数学教育的价值与数学教育改革

历史上每一次重大的数学教育改革 ,无不关涉到数学教育价值的抉择与建构 ;数学教育的“训练价值”与“实用价值”、“知识价值”与“能力价值”一直处在“钟摆”与“嬗变”之中 ;新世纪的数学教育、尤其是数学课程改革 ,应该把握住数学的本质特征和根本特点 ,在提高学生的数学素质 (数学知识、技能和思想、方法 ,数学概括、抽象和推理、证明能力等 )的基础之上 ,促进学生理性和非理性充分、和谐地发展。     

Fluid reasoning,working memory and planning ability in assessment of risk for mathematical difficulties

ABSTRACT

The demands on mathematical problem-solving have increased in almost all school systems internationally and may constitute a barrier for children with special educational needs (SEN). This study explored the role of fluid reasoning (FR), working memory (WM) and complex executive function of planning (EF) in children (N = 62) referred for assessment of SEN, and specifically of risk for mathematical difficulties (MD). Performances on FR, WM and complex EF of planning were used to predict risk for MD. Results showed that planning ability predicted children at risk for MD, beyond FR or WM ability, when comparing with children not at risk for MD. It was concluded that assessing the complex EF of planning in addition to FR and WM ability is crucial in identifying children at risk for MD. The importance of understanding how planning ability affects children’s mathematical problem-solving is discussed, in relation to assessment and teaching practices.     

A structural model of algebra achievement: computational fluency and spatial visualisation as mediators of the effect of working memory on algebra achievement

The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students’ algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT‐M) to determine whether the pattern of relations is similar for different types of higher level maths achievement. Structural equation modelling was used to test the effects of working memory, 3D spatial ability, and computational fluency on both types of higher order maths achievement. Computational fluency had the strongest effect on algebra achievement, with 3D spatial ability and working memory showing moderate effects. In contrast, 3D spatial ability had a stronger effect on SAT‐M scores than did computational fluency. Computational fluency and 3D spatial ability completely mediated the effect of working memory for both algebra and SAT‐M achievement.     

Impacts of the universal primary education policy on educational attainment and private costs in rural Uganda

While some governments in Sub-Saharan Africa have abolished tuition to achieve universal primary education (UPE), few studies have examined the impacts of the UPE policy beyond school enrolment. This study estimates the impact of the UPE policy in Uganda on overall primary education attainments by using data including 940 rural households. We find that UPE has decreased delayed enrolments and increased grade completion rates up to the fifth grade and its effects are especially large among girls in poor households. Yet, schools in Uganda still face further challenges in terms of low internal efficiency and the unequal quality of education.     

Alleviating or exacerbating disadvantage: does school attended mediate the association between family background and educational attainment?

ABSTRACT

Opportunities for social mobility are generated by education systems designed to alleviate the effects of social origin by providing equality of opportunities and resources. The persistence of the strong association between socioeconomic status (SES) and child’s educational achievement and attainment suggests that social origin continues to play an integral role in the educational outcomes of successive generations of Australians. Sociologists draw on a range of theoretical perspectives to explain this association including Bourdieu’s cultural and social capital theories. Using data collected by the Longitudinal Survey of Australian Youth 2009 (LSAY09) project, I examine the associations between student SES, school SES and two outcome variables: Programme for International Student Assessment (PISA) score and university enrolment. The results indicate that low SES students attending high SES schools perform better on PISA tests than low SES students attending low SES schools. After controlling for PISA score, low SES students were less likely than their high SES peers to enrol at university. Furthermore, students attending low SES schools were less likely than their peers attending high SES schools to enrol at university, net of their individual SES and their PISA scores.     

Getting Real: Exploring the perceived disconnect between education theory and practice in teacher education

This article, inspired in part by the Levine report that criticizes teacher education programs in the United States for being out of touch with practices that work in real classrooms, is a self-study that explores the rift between educational theory, particularly theory that pushes for social constructionist, child-centered approaches to teaching, and teaching practices in majority African-American, inner-city schools. The authors conducted this year-long self-study to answer the question: What could the college's education program do to improve preparation for teaching in inner-city schools? Through their year-long collaboration in a middle-school writing classroom in an inner-city charter school, the authors examined what a prospective teacher learned in his education program that helped and hindered him and then explored how the successful approaches he developed as a new teacher could be incorporated into the college's preservice program.     

