Characterising and developing vocational mathematical knowledge

In this introductory article, I argue why this special issue focuses on the question of how the mathematical knowledge required at work can be characterised and developed in vocational education and workplace training. After some words on the importance of this subfield of mathematics education and the need to rethink metaphors of learning in this area, I summarise the structure of the special issue and highlight a few main points raised in the various contributions.     

关于发展高校科技企业的几点认识

本文结合高校科技企业管理的正反经验,对此类企业今后的提出了自己的认识：肾校企分开原则;加强骨干队伍建设;建立产权激励机制;努力进行技术创新。     

Working with artefacts: gestures, drawings and speech in the construction of the mathematical meaning of the visual pyramid

This paper reports a part of a study on the construction of mathematical meanings in terms of development of semiotic systems (gestures, speech in oral and written form, drawings) in a Vygotskian framework, where artefacts are used as tools of semiotic mediation. It describes a teaching experiment on perspective drawing at primary school (fourth to fifth grade classes), starting from a concrete experience with a Dürer’s glass to the interpretation of a new artefact. We analyse the long term process of appropriation of the mathematical model of perspective drawing (visual pyramid) through the development of gestures, speech and drawings under the teacher’s guidance.

高校数学实验开展与建设的理论研究

数学实验为数学的思想与方法注入了更多、更广泛的内容。如何开展数学实验是数学教学工作者及科研人员面临的重要问题。文中通过理论分析的方式阐明了数学实验开展的必要性、实验室建设结构及实验教学方法和模式。目的在于为高校数学实验开展及建设提供参考。     

Teaching care ethics: conceptual understandings and stories for learning

An ethic of care acknowledges the centrality of the role of caring relationships in moral education. Care ethics requires a conception of ‘care’ that differs from the quotidian use of the word. In order to teach care ethics more effectively, this article discusses four interrelated ways that teachers’ understandings of care differ from care ethics: (1) conflating the term of reference ‘care’ with its quotidian use; (2) overlooking the challenge of developing caring relationships; (3) tending toward monocultural understandings of care; and (4) separating affect and intellect. Awareness of these conceptions of care supports teacher educators to teach care ethics in more meaningful and relevant ways. We explore stories and their dramatization as a medium to facilitate effective and in-depth teaching of care ethics.     

Teaching as mediation: The cogenerative dialogue and ethical understandings

The mediation by teachers of the many activity systems that constitute any given class has traditionally been an ignored aspect of teaching. In this paper we argue that the teacher's responsibility for this mediation exists and must therefore be accounted for in the praxis of teaching. In addition we argue for the cogenerative dialogue as one viable solution for teachers to mediate in an ethically responsive manner. We construct these arguments because teachers must be better prepared to understand their complex role in the classroom along with their ethical responsibility to the students for the effective negotiation of the systems they navigate each day.     

Didactics: Swedish and Norwegian understandings compared by a Norwegian

A debate concerning didactics as a concept and research field has been conducted in Sweden during the 1980s. This article presents central points of view from this debate, and discusses them on the basis of a Norwegian understanding of didactics. From this perspective the author holds that the Swedish discussion of didactics may appear somewhat near‐sighted. The conclusion drawn is that the primary task of didactics must be the establishment of a basis for the attainment of more knowledge about, better understanding of, and deeper insight into education. Such a task is scarcely best solved through a fight over the right understanding of didactics. A better strategy would comprise efforts at fruitful dialogue and focus on research aimed at illuminating all aspects of education and its influencing factors.     

Discourses at the boundary spaces: developing a fluent transition from preschool to school

This article examines the preschool–school transition in the Finnish school system from institutional and professional perspectives. It takes place in a context in which the fluent transition from preschool to primary school is supported by developing joint lessons for preschool and primary school children. Transition is seen as a process in which culturally and historically constructed institutional boundaries form an arena for professional learning. The study focuses on boundary work and boundary spaces. Boundaries are seen as spaces where resources from different practices are brought together to expand interpretations of multifaceted tasks. The data are analyzed from a discursive perspective. The study investigates how professionals create new forms of activity when collaborating in boundary spaces. Three discursive frames were identified. The first is called the ‘initiative frame’, the second the ‘consensus frame’ and the third the ‘collaboration frame’. These frames are considered in relation to creating new, shared practices and a common object of activity.     

Student understandings of acids and bases: A two year study

Conclusion This study had indicated that further research needs to be done into the examination of how subsequent learning will interact with knowledge previously gained. Does the learning of new knowledge in relation to previously understood knowledge cause interference (Biggs & Telfer 1986) or does it result in some confusion culminating in lack of linkages (Osborne & Freyberg, 1985)? Can the benefits of constructivism be built upon when using other strategies? These are some of the questions which arise from the results obtained in this study. This study does not provide any definitive solution to the questions; however it does show that long term retention of concepts learnt using a constructivist strategy does occur.     

Comparing action gestures and classifier verbs of motion: evidence from Australian Sign Language, Taiwan Sign Language, and nonsigners' gestures without speech

Recent research into signed languages indicates that signs may share some properties with gesture, especially in the use of space in classifier constructions. A prediction of this proposal is that there will be similarities in the representation of motion events by sign-naive gesturers and by native signers of unrelated signed languages. This prediction is tested for deaf native signers of Australian Sign Language (Auslan), deaf signers of Taiwan Sign Language (TSL), and hearing nonsigners using the Verbs of Motion Production task from the Test Battery for American Sign Language (ASL) Morphology and Syntax. Results indicate that differences between the responses of nonsigners, Auslan signers, and TSL signers and the expected ASL responses are greatest with handshape units; movement and location units appear to be very similar. Although not definitive, these data are consistent with the claim that classifier constructions are blends of linguistic and gestural elements.     

