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Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university 在新冠肺炎危机期间,通过改用在线形式来提高数学补救课程的效果:来自德国一所大学的证据
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2021-11-01 DOI: 10.1093/teamat/hrab013
Stefan Büchele;Michael Liebendörfer;Elisa Lankeit
Due to the COVID-19 crisis, many courses have been offered digitally. Using data from n = 1,173 business students participating in a preparatory mathematics course at a German university that covered the same content as in 2018, 2019 and 2020, we examine how students’ participation and the effect of the preparatory course changed. The data show that the participation rate has fallen slightly, but students’ participation is rather similar to preceding years. Interestingly, students have participated more intensively. There are clear signs of dishonesty in the self-test (use of a calculator) and significant changes in predictors of performance. In particular, the effect of students’ engagement in the course on their performance substantially increased. Further, we found a gender gap in performance affecting women. Finally, the data show that digital courses can be as effective as on-campus courses.
由于新冠肺炎危机,许多课程都以数字方式提供。使用来自n=1173名参加德国一所大学数学预科课程的商学院学生的数据,我们研究了学生的参与度和预科课程的效果是如何变化的。数据显示,参与率略有下降,但学生的参与率与前几年相当相似。有趣的是,学生们的参与度更高。自我测试(使用计算器)中有明显的不诚实迹象,表现预测因素也有显著变化。特别是,学生参与课程对他们表现的影响大大增加。此外,我们发现女性在表现方面存在性别差距。最后,数据表明,数字课程可以和校园课程一样有效。
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引用次数: 3
Using peer instruction in an analysis course: a report from the field 在分析课程中使用同伴指导:来自现场的报告
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2021-02-01 DOI: 10.1093/teamat/hraa013
Leander Kempen
This paper is meant to give some kind of manual instruction for the use of audience response systems for performing peer instruction in class. The different aspects one has to take into account when trying to implement this method are presented. In all of the sections, additional links and references are provided. The author reports on and reflects on his individual decisions when conducting peer teaching in an analysis course at the university. Finally, the results of the corresponding evaluation are presented and discussed.
本文旨在为课堂上使用受众反应系统进行同伴教学提供某种手动指导。介绍了在尝试实现这种方法时必须考虑的不同方面。在所有章节中,都提供了额外的链接和参考资料。作者报告并反思了他在大学分析课程中进行同伴教学时的个人决定。最后,给出并讨论了相应的评价结果。
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引用次数: 4
Mathematics support centres’ online presence: provision in Ireland and the UK in 2018 数学支持中心的在线存在:2018年在爱尔兰和英国提供
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2021-02-01 DOI: 10.1093/teamat/hraa010
Ciarán Mac an Bhaird;Peter Mulligan;James O'Malley
Mathematics Support Centres are available in the majority of Higher Education Institutions in Ireland and the UK. Whilst the online presence of these centres appears to be increasing, there is little research to date which considers its breadth or effectiveness. In this paper we consider the results of a survey on the online presence of support centres in Ireland and the UK. We discuss the opportunities that arise from such a presence, the challenges that exist and what the results of the survey mean for individual practitioners and the wider mathematics support community.
爱尔兰和英国的大多数高等教育机构都设有数学支持中心。虽然这些中心的在线存在似乎在增加,但迄今为止,很少有研究考虑其广度或有效性。在本文中,我们考虑了一项关于爱尔兰和英国支持中心在线存在的调查结果。我们讨论了这种存在带来的机遇、存在的挑战以及调查结果对个体从业者和更广泛的数学支持社区意味着什么。
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引用次数: 9
Student attitudes towards linear algebra: an attempt to roll back the fog 学生对线性代数的态度:拨开迷雾的尝试
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2021-02-01 DOI: 10.1093/teamat/hraa012
Barry J Griffiths;Samantha Shionis
In this study, we look at student perceptions of a first course in linear algebra, focusing on two specific aspects. The first is the statement by Carlson that a fog rolls in once abstract notions such as subspaces, span and linear independence are introduced, while the second investigates statements made by several authors regarding the negative emotions that students can experience during the course. An attempt is made to mitigate this through mediation to include a significant number of applications, while continually dwelling on the key concepts of the subject throughout the semester. The results show that students agree with Carlson's statement, with the concept of a subspace causing particular difficulty. However, the research does not reveal the negative emotions alluded to by other researchers. The students note the importance of grasping the key concepts and are strongly in favour of using practical applications to demonstrate the utility of the theory.
