Some Reflections on Motivating Situations and Situational Teaching

Debates about the crisis of school teaching in the Western world have focused more on education as a state of the art and on psychological problems of either teachers or pupils than on situational features which are of importance for teaching and learning situations. In applying K. R. Popper's propensity theory and his idea of situational logic, a preliminary analysis of problem situations is attempted with the aim of identifying biopsychological situational elements in children's preschool life‐conditions that could be simulated at school in their first years thereby enabling them to draw upon already acquired knowledge and skills. Two principal ways of acquiring experience — one instructive, the other selective — are described and discussed in relation to learning, exploration and play. It is argued that, while selection procedures are found in exploration, play and the like, instruction procedures are most often used in teaching situations despite growing evidence that instruction learning is less motivating than learning by action and selection, as various experiences with situational teaching indicate.     

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.     

Learning by Seeing by Doing: Arithmetic Word Problems

"Learning by doing" in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children's ability to "see" significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children's ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children's own word problems; play with dynamically linked representations with attention to children's prior connections; and systematic problem variation based on empirically determined level of difficulty.     

高等数学教学中创设情境的探究

现今大学生普遍认为高等数学难学,学习高等数学的兴趣不高。要改变这一现状就要努力探究如何利用学生已有的认知结构,挖掘数学思想、利用数学史实和知识间的辩证关系、利用具体实例抽象出数学概念,通过在学生认知冲突等方面创设情境,让学生在情境中感性地探索、发现、理解和掌握高等数学的内容、思想和本质。     

Developing Students’ Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the practitioners in the extra-mathematical domain. For students to experience the significance of different scientific practices and cultures for the function and status of mathematical modeling in other sciences, students need to be placed in didactical situations where such differences are exposed and made into explicit objects of their reflections. It can be difficult to create such situations in the teaching of contemporary science in which modeling is part of the culture. In this paper we show how history can serve as a means for students to be engaged in situations in which they can experience and be challenged to reflect upon and criticize, the use of modeling and the significance of the context for the function and status of modeling and models in scientific practices. We present Nicolas Rashevsky’s model of cell division from the 1930s together with a discussion of disagreement between him and some biologists as one such episode from the past. We illustrate how a group of science students at Roskilde University, through their work with this historical case, experienced that different scientific cultures have different opinions of the value of a model as an instrument for gaining scientific knowledge; that the explanatory power of a model is linked not only to the context of its use, but also to the underlying philosophical and theoretical position held by the modeler(s) and the scientists discussing the model and its use. The episode’s potential to challenge students to reflect upon and criticize the modeling process and the function of models in an extra mathematical domain is discussed with respect to the notions of internal and external reflections.     

The role of gestures in the mathematical practices of those who do not see with their eyes

In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the appropriation of practices associated with the sets of artefacts that have historically come to represent the body of knowledge we call mathematics. This process of appropriation involves a coordination of a variety of the semiotic resources??spoken and written languages, mathematical representation systems, drawings, gestures and the like??through which mathematical objects and relationships might be experienced and expressed. To highlight the connections between perceptual activities and cultural concepts in the meanings associated with this process, we concentrate on learners who do not have access to the visual field. More specifically, we present three examples of gesture use in the practices of blind mathematics students??all involving the exploration of geometrical objects and relationships. On the basis of our analysis of these examples, we argue that gestures are illustrative of imagined reenactions of previously experienced activities and that they emerge in instructional situations as embodied abstractions, serving a central role in the sense-making practices associated with the appropriation of mathematical meanings.     

Guided Play: Where Curricular Goals Meet a Playful Pedagogy

Decades of research demonstrate that a strong curricular approach to preschool education is important for later developmental outcomes. Although these findings have often been used to support the implementation of educational programs based on direct instruction, we argue that guided play approaches can be equally effective at delivering content and are more developmentally appropriate in their focus on child‐centered exploration. Guided play lies midway between direct instruction and free play, presenting a learning goal, and scaffolding the environment while allowing children to maintain a large degree of control over their learning. The evidence suggests that such approaches often outperform direct‐instruction approaches in encouraging a variety of positive academic outcomes. We argue that guided play approaches are effective because they create learning situations that encourage children to become active and engaged partners in the learning process.     

