Two Mechanisms for Understanding Mathematical Concepts in Terms of Fictive Motions

This article discusses two mechanisms through which understanding static mathematical concepts (basic and more advanced mathematical concepts) in terms of fictive motions or motion events enhance our understanding of these concepts. It is suggested that at least two mechanisms are involved in this enhancing process. The first mechanism enables us to employ both the motor system and the visual system as two contributing cognitive resources to process the static concept. When one representation of a mathematical concept is transformed into another representation, there is a shift in the mode of processing. This shift facilitates the process of employing new cognitive resources such as the motor and visual systems. The second mechanism, which is a special form of mental simulation, enables us to simulate the process of formation of the static concept, which, in turn, makes it easier for us to understand the structure and properties of the static concept.     

先行组织者模式在中小学英语音标教学中的应用

奥苏伯尔的先行组织者模式强调在学习者接受新观念时 ,要重视学习者的认知基础。在进行教学时 ,如果没有上位观念可以同化新观念 ,教师就应该在引入新观念时先介绍先行组织者 ,然后用其同化新观念。本文分析了目前英语音标教学方面的不足 ,并试图运用先行组织者模式来解决这些问题 ,以使学习者能够在今后的英语学习中更深刻地理解和运用音标     

For want of a better word: unlocking threshold concepts in natural sciences with a key from the humanities?

The process of identifying threshold concepts invites experts to reflect on their discipline in a new way with the ultimate goal of improving learning and teaching. During a workshop to identify threshold concepts in biochemistry, we asked a group of natural scientists to explore ‘signification,’ a threshold concept from the humanities, as a mechanism to push them out of their comfort zones and recall how it feels to experience learning from a student’s perspective. In addition to accomplishing this goal, we subsequently realized that signification could also help us uncover and remedy ways in which use of scientific terminology impedes learning in biochemistry. Using the results of a survey of university teachers that aimed at refining a list of possible threshold concepts, we present three scenarios to illustrate the challenges that teachers and students encounter when attempting to cement a label (the signifier) and a concept (the signified) into a coherent sign. Based on these findings, we propose that teachers can better explore threshold concepts if they carefully consider the role terminology plays in learning and teaching. Thus we describe the ‘terminological canyon’ through which university teachers must journey in order to produce effective learning and teaching activities related to the threshold concepts. While the work described here pertains to biochemistry, we believe the process and findings can be generalized to a broad range of disciplines.     

Natural language as a tool for analyzing the proving process: the case of plane geometry proof

In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, 1938). Thanks to “verbal thought”, language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, 1975). So, it appears language can be studied as a cognitive process (Chomsky, 1975). In this investigation, I study language as a means for making the cognitive process explicit. In particular, I analyze the role of the verbalization produced by pairs of students solving a plane geometry problem. The basic idea of my research is that, during the resolution process of a plane geometry problem, natural language can play roles beyond that of communication: Natural language can be seen as a tool for supporting students’ cognitive processes (Robotti, 2008), and, at the same time, it can also be seen as a researchers’ tool which allows us to shed light on the evolution of students’ cognitive processes. With regard to language as researchers’ tool, I show how natural language (in our case, students’ verbalization during resolution of a plane geometry problem) can be used by the researcher to make explicit, to study, and to describe the development of the students’ cognitive processes during the resolution process. To this end, I present a model I have developed that allows us to identify, in students’ verbalization, different phases of their cognitive processes.     

隐喻在英语财经新闻中的应用

认知语言学认为,隐喻是人类基本的认知方式之一,是人类通过结构清晰的始源概念来解释结构相对模糊的目标概念,是我们理解抽象概念和现象的主要途径。英语财经新闻中常借助隐喻的不同类型如结构隐喻、方位隐喻、本体隐喻等来描述和解析经济活动中的抽象概念和专业术语,使抽象的财经新闻变得通俗易懂、形象生动。     

Threshold concepts about online pedagogy for novice online teachers in higher education

ABSTRACT

The use of threshold concepts to define key points of curricula is a relatively recent development in educational research. Threshold concepts represent crucial stages of learning, the acquisition of which enables learners to progress from one level of achievement to another. In this context, the learner is described as passing through an unsettling liminal space in which they may encounter troublesome knowledge and experience uncertainty or anxiety. When applied to online pedagogy in higher education contexts, academic staff become the learners as they extend their on-campus teaching knowledge into the online realm. In this setting, the identification of threshold concepts has the potential to inform the content of professional development (PD) programmes for novice online teachers. Because little research has yet been reported on threshold concepts associated with online teaching, this study identified these threshold concepts and investigated their specific nature. Funded by an Office for Learning and Teaching Australia Grant, the project employed a mixed-methods research approach. A mixture of qualitative and quantitative data was gathered from responses to questionnaires and reflective journal entries provided by university educators who were teaching in online contexts. Also, experts in the fields of PD, online teaching and threshold concepts were consulted using a modified Delphi technique that incorporated two rounds of surveys. Results of this study are discussed in association with potential applications to PD design for novice online educators, informed by the most fundamental learning experiences encountered by their more experienced colleagues.     

