Proof and application

This paper outlines an epistemological conception which attempts to relate the formal aspects of mathematical proof to its pragmatic dimensions. In addition to the key concept of application, the paper makes use of several concepts from the domain of analytical philosophy, to present a view of proof that might best be categorized as a dialectical one. A number of implications for teaching are discussed.     

Integrating Mathematical Learning During Caregiving Routines: A Study of Toddlers in Swedish Preschools

In recent years the interest in preschool mathematics has increased. However, studies seldom focus on children under the age of three and research is scarce on the early use of mathematics observed in natural settings. This article reports a study of mathematical possibilities during diaper changing in a preschool setting. A diaper change can be a communicative moment when the child can experience mathematics with a professional preschool teacher, but it can also be a moment of mechanical routine with no pedagogical context. The intention of the study presented here was to investigate the mathematical potential preschool teachers described in relation to diaper changing and to examine the ways this potential was put into action. Both similarities and differences emerged regarding the mathematical potential preschool teachers described in relation to diaper changing and the mathematical content that they were observed to communicate. The results show that it is possible to communicate mathematical content in a pedagogical way during diaper changes, making this routine a learning opportunity for children. However, the results also show variations in the observed range and context of such communication, and therefore the potential for mathematical learning during diaper changes seems to differ widely.     

几种不同的活化能及其应用

本文叙述了几种不同的活化能及它们之间的关系,明确了活化能的物理意义,并由此讨论了活化能的重要应用。     

“Everyone Has to Find Themselves in the Story”: Exploring Minority Group Representation in the Citizenship Curriculum in Northern Ireland and Israel

ABSTRACT

This article explores understandings of minority group representation in citizenship education in Northern Ireland and Israel, from the point of view of students, teachers, and policy makers. It is set against the background of the minority–majority group dichotomy within societies divided along ethnonational lines, and the challenge of delivering a common citizenship curriculum to a diverse group in such a context. Starting with interpretations of international law that state that education should be culturally appropriate and flexible to the needs of a particular community, the article considers several interrelated ideas: proportional representation of the minority in educational governance, students being able to “find themselves in the story” of the curriculum, and the debate over a common versus a differentiated curriculum. Interjurisdiction comparisons allow for exploration of varied understandings of citizenship education as socialization, and of potential responses to the challenge of balancing unity and diversity in a divided or multicultural society.     

The process of early self-control: an observational study in two- and three-year-olds

Metacognition and Learning - Early individual differences in self-control are predictive of numerous developmental outcomes, such as physical health and risk-taking behaviours. Therefore, it is...     

Quality of Teaching and Dropout Risk: A Multi-Level Analysis

The purpose of this study is to examine how the quality of teaching contributes to a sense of belonging and satisfaction, while considering students' personal and socioeconomic variables, in explaining the risk of dropping out of school. Two thousand, eight hundred and seventy 4th- to 9th-grade students from 105 classes in 18 schools participated in this research. A 3-level HLM6 analysis was performed: Students, classes, and schools. Findings showed the effect of the type of school (traditional vs. experimental) on the connections between quality of teaching and dropout risk; these connections are stronger in traditional schools. The conclusion was that quality of teaching plays an important role in decreasing the risk of dropout. Teaching quality has a significant effect on students' satisfaction and their sense of belonging, thereby affecting the risk of dropout.     

Exploring one student’s explanations at different ages: the case of Sharon

This study describes the types of explanations one student, Sharon, gives and prefers at different ages. Sharon is interviewed in the second grade regarding multiplication of one-digit numbers, in the fifth grade regarding even and odd numbers, and in the sixth grade regarding equivalent fractions. In the tenth grade, she revisits each of these concepts again. The study investigates the different forms Sharon’s explanations take at different ages as well as how she perceives the nature of mathematical explanations at different ages. Sharon’s explanations are also used to investigate her conceptualization of the number zero, a concept which runs across the curriculum at different ages. Finally, the study explores a method for investigating the long-term mathematical development of one student. Implications for future research are discussed.     

Relations of power and knowledge: university–industry relations in business studies in Finland

In the globalized neoliberal economy, business schools and business science has become a dominant societal institution and discourse. However, this has not directly strengthened the position of business schools in the societal networks of power. This paper examines this paradox by depicting who are the actors in the field and how these actors seek to influence what passes as legitimate knowledge in the discipline of business studies. Informed by actor network theory (Latour in Reassembling the social: an introduction to actor-network theory. Oxford University Press, Oxford, 2005) and drawing on the antenarrative analysis (Boje in Narrative methods for organizational and communication research. Sage Publications, London, 2001), the paper considers the understated dynamics of negotiation over the form and content of academic knowledge in a local context (cf. Alferoff and Knights in Br J Manag 20(1):125–142, 2009). The paper depicts the change that has occurred from the early 1990s till today. First, the potentially influential actors will be identified. Second, two maps of networks in different points of time will be traced. In the contemporary network, the gatekeeper role of business schools is undermined by new prominent actors. The paper shows how business schools, instead of gaining a high power position, are now more dependent on a variety of other actors, who increasingly define what passes as relevant and valid knowledge in business studies.