房地产行业融资方式研究

在房地产的发展过程中,资金扮演着重要的角色。本文从我国的国情出发,并借鉴了各国房地产企业融资的经验,首先介绍了我国房地产企业在融资方面的发展状况以及基本的融资理论,然后对企业的融资手段一上市、房地产基金、债券等做了完整的介绍和阐述。并具体分析了各种融资手段的利弊及可操作性。     

Secondary School Students’ Construction and Use of Mathematical Models in Solving Word Problems

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15–16 years old). Four levels of the development of constructing and using mathematical models were identified using a constant-comparative methodology to analyse the student’s problem-solving processes. Identifying the general in the particular and using the particular to endow the general with meaning were the key elements employed by students in the processes of construction and use of models in the different situations. In addition, attention was paid to the difficulties that students had in using their mathematical knowledge to solve these situations. Finally, implications are provided for drawing upon student’s use of mathematical models as conceptual tools to support the development of mathematical competence from socio-cultural perspectives of learning.     

Taking Shape: Supporting Preschoolers' Acquisition of Geometric Knowledge Through Guided Play

Shape knowledge, a key aspect of school readiness, is part of early mathematical learning. Variations in how children are exposed to shapes may affect the pace of their learning and the nature of their shape knowledge. Building on evidence suggesting that child‐centered, playful learning programs facilitate learning more than other methods, 4‐ to 5‐year‐old children (N = 70) were taught the properties of four geometric shapes using guided play, free play, or didactic instruction. Results revealed that children taught shapes in the guided play condition showed improved shape knowledge compared to the other groups, an effect that was still evident after 1 week. Findings suggest that scaffolding techniques that heighten engagement, direct exploration, and facilitate “sense‐making,” such as guided play, undergird shape learning.     

大学生数学应用能力的培养和探索

首先论述了培养大学生数学应用能力的重要性和迫切性,然后对现阶段大学数学应用能力培养的现状和原因进行了分析,最后指出开展数学建模活动和开设数学实验课程是培养大学生数学应用能力的有效途径。     

Word problems and mathematical reasoning-A study of children''s mastery of reference and meaning in textual realities

The mastery of word problems is seen as an important test of mathematical ability. When solving such problems, students supposedly go beyond rote learning and mechanical exercises to apply their knowledge to realistic problem situations in which mathematical reasoning becomes an important instrument for making concrete judgements. Research shows that performance on word problems is often surprisingly poor. Non-realistic, and even logically inconsistent, answers to word problems are often accepted by students, and there are many signs that students seldom make so-called realistic considerations when applying their mathematical knowledge to real world events. The study reported is a follow-up of the work by Verschaffel, De Corte, and Lasure (1994) in which the difficulties students have in making realistic considerations were clearly illustrated. In the present study, students (10–12 years of age) worked in groups, and the tasks given (estimating distances) were introduced as part of a general discussion of how to calculate distances to school. Results show that the participants were clearly able to entertain different assumptions regarding how to measure distances, and they make distinctions between alternative options when discussing, for instance, the distance between two villages as indicated on a road sign on the one hand, and when talking about the shortest possible distance on the other. It is argued that the problem of what constitutes a realistic consideration when solving word problems is far from simple but has to be understood in context.     

基于五环节教学的体育微课设计模式探讨

五环节教学模式,即“问题激活”“自主探究”“尝试应用”“分组展示”“改进与完善”。基于五环节教学模式的体育微课以“解决体育问题”为核心设计教学内容,将运动知识、技能的掌握过程呈现在不同的问题情境中,并在问题情境中突出五环节,从而增强体育教学的可操作性。     

Squishing Circuits: Circuitry Learning with Electronics and Playdough in Early Childhood

While circuitry lessons have traditionally been first introduced in late elementary school, they remain challenging conceptually for undergraduates in physics and engineering courses. Seeking to provide a higher quality and earlier introduction to circuitry learning for young children (ages 3–5), this paper investigates the affordances of utilizing the Squishy Circuits toolkit, a circuitry kit that combines circuit components and playdough, as a first introduction. Our study engaged 45 children across three nursery school classrooms in open-ended play with Squishy Circuits toolkits for seven sessions over a period of 2 weeks. Here, we focus on six children in one focal classroom in order to illustrate the concepts that children are developing during play and open exploration with the kits and a range of crafting materials. Findings indicated that the Squishy Circuits toolkit enabled children to explore concepts important to circuitry learning, including current flow, polarity, and connections. Additionally, analysis of whole class conversations before and after the circuitry explorations indicated significant gains in children’s ability to discuss circuitry concepts over the course of the study. Through individual case studies, we illustrate how children enacted these concepts through their play and how the transparency afforded by the toolkit make the big ideas of circuitry visible. This work serves to illustrate how very young children can successfully begin to engage with science topics commonly introduced in later elementary school when those topics are framed through play and discovery with transparent and malleable materials.