Threshold concepts in research education and evidence of threshold crossing

Most work on threshold concepts has hitherto related to discipline‐specific undergraduate education, however, the idea of generic doctoral‐level threshold concepts appeared to us to provide a strong and useful framework to support research learning and teaching at the graduate level. The early work regarding research‐level threshold concepts is further developed and reported in this paper using research carried out with supervisors into their identification of threshold concepts and research students' crossing of these thresholds. The research was conducted in two stages involving 65 experienced research supervisors across six countries (Australia, England, Jamaica, Malaysia, New Zealand and Trinidad) and across Humanities, Social Sciences, Engineering and IT and the Sciences. The first stage involved written responses from 26 experienced supervisors related to the learning challenges experienced by research students and their supervisors. The second stage of the research involved in‐depth interviews with 39 supervisors regarding student learning challenges and successes at the research level. Responses were analysed, resulting in the identification of six possible generic research threshold concepts, which evidence themselves in the quality and level of the students' work at different stages in that work: argument; theorising; framework; knowledge creation; analysis and interpretation; and paradigm. The data analysis also suggests a number of indicators that signal when learners have crossed conceptual thresholds to gain, articulate and put into practice one or more of these threshold concepts in their research learning.     

概念的认知表达——框架、认知域及理想化的认知模式之比较

框架、认知域及理想化的认知模式是认知语言学中表达概念的三个重要术语.对三者在细致分析的基础上进行对比研究,有助于我们正确使用这些概念,加深对认知语言学的理解.     

Shifting relations with the more-than-human: six threshold concepts for transformative sustainability learning

Using the iterative process of action research, we identify six portals of understanding, called threshold concepts, which can be used as curricular guideposts to disrupt the socially constituted separation, and hierarchy, between humans and the more-than-human. The threshold concepts identified in this study provide focal points for a curriculum in transformative sustainability learning which (1) acknowledges non-human agency; and (2) recognizes that the capacity to work with multiple ways of knowing is required to effectively engage in the process of sustainability knowledge creation. These concepts are: there are different ways of knowing; we can communicate with non-human nature and non-human nature can communicate with us; knowing is relational; transrational intuition and embodied knowing are valuable and valid ways of knowing; worldview is the lens through which we view reality; and the power of dominant beliefs (represented in discourse) supports and/or undermines particular ways of knowing and being as in/valid.     

The dolphin’s grammatical competency: Comments on Kako (1999)

Kako (1999) reviews the evidence for syntactic competencies in several animal species exposed to artificial language systems, emphasizing the importance of core syntactic properties such as argument structure and closed-class items. We present evidence from our dolphin studies for the acquisition of the closed-class functionality of demonstratives, prepositions, conjunctions, and locatives. Sensitivity to argument structure is also evidenced by wholly untrained and consistent interpretations of the dolphin to probes of anomalous syntactic structures. These results are generated within our comprehension-based paradigm, which enables us to provide convincing objective evidence for the development and generalization of concepts by the dolphin subject. Demonstrations of animal language competencies may illuminate certain aspects of human linguistic competence by suggesting that the particular modeled subsets can derive from general cognitive mechanisms, rather than language-specific ones.     

信念的形成

人类认识的发展经历了三个阶段，即感性、知性和理性，只有理性阶段才能形成理念，才为信念的形成提供了认识论基础。理性与知性相比有很大区别；知性以概念、判断、推理为形式，只能获得片面性知识，只能给人以是即是，非即非的形而上学思维方式；而理性是建立在多种规定性综合统一逻辑论证基础上的，最整体性和具体性的理性重构，给人提供智慧和理念，教给人一种辩证的思维方式，所以，理念和实践各环节综合，就使理念转变为信念，成为人的精神支柱。     

From Alternative Education to The Mainstream: approaches in Canada and Germany to Preparing Learners to Live in a Changing World

There has been a shift in the core idea of schooling in both Germany and Canada: While schools have traditionally focused on cognitive development, they now increasingly focus on ‘engaged learners’ and use integrated settings to support their cognitive, metacognitive and social-emotional development. In line with the theme ‘Learning to Be’, we argue that beliefs about the purpose of schooling are shifting from a narrow, knowledge-based approach to understanding that students need knowledge, skills and attitudes to succeed in their private, public and professional lives as adults. To this end, pedagogical concepts developed in alternative education are increasingly being implemented by mainstream schools. This article examines this significant development in Germany and Canada. We analyse current examples from mainstream schools, highlighting how they use alternative pedagogical concepts to transform the ways in which students come to know themselves as learners. In both countries, this process has been simultaneously bottom-up, driven by early-adopter schools, and top-down, driven by public awards or broad public initiatives.     

