Making Explicit the Analysis of Students’ Mathematical Discourses – Revisiting a Newly Developed Methodological Framework

Sfard and Kieran [Kieran, C., Educational Studies in Mathematics 46, 2001, 187–228; Sfard, A., Educational Studies in Mathematics 46, 2001, 13–57; Sfard, A. and Kieran, C., Mind, Culture, and Activity 8, 2001, 42–76] have developed a methodological framework, which aims at characterizing the students’ mathematical discourses while they are working in groups. In this study, I focus on an important aspect of this methodological framework, namely the interactive flowcharts. The aim of this study is to suggest two complementary analyses for the construction of the interactive flowcharts: an additional analysis by means of the analytical construct of contextualization as well as an analysis of types of mathematical discourses. Based on data from a study of how four groups of Swedish engineering students collaboratively construct concept maps in linear algebra. I show that the two complementary analyses make the construction of the interactive flowcharts more coherent and transparent, and hence, more reliable. Furthermore, the two complementary analyses dramatically changed the picture as to whether the studied discourses were to be seen as mathematically productive or not. In the end of the article, I discuss the possibilities of performing the suggested additional analyses within the original methodological framework.     

"大槐树移民"与明初的垦荒政策

"大槐树移民"是中国移民史上一次重要的移民活动,是明王朝建立初年大力推行和奖励屯田垦荒政策的直接表现;山西是明初移民的主要迁出地,但移民并不是只移大槐树下的洪洞县人,而是将山西各个地方的人都集中在这里,然后再迁往全国各地;"大槐树移民"有利于明初农业生产的恢复与发展,在我国人口史和社会发展史上具有深远的意义和影响.     

Parental perceptions of life context variables for involvement in their young children's education

The purpose of this study was to discover Turkish parents’ perceptions of life context variables, including personal knowledge and skills and personal time and energy for involvement activities in their young children's education. The scales used in this study were based on parents’ self-report, and included: (1) Parental Perceptions of Personal Knowledge and Skills for Involvement Activities and (2) Parental Perceptions of Personal Time and Energy for Involvement Activities. Moreover, a demographic survey was developed and used as the second instrument in this study. The results suggested that parents as a group tend to have positive perceptions of life context variables for involvement in their young children's education and their income is the strongest predictor of these perceptions.     

Literacy as a social practice in the early years and the effects of the arts: a case study

Literacy as a social practice has a fundamental role in children’s lives especially in the early years context, in which social interactions are in the centre of knowledge achievement. Several pieces of research investigate the positive contribution of the arts in children’s literacy development in the early years settings. However, most of them focus on the aspect of emergent literacy and phonological awareness, with some indirect arguments about literacy as a social practice. Having this in mind and the importance of literacy as a social practice, this project was designed. The purpose of this paper is to examine the effects of the arts in the development of literacy as a social practice in the early years settings. The intervention used the ‘Play and Learn through the Arts’ (PLA) programme for a full school year in a case study with 5–6-year-old children in Greece. The outcomes were measured using authentic assessment techniques and a semi-structure interview. The findings showed the positive contribution of the arts in the development of literacy as a social practice in the early years setting.     

Rural classroom environments as contexts for teacher-child relationships

The authors examined the associations between observed classroom management and teacher-child relationships with individual children during kindergarten and Grade 1. We used a sample of nonstruggling and struggling readers and their teachers in rural schools in the Southeastern United States to examine whether gender and struggling reader status explained associations between classroom management and conflictual or close teacher-child relationships. After controlling for child- and teacher-level characteristics, results from multilevel model analyses indicated that stronger classroom management was significantly related to less teacher-rated conflict, but was not related to teacher-rated closeness. Gender was a significant moderator, with boys who were in classrooms with lower levels of classroom management having poorer teacher-child relationships as rated by their teachers. Struggling reader status was not a significant moderator of the association between classroom management and teacher-child relationships.     

论蒙古族早期创世说中的生态观

世界是由物质组成的还是意识或上帝的创造物,这一哲学基本问题是贯穿整个人类认识史并争论极为激烈的问题。针对这一问题蒙古先民们也进行过反思并得出截然相反的两种观点:一种观点认为世界是由物质组成的;另一种观点便是创世说,认为世界是“腾格里”(天)或“布儿罕”(佛祖)创造的产物。这种观点主要集中在早期蒙古的神话故事、英雄史诗、图腾崇拜和萨满教当中。我们应发现其中的合理成份并使其运用或服务于今天人们的社会-生态实践活动,以达到古为今用的目的。     

What troubles early childhood educators in New Zealand: a 20-year cross-sectional study of ethical difficulties in early childhood practice

For more than 20 years, the New Zealand early childhood (EC) sector has had guidance about how to deal with situations of ethical difficulty in daily practice through the ECE Code of Ethics. This paper reports on three surveys undertaken at 10-year intervals that sought to understand EC educators’ experiences of such situations, and how they addressed them within their EC settings. An analysis of educators’ stories of ethically troubling situations from the three data-sets traced shifts and similarities in the content reported, and in how educators responded to these challenges over the two-decade period. We situate this analysis alongside changes in the New Zealand ECE policy context during the same time frame. We argue that a connection exists between the reported situations and teachers’ responses to them, and changes within the policy and professional context of daily EC practice.     

关于洛南猿人生活时代研究的回顾与展望

洛南猿人自1977年被发现以来,我国学术界对其生活时代的认定,存在着三种相差十分悬殊的观点,即:距今100万年以上;距今50万年左右;距今30多万年以内。本文认为这是不正常的现象,因此,呼吁学术界有关专家组成“合议庭”对此悬案进行“终审”。     

The Anthropology of Meaning

Meaning is one of the recent terms which have gained great currency in mathematics education. It is generally used as a correlate of individuals' intentions and considered a central element in contemporary accounts of knowledge formation. One important question that arises in this context is the following: if, in one way or another, knowledge rests on the intrinsically subjective intentions and deeds of the individual, how can the objectivity of conceptual mathematical entities be guaranteed? In the first part of this paper, both Peirce's and Husserl's theories of meaning are discussed in light of the aforementioned question. I examine their attempts to reconcile the subjective dimension of knowing with the alleged transcendental nature of mathematical objects. I argue that transcendentalism, either in Peirce's or Husserl's theory of meaning, leads to an irresolvable tension between subject and object. In the final part of the article, I sketch a notion of meaning and conceptual objects based on a semiotic-cultural approach to cognition and knowledge which gives up transcendentalism and instead conveys the notion of contextual objectivity.     

Weighing up the Influence of Context on Judgements of Mathematical Literacy

Mathematical literacy, viewed as a set of ideas involving applications of mathematics to real-world contexts, has recently featured in curricular discussions about the aims for mathematics education. This article explores the effect that differences in the way that a mathematical task is contextualised can have on students’ mathematical arguments and, therefore, on their perceived levels of mathematical literacy. Seventy-two students’ responses to three similar measurement tasks are described according to Kaiser and Willander’s levels of mathematical literacy. The arguments used for assigning each level of mathematical literacy are then investigated for the presence of specific macro- and micro-linguistic features. The context of the task affects what students perceive to be most relevant approaches to use, which are reflected in the arguments they give; this, in turn, affects external judgements of their level of mathematical literacy.