Cognitive style and mathematics anxiety among high school students

The recent concern over declining mathematics achievement test scores has drawn attention to mathematics anxiety. One possible cause of the development of mathematics anxiety is cognitive learning style. The authors investigated the association of field dependent/independent cognitive style with mathematics anxiety. A three-way analysis of variance (cognitive style by achievement level by sex) was performed on math anxiety scores of 481 secondary students. Findings indicated that field dependent learners experienced more mathematics anxiety than did field independent learners. Interactions between sex and cognitive style and between achievement level and cognitive style also were significant. Implications for instruction and for future research are discussed.     

Emerging Trends in Mathematics Education for People with Down Syndrome: Current Research and Future Directions

ABSTRACT

In September 2017, a group of researchers met for the first conference devoted to the singular purpose of exploring a neglected field – the learning of mathematics by individuals with Down syndrome. This special issue is a result of that first meeting and identifies three emerging trends in the mathematics education of learners with Down syndrome: the goals, content, and pedagogy. Education is central to the goal of improving an individual’s quality of life and only recently has the impact of mathematics been fully comprehended. Many researchers continue to explore the development of the concept of number and there is still much to learn. As a new development, we see that interest is now expanding to explore other areas of mathematics. We still have a long way to go to understand how best to open the doors of mathematics to all learners with Down syndrome. We conclude by offering six areas requiring immediate future research in the field of mathematics and Down syndrome.     

Rethinking Learner-Centred Education: Bridging Knowledge Cultures

Abstract

This article argues that learner-centred education needs to shift from a discussion only on pedagogical activities such as group-work and other cooperative learning strategies. It suggests that the focus of learner-centred education should be on the cultural world of the African child and how this influences the way in which he/she learns Western science. The African child often experiences cognitive dissonance/perturbation when learning Western science. The article draws on insights from the theory of collateral learning which was originally developed by Jegede. It argues that unless policymakers and teachers take into consideration the cultural frameworks of learners, there will not be a sound basis for improving school science and school mathematics in South Africa. Spending more on resources and increasingly testing learners, as is currently done in South Africa, will not improve school science in South Africa. Improving school science in part depends on rethinking leaner-centred education, which means critically looking at the important role that cultural frameworks of learners play in learning Western science.     

Prospective elementary teachers’ aesthetic experience and relationships to mathematics

Previous research has adopted various approaches to examining teachers’ and students’ relationships to mathematics. The current study extended this line of research and investigated six prospective elementary school teachers’ experiences in mathematics and how they saw themselves as learners of mathematics. One-on-one interviews with the participants were conducted, and their written reflections were collected. A grounded-theory approach and a framework for analyzing mathematics identities were adopted in data analysis. The findings showed that the participants’ development of obligations-to-oneself was associated with not only their opportunity to exercise conceptual agency but also their aesthetic experience with mathematics. Their views on themselves as learners of mathematics had cognitive, affective, and aesthetic dimensions. The findings suggest that teachers and students can engage in a reflection on their aesthetic involvement in doing mathematics. There is a need for a local theory of aesthetics in K-12 mathematics.     

The effect of a pre-university mathematics bridging course on adult learners’ self-efficacy and retention rates in STEM subjects

In August 2008, the Mathematics Learning Centre at the University of Limerick initiated a mathematics bridging course, entitled ‘Head Start Maths’, to provide mathematics revision for adult learners about to embark on science or technology degree programmes. The aim of Head Start Maths was to revise mathematics fundamentals before the commencement of third-level education so as to lessen the anxiety levels of adult learners towards mathematics. Negative preconceptions have been noted as being of major concern with adult learners, both preconceptions of mathematics in general and also of their own abilities. In addition to this, it was hoped that Head Start Maths might lead to increased retention rates among adult learners and lead to less dropouts within the first semester. Results found that there were statistically significant increases in self-efficacy scores across some, but not all, of the mathematical topic areas and that there was an increase in the retention rates of adult learners who participated in Head Start Maths compared to those who did not.     

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.

     

基于认知诊断的英语阅读研究述评

认知诊断是在现代认知心理学和心理测量学、现代统计数学以及计算机科学基础上发展起来的一种新的诊断技术。它能够科学地描述测试中所包含的认知属性,准确地诊断学习者的语言技能结构,促进个性化的语言教学,因而在英语教育领域,尤其是英语阅读测试中得到了广泛应用,并引起了国内外学者的关注。本文从认知诊断研究的发展、理论基础、在英语阅读测试中的应用、现有研究的难点和不足等方面对认知诊断进行了综述,以期促进认知诊断在英语教学中的应用。     

从高等代数教学改革实践谈高师数学教学改革

目前,义务教育数学课程正在进行深刻地变革,作为为义务教育培养合格数学师资的高师数学教育也应顺应时代发展,开展教学改革的探索与实践。以高等代数课程教学改革的实践为例,以培养学习者的数学素质为目标,探索高师数学教学改革模式,以期提升人才培养规格。     