在这项研究中,我们观察了学生对线性代数第一门课程的看法,重点关注两个具体方面。第一种是卡尔森的说法,即一旦引入子空间、跨度和线性独立性等抽象概念,就会出现迷雾,而第二种则调查了几位作者关于学生在课程中可能经历的负面情绪的说法。试图通过调解来缓解这种情况,包括大量的应用程序,同时在整个学期中不断深入研究该学科的关键概念。结果表明,学生们同意Carlson的说法,子空间的概念造成了特别的困难。然而,这项研究并没有揭示其他研究人员所暗示的负面情绪。学生们注意到掌握关键概念的重要性,并强烈赞成使用实际应用来证明理论的实用性。
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引用次数: 2
On the classic paradox of infinity and a related function 关于经典的无穷大悖论及其相关函数
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2021-02-01 DOI: 10.1093/teamat/hrab001
Chanakya Wijeratne;Rina Zazkis
In this study we consider a classic paradox of infinity and its variations and suggest how the sources of misleading intuition can be analysed using the concept of uniform convergence of functions. We then examine how six mathematics honour students engage with a variation of the paradox. Despite their advanced mathematical training, the participants experienced considerable difficulty in addressing the presented paradoxical situation. Drawing on data from written responses and individual interviews, we describe the students’ approaches in an attempt to reconcile their intuitive perceptions with their mathematical computations.
在这项研究中,我们考虑了一个经典的无穷大悖论及其变体,并建议如何使用函数一致收敛的概念来分析误导直觉的来源。然后,我们研究了六名数学荣誉学生是如何参与悖论的变体的。尽管他们接受了高级数学训练,但参与者在解决出现的矛盾情况方面遇到了相当大的困难。根据书面回复和个人访谈的数据,我们描述了学生的方法,试图将他们的直觉与数学计算相协调。
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引用次数: 0
Further Mathematics, student choice and transition to university: part 2—non-mathematics STEM degrees 继续数学、学生选择和大学过渡:第二部分——非数学STEM学位
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2021-02-01 DOI: 10.1093/teamat/hrab004
Sofya Lyakhova;Andrew Neate
This is the second paper reporting the results of a study investigating student choices of optional post-16 advanced-level (A-level) Mathematics and Further Mathematics qualifications in the UK and their impact on the transition from school to university mathematics. Here, the opinions of non-mathematics Science, Technology, Engineering and Mathematics (STEM) undergraduate students (all of whom had previously studied A-level Mathematics) were accessed via a survey and individual interviews. The study found that Further Mathematics qualifications are perceived as advantageous for non-mathematics STEM degrees by students once they are at university but not when making A-level choices. While the students often perceived mathematics positively, this appears to influence the choice of A-level Mathematics but not Further Mathematics. The lack of support from teachers and parents, the lack of perceived utility of Further Mathematics qualifications and a perception that Further Mathematics is only useful for studying a mathematics degree could all be factors affecting the uptake of Further Mathematics. The identified perceived impact of Further Mathematics on the university transition is linked to studying more pure mathematics which may give students a better understanding of how to apply mathematics in the context of their degree. Some comparisons between the findings in Parts 1 and 2 of the study are included which suggests that the Further Mathematics qualification is better serving students intending to study a non-mathematics STEM degree rather than mathematics itself.
