Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review of ethnomathematics

This paper is a critical review of the ethnomathematics literature and classifies ethnomathematics according to where it might stand in relation to the teaching of formal, academic mathematics. This paper investigates what it sees as four possibilities: ethnomathematics should replace academic mathematics, ethnomathematics should be a supplement to the mathematics curriculum, ethnomathematics should be used as a springboard for academic mathematics and ethnomathematics should be taken into consideration when preparing learning situations. We argue that it is only through the lens of formal, academic mathematics sensitive to cultural differences that the real value of the mathematics inherent in certain cultures and societies be understood and appreciated.This revised version was published online in October 2005 with corrections to the Cover Date.     

A Comment on: Rowlands & Carson ``Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review'

The critique of ethnomathematics by Rowlands and Carson that appeared recently provides an opportunity to open debate on cultural issues in mathematics. This response argues that such debate must be based on contemporary writing in the field, and should not focus on extreme views within the political justification for ethnomathematics. It addresses some of the philosophical questions raised by Rowlands and Carson, and the relationship of the field with indigenous knowledge is raised. We also suggest that the role of ethnomathematics in mathematics education is now predominantly an empirical matter,and comment on some preliminary results from recent studies that indicate a positive role for culturally-based curricula. This revised version was published online in August 2006 with corrections to the Cover Date.     

Making sense of number sense: implications for children with mathematical disabilities

Drawing on various approaches to the study of mathematics learning, Gersten, Jordan, and Flojo (in this issue) explore the implications of this research for identifying children at risk for developing mathematical disabilities. One of the key topics Gersten et al. consider in their review is that of "number sense." I expand on their preliminary effort by examining in detail the diverse set of components purported to be encompassed by this construct. My analysis reveals some major differences between the ways in which number sense is defined in the mathematical cognition literature and its definition in the literature in mathematics education. I also present recent empirical evidence and theoretical perspectives bearing on the importance of measuring the speed of making magnitude comparisons. Finally, I discuss how differing conceptions of number sense inform the issue of whether and to what extent it may be teachable.     

论民族数学及其教育

论述了民族数学的含义,另外,认为民族数学在数学教育中应该发挥积极的效应.     

Politics in an Indian canyon? Some thoughts on the implications of ethnomathematics

Working with Navajo Indian informants in Arizona, USA we became aware of the capabilities of children and adults to find their way in vast and clearly “chaotic” canyons. One thing we did was describe what people actually did and said about their ways to find the way back home in such contexts. A second one was to use these data in order to build a curriculum book for a bicultural school on the Navajo reservation. We start from this example to ask what the political choices are, which we confront when working with such material: how much mathematics (or is it Mathematics) is needed in daily life? And what mathematics should we promote or develop, without becoming colonialist again? In Section 2, we discuss the meaning and the status of ethnomathematics, proposing that it would be the generic category which allows for a more systematic and comparative study of the whole domain of mathematical practices. In Section 3, we introduce the concept of multimathemacy (after multiliteracy) to discuss the political agenda of ethnomathematics. We argue that multimathemacy should be the basis of the curriculum in order to guarantee optimal survival value for every learner.     

文化批评和比较文学定义

比较文学的定义应该体现学科发展的新特点,重视文化批评的意义。但是,如果把"探讨文化差异"当作比较文学区别于其他文学研究的根本标志,那是不妥当的。比较文学的基本要求是研究对象必须跨越民族界限,没有跨民族意义的文学研究,即使是重点探讨文化差异,也不是比较文学。否则,就会把比较文学消解于一般的文化研究之中。所以,文化批评在当前虽然应该强调,却不应成为界定比较文学的依据。有关比较文学定义争论的历史说明,准确地把握学科的特定研究领域和学科的基本特征,是为比较文学下定义的关键。     

Differentially positioned language games: ethnomathematics from a philosophical perspective

This paper discusses a new philosophical perspective for ethnomathematics which articulates Ludwig Wittgenstein’s and Michel Foucault’s theoretical notions. It is conceived as a theoretical toolbox which allows the analysis of, on the one hand, the mathematical language games of different forms of life and their family resemblances and, on the other hand, the Eurocentric discourses of academic and school mathematics and their effects of truth. Based on fieldwork done in rural forms of life in the south of Brazil, examples of the use of this perspective are presented. The paper analyzes language games of those different forms of life and the school mathematics discipline, highlighting the complex network of learning and powers that makes other mathematics than that known as the mathematics be positioned “in a void” in school curricula.     

The End of Innocence: A Critique of 'Ethnomathematics'

Ethnomathematics originated in the former colonies, in response to the Eurocentrism of the history of mathematics, mathematics itself and mathematics education. It has also found expression in several other contexts. It is a part of the broader framework that elaborates the social and political dimensions of mathematics and mathematics education but especially, the dimension of culture. This focus on culture examined in the unique context of South Africa makes visible both conceptual difficulties in its formulation and also difficulties with respect to its interpretation into educational practice. This paper explores a critique of ethnomathematics using the South African situation and conceptual tools of a critical mathematrics education.     

