedagogics, although not in the classical sense of an absolute and self‐sufficient identity, and it develops one particular ontological theory of pedagogical practice viewed from a life‐world approach with the ambition of suggesting a theoretical point of departure for pedagogical research.     

Inquiry-based science education: towards a pedagogical framework for primary school teachers

Inquiry-based science education (IBSE) has been promoted as an inspiring way of learning science by engaging pupils in designing and conducting their own scientific investigations. For primary school teachers, the open nature of IBSE poses challenges as they often lack experience in supporting their pupils during the different phases of an open IBSE project, such as formulating a research question and designing and conducting an investigation. The current study aims to meet these challenges by presenting a pedagogical framework in which four domains of scientific knowledge are addressed in seven phases of inquiry. The framework is based on video analyses of pedagogical interventions by primary school teachers participating in open IBSE projects. Our results show that teachers can guide their pupils successfully through the process of open inquiry by explicitly addressing the conceptual, epistemic, social and/or procedural domain of scientific knowledge in the subsequent phases of inquiry. The paper concludes by suggesting further research to validate our framework and to develop a pedagogy for primary school teachers to guide their pupils through the different phases of open inquiry.     

Developing pedagogical practices in Myanmar primary schools: possibilities and constraints

This paper presents the findings of a baseline study of pedagogic practices used by Myanmar primary teachers in the teaching of mathematics and Myanmar language at Grades 3 and 5. The main purpose of the baseline study was to inform the design of teacher education programmes and allow for subsequent evaluations of interventions designed to improve the quality of primary education. It found that the majority of observed lessons (n = 728) used a transmission model of teaching in which the teacher often used a chalkboard and/or textbook to transmit recipe knowledge for recall and there was little variation across the teaching of mathematics and Myanmar language at Grades 3 and 5. Drawing on evidence from the baseline, the paper explores the training needs of primary teachers in Myanmar in the light of proposed reforms to teacher education at the pre- and in-service stages.     

Supporting higher levels of reflection among teacher candidates: a pedagogical framework

An integrated mathematics and science methods course was designed to focus on the knowledge, skills, and beliefs of teacher candidates. Teacher candidates were involved in experiences that would prompt them to consider the influence of their experiences on their beliefs, the influence of their beliefs on their instructional decisions and the impact of those decisions on their effectiveness as teachers. Three teacher candidates who exhibited high levels of reflection and who made significant changes in the ways that they thought about mathematics and the teaching/learning process were chosen for study. Two themes related to this cognitive change emerged: a more complex, sophisticated understanding of the nature of mathematics; and an increased focus on children's thinking to guide instruction. Three program components having a major impact on these students' reconceptualization were reflection on past experiences, engagement in mathematical problem‐solving and opportunities to act on new beliefs.     

Classroom management in urban schools: proposing a course framework

ABSTRACT

Students of color in urban areas experience a multitude of intersecting oppressive structures that influence their behavior in schools. As a result, teachers in these schools often face distinct student behavior challenges to which they are often ill-equipped to respond. Colorblind approaches to student misbehavior, those that do not acknowledge students’ environments and cultures, are often punitive in nature and result in consequences that are not in students’ best interests. We propose, then, that preservice teachers who aim to teach in urban schools are required to consider contextual and cultural influences on student behavior as part of their teacher preparation coursework. Drawing upon existing scholarship, we propose a course framework that focuses exclusively on techniques that cultivate strong student-teacher relationships and academically supportive student behaviors. The framework consists of five thematic units: 1) trauma-informed and trauma-sensitive classrooms, 2) facing cultural conflicts, 3) culturally informed care, 4) culturally relevant/responsive classroom management, and 5) restorative discipline philosophy and practices.     

