数学思维差异的个性化比较

问题解决是具有目的性和一系列认知操作的过程,问题解决者根据面对的问题条件在头脑中进行转化,形成关于问题的内在表征,寻找在问题空间中蕴涵着的中间环节,达到解决问题的目的.在这一过程中转化策略的选择具有明显的个性思维差异,决定策略的主导因素是其数学思维模式.     

民族高校概率论与数理统计教学的探究

概率论的起源与博弈有关,它最近几十年在自然科学和社会科学等方面应用广泛。概率论与数理统计是研究随机现象统计规律性的学科,是我国各类高等学校工科、理科、管理学及经济学等各专业的基础性课程,是学生学习高等数学后的后续课程,学习本课程需要微积分作为基础。概率论与数理统计研究的一些对象带有随机性、不确定性,并且它和实际生活有着紧密的联系,它的理论与方法已广泛应用于自然科学、社会科学、工程建设、军事科学、生物工程和众多经济领域之中,如经济管理、金融工程、保险精算、经济预测等。概率论与数理统计是高校重要的数学基础课之一,本文探讨了民族高校概率论与数理统计这门课程进行分层教学和激发学生学习的主动性方式,并提高了教学质量。     

A study of pupils' conceptions and reasoning in connection with 'microbes', as a contribution to research in biotechnology education

Biotechnology uses genetically modified bacteria or viruses. Students' conceptions about 'microbes' tends to condition their understanding of biotechnology. This study focuses on the reasoning behind their conceptions. It is assumed that students' conceptions are themselves conditioned by the status given to diseases, by a hygiene-oriented culture, by layman's and school knowledge, personal experiences, socio-cultural mediation and linguistic confusions. It is essential to take all these factors into consideration in any project involving biotechnology education.     

Investigating pupils' images of mathematicians

This paper describes a research project that had two goals: (1) to design and develop a tool with which to investigate pupils' images of mathematicians; and (2) to use the device to compare those images held by lower secondary pupils (ages 12–13) in five countries. We report that with small cultural differences certain stereotypical images of mathematicians are common to pupils in all of these countries and these images indicate that for pupils of this age mathematicians and the work that they do are, for all practical purposes, invisible. This revised version was published online in July 2006 with corrections to the Cover Date.     

数学创新教育课堂教学评价初探

对数学创新教育课堂教学评价的价值取向、评价主体、对象、指标体系以及评价的方法、方式等问题进行了探讨。     

Teachers' predictions and pupils' destinies: A West African survey

This article presents a case study of the primary schooling and post-primary careers of a group of West African pupils. Their school performance and later careers were studied in relation to a number of variables, some relating to the school itself, others to background factors. Among the most important of the former were the predictions made by teachers about the pupils' ability to succeed. While teachers' predictions tended to be fairly accurate, they also functioned to some extent as self-fulfilling prophecies. The study shows that socio-economic and cultural variables are as important as school variables in explaining variations in former pupils' geographical location and socio-economic position eight to nine years later. The study has implications in relation to the improvement of the quality of primary education, since out-of-school variables cannot be manipulated through educational policies alone.

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Zusammenfassung In dem vorliegenden Artikel werden Ergebnisse einer westafrikanischen Studie dargestellt, die sich mit dem Schulbesuch und mit der Laufbahn nach abgeschlossenem Schulbesuch beschäftigt. Die Ausbildung der Schüler in zwei senegalischen Dörfern und ihre Laufbahn nach der Ausbildung werden im Verhältnis zu gewissen Schulvariablen und Hintergrundsvariablen studiert. Unter den erstgenannten waren die Voraussagen der Lehrer über die Möglichkeit der Schüler, von einer Klasse in die nächste versetzt zu werden, wichtig. Die Annahmen der Lehrer waren ziemlich sicher, aber sie funktionierten auch in hohem Grade als selbsterfüllende Prognosen. Die Studie zeigt, daß sozioökonomische und kulturelle Variablen genauso aussagekräftig sind wie Schulvariablen, wenn man die Unterschiede in dem geographischen Wohnort und in der sozioökonomischen Position der früheren Schüler acht bis neun Jahre später erklären will. Das hat Implikationen für eine Menge Richtlinien und Vorschläge, die in den letzten Jahren im Hinblick auf die Verbessergung der Qualität der Schule vorgelegt wurden, weil sich die Variablen außerhalb der Schule durch rein bildungspolitische Maßnahmen nicht manipulieren lassen.

