Using symbolic interactionism insights as an approach to helping the individual with Asperger's syndrome overcome barriers to social inclusion

This article outlines a case for using symbolic interactionism as a tool to help individuals with Asperger's syndrome reconcile situations in which communication might prove challenging. This study builds on previous work carried out by the author which describes an autoethnographical approach to help the individual with Asperger's syndrome gain insights into ways to engage effectively with the social situations they encounter. It is well documented that those with Asperger's syndrome find many social situations challenging and that commonly understood verbal and non‐verbal communication ‘signs’ and ‘symbols’ may be difficult for them to interpret in ways intended by others. It is within this context that the work seeks to examine communication issues in terms of the symbolic interactionism notion of the ‘Me’ and how this understanding can help the individual with Asperger's syndrome model their own behaviour from a symbolic interactionism point of view. The article begins with a discussion of the background to the research and how an inability to read the communication ‘signs’ and ‘symbols’ around them can make it difficult for the learner with Asperger's syndrome to have a commonly held understanding of the social setting in which he or she operates. The work gives a personal insight from a person with Asperger's syndrome into how symbolic interactionism coupled with autoethnography can be used as tools to enable the learner with Asperger's syndrome to explore the nature of communication patterns under such circumstances. The work includes vignettes which highlight experience from such a personal perspective.     

交际中调距现象--从人称指示语更换说起

本文以心理距离为参照点,以汉语日常会话为语料,在语用视点和语用移情及离情理论框架下,探究人称指示语的更换在交际中所起的调距作用和取得的语用效果。通过分析发现,第一人称指示语换指第二或第三人称指示语时,前者拉近了说话人和听话人间的心理距离,增强了话语的亲和力,后者拉近了说话人与第三方间心理距离,便于听话人感受说话人对第三方的情感和立场;第二人称指示语换指第一或第三人称指示语时,前者将听话人移位于说话人位置,两者间心理距离消失,激起情感共鸣,后者将心理距离由远拉近,强化说话人负面情绪,多为严厉批评;第三人称指示语换指第一或二人称指示语时,两者都将心理距离拉远,不同之处在于前者弱化自我意识以增强客观性,后者通过模糊听话人身份来提高礼貌程度。     

An analytical framework for analyzing student teachers’ verbal interaction in learning situations

This paper focuses on the study of student teachers’ verbal interaction in learning situations generated in a classroom corresponding to a mathematics methods course. In our work, we incorporate two ‘ways of seeing’ a group: as an entity or as a set composed of individualities. We present an analytical framework that considers two dimensions connected with these ways of seeing the group and four variables corresponding to these dimensions, through which the verbal interaction between student teachers in a group can be considered. As regards the first dimension, the variables included are specific language, cognitive processing, social processing; the second dimension considers the relational variable. We describe each of the different variables that form the framework, and how this framework allows us to analyse the verbal interaction in three groups of student teachers. We believe that building analytic frameworks that allow the study of verbal interaction in detail is worthwhile in the educational field due to their important role in the analysis of learning-teaching processes.     

数学史融入数学教学研究的若干思考

中国数学课程改革提出将数学史融入数学教学,可是在教学实践中存在教学设计不高、课堂教学效果不佳等问题.为了有效解决这些问题,数学史融入数学教学的研究应关注3个主要课题:(1)应如何评价数学史融入数学教学的教学案例及其教学效果;(2)是否为教师开展数学史融入数学教学创造了必要条件;(3)为了达成数学史融入数学教学的目标,应该做些什么.     

论高职学院数学的分层教学

高职数学教学目标分为三个层次,在教学实践上可按三个阶段实施。第一阶段为基本知识的学习,掌握基本概念、基本方法和最基本的运算;第二阶段为理论及运算技巧的学习;第三阶段为数学建模的学习。第一阶段是最重要也是最基础的,是必修课程,二三两个阶段为选修课。     

职前中学数学教师解题能力的培养

解题是中学数学教师的基本功之一,但目前职前中学数学教师在解题方面的能力比较弱。因此,需要有效地、全面地提高职前中学数学教师解题的能力。具体来说,需要系统地、有计划地培养职前中学数学教师解题能力。在第一学年研读中学数学课标和教材,强化中学数学的概念性知识;在第二学年熟练掌握中学数学解题中的解题思想和方法;在第三、四学年对解题中的有意识控制的知识进行训练。同时,将解题的书面表达、口头表达的训练融入每一个阶段当中。     

Pedagogical content knowledge and the teaching of outdoor education

This theoretical paper examines the concept of pedagogical content knowledge (PCK) and explores how it might contribute to conversations around quality teaching and learning in outdoor education. This paper begins by summarizing the historical and contemporary literature, including issues of definitions, curriculum, content, and pedagogy in outdoor education. We then review the concept of PCK, its history, and contributions to other subject areas, including mathematics. We present a framework for PCK from the field of mathematics education and propose a 'modified' PCK framework for outdoor education. We postulate that this framework might help articulate knowledge areas needed by a teacher of outdoor education, and how these differ from and are similar to those required in other subject areas. We conclude by exploring how the idea of PCK and the modified framework might add to existing understandings of what it means to provide high quality outdoor education teaching and learning experiences.     