Effective integration of ICT in Singapore schools: pedagogical and policy implications

This paper examines and analyses where and how information and communication technologies (ICT) are integrated in Singapore schools to engage students in higher-order thinking activities. Taking the activity system as a unit of analysis, the study documents the actual processes and sociocultural elements that engage students in higher-order thinking. By employing methods such as observations, focus group discussions with students, and face-to-face interviews with teachers, ICT-coordinators and principals, an account of how the activity systems within and between classrooms, and the schools are generated. Based on the analysis of the data from 10 schools, issues in the learning environment are discussed: Necessary (classroom management and orienting activities) and sufficient conditions (scaffolding activities and supporting school policies) for effective ICT integration in the classroom. The account also highlights the constraints of time and lack of knowledge and experience in the contexts that the teachers are working under, and how these constraints are addressed by supporting school policies in the larger sociocultural setting of the school. This account provides a sample of pedagogical and sociocultural issues that are discussed over the course and at the end of the project. Like a good guidebook, the study sensitizes the audience to what is likely to happen given a particular objective, constraint, or design.     

Systems-psychodynamics in schools: a framework for EPs undertaking organisational consultancy

This article considers how a framework for understanding group and organisational behaviour, systems-psychodynamics, can be utilised by educational psychologists taking up an organisational consultancy role to work with schools as whole systems. It outlines the three main theories that constitute a systems-psychodynamic perspective and considers how the approach has been used by educational psychologists. Two case studies are presented that explore how psychoanalytic concepts such as splitting, projection, use of counter-transference, social defences and others can be applied. Key themes from the case studies are analysed and salient details discussed. The article then discusses implications for practice and further areas of study.     

Pre-service teachers' pedagogical learning during practicum placements in special schools

This paper discusses the pedagogical learning of some South African pre-service teachers during a practicum in ‘special’ schools. Besides promoting their understanding of diversity, these pre-service teachers noticed aspects of pedagogy that had been less visible to them during previous practicum sessions in ‘mainstream’ schools. An analysis of focus group interviews, Facebook posts, and journal entries suggests that their attention was drawn to the value of multiple representations of core concepts, lesson pacing and behavior management in responding to learning differences. Observing and teaching in special schools enabled some tacit aspects of their developing practice to become more explicit.     

Decision-making models in a Tunisian university: Towards a framework for analysis

Abstract

This study investigates how decisions are made in Tunisian public higher education establishments. Some factors are identified as having a potentially significant impact on the odds that the decision-making process follows the characteristics of one of the most well known decision-making models: collegial, political, bureaucratic or anarchical model. For this, this investigation was based on some statistical methods related to qualitative variables and allowing to measure whether the hypotheses, identified through an inductive analysis, are expressible in the same terms and with the same acuteness in all Tunisian public higher education establishments. In particular, the results showed that how decisions are made is related to the nature of the decision itself: collegiality for pedagogic and scientific decisions, bureaucratic for decisions related to institutional management and politic for academic personnel decisions. This finding can help the university leadership to evaluate and improve the governance in the higher education establishment.     

Towards a pedagogical model for science education: bridging educational contexts through a blended learning approach

This paper proposes a design framework to support science education through blended learning, based on a participatory and interactive approach supported by ICT-based tools, called Science Learning Activities Model (SLAM). The development of this design framework started as a response to complex changes in society and education (e.g. high turnover rate of knowledge, changing labour market), which require a more creative response of learners to the world problems that surround them. Many of these challenges are related to science and it would be expected that students are attracted to science, however the contrary is the case. One of the origins of this disinterest can be found in the way science is taught. Therefore, after reviewing the relevant literature we propose the SLAM framework as a tool to aid the design of science courses with high motivational impact on students. The framework is concerned with the assumption that science learning activities should be applicable and relevant to contemporary life and transferable to ‘real-world’ situations. The design framework proposes three design dimensions: context, technology and pedagogy, and aims at integrating learning in formal and informal contexts through blended learning scenarios by using today’s flexible, interactive and immersive technologies (e.g. mobile, augmented reality, virtual reality).