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Resumen Este artículo presenta los resultados de un estudio que se ocupa de la enseñanza primarla y de las carreras post-primarias en un grupo de alumnos de Africa Occidental. La formación que recibieron los alumnos en dos pueblos senegaleses y las carreras que hicieron después de la escuela se estudian en cuanto a determinadas variables; relacionadas con la escuela misma y con el medio. Una de las más importantes de la primera catgoría eran las predicciones que los maestros hacían sobre las posibilidades que tendrían los alumnos de pasar al grado superior. las suposiciones de los maestros eran bastante acertadas, pero también funcionaban, en bueno grado, como pronósticos que se cumplirían automáticamente. El estudio demuestra que las variables socioeconómicas y culturales son tan importantes como las variables escolares, si se quieren explicar, ocho u nueve años desputés, las diferencias en localizatión geográfica y posición socioeconómica de los antiguou alumnos. Esto tiene implicaciones en una cantidad de directivas y sugerencias que se presentaron en los ültimos años para mejorar la calidad de la enseñanza primaria, ya que las variables del entorno extra-escolar no pueden manipularse a través de meras medidas de política educacional.

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Résumé Cet article présente une étude de cas en Afrique Occidentale se rapportant à l'enseignement primaire et aux carrières post-primaires, le succès scolaire des élèves ainsi que leurs carrières sont examinés par rapport à des variables scolaires et des variables concernant le milieu de l'élève constituent les variables importantes. Ces prédictions sont pluôt exactes, mais dans une certaine mesure elles relèvent de la prédiction qui s'accomplit automatiquement. L'étude démontre que les variables socio-économiques et culturelles sont aussi importantes que les variables scolaires; elles expliques les variations les variations dans la localisation géographique ainsi que le statut socio-économique de l'élève entre huit ans et neuf ans plus tard. Ceci a des implications pour un grand nombre de suggestions soumises récemment pour améliorer la qualité de l'enseignement primaire primaire étant donné qu'il est impossible de modifier les variables extra-scolaires uniquement à travers la politique de l'éducation.

     

Investigating pupils' questions in the primary classroom

The paper presents the findings of a coding system applied to the questions generated by primary school pupils to a narrative text. The coding schedule proved consistent across university and teacher researchers. The results and discussion centre on the question type and the degree of understanding displayed by pupils. Suggestions are put forward for the use of a community of inquiry approach to question generation as a means of empowering pupils and allowing the speaking and listening requirements of the National Curriculum to be met in a holistic manner.     

数学思想及解题技巧初探

数学是一门运用非常广泛的基础性学科,数学思想是教学精髓所在,在解题教学中应加强数学思想方法的引导渗透,从引导建立直觉认识开始,逐步开启学生的理性认知,培养灵活应用数学思想的素养。教师要根据不同阶段、不同水平层次学生的实际情况,分类分批地渗透数学思想方法。在倡导素质教育的背景下,让学生将数学思想运用于小学习题解题,是培养学生发散性思维的重要环节。据此,建议把全班学生分成若干组,让学习成绩好的学生扮演小老师角色,在课外帮助差生解答疑难问题,可以取得一举两得的效果。     

Creativity and pupils' experience of school

Based on the analysis of interviews with children, this article links what we know about the way in which they learn with their views of creativity. Whilst pupils have a crisp view of the nature of creativity, which links them to well-established philosophical views, this contrasts both with the vaguer notions of the term and with their experience of school.     

Pupils' mathematical performance in grades 3 and 6. A longitudinal study

The main purpose of this study was to analyse how pupils, differing in achievement levels in mathematics, performed operations with numbers and solved mathematical problems. What strategies did they use in different grades when they performed the operations and solved the problems correctly, and what types of errors were involved when they solved an item incorrectly? What types of errors disappear and what types of errors remain at a later grade? Five groups of pupils, comprising a total number of 900, who have shown different developments in mathematical achievement from grades 3 to 6 have been studied. When the pupils solved items correctly they used the same strategies irrespective of their total results. However, when they made errors they used a number of different strategies. The results of this study implicate that it is very essential that the teaching be individualised and built upon how the pupils think when solving mathematical problems.     