建构主义与认知主义教育思想的比较研究

当前比较盛行于教育界的建构主义教育思想与传统的认知主义有深刻的渊源关系,两者存在若干共同之处,但作为两种不同的理论,两者更存在很多细微的差异。为了更深入地把握这两种重要的理论,文章主要从知识观、学习观和教学观等方面对这两种理论进行了初步的比较。     

The association between education and society: The educational struggle for Korean identity in Japan 1945–1948

This study attempts to elucidate the idea that education reflects the contemporary social structure. This inference is focused on the educational struggle for Korean identity led by the Korean Federation in Japan (KFJ) during 1945– 1948. The KFJ disseminated the educational movement for Koreans in Japan (Zainichi). The General Head Quarters (GHQ) suppressed Korean identity education (KIE) and tried to disrupt the activities of the KFJ. KIE was identified and destroyed during the HanShin educational struggle as part of the conflict with the GHQ. However, HanShin movement survived to form the basis for the new start of the Korean educational movement in Japan and has served as the cornerstone of KIE. This case elucidates the ways in which education is strongly associated with the social structure and the status quo.     

Developing mathematical thinking in the primary classroom: liberating students and teachers as learners of mathematics

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011–2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. Particular attention is given to the epistemological positioning of the researchers as this influenced both the curriculum design process and also the theoretical framing of the research study which are both described. The project was set up within a design research framework, which aimed to promote classroom-based action research on the part of participants through the course and also research by the university researchers into the process of curriculum development. The research questions focused on the teachers’ confidence, competence, attitudes and beliefs in relation to mathematics and their expectations and experiences of the impact on pupil learning arising from this course. Empirical data were drawn from pre- and post-course surveys, interviews and observations of the discussion forums in the online environment. Findings from this study highlight the way the course had a transformational and emancipatory impact on these teachers. They also highlight ways in which the ‘framing’ of particular aspects of the curriculum had an oppressive impact on learners in the ways that suppressed creativity and limited the exercise of learner autonomy. Furthermore, they highlight the ways in which a number of these teachers had experienced mathematics as a school subject in very negative ways, involving high levels of ‘symbolic violence’ and of being ‘labelled’.     

关于高师数学模型课及其教学的一些思考

讨论了高师开设数学模型课程的意义,明确了数学模型课程的教学侧重点,给出了一些行之有效的教学方法．     

关于大、中、小学持续艺术教育教学的研究

大、中、小学艺术教育衔接出现断流现象的原因可归为规则与条件两个方面。规则原因指的是高师中一些不适应大、中、小学连续发展的规定或不成文的规则,包括入学考试、教学和实习。条件原因指的是组成教学的双方——学生与教师中存在的不适合高校教育与中小学教育有效连接的原因。     

Rethinking assessment and inequality: the production of disparities in attainment in early years education

Despite decades of research and debate, the issue of unequal outcomes continues to be a concern in educational systems worldwide. In England, published data relating to pupils’ attainment across ethnic groups and by class indicators has been used to demonstrate continued inequalities in schools. This article attempts to deconstruct the relationship between assessment results and inequality by questioning the assumption that results only record inequality, rather than being implicated in its production. Interview data related to the case of a statutory teacher assessment system in early years education are used to show how assessment results may be influenced by pressure from external advisors, who only recognise certain patterns of results as intelligible. These recognisable patterns, it is argued, relate to wider discourses of class, race and the ‘inner city’, through which the pupils in these schools are constituted as inevitably low attaining. In addition, monitoring systems based on ‘value added’ methodologies provide an incentive to deflate assessment results in this first year of school. The article concludes that we need to rethink exactly what apparent disparities in assessment results actually represent, particularly given the increasing use of teacher assessment in the school system in England.     

Mathematics anxiety and working memory: Longitudinal associations with mathematical performance in Chinese children

The link between mathematics anxiety and mathematical performance in young children remains inconclusive. The present study examined the longitudinal associations between mathematics anxiety and mathematical performance (calculation and story problem solving) in 246 Chinese children followed from second to third grade. Multiple regression analyses showed that mathematics anxiety made independent contributions to mathematical performance beyond non-verbal intelligence, working memory, number skills, general and test anxieties. However, mathematics anxiety does not affect all children and all kinds of mathematical performance equally. Mathematics anxiety has a more pronounced impact on mathematical problems that require more processing resources, as opposed to simple arithmetic problems and straightforward story problems and children who are higher in working memory are more vulnerable to its deleterious impacts.     

