The Illusion of Linearity: Expanding the evidence towards probabilistic reasoning

Previous research has shown that – due to the extensive attention spent to proportional reasoning in mathematics education – many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the ‘illusion of linearity’. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. In this article, the empirical evidence for this phenomenon is expanded to the domain of probabilistic reasoning. First, we elaborate on the notion of chance and provide some reasons for expecting the over generalization of linear models in the domain of probability too. Afterwards, a number of well-known and less-known probabilistic misconceptions are described and analysed, showing that they have one remarkable characteristic in common: they can be interpreted in terms oft he improper application of linear relations. Finally, we report on an empirical investigation aimed at identifying the ability of 10^th and12^th grade students to compare the probabilities of two binomial chance situations. It appears that before instruction in probability, students have a good capability of comparing two events qualitatively, but at the same time they incorrectly quantify this qualitative insight as if the variables in the problem were linked by a linear relationship. Remarkably, these errors persist after instruction in probability. The potential of this study for improving the teaching and learning of probability, as well as suggestions for further research, are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Students and school characteristics related to elementary school students' views of the nature of science

The purpose of this study is to investigate student- and school-level factors that help to explain the difference in the nature of science (NOS) views. Overall, the design of this study is correlational. The sample consisted of 3062 students enrolled in the sixth, seventh, and eighth grades of elementary schools in Turkey. A hierarchical linear modelling was selected as a modelling technique. This study has established the importance of the student's socioeconomic background, learning approaches undertaken, self-efficacy, and motivational goals in the formation of their NOS views. The findings reveal that quality of both the physical infrastructure of schools and the educational resources in schools, parent educational levels, student achievement, self-efficacy, experience of meaningful learning, and learning goal orientation are positively related to different dimensions of student NOS views. Additionally, performance goal orientation and rote learning approaches have a negative relationship with different dimensions of student NOS views.     

Inclusion in action: an in-depth case study of an effective inclusive secondary school in the south-west of England

This paper represents the outcomes of an in-depth case study of a secondary school in the south-west of England, identified as inclusive by the local education authority (LEA). The study, which formed the second part of a ‘bricolage’ approach, utilized ethnographic research methods, with the aim of investigating inclusion in a holistic way, at the school level. Data were collected through interviewing of a variety of school constituencies and participant observation. The analysis suggested that: (a) the participants were enculturated into the integration model; (b) although there were strong perceived academic benefits for the included students, the evidence is contradictory regarding the social outcomes of inclusion; (c) successful implementation of inclusion requires restructuring of the physical environment, resources, organizational changes and instructional adaptations; and (d) there was a perceived need for ongoing professional development. The findings reported in this investigation may be used to illuminate current practice in the LEA and to provide directions for formulating policies to support ‘inclusive practice’ in ways which are acceptable to teachers, parents and students.     

Turkish grade 10 students' and science teachers' conceptions of nature of science: A national study

This study aimed to assess grade 10 Turkish students' and science teachers' conceptions of nature of science (NOS) and whether these conceptions were related to selected variables. These variables included participants' gender, geographical region, and the socioeconomic status (SES) of their city and region; teacher disciplinary background, years of teaching experience, graduate degree, and type of teacher training program; and student household SES and parents' educational level. A stratified sampling approach was used to generate a representative national sample comprising 2,087 students and 378 science teachers. After establishing their validity in the Turkish context, participants were administered a questionnaire comprising 14 modified “Views on Science‐Technology‐Society” (VOSTS) items to assess their views of certain aspects of NOS. A total of 2,020 students (97%) and 362 teachers (96%) completed the questionnaire. Participant responses were categorized as “naïve,” “have merit,” or “informed,” and the frequency distributions for these responses were compared for various groupings of participants. The majority of participants held naïve views of a majority of the target NOS aspects. Teacher views were mostly similar to those of their students. Teacher and student views of some NOS aspects were related to some of the target variables. These included teacher graduate degree and geographical region, and student household SES, parent education, and SES of their city and geographical region. The relationship between student NOS views and enhanced economic and educational capitals of their households, as well as the SES status of their cities and geographical regions point to significant cultural (specifically Western) and intellectual underpinnings of understandings about NOS. © 2008 Wiley Periodicals, Inc. J Res Sci Teach 45: 1083–1112, 2008     