远程在场的知识延展与存在收缩——对在线教育的存在论阐释

随着通信技术的发展与教育现代化进程的推进,在线教育得到了广泛的应用。以存在论视角对在线教育进行分析可以发现,在线教育虽然为教育提供了远程在场与知识延展的手段支撑,但同时也面临学生存在空间收缩的危机。远程在场使知识得以延展的同时易出现知识内化片面且断裂的现象;界面化与符号化使知识跨地域传输的同时易导致学生学习成为一种脱节于真实经验与应用的存储。溯其原因在于远程在场存在收缩而导致的学生认知局限,身体缺席而导致的学生主体冲突,技术呈现中的情境残缺而导致的学生片面发展。因此,在线教育应重述“在场”的意义,区分现实与虚拟的课堂,明确虚拟是现实教学的辅助,以真实经验引领虚拟感知。     

School mathematics in the era of globalization

This essay reviews the principles motivating contemporarycritical mathematics discourses. Drawing from varied critical discourses including ethno-mathematics, critical theory, post-structural theory, and situated and ecological cognition, the essay examines the pragmatics of critiques to the privileged role of school mathematics in the era of globalization. Critiques of modern school curricula argue that globalization practices linking education to technological and economic development are increasing, and the curriculum is being re-defined through discourses of privatization, national standards, and global competitiveness. Globalization has reinforced the utilitarian approach to school mathematics and the Western bias in the prevailing mathematics curricula, as well as helped to globalize pervasive mathematical ideologies. In most instances, a newfound status that mathematics is enjoying in this era of globalization is not well deserved, as school mathematics can no longer be considered culturally, socially, politically, nor economically neutral. In particular, school mathematics is increasingly critiqued as a cultural homogenizing force, a critical filter for status, a perpetuator of mistaken illusions of certainty, and an instrument of power. With such concerns it is becoming more evident that mathematics learning and education have implications for building just and democratic societies. As an African female scholar who is now living in Canada, I reflect on what the critical stance might mean for contexts with which I am familiar. I discuss the challenges of school mathematics with a view to improving curriculum and pedagogy so as to raise the awareness of teachers and learners to the questionable assumptions from which mathematics derives its prestige. The mathematics curriculum is central to cultivating values as well as fostering the conscientization of learners.     

The Future of the Discipline? Mathematics and the <Emphasis Type="Italic">Undergraduate Ambassadors Scheme</Emphasis>

The crisis in UK mathematics education, both in schools and universities, has been widely reported. Currently, 24% of full-time mathematics teachers in English secondary education have `weak’ or `nil’ qualifications in the subject, 31% of secondary mathematics teachers are now over the age of 50, and it is estimated that England alone is short of 3500 qualified mathematics teachers. Furthermore, studies suggest that UK mathematics undergraduates often lack confidence in several key skills essential for teaching, and the availability of attractive careers for mathematics graduates impacts upon the numbers entering the profession, thus risking a spiral of decline. This paper recounts the development of a unit of study in the Faculty of Mathematical Studies at the University of Southampton, England, in conjunction with a new national initiative entitled the Undergraduate Ambassadors Scheme (UAS). This aims to address the crisis in UK mathematics education through the training and placement of final year undergraduates as teaching assistants in local schools, with a view to promoting mathematics as a university choice to the broadest possible constituency, whilst simultaneously developing those key skills in which undergraduates regularly feel least confident, and facilitating an insight into teaching as a career option. The paper also provides a detailed evaluation of this new initiative, together with the recent comments of students who, having completed the UAS unit, have progressed subsequently to postgraduate teacher education.     

Mathematics professional development for elementary teachers: Building trust within a school-based mathematics education community

Despite increased attention in professional development to building communities of teachers, few studies have investigated the development of trust in these communities. This paper presents issues related to trust in a professional development project at an elementary school. The project aimed for school-based elementary teachers and university-based mathematics educators to work together to improve mathematics instruction at the school by developing a mathematics education community of learners, where learners were conceived of as both the teachers and the mathematics educators. This paper addresses the following question: What factors in the project supported the development of trust among mathematics educators and teachers as the community was formed? More specifically, the paper is about one aspect of trust, namely, building school-based elementary teachers’ trust in the university-based mathematics educators. We point to three factors that helped the development of trust and we use care theory to further understand and discuss these factors in the context of in-service teacher education initiatives.     

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.     

Is There a Role for Executive Functions in the Development of Mathematics Ability?

ABSTRACT— This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based approaches to understanding the ways in which children become proficient in mathematics. Task analysis indicates that executive cognitive functions likely operate in concert with procedural and conceptual knowledge and in some instances might act as a unique influence on mathematics problem-solving ability. It is concluded that consideration of the executive cognitive demand of mathematics can contribute to research on best practices in mathematics education.     

高效率数学教学方法的实践与思考

高效率数学教学方法能够促进数学学习者始终保持浓厚的数学学习兴趣、数学认知成绩好并维持在稳定状态.认为:其教学模式是以多元化、多层面为指导思想,全面实施人性化的民主讨论方法.具体表现为:数学课堂教学的师生积极互动与共同发展,它既能保持学生创造性思维的独立性和自主性,又能平等协商与合作交流,从而感悟数学是做出来的.只有这样,才能让数学学习者感受和体验数学问题的产生、发现、应用过程,并从亲身经历中,再次体悟到数学学习是一个艰辛的再创造再发现的过程.     