Maxine Greene and the democratic project in education: signposts for the Irish educational system

This paper considers the work of philosopher Maxine Greene as it pertains to the democratic project in education, with a particular focus on the Irish educational context. The author considers the extent to which specific aspects of the educational concerns raised by Greene, with respect to the realisation of the democratic project in the context of post-industrial hi-tech societies, might help to illuminate certain educational challenges that are currently being faced in hi-tech post-modern societies. Greene has been regarded as a luminary in the educational field, both within the United States and beyond. She is principally concerned with espousing a conception of the educational project that allows for the flourishing of human freedom. It is anticipated that aspects of the Irish reality, especially in the wake of the Celtic tiger, might be able to resonate with certain aspects of the concerns raised by Greene.     

论体育教学中师生关系及对学校体育教学的影响

本文采用文献法、问卷调查法、数理统计法等,针对体育教学中师生关系及对学校体育教学的影响,对泉州市3所大学、3所中学和3所小学的300名学生和60名体育教师进行了调查研究。结果表明：体育教学中师生关系总体评价较好;在影响师生关系因素和体育教师的职业认知上体育教师和学生存在差异。建立良好的师生关系是学校体育教学顺利进行的前提。     

Parental aspirations for their children's educational attainment and the realisation of universal primary education (UPE) in Kenya: Evidence from slum and non-slum residences

There is a sound research base attesting to the importance of parental involvement and to the many potential benefits it can offer for children's education. This study sought to examine differences in parental aspirations (as a mechanism of parental involvement in their children's education) for their children's educational attainment between slum and non-slum residing parents in Kenya. The study used cross-sectional household data for a sample of 4065 parents, collected in 2007 by the African Population and Health Research Centre (APHRC) in Nairobi. A multinomial logistic model was used for the analysis to explore the factors determining parental aspirations. The results indicate the following: (i) that parents who live in the slums have lower aspirations for their children's educational attainment when compared to those who live in non-slum areas; (ii) that parents in the slums have aspirations for higher levels of educational attainment for their children than their own levels of education. We conclude that parents in urban Kenya have a strong belief in the education of their children irrespective of their slum or non-slum residence but aspirations are higher in non-slums than in slums.     

高职数学教学中数学文化的融入探索与实践

文章借鉴了一些本科院校开设数学文化课的经验,结合高职院校的实际情况,提出了在开设高职数学课的同时进行数学文化的融入,以及如何在高职数学教学中寻找数学文化的融入点,结合具体实例探索如何挖掘若干数学题材中的文化意义,并将其融入到高职数学教学中去,把传授数学知识和揭示数学文化相结合,从而提升学生的人文素养和创新精神。     

Ethnic composition of the class and educational performance in primary education in The Netherlands

This article examines the effect of the ethnic composition in the school class on school performance in primary education, using COOL 2008 data for The Netherlands. We make an important distinction between the proportion of migrant children and the diversity with regard to the different ethnic groups in a school class. Due to the strong correlation between these 2 variables, we employ a residualized score of diversity on the proportion of migrants. The diversity indicator, which indicates the level of diversity given a particular share of migrant children, is negatively related to reading comprehension in Grade 8. For other grade years, we find little support for negative effects of diversity net of the share of migrants in a class.     

Teaching and learning in the special education setting: agency of the diagnosed child

ABSTRACT

This article is based on an extensive study of teaching-learning processes in special educational settings organised for children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD). There is a general assumption that children’s learning will be supported through placement in a special class with few students and one or more teachers present. The issues explored concern what educational practices unfold in these settings, i.e. what are the children learning, and how do they participate in the activities? The empirical study is based on video-recorded classroom interaction in eight ADHD-classes during a period of seven years, in total about 200 h. The results show that the interactional format dominating is characterised by one teacher instructing one child at a time. These situations usually seem to follow the well-known Initiative-Response-Feedback (I-R-F) structure. The contributions from the children are generally minimal, and there is no indication that the student’s role in such dyads is more active. Thus, there is little evidence that children’s learning will improve and that they become more focussed and assume a more participatory role in the interactional formats offered in special classes. Also, it is not obvious how experiences of this kind will prepare children for a return to regular classroom or develop towards becoming active citizens.     