COGNITIVE LOAD THEORY AND THE ACQUISITION OF COMPLEX COGNITIVE SKILLS IN THE ELDERLY: TOWARDS AN INTEGRATIVE FRAMEWORK

The purpose of this article is to explore the advantages of instructional formats based on cognitive load theory for elderly learners engaged in the acquisition of complex cognitive skills. A great body of research has demonstrated that cognitive aging is accompanied by a reduction of working - memory capacity, a general slowing of mental processes, and a decline of the ability to repress irrelevant information. The core idea of cognitive load theory is that working - memory capacity is limited and should therefore be managed with great care and discretion. Cognitive load theory claims that this can be achieved by minimizing the level of extraneous cognitive load, which is the portion of load that does not contribute to schema acquisition, and by maximizing the level of germane cognitive load, which directly contributes to the construction of cognitive schemata. Since instructions based on cognitive load theory deal with cognitive limitations, in that they lead to an efficient use of the available resources, it was hypothesized that they are especially effective when elderly people are involved. This idea was analyzed by means of a framework merging cognitive load theory with the aforementioned research findings concerning cognitive aging. It was concluded that cognitive load theory, enabling elderly people to acquire new complex skills, can be regarded as an essential guide for educational gerontology.     

关联理论视野中的习语及其变体的理解机制阐释

关联理论为人类的认知本质设定了强有力的语用规范,为辨别区分可接受性和不可接收性语言变体提供了一条准绳,可以比较充分地阐释习语及其变体。在关联理论框架背景下,当听到不熟悉的习语形式时,受话者脑中会构建出一个定语式的、被充分理解的特定概念,并最终将其发展成为自身词汇库中的一个稳定项目。在理解习语变体的过程中,语链中蕴涵的变体概念及其组成要素会被激活,其间的部分信息还被评估并复制到一个新的特定概念中。这一过程必然生成原本习语形式无法达到的额外认知效果。     

新闻动态失实问题浅析

新闻的真实是一个动态的概念和过程。事实的变动是新闻赖以存在的依据。而事实的变动在为我们提供可供报道的新闻素材的同时,也增加了我们对事变的认识与把握的难度。动态真实的理念是对传统新闻观的纠偏。防范动态性新闻失实的策略是注重交代消息的来源以及获取信息的时间,变静态、结论式的平面报道为动态、过程式的立体报道,新闻的时效性必须服从动态真实性,报道策划要有预见性与应变性,注意截稿时间与新闻细节的交代,实现传统媒体与网络媒体的互动。     

Model based learning as a key research area for science education

A framework is presented for thinking about cognitive factors involved in model construction in the classroom that can help us organize the research problems in this area and the articles in this issue. The framework connects concepts such as: expert consensus model, target model, intermediate models, preconceptions, learning processes, and natural reasoning skills. By connecting and elaborating on these major areas, the articles in this issue have succeeded in moving us another step toward having a theory of conceptual change that can provide guidance to teachers in the form of instructional principles. Taken together, the articles remind us that individual cognition, while not the only factor in learning, is a central determining feature of learning. However, we must work to further develop the present partial theory of conceptual change to fill in the missing cognitive core of the present shell.     

中德文化与语言差异简析

中国人和德国人在哲学思想、文化理念、语言使用、生活习俗等方面的某些认知差异具体表现在:对哲学思辨、皇帝宗教、道家理论等问题的看法各异, 在做客、送礼、饮食、服饰等方面的生活习俗不同,从而使得中德两国的跨文化交际不时出现误解或者障碍.认真分析对比这种民族文化差异,有助于进一步了解日耳曼民族的文化内涵与风土人情,掌握德语的使用特点.     

Threshold concepts in higher education: a synthesis of the literature relating to measurement of threshold crossing

In relation to teaching and learning approaches that improve student learning outcomes, threshold concepts have generated substantial interest in higher education. They have been described as ‘portals’ that lead to a transformed way of understanding or thinking, enabling learners to progress, and have been enthusiastically adopted to inform teaching approaches and curriculum design. A growing body of literature has critiqued the relevance and applicability of the threshold concept theory and identified threshold concepts relevant to specific disciplines. More recent research has identified how students cross these thresholds and provided measures of the successful acquisition of threshold concepts. This literature synthesis critiques existing evidence on threshold crossing and acquisition to provide a succinct and informative overview of the outcomes to date. Key questions relevant to educators and researchers investigating whether students acquire the threshold concepts associated with their teaching, arose from the literature synthesis. These were: whether or not threshold crossing can be measured; how variation in student learning can be addressed during measurement; tools that can be used for measuring threshold crossing; whether the way units or concepts are taught should alter prior to measurement, and the challenges and limitations of measuring threshold crossing.     

英语专业学生写作中隐喻思维的培养

对英语专业的学生来说,写作中输入隐喻的概念是帮助学生提高写作质量,克服写作中问题的方法之一。要帮助学生建立隐喻恩维,就要从认知概念上着手并加以实践训练,才能增加学生对于这个思维方式的认识和适应,并在将来写作中主动的采用隐喻,以达到激发学生的写作兴趣,改善写作质量的目的。