小学生语文阅读能力的培养

小学生语文阅读能力对学生语文课的学习有着重要的影响,阅读能力的提高有助于学生理解和巩固学习,有利于提高学生的表达能力与写作能力,对学生语文学习综合能力的提高起着推动的作用。本文主要就小学生语文阅读能力的培养进行分析,提出了快速提高学生阅读能力的策略,希望为促进小学生语文阅读能力的提高提供一些参考。     

Including pupils' faith background in primary religious education

In this article, Julia Ipgrave takes the idea of inclusion beyond the field of special educational needs to incorporate the needs of children with different faith backgrounds in the religious education (RE) class. She recommends that teachers respect the integrity of their pupils' faith backgrounds by making room for the children's own experiences and perspectives on the traditions to which they belong. Suggestions are made as to how to give equal value to the different faith and non‐faith backgrounds of children in Religious Education lessons. As well as feeling valued, pupils also need to feel safe. The article argues that the children's interests are best served, not by avoiding sensitive and controversial areas of religion, but by establishing a framework of openness and respect within which children can express their views with confidence, differences can meet and pupils and teachers listen to and learn from each other.     

A mathematical model of symmetry based on mathematical definition

Tolerance is imperative for seamless integration of CAD/CAM (Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarfy: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis. Project supported by the National Natural Science Foundation of China for Innovation Research Groups(No.60021201) and NSFC(Nos.59705022 & 69973045).     

Exploring pupils' perceptions of teacher racism in their context: A case study of Turkish and Belgian vocational education pupils in a Belgian school

This article employs ethnographic data gathered from one Belgian (Flemish) secondary school to explore the meaning Belgian and Turkish‐speaking minority pupils enrolled in technical and vocational education attach to teacher racism and racial discrimination, and to explore variations between pupils in making claims of teacher racism. A symbolic interactionist framework is employed to explore how pupils define teacher racism and how a particular context and interactions between pupils and teachers informs pupils' perceptions of racism. This article builds on a strong research tradition in British sociology of education on racism and discrimination by focusing the analysis on pupils' perceptions of such incidents and by investigating how racism is experienced by a generally neglected group of Turkish minority pupils in a particular Belgian education context.     

Primary pupils' experiences of different types of grouping in school

There has been little research on pupils' experiences of ability grouping. This study aimed to explore the perceptions of primary‐aged pupils regarding the purpose and practice of within and between class ability grouping; their experiences of those practices; and how their attitudes to school, self‐perceptions and behaviour were affected. The study was undertaken in six primary schools adopting different combinations of grouping practices including streaming, setting, within‐class ability and mixed ability grouping. Six pupils, of high, moderate or low ability, mixed in gender, in each Key Stage 2 class were interviewed in each school. The findings showed that pupils were aware of how and why they were grouped and accepted the rationales provided. Attitudes towards school were not affected by grouping structures, but pupils' awareness of their place in the pecking order and the nature of teasing in the school were, although these were mediated by school ethos factors.     

从一节优秀课谈数学教学中的情感调控

情感，作为人对客观事物的态度，是人的需要和客观事物之间的关系的反映。人的认识活动与人的情感紧密联系，进行情感教学不仅可以促进和补偿学生的智力活动，提高教学质量，而且对培养良好的个性，提高人的素质有着重要的意义。前不久，笔者听了一节数学优秀课《商不变的规律》。这节课之所以成功，其中一个重要原因是教师实施了合理的情感调控，充分发挥了情感信息功能，成功调动了全体学生主动学习的积极性。整节课有矛盾的困扰，有紧张的沉思，有不服气的争辩，更有问题解决后的欢欣，情感的彩带贯穿于教学的始终。数学是一门美感性很强…     

A bridging study analyzing mathematical model construction through a quantities-oriented lens

Educational Studies in Mathematics - Mathematical modelling is endorsed as both a means and an end to learning mathematics. Despite its utility and inclusion as a curricular objective, one of many...