关于英语专业蒙古族学习者英语学习策略的研究

随着我国民族高等教育的发展,少数民族英语学习者学习策略的研究受到越来越多的外语教育者的关注。笔者从学生不同阶段策略使用的差异性、考试成绩与策略使用的差异性等几个方面进行了分析描述,得出结论：策略使用频率由高到低为：认知策略（元认知策略（记忆策略（社交策略（补偿策略（情感策略;记忆策略和情感策略在不同的学习阶段存在差异,其他策略不存在差异;入学成绩与其学习策略中的认知策略和补偿策略具有相关性。     

基于MQI评估系统的大班数学集体活动质量分析及其启示

数学是学前儿童学习和入学准备的重要领域,也是学前教育质量监测的重要方面。MQI评估系统作为一种评估数学课堂教学质量的框架,体现了最新数学教育观念,突出了数学的学科特性和认知要求,强调儿童的主动参与和生成性的教学过程,可同时对教师的教和儿童的学进行评估。本研究使用MQI评估系统对我国幼儿园大班数学集体活动的质量进行考察,结果表明除数学意义建构和数学语言之外,数学丰富度领域各维度表现水平不高;教师对儿童行为进行处理和反馈的水平较低;大多数活动片段中不存在数学表达和语言上的错误及不严密性问题;儿童参与有意义的解释或者提问和推理较少,参与活动的认知要求不高。幼儿园大班数学集体活动质量受到集体教学中"教"与"学"的关系、教师对数学领域知识和儿童数学发展目标的认知、教师评价儿童数学思维的能力及师幼互动技巧、教师培训与考核的侧重点等因素的影响。我国学前教育界应重视数学教育活动的过程性质量,关注儿童数学学习过程性能力的发展,并应在借鉴MQI评估系统的基础上开发适合我国幼儿园数学教育实践的质量评估系统。     

Simplest Shapes First! But Let's Use Cognitive Science to Reconceive and Specify What “Simple” Means

Children's informal and formal learning experiences with geometric shapes currently result in misconceptions that persist into adulthood. Here, we combine research from mathematics education as well as cognitive science pertaining to concepts, categories, and learning strategies to propose a more optimal progression that is better specified and justified than the current standards. To do so, we reframed what constitutes a “simple” shape from perceptual simplicity to simplicity of properties. Our Property-Based Shape Sequence uses property-based criteria of what makes shapes “simple” and progresses in a way that affords opportunities for learners to develop hierarchical conceptions of two-dimensional and three-dimensional shapes. Our goals are threefold: (1) recommend an optimal, mathematically-correct shape learning sequence, (2) correct misconceptions that adults and children harbor about shapes, and (3) encourage cross-disciplinary collaborations between mathematics education and psychology researchers to validate the proposed learning sequence.     

同伴互评对学习者知识建构过程的实证研究——基于时间序列的认知网络分析

同伴互评能够促进学习者高阶认知能力的发展。文章采用认知网络分析法,以课程进程中四次作业的同伴互评评语为分析对象,从时间序列视角探索同伴互评对学习者知识建构的过程影响与差异影响,剖析出在高校课程教育中"以评促学"的作用机理。研究发现:同伴互评能有效提高学习者深层次的知识建构,帮助学习者在更高阶认知结构上进行知识构建;在同伴互评策略支持下,高、低元认知自我调节能力水平学习者与整体学习者的知识建构过程趋同,即都经历了从浅层学习到深度学习的发展过程;但是,对于高水平元认知自我调节能力组学习者而言,同伴互评在提升学习者认知结构的综合性和深层次的建构方面,有更加明显的作用。     

Those who can, teach: addressing the crisis in mathematics in UK schools and universities

The crisis in UK mathematics education, both in schools and universities, has been widely reported in the national media. A recent study shows that 26% of full-time mathematics teachers in UK schools have no qualification in the subject, and that 31% of all UK schools' mathematics teachers are now over the age of 50. The crisis in school mathematics has impacted on much of the university sector, with some departments under threat of closure and widespread difficulties experienced in student recruitment. The availability of attractive careers for mathematics graduates impacts upon the numbers choosing to enter teaching, thus risking a spiral of decline. Furthermore, studies suggest that UK mathematics graduates often lack confidence in several key skills essential for teaching, such as presenting information effectively, working in teams, and written communication. This paper recounts the development of a unit of study in the Faculty of Mathematical Studies at the University of Southampton, England, in conjunction with a new initiative, the Undergraduate Ambassadors Scheme, which seek to address the crisis in UK mathematics education through the training and placement of final year undergraduates as teaching assistants in local schools. This with a view to promoting mathematics to the broadest possible constituency as a university choice, whilst simultaneously developing those key transferable skills in which undergraduates regularly feel least confident, and allowing undergraduates to experience a flavour of teaching as a career option.