Basic education as the first stage of lifelong education: Aspects of a working concept for curriculum integration and educational development in third world countries

Present educational systems are inflexible due to their tendency to perpetuate the familiar. They escalate costs, promote institutionalization and have the notion of failure built into the system. Strategies for educational reform include such ideas as Basic Education, Lifelong Education and relating education to production.In 1976 African Ministers of Education expressed belief that Basic Education defined in terms of minimum learning needs is the best means of providing mass education. Complementary systems must be integrated with traditional.Key elements in a strategy oriented to basic needs are participation and integration. A learning-needs approach to curriculum planning should concentrate on e.g., health, food and literacy; implementation requires a new approach in teacher education, content of education and examinations. The further a school is from the capital city the less it can live up to planner's requirements. The official and the actual curriculum in any school need to be integrated. Local skills should develop as an outcome of participation.Hypotheses concerned with a community's organizational infrastructure, its participation in planning, and its rural exodus require research and testing.

---

Zusammenfassung Durch ihre Tendenz, am Gewohnten festzuhalten, sind die heutigen Bildungssysteme unbeweglich. Sie verursachen steigende Kosten, fördern Institutionalisierung und tragen die Vorstellung des Versagens in sich. Zu Strategien für Bildungsreform gehören Konzepte wie Elementarbildung, lebenslanges Lernen und produktionsbezogene Bildung.Im Jahre 1976 sprachen afrikanische Bildungsminister ihre Ansicht aus, dass Elementarbildung — definiert als ein erforderliches Minimum an Lernen — die beste Lösung für Massenbildung darstellt. Komplementäre Systeme müssten mit den traditionellen integriert werden. Schlüsselelemente in einer auf Elementarbedürfnisse abgestellten Strategie sind Teilnahme und Integration. Ein entsprechender Ansatz zur Curriculumplanung sollte sich zum Beispiel auf Gesundheid, Ernährung und Alphabetismus konzentrieren. Die Durchführung dieser Strategie erfordert eine Neu-Orientierung der Lehrerausbildung, Lerninhalte und Prüfungen. Je weiter eine Schule von der Hauptstadt entfernt ist, desto weniger kann sie den Anforderungen der Planer entsprechen. Daher müssen in jeder Schule das offizielle und das tatsächliche Curriculum integriert werden. Örtlich benötigte Fertigkeiten werden sich als Folge aktiver Teilnahme entwickeln.Hypothesen zur organisatorischen Infrastruktur der Gemeinden, zu deren Beteiligung an der Planung und zur Abwanderung aus ländlichen Gegenden sollten durch Forschung und Tests überprüft werden.

---

Résumé Les systèmes éducatifs actuels sont figés du fait de leur tendance à perpétuer une routine familière. Ils deviennent de plus en plus coûteux, incitent à l'institutionalisation et insèrent une notion d'échec dans la structure même de l'éducation. La stratégie des réformes de l'éducation dans chaque pays doit porter sur l'éducation de base, sur l'éducation permanente et sur la relation de l'éducation à la production.En 1976, les ministres africains de l'éducation ont exprimé leurs convictions que l'éducation de base — c'est-à-dire celle qui répond aux besoins minimum d'instruction — est le meilleur moyen d'assurer l'éducation des masses. Les systèmes complémentaires doivent être intégrés aux systèmes traditionnels.Les points-clés d'une stratégie orientée sur les besoins minimum sont la participation et l'intégration. La planification d'un curriculum, pour être adaptée aux besoins essentiels, devrait se concentrer, par exemple, sur la santé, la nourriture et l'alphabétisation; la mise en uvre exige une nouvelle approche de la formation de l'enseignant, des programmes différents et d'autres systèmes de sanction des études. Plus une école est éloignée de la capitale et moins elle peut se hausser au niveau des exigences posées par l'auteur du projet. Quelle que soit l'école, le curriculum officiel et le curriculum réel doivent être intégrés. La participation devrait aider au développement des ressources de l'endroit, des aptitudes humaines et de l'artisanat local.Certaines hypothèses ayant pour objet l'organisation de l'infrastructure d'une communauté, sa participation au planning et son exode rural, demandent à être soumises à des recherches et à des expériences plus approfondies.