Beyond words: the importance of gesture to researchers and learners

Gesture has privileged access to information that children know but do not say. As such, it can serve as an additional window to the mind of the developing child, one that researchers are only beginning to acknowledge. Gesture might, however, do more than merely reflect understanding-it may be involved in the process of cognitive change itself. This question will guide research on gesture as we enter the new millennium. Gesture might contribute to change through two mechanisms which are not mutually exclusive: (1) indirectly, by communicating unspoken aspects of the learner's cognitive state to potential agents of change (parents, teachers, siblings, friends); and (2) directly, by offering the learner a simpler way to express and explore ideas that may be difficult to think through in a verbal format, thus easing the learner's cognitive burden. As a result, the next decade may well offer evidence of gesture's dual potential as an illuminating tool for researchers and as a facilitator of cognitive growth for learners themselves.     

Teacher-student relationship and mathematical problem-solving ability: mediating roles of self-efficacy and mathematical anxiety

Abstract

This study investigated the mediating roles of self-efficacy and anxiety on the effects of teacher–student relationship on mathematical problem-solving ability. A total of 1667 fifth graders from central China participated in the large-scale survey. The findings indicated that (1) teacher–student relationship had a direct and positive effect on students’ mathematical problem-solving ability; (2) the positive link between teacher–student relationship and mathematical problem-solving ability was partially mediated through self-efficacy; (3) the teacher–student relationship affected students’ mathematical problem-solving ability through self-efficacy and maths anxiety, but the effect of self-efficacy on mathematical anxiety was smaller. Implications for the importance of teacher–student relationships in education as well as suggestions for future research are discussed.     

贯一学习系统设计：有效的教学、学习和技术

人们带着巨大的并且常常是盲目的热情追求着连接教学、学习和技术的理论和模式。技术的发展激发了研究者和教育者去拓展学习的概念和学习环境的设计，这引发了对不同方法的睿智性和正当性的争论。由此，需要发展一个更具原则性的方法来连接教学、学习和技术。文章提出了贯一学习系统设计的标准和理论基础，及一个理论、研究、假设和方法之间的连接试验。     

When victims don't cry: children's understandings of victimization, compliance, and subversion

How do children understand situations in which the targets of moral transgressions do not complain about the way they are treated? One-hundred and twenty participants aged 5, 7, 10, 13, and 16 years were interviewed about hypothetical situations in which one child ("transgressor") made an apparently unfair demand of another child ("victim"), who then responded by either resisting, complying, or subverting. In general, 5-year-olds judged compliance positively and resistance negatively and 7- to 16-year-olds judged resistance positively and compliance negatively; all but 16-year-olds judged subversion negatively. Most participants judged the transgressor's actions negatively, regardless of how the victim had responded. The findings are discussed in terms of their implications for children's developing understandings of victimization.     

A study of multimodal motherese: the role of temporal synchrony between verbal labels and gestures

This study examined European American and Hispanic American mothers' multimodal communication to their infants (N = 24). The infants were from three age groups representing three levels of lexical-mapping development: prelexical (5 to 8 months), early-lexical (9 to 17 months), and advanced-lexical (21 to 30 months). Mothers taught their infants four target (novel) words by using distinct objects during a semistructured play episode. Recent research suggests that young infants rely on temporal synchrony to learn syllable-object relations, but later, the role of synchrony diminishes. Thus, mothers' target and nontarget naming were coded for synchrony and other communication styles. The results indicated that mothers used target words more often than nontarget words in synchrony with object motion and sometimes touch. Thus, multimodal motherese likely highlights target word-referent relations for infants. Further, mothers tailored their communication to infants' level of lexical-mapping development. Mothers of prelexical infants used target words in synchrony with object motion more often than mothers of early- and advanced-lexical infants. Mothers' decreasing use of synchrony across age parallels infants' decreasing reliance on synchrony, suggesting a dynamical and reciprocal environment-organismic relation.     

New understandings of communities and ourselves: community-based participatory research with Alaska Native and Lower 48 youth

In the summer of 2014, students from universities in the contiguous United States (Lower 48) and Inupiat youth from Alaska carried out a pilot project as participants/co-researchers in a process called Intergenerational Dialog, Exchange, and Action (IDEA). This action-oriented, community-based, and participatory research method was first developed in 2008, as a platform for structuring dialog between adults, Elders and youth within a community, and for extending resonant ideas emerging from these discussions through Photovoice and digital storytelling amongst youth participants. This pilot study was designed to investigate the feasibility and potential of university students from the Lower 48 and Indigenous youth from Alaska to carry out the IDEA process together as co-researchers. The results of the pilot suggest that it is both possible and meaningful for IDEA to be conducted by a team of youth co-researchers. We found that participation in IDEA expanded the perspectives of youth co-researchers from both Alaska and the Lower 48 in parallel, yet different ways. Exploring the strengths of older community members, being exposed to different ways of living and being, and having opportunities to reflect on and build narratives around these ideas, allowed all the co-researchers to develop a new understanding of their own communities and their roles and responsibilities within them. This paper shares youth co-researcher reflections of the process and the ways in which the process prompted these new perspectives about themselves, their respective communities and their roles within them.