Plato, Pascal, and the dynamics of personal knowledge

Abstract educational practices are to be based on proven scientific knowledge, not least because the function science has to perform in human culture consists of unifying practical skills and general beliefs, the episteme and the techne (Amsterdamski, 1975, pp. 43–44). Now, modern societies first of all presuppose regular and standardized ways of organizing both our concepts and our institutions. The explanatory schemata resulting from this standardization tend to destroy individualism and enchantment. But mathematics education is in fact the only place in which to treat the human subject’s relationship with mathematics. And that is what mathematics education is all about: make the human subject grow intellectually and as a person by means of mathematics. At first sight, mathematics, in its formal guise, seems the opposite of philosophy, because philosophy constructs concepts (meanings), whereas mathematics deals with extensions of concepts (sets). We shall, however, turn this problem into an instrument, using the complementarity of intensions and extensions of theoretical terms as our main device for discussing the relationship between philosophy and mathematics education. The complementarity of the “how” and the “what” of our representations outlines, in fact, the terrain on which epistemology and education are to meet.     

The Evolution of Thought

We investigate the evolution of thought using the method of historical reconstruction, the theory of the cultural and historical determinism of psychological development, data on the relationship between morphological studies, modern findings about child development, and the scientific understanding of neural morphogenesis. We argue for classifying protothinking as a separate category to describe a stage when the person thinks objectively without being aware of this process. It is shown that protothinking is a transitional stage between animal thinking and human verbal thinking. We devote particular attention to the process whereby words and verbally expressed thoughts originated. We formulate the conditions that make it possible to trace the process of how speech came into being as sound combinations that are designed to express thought. It is emphasized that individuals are always responsible for discovering words for themselves. We discuss the origins of language, and we note the creative nature of this process.     

Getting at the Mathematics: Sara’s Journal

In this paper, we discuss issues in planning and conducting research into mathematics learning. We emphasize two central themes: (a) the learners mathematics (especially the issues and ideas, in given problem situations, that learners choose to think about and to present) and (b) the kinds of knowledge that learners may be building (including their ideas about what mathematics is, and how people do, learn, use, communicate and understand it). While the first theme is at least partly mathematical, the second interweaves cognition and epistemology. Anchored in student data from an extended classroom teaching experiment in the mathematics of change, we focus on key choices needed to build narratives to help researchers capture, in detail, how students engage with mathematics in extended problem explorations.     

Learning Mathematics for Teaching: From a Teachers' Seminar to the Classroom

A successful practice grounded in the principles that guide the current mathematics education reform effort requires a qualitatively different and significantly richer understanding of mathematics than most teachers currently possess. However, it is not as clear how teachers' mathematical understandings develop and how those understandings affect instruction. This paper explores two avenues for K-6 teachers' mathematical development, (a) engagement in inquiry into mathematics itself, and (b) investigation of children's mathematical thinking, illustrating how the need for these two kinds of investigations arises in classroom situations and how they can be pursued in a professional development setting.     

A Conceptual Framework for Learning to Teach Secondary Mathematics: A Situative Perspective

This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations -- mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By participating over time in these varied contexts, mathematics teachers refine their conceptions about their craft -- the big ideas of mathematics, mathematics-specific pedagogy, and sense of self as a mathematics teacher. This framework guides a research project that traces the learning trajectories of teachers from two reform-based teacher preparation programs into their early teaching careers. We provide two examples from this research to illustrate how this framework has helped us understand the process of learning to teach. This revised version was published online in July 2006 with corrections to the Cover Date.     

Characterization of an Ordinary Teaching Practice with the Help of the Theory of Didactic Situations

In this paper, we use the theory of didactic situations to characterize a mathematics teaching practice, currently used in secondary schools in France, which we have called interactive synthesis discussion. We have studied this practice in ordinary classes, i.e. classes where the researcher intervenes neither in the preparation nor in the management of the lessons. We have looked at the didactic situations the teacher chooses, and how he manages his teaching project, the students’ work in the classroom and at home, and classroom interactions. We present two case studies of experienced teachers, one in grade 8, and the other in grade 10.     