History,identity, and the school curriculum in Northern Ireland: an empirical study of secondary students' ideas and perspectives

This study reports results of an empirical investigation of secondary students' conceptions of history and identity in Northern Ireland. Interviews with 253 students from a variety of backgrounds indicate that they initially identify with a wide range of historical themes, but that these identifications narrow as they study the required national curriculum during the first 3 years of secondary school. Often, they draw selectively from the formal curriculum in order to support their developing identification with the history of their own political/religious communities. This process is most apparent among boys, at predominantly Protestant schools, and in schools located in areas of conflict. These findings suggest that to address history's role in ongoing community conflict, educators may need to challenge more directly the beliefs and assumptions held by students of varied backgrounds, as well as to provide a clearer alternative to the partisan histories encountered elsewhere.     

中等职业学校的定位与发展:透视供求矛盾中隐含的问题

文章基于文献研究,剖析作为供应方的中等职业学校与作为需求方的企业等用人单位之间的矛盾,即供求错位。通过对这种错位现象的剖析,把握当前中等职业学校发展的问题所在,同时,结合专家学者的研究,对中等职业学校的定位和发展提出一些建议。     

“中国”“美国”“巴西”数学教材“比和比例”内容的比较研究

选取中国、美国、巴西的6年级较主流数学教材,比较教材中“比和比例”的相关章节．3个国家教材的问题定位、认知需求问题的分布和结构均较为相似,组织方式均为螺旋式非线性,很少涉及信息技术运用和数学史情境．对于“比和比例”的内容应从学生数学学习持续发展的角度给予关注．对于教材编写中问题情境的设计,可以适度增加不同主题间数学情境问题所占比重,对于开放式、半开放式问题的设计与相应学段学生心理发展水平和已有知识经验基础相匹配,寻求非数学情境问题类型的多样化．3个国家的数学教材基于熟悉情境的问题比例较高,基于陌生情境的反思式问题占比偏低．     

美国农村中小学校长成长模式的变革及启示

美国农村中小学校长成长的传统模式存在着入选范围的狭窄与高质量人选的日益匮乏及培养中理论与实践相脱节的弊病,职后面临客观环境的巨大压力与专业发展的缺失而导致中途离职现象日益加剧。政府采取了拓宽入选范围、改革培养模式、提高工资福利待遇与社会地位、促进专业的可持续发展、改革评价机制等措施来促进校长成长模式的变革。     

人性之谜的追寻——对纳博科夫和《洛丽塔》两个谜的解释

《洛丽塔》是纳博科夫在企图表现自己“原始幻觉”的欲望下所创造的白日梦或幻想小说。作在作品中力图去追寻人性中的某种状态或某个形象,并欲将其视为是自己的“我”,从而揭示了人性个体所具有的幻想性和异化性。小说以凸现个体生命为指归,对人类深不可测的灵魂和人性之谜作一次大胆而谨慎的探险,“至深呼唤至深”是它的话语动力,对生存,生命的追问是它的基本态势,“始于性而终于爱”是它的精神向度。     

美国中小学理财教育实施路径研究

理财教育是美国学校课程的一项重要内容,文章把美国中小学理财教育的实施路径归纳为立法、理论研究、课程模式、社会组织参与等方面,以期为美国中小学理财教育的后续研究做好铺垫。     

Patterns of students' and teachers' interactions in learning centres: a case study of three teacher leaders in an elementary school

This study investigated the instructional practices of three teacher leaders employed in a diverse, elementary school in the USA. Through extended observations, it was found that learning centres occupied a central role in the organisation and learning in each of the classrooms. Bernstein's theory of classification and framing was used to analyse the patterns of classroom interactions and identify the skills and values from learning centres. This research critically examined the role centres play in developing academic and social skills in learners, including those learners from lower socio-economic backgrounds and English language learners (ELL). Learning centres were constructed on an expectation that learners made self-initiated decisions, collaborated with peers, and contributed to the development of students' academic, linguistic, and social skills in students of colour, students from lower socio-economic class backgrounds, and ELL.     

