Semiotic systems,culture and early mathematical knowledge / Sistemas semióticos,cultura y conocimiento matemático temprano

Abstract

In this introduction to the issue Semiotic tools in early mathematical knowledge, we offer a theoretical perspective that provides meaning to the different contributions. We begin by reviewing three perspectives bearing an important influence on the study of mathematical development in childhood (the Piagetian, the information processing and the neonativist perspectives). Next, we underscore the need for developmental studies in this domain to consider the semiotic component, and hence the socio-cultural component, in depth. The contributions that form this volume — a theoretical article, five papers and four short reports of empirical studies and a review of an instructional approach — illustrate different ways of including the semiotic component in the study of children’s mathematical knowledge.     

A first grade student’s exploration of variable and variable notation / Una alumna de primer grado explora las variables y su notación

Abstract

This paper presents a case study of a first grade student to illustrate the diversity of her understandings related to variables and variable notation. While prior research has documented secondary school students’ difficulties with variables and variable notation, we identify many productive understandings in this much younger student, leading us to question the prevailing argument that students might have difficulties with variables due mostly to their own limitations. We draw our data from a teaching experiment that explored functional relationships. Individual interviews were carried out with a subset of the students in the experiment prior to, as well as mid-way through and at the end of the experiment. This paper focuses on a set of three interviews with one of the first grade students. We illustrate the shifts that occurred in the student’s understandings about variables and variable notation across as well as within each of the three interviews.     

An analysis of coping profiles and adjustment in persons with rheumatoid arthritis

This study examined dispositional and situative antecedents of vigilant and avoidant coping behavior. Seventy-two subjects were classified in coping style on the basis of their responses to the vigilance and cognitive avoidance scales of the Mainz Coping Inventory (MCI, Krohne, 1989), and alternatively, on their trait anxiety and defensiveness scores (cf. Weinberger, Schwartz, & Davidson, 1979). In a subsequent laboratory task, subjects were exposed to various conditions of predictability of an aversive event. In anticipation of an aversive loud tone, coping behavior was operationally defined as choosing to listen either to a warning channel (i.e., vigilance) or instead to music (i.e., avoidance). Probability of occurrence of a warning signal while listening to the warning channel varied across trials, being either 0%, 33%, 66%, or 100%. Subjects were exposed to each level and were informed about the respective probability in advance. In general, listening to the warning channel increased with an increase in the probability of the warning signal. However, four groups of subjects who differed in their pattern of coping behavior across trials were observed: rigid-avoidant copers (always listening to music), rigid-vigilant copers (always monitoring the warning channel), flexible copers (switching from music to warning channel with increasing probability of warning), and inconsistent copers (vacillating between music and warning channel regardless of probability of warning). Coping style classifications did not show substantial associations with coping behavior. However, subjects demonstrating the inconsistent coping pattern scored high on trait anxiety.     

积极情绪对视觉注意的调节及其机制

在积极心理学思潮的推动下, 已有研究不但发现积极情绪扩展了空间和时间注意范围、增加了注意灵活性, 而且发现在积极情绪下个体对积极刺激表现出了注意偏向。对这些现象, 先前研究主要以积极情绪的扩展与建构理论、情绪信息等价说等理论来加以解释。但这些理论主要从宏观上强调情绪信息对注意加工的启动或积极情绪对注意资源分布的调节, 并不能清楚地揭示积极情绪对注意调节的内在机制。神经生化机制研究发现, 这些现象可能与多巴胺系统对注意控制能力的调节以及积极情绪对初级视觉皮层编码的调节有关。将来研究者可以基于不同的种类的注意选择和注意模型来进一步拓展积极情绪对注意调节的研究, 同时注重对其机制的探讨和理论的整合与创新。