这是第二篇报道研究结果的论文,该研究调查了英国学生对16岁后高级数学(a-level)和继续数学资格的选择及其对从学校到大学数学过渡的影响。在这里,非数学科学、技术、工程和数学(STEM)本科生(他们都曾学习过A级数学)的意见是通过调查和个人访谈获得的。研究发现,学生一旦上了大学,就会认为进一步数学资格对非数学STEM学位有利,但在选择A-level时则不然。虽然学生通常对数学有积极的看法,但这似乎会影响A级数学的选择,而不会影响进一步数学的选择。缺乏教师和家长的支持,对继续数学资格缺乏效用,以及认为继续数学只对学习数学学位有用,这些都可能是影响继续数学学习的因素。进一步数学对大学转型的影响与学习更纯粹的数学有关,这可能会让学生更好地理解如何在学位背景下应用数学。该研究第1部分和第2部分的研究结果之间的一些比较表明,继续数学资格证书更适合于打算学习非数学STEM学位的学生,而不是数学本身。
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引用次数: 3
Mathematics is different: student and tutor perspectives from Ireland and Australia on online support during COVID-19 数学不同:来自爱尔兰和澳大利亚的学生和导师对新冠肺炎期间在线支持的看法
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2021-01-01 DOI: 10.1093/teamat/hrab014
Claire Mullen;Jim Pettigrew;Anthony Cronin;Leanne Rylands;Donald Shearman
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引用次数: 0
Investigating the affordances of a flipped mathematics classroom from an activity theoretical perspective 从活动理论的角度考察翻转数学课堂的可供性
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2020-08-01 DOI: 10.1093/teamat/hraa011
Helge Fredriksen
Flipped Classroom as a pedagogical framework has gained popularity at secondary and tertiary levels of mathematics education, but there is a lack of research based on a solid theoretical foundation. This article considers the flipped mathematics classroom from the perspective of affordances and cultural–historical activity theory. The empirical background is based on semi-structured interview data from eight first-year computer-engineering students following 1 year of flipped classroom teaching. The thematic analysis of the data indicates that the flipped format offers a range of affordances at various levels of the activity system. This article advances research on affordances for mathematical learning in a flipped classroom pedagogical frame, presenting operational affordances out-of-class, action affordances at the mathematical task level and finally activity affordances at the collective level.
翻转课堂作为一种教学框架在中等和高等数学教育中越来越受欢迎,但缺乏基于坚实理论基础的研究。本文从可供性和文化历史活动理论的角度来思考翻转数学课堂。实证背景基于八名计算机工程一年级学生在翻转课堂教学一年后的半结构化访谈数据。对数据的主题分析表明,翻转格式在活动系统的各个层面提供了一系列可供性。本文对翻转课堂教学框架下数学学习的可供性进行了研究,提出了课堂外的操作可供性、数学任务层面的行动可供性,以及集体层面的活动可供性。
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引用次数: 1
Maths Sparks engagement programme: investigating the impact on under-privileged pupils’ attitudes towards mathematics 数学火花参与计划:调查对弱势学生数学态度的影响
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2020-08-01 DOI: 10.1093/teamat/hraa009
Aoibhinn Ni Shuilleabhain;Anthony Cronin;Mark Prendergast
In this paper we explore the attitudes of under-privileged secondary school pupils in Ireland towards mathematics and investigate the impact of attending a 4-week engagement programme on these attitudes. The pupils involved in this research attended schools recognized by the Department of Education & Skills as socio-economically deprived. Pupils attending these schools, known as Delivering Equality of Opportunity in Schools (DEIS), are 40% less likely than their counterparts in non-DEIS schools to pursue mathematics at a higher level in state examinations (Smyth, E., Mccoy, S. & Kingston, G., 2015, Learning From the Evaluation of DEIS. Dublin: Economic and Social Research Institute). However, little research has reported on these pupils’ experiences of and attitudes towards mathematics at senior secondary level. An engagement programme entitled ‘Maths Sparks’ was purposefully designed for secondary pupils from DEIS schools, with the aim of positively influencing their attitudes towards and confidence in mathematics. The programme consisted of weekly out-of-school workshops exploring extra-curricular mathematics topics, designed and delivered by undergraduate mathematics students. Questionnaires were utilized to evaluate pupils’ attitudes towards mathematics before and after their participation in the programme. Despite its relatively short time frame, qualitative and quantitative analysis suggests an increase in participating pupils’ attitudes towards, enjoyment of and self-confidence in mathematics due to their participation in the programme. Findings also suggest that while these pupils liked the subject of mathematics, their experience of learning the subject in school was not always positive and was sometimes hindered by the absence of higher-level mathematics as an option in school. The high-stakes examination content and teachers’ beliefs in the ability of their students also sometimes negatively impacted learners’ intentions to pursue mathematics at a higher level. Findings suggest that longitudinal mathematics engagement programmes, which focus on problem solving, involve extra-curricular mathematical concepts and are presented by undergraduate mathematics students, may provide a valuable way of positively impacting pupils’ intentions to pursue the subject.