Cognitive play and mathematical learning in computer microworlds

Based on the constructivist principle of active learning, we focus on children's transformation of their cognitive play activity into what we regard as independent mathematical activity. We analyze how, in the process of this transformation, children modify their cognitive play activities. For such a modification to occur, we argue that the cognitive play activity has to involve operations of intelligence which yield situations of mathematical schemes.We present two distinctly different cases. If the first case, the medium of the cognitive play activity was a discrete computer microworld. we illustrate how two children transformed the playful activity of making pluralities into situations of their counting schemes. In the second case, the medium was a continuous microworld. We illustrate two children's transformation of the playful activity of making line segments (sticks) into situations of their counting schemes. We explain one child's transformation as a generalizing assimilation because it was immediate and powerful. The transformation made by the other child was more protracted, and social interaction played a prominent role. We specify several types of accommodations induced by this social interaction, accommodations we see as critical for understanding active mathematics learning. Finally, we illustrate how a playful orientation of independent mathematical activity can be inherited from cognitive play.     

激活学生数学思维培养学生创新意识

培养学生的创新能力是当前教育教学研究的重要课题。本文主要从创设情景、营造探究氛围、发挥学生的主体作用以及评价学生的课堂活动等方面探讨激活学生的数学思维,培养学生创新意识的意义。     

Students’ understanding of the number line / Estudiantes pensando en la recta numérica

We studied the conceptions of students coming from secondary education and university regarding the number line as a representation of real numbers. In the context of a wider questionnaire, 307 students were presented with a task consisting of two verbal items and one graphic item related to the number line. The students were all at different levels in their study of mathematics (in the third, fourth or fifth year of secondary education, or at the beginning or advanced stage of a university degree in mathematics, biology or physical education). A gradient in the depth of the students’ conceptions, associated with the level of their studies in mathematics, was found. This gradient extends from the estrangement of facing the problem or a conception of a drawn or physical matter line, which was associated with students with a lower level of mathematical studies, passing through a vision centred around potential numeric density or a line containing points (discrete), up to an instrumental conception of the line as supportive of magnitudes in advanced students of biology and focusing on continuity sustained by advanced students of mathematics.     

Using Intuition From Everyday Life in 'Filling' the gap in Children's Extension of Their Number Concept to Include the Negative Numbers

We report here an instructional method designed to address the cognitive gaps in children's mathematical development where operational conceptions give rise to structural conceptions (such as when the subtraction process leads to the negative number concept). The method involves the linking of process and object conceptions through semiotic activity with models which first record processes in situations outside mathematics and subsequently mediate activity with the signs of mathematics. We describe two experiments in teaching integers, an interesting case in which previous literature has focused on the dichotomy between the algebraic approach and the modelling approach to instruction. We conceptualise modelling as the transformation of outside-school knowledge into school mathematics, and discuss the opportunities and difficulties involved. This revised version was published online in July 2006 with corrections to the Cover Date.     

How Automatically Do Readers Infer Fictional Characters' Emotional States?

We propose that reading stories, such as a narrative about a character who takes money from a store where his best friend works and who later learns that his best friend has been fired, stimulates readers to activate the knowledge of how the character feels when he finds out that his best friend has been fired from a job for something he did. In other words, we propose that readers infer fictional character's emotional states. In this article, we first review two series of laboratory experiments (Gernsbacher, Goldsmith, & Robertson, 1992; Gernsbacher & Robertson, 1992) that empirically tested this hypothesis by measuring participants' reading times to target sentences that contained emotion words that matched (e.g., guilt) or mismatched (e.g., pride) the implied emotional state. We then present a third series of laboratory experiments that tested how automatically such knowledge is activated by using a divided- attention task (tone-identification, per-sentence memory load, or cumulative memory load) and by comparing target-sentence reading time when the emotional state is explicitly mentioned versus only implicit.     

Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance

This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of working memory. Concurrent analyses indicated that mathematics anxiety represents a unique source of individual differences in children’s calculation skills and mathematical applications, but not in children’s geometric reasoning. Furthermore, we found that higher levels of mathematics anxiety in second grade predicted lower gains in children’s mathematical applications between second and third grade, but only for children with higher levels of working memory. Overall, our results indicate that mathematics anxiety is an important construct to consider when examining sources of individual differences in young children’s mathematical performance. Furthermore, our findings suggest that mathematics anxiety may affect how some children use working memory resources to learn mathematical applications.     

《西厢记》的人称代词

从《西厢记》中的人称代词,归纳出它的人称代词系统:第一人称用"我"、"俺"、"喒"、"咱",第二人称用"你"、"您",第三人称用"他"。"我"和"俺"对立主要体现在作不同的句子成分。"您"字已经出现了单数的用法,但是还没有完成表敬称这一转变。元代北方汉语的第三人称代词实际上只有一个"他","们"字在书中用得极少。