从中学物理教育探究科学态度及其评价(下)

三、结论与建议 １．主要结论 经过上文实验、分析与对比，可以得出如下结论。 ①《中学生科学态度评价量表》中的各个评价指标得到了我国部分科学教育界人士的认同与支持，符合中国的文化传统和思想认识；而且统计计算过程科学严谨；指标覆盖了态度的三种成分，内容较为完整、丰富，因此在内容效度方面具有一定的有效性。 ②经过样本测试，《中学生科学态度评价量表》与被试的物理考试成绩之间呈现高度正相关，与国外的《科学态度问卷》之间呈现一定的正相关，这进一步说明该量表具有一定的有效性和可靠性。 ③《中学生科学态度评价量表》…     

An explicit and reflective approach to the use of history to promote understanding of the nature of science

Monk and Osborne (Sci Educ 81:405–424, 1997) provide a rigorous justification for why history and philosophy of science should be incorporated as an integral component of instruction and a model for how history of science should be used to promote learning of and about science. In the following essay we critique how history of science is used on this model, and in particular, their advocacy of a direct comparison of students’ conceptions of scientific phenomena with those of past scientists. We propose instead an alternative approach that promotes a more active engagement by inviting students to engage in the sort of reasoning that led past scientists to reach insights about scientific phenomena. As an example we describe in detail two lesson plans taken from an eight-class unit developed with reference to the history of research on sickle-cell anemia. These lessons demonstrate how an open-ended, problem-solving approach can be used to help students deepen their understanding of science. Throughout the unit students are invited to explicitly and reflectively consider the implications of their reasoning about the disease for their understanding of nature of science issues. The essay draws attention to how this alternative approach actually more closely aligns with the constructivist rationale Monk and Osborne have articulated. It concludes with a brief summary of empirical research demonstrating the efficacy of this approach.

概念图在中小学数学教学中的应用

90年代末概念图传入我国,并在教育领域取得一定的成果。从概念图的内涵出发,以概念图在中小学数学教学中应用的意义和策略展开议论。结合前人的研究成果,试图探讨在中小学数学教学中如何通过构建概念图进行有效教学的问题。     

检视我国商业银行存差放大

结合我国10年来存差的变化,从银行自身和其经营环境分析存差的形成,这其中虽有银行主动选择的因素,也有银行在竞争激烈、资金价格不稳定、客户需求多样化状态下被动接受的因素。存差长期放大的结果极易导致商业银行信贷资金供求结构失衡、盈利水平下降、货币政策传导渠道受阻等弊端,因此应强化信贷业务和其他增值服务并重的观念,顺应宏观调控意图来优化信贷结构;努力拓宽银行主动负债渠道;通过改善金融生态来增加有效的信贷供给。     

试析基于教师专业成长的小课题研究——以巴州中小学教师继续教育为例

本文通过对巴州中小学教师的教育科研现状的调查,分析了中小学教师的科研能力、科研需求,结合继续教育对教师专业素养的提升作用,阐述了小课题研究是适合中小学教师进行校本研修的有效形式。     

CET听力比重增加的必然性及其后势分析

全国大学英语等级考试（CET）自1987年正式实施以来,其听力理解部分的题量和分值比例不断增加,结合我国社会发展及英语教学改革的实际来看,这有其必然性;但这种变化趋势对现实的英语教学改革以及学生的能力发展和成长等方面既有积极影响也有消极影响,要辩证看待。     

线束交比的几何意义和三角形面积比方法

本文通过对线束比和三角形面积比方法较为简洁地证明蝴蝶定理的分析,找出了高等几何与初等几何之间的一种联系,为解决一类几何问题提供了有效的方法。     

Academic risk factors and deficits of learned hopelessness: a longitudinal study of Hong Kong secondary school students

The aim of the present study is to explore a causal model of academic achievement and learning‐related personal variables by testing the nature of relationships between learned hopelessness, its risk factors and hopelessness deficits as proposed in major theories in this area. The model investigates affective–motivational characteristics of students such as prior academic failures, academic attributional style, self‐efficacy, thoughts about intelligence, school values, learned hopelessness, self‐esteem, learning strategy effectiveness and academic achievement, and the relationships among them. A sample of 741 Hong Kong secondary students completed a series of scales over a school year. As expected, prior achievement was the best predictor of subsequent achievement. The next best predictors were perceived learning difficulties and learned hopelessness. This in turn leads to disengagement from schooling and students taking on most responsibility for their failing. Recommendations for teachers and schools to ameliorate these beliefs may redress the move towards hopelessness.