论文学

文学是个非常古老的精神活动、精神形式,但人们对它既熟悉又陌生,熟知却未必真知。加上西方20世纪80年代发生了文学的＂文化转向＂后,文学的疆界变得无限开阔,而其自身的界定也面临空前的危机。因此,对＂文学是什么＂的回答就成了一个迫切的学术问题。而此前的＂形象论＂、＂表现论＂和＂审美意识形态论＂文学观都存在着严重不足,故而需要另辟蹊径,再进行新的界定。新的结论是：从其本源上看,文学是一种高级的魅态文化形式;从其历史面貌上看,文学是个历史性的家族,表现为文学观、特征论、形式定位、流派形态,同时还呈现为杂化和纯化的周期性变奏;从本质的抽象定义看,文学则是象征性的语言艺术,它不以科学和实用为目的,而以想象性超越和诗性的解放为旨归。中国当代文学的致命危机就是＂象征性＂传统谱系的断裂。     

论冯沅君与庐隐的女性悲剧意识

＂五四＂时期是妇女解放和思想启蒙的时期,又是中国女性文学发生和崛起的时期。作为作家的冯沅君和庐隐同是＂五四＂的产儿,她们关注女性的命运,寻找女性的出路,以女性的独特视角反映了在传统与现代对立中的女性心理与悲剧命运,书写了众多的悲剧女性形象,对＂五四＂女性文学的开掘与发展无疑具有拓荒的价值与意义。     

The Definition, Assessment, and Mitigation of State Boredom Within Educational Settings: A Comprehensive Review

Mitigating the situational factors that give rise to state boredom is a consistent challenge facing educators. Despite the growing amount of literature devoted to the construct, the field has yet to arrive at a consensus regarding a clear theoretical or operational definition. Subsequently, inconsistencies exist in the assessment methodologies, research findings lack generalizability, and strategies for mitigation in educational settings remain elusive. In this cross-disciplinary analysis, the extant literature on state boredom is critically reviewed and synthesized, and a two-dimensional definition of state boredom as an unpleasant (subjective), low-arousal (objective) experience is proposed. Findings from the technological advances of the last decade that allow for the objective measurement of physiological states are used to inform recommendations for empirically sound assessment methodologies. Finally, the proposed definition of state boredom and related assessment strategies are discussed with respect to implications for enhancing educational practices.     

中西比较语境中的文学界定

审美作为文学定义的种差,既是从内容也是从形式上区分文学与非文学:文学内容具有非功利、非理性特征,文学语言具有含混性、多义性,文学文本具有空白性、解释的主观性等等。文学定义的属概念反映文学的共性。"文本"作为属概念,可以兼容文学的多层面、多角度属性,兼容多学科观念和方法,普遍适用于中西语境。将文学定义为一种审美文本,与文学是一种语言艺术、文学是一种审美意识形态是等价的,但是可以避免用语潜含的历史分歧,可以彻底解决近年中国学界有关文学界定和文学研究边界的争议。     

关于乡土文学理论的一点思考

对于乡土或地域文学这一概念的使用,人们还有很多方面的争议.争议的焦点在于:无论是世界文学,还是国家或民族的文学,都离不开特定的历史社会背景,再提“乡土“、“地域“这类概念有无必要?通过检索我国的乡土文学理论,对其作了一些思考.     

"文献"芻议

“文献”是一个至少在春秋末期就已经出现的概念。然而在历史上,该词随着使用语境的不同,其含义也时广时窄。大致而言,“文”的含义没有什么变化,而“献”的范围则呈日益狭窄的趋势,这与参与文献研究的人自身视野的变化有关。其次,本文以现代视野重新审视了现当代学者的观点,认为在目前的“文献”定义乃现当代图书馆、情报学的定义,在相当程度上混淆了“文献”和“文物”的界限,并不惬合于实际;另外,在科技和社会快速发展的今天,应该重新界定“文献”,将新产生的电子文献等收纳于内。最后,“文献”一词,目前尚未有适合的对应外语翻译。     

A sense of belonging among Australian university students

ABSTRACT

This study was designed to explore what students perceive as essential factors influencing their sense of belonging. Gaining insight into what students perceive as influencing their sense of belonging enables design of interventions to foster that sense of belonging. Two hundred and nine students from a university in Sydney responded to the question: ‘What would help you to feel that you belong at Macquarie University?’ Results showed students most frequently identified people as instrumental in feeling that they belonged at university. Students also reported that places where there is respect, and where others are accepted, contributed to their feelings of belonging. Lastly, opportunities to interact with other students, such as within clubs, societies and at events, were reported by students to contribute to their feelings of belonging. Findings of the current study are discussed in relation to existing literature, to develop approaches that may enhance university students’ sense of belonging.