在本文中,我们探讨了爱尔兰弱势中学生对数学的态度,并调查了参加为期4周的参与计划对这些态度的影响。参与这项研究的学生就读于教育和技能部认定的社会经济贫困学校。这些学校被称为“实现学校机会平等”(DEIS),与非DEIS学校的学生相比,就读这些学校的学生在州考试中追求更高水平数学的可能性低40%(Smyth,E.,Mccoy,S.和Kingston,G.,2015,从DEIS的评估中学习。都柏林:经济和社会研究所)。然而,很少有研究报道这些学生在高中阶段的数学经历和态度。有目的地为DEIS学校的中学生设计了一项名为“数学火花”的参与计划,目的是积极影响他们对数学的态度和信心。该方案包括由数学本科生设计和举办的每周校外讲习班,探讨课外数学主题。问卷被用来评估学生在参加该项目前后对数学的态度。尽管时间相对较短,但定性和定量分析表明,由于参与该项目,参与学生对数学的态度、享受和自信有所提高。研究结果还表明,虽然这些学生喜欢数学科目,但他们在学校学习该科目的经历并不总是积极的,有时会因为学校没有更高级别的数学作为一种选择而受到阻碍。高风险的考试内容和教师对学生能力的信念有时也会对学习者追求更高水平数学的意图产生负面影响。研究结果表明,专注于解决问题、涉及课外数学概念并由数学本科生提出的纵向数学参与计划,可能为积极影响学生学习该学科的意愿提供了一种有价值的方式。
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引用次数: 3
Construction of the concept of pairability in comparing infinite sets in the individuals’ mind: an APOS approach 在比较个体头脑中的无限集合时构建可配对性概念:APOS方法
IF 0.8 Q3 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2020-08-01 DOI: 10.1093/teamat/hraa008
Mohadaseh Mahdiyan;Ali Barahmand
This study focuses on the concept of pairability as a fundamental metaphorical concept in the Cantorian set theory regarding comparison of infinite sets. In this theory, pairability appears in a hierarchical manner of generating and developing as a one-to-one correspondence by arrows in finite, and then in infinite states, a bijection map through an explicit formula and the concept of cardinality. Adapting these hierarchical components of pairability and the APOS theory, about description of constructing and understanding a mathematical concept in a hierarchical manner, this study examines the construction of the concept of pairability in the individuals’ mind. In this way, their imaginations of pairability and practical performances in different situations will also be surveyed. In so doing, a total of 20 mathematics teachers and university lecturers holding at least an M.Sc. degree in mathematics were chosen. To collect the data, interviews were conducted in which the participants not only answered questions about the concept of the various types of pairability but also compared infinite countable sets in different situations. Our findings revealed that a bijection map via an explicit formula was the individuals’ dominant conception of pairability and most of the incorrect answers were related to unsuccessful attempts to recall a formula or method as the only possible way, and the encapsulated concept of cardinality was used less frequently in practice. Therefore, there was not a total schema of actions, processes and objects of the concept of pairability in the individuals’ mind.
本研究的重点是可配对性的概念,这是康托尔集合论中关于无限集合比较的一个基本隐喻概念。在这个理论中,可配对性以一种分层的方式出现,即在有限状态下通过箭头生成和发展为一对一的对应关系,然后在无限状态下通过显式公式和基数概念生成双射映射。本研究将可配对性的这些分层组成部分与APOS理论相结合,以分层的方式描述构建和理解数学概念,考察了可配对性概念在个体头脑中的构建。通过这种方式,他们对可配对性的想象和在不同情况下的实际表现也将被调查。在这样做的过程中,共选择了20名至少拥有数学硕士学位的数学教师和大学讲师。为了收集数据,进行了访谈,参与者不仅回答了关于各种类型的可配对性概念的问题,还比较了不同情况下的无限可数集。我们的研究结果表明,通过显式公式的双射图是个体对可配对性的主要概念,大多数错误答案与试图回忆公式或方法作为唯一可能的方法的失败有关,而基数的封装概念在实践中使用频率较低。因此,在个体的头脑中,并没有一个关于可配对性概念的行动、过程和对象的完整模式。
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引用次数: 0
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Teaching Mathematics and Its Applications
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