     

Type A behavior in preschool children

Type A behaviors were observed in a group of 48 preschool children in different free-play and competitive situations. Interrater reliability was assessed on the Matthews Youth Test for Health (MYTH), and the children's and their parents' type A scores were compared. Scores on the MYTH were used to classify children as either type A or type B. Comparisons were made between type A and type B children's play in classroom and in laboratory situations. For the laboratory situations, 24 same-sex type A-type B dyads were formed, and the dyads were observed in free play, followed by car racing, by a tower-building contest, and by an interview. Type A children more frequently showed annoyed facial expressions, gross motor activity, interruptions during classroom free play, and gross motor activity and aggressive play with an inflatable Bobo doll during the laboratory free-play situation. Type A children more often won the car race and the tower-building contest, and they answered a greater number of questions and more frequently answered first during the interviews. These data are consistent with other findings on type A behavior in preschool children and suggest that the behavioral dimensions of type A (competitiveness and impatience-aggression) may emerge as early as the preschool years, particularly in competitive situations.     

小学数学应用题教学的基本策略

小学阶段的数学学习仍然处于启蒙阶段,这一时期要培养起学生对数学学习的兴趣,尤其是与我们日常生活联系密切的应用题教学。教师要善于利用有效的教学策略来培养学生对应用题知识的学习兴趣,引导学生发觉解答应用题的乐趣,让学生充分发挥自身主观能动性,对应用题展开深入的思考和探索,在积极探索的过程中,发展学生的数学思维能力和自主学习能力,为学生未来深度学习数学知识打下坚实的基础。     

数学探究课堂教学个案研究--兼谈教师的适应与挑战

数学探究课如何组织 ,许多教师感到困难和困惑 ,以“四边形的内角和”的探究教学为案例进行评析。教师应有宽厚扎实的数学功底 ,具备能创设问题情景、能在教学中搭适当的“脚手架”的技术 ;树立“以学生发展为本”和“学生参与”的教学观念 ,具有能进行灵活的教学设计和加工、采用对话与交往的形式进行教学的技能 ,把握“讲授”与“探究”的适度平衡。     

The World According to Johnny; A Coping Perspective in Mathematics Education

Students in mathematical problem-solving situations often experience confusion and loss of meaning. In these situations, affective and social factors are as much part of the student's thinking and behavior as are cognitive factors. These additional factors might include, for example, the need to make sense and the need to meet expectations of the authority figure involved (e.g., teacher or researcher). In this paper we attempt to analyze students' productions, taking into account such additional affective and social factors. To this end, we have tried to reproduce the student's voice in what we call virtual monologue. It consists of a monologue in the student's voice given in first person language, in which we try to describe as vividly and as faithfully as we can our picture of what might be going on in the student's mind during such situations.     

"嵌入式系统"开放实验室建设与实践

针对当前嵌入式人才培养过程中存在的重理论轻实践问题,介绍了我校嵌入式系统开放实验室2007年以来的实践教学经验.对开放过程中的课程内容、教学手段、教材建设、以开放实验为基础的大学生科技竞赛等方面进行了探索与实践.开放运行以来所取得的成果表明,开放实验室在培养大学生创新精神和实践能力方面发挥了重要作用.     

Value orientations in relation to mathematical self-esteem: An exploratory study of their role in mathematical achievement among German, Israeli, and Canadian 14-year-olds

The present paper offers an exploration of the role achievement values play in the generation of mathematical achievement as measured in school grades and test scores. Based on a comparative study of 1665 German, Israeli, and Canadian 14-year-olds two hypotheses are tested. First, it is assumed that achievement value preferences have a dual role in the generation of high academic performance. On the one hand, they are assumed to facilitate a high achievement-related self-esteem, which itself is a strong covariate of good academic performance. On the other hand, they are expected to sensitize for achievement pressure from parents, which in turn increases anxiety, and henceforth lowers the achievement-related self-esteem. Secondly, it is assumed that one will find cross-cultural variation in the strength of the two postulated effects. The “positive” role of achievement values is assumed to be stronger in cultures with a more positive view on achievement (Canada, Israel), whereas the “negative” role is assumed to be stronger in cultures with a less positive view on achievement (Germany). Hypotheses were tested in a structural equation modeling frame, and are essentially confirmed. Effect sizes are, however, low, and confirmation pertains almost exclusively to grades, not to test scores as measures of mathematical abilities.