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Best practices for teaching the concept of the derivative: Lessons from experienced calculus instructors 导数概念教学的最佳实践:经验丰富的微积分教师的教诲
Q1 Mathematics Pub Date : 2024-04-01 DOI: 10.29333/ejmste/14380
T. Mkhatshwa
Much research has reported on difficulties exhibited by students when working with the concept of the derivative in first-semester university calculus. In an effort to generate and share a resource on effective instructional practices related to the teaching of the concept of the derivative, a 12-item questionnaire was administered to experienced calculus instructors in the United States. Most of the 10 experts who participated in this study considered providing ample examples and practice problems, using graphing utilities such as Desmos and GeoGebra, and employing problem solving strategies in the teaching of the concept of the derivative to be effective in supporting students learn about the concept of the derivative, among other things. These experts further remarked on representations of the concept of the derivative and real-world contexts they typically use in their teaching of the concept, in addition to providing rationales for the choice of real-world contexts they typically use in their teaching of the concept. Recommendations for instruction are included.
许多研究报告都指出了学生在大学微积分第一学期学习导数概念时遇到的困难。为了生成和共享与导数概念教学相关的有效教学实践资源,我们向美国经验丰富的微积分教师发放了一份包含 12 个项目的调查问卷。参与此次研究的 10 位专家中的大多数认为,在导数概念的教学中,提供充足的例题和练习题、使用 Desmos 和 GeoGebra 等图形工具、采用问题解决策略等,都能有效地帮助学生学习导数概念。这些专家还就导数概念的表征和他们在导数概念教学中通常使用的真实世界情境发表了看法,并就他们在导数概念教学中通常使用的真实世界情境的选择提供了理由。此外,还包括教学建议。
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引用次数: 0
Metacognition in mathematics education: From academic chronicle to future research scenario–A bibliometric analysis with the Scopus database 数学教育中的元认知:从学术编年史到未来研究设想--利用 Scopus 数据库进行的文献计量分析
Q1 Mathematics Pub Date : 2024-04-01 DOI: 10.29333/ejmste/14381
Hoang Thi-Nga, Vu Thi-Binh, Tien-Trung Nguyen
Originally introduced by psychologists, metacognition has attracted considerable interest within academic spheres and has transformed into a significant research focal point in the field of mathematics education, commonly denoted as ‘mathematical metacognition.’ This investigation constitutes the primary endeavor to comprehensively examine all publications within the Scopus database related to metacognition in mathematics education (MiME). The data encompasses a total of 288 documents, authored by 653 individuals hailing from 58 different countries and territories and disseminated across 162 diverse sources. Notably, this examination delineates two distinct developmental phases, with a particularly pronounced surge in publications emerging from the year 2016 onward. Although Asia has two representatives in the top-10 in terms of number of publications (China and Indonesia), authors from developed countries have made significant contributions to research on MiME, especially the United States, Germany, Turkey, and Belgium. Among the 15 most influential academic journals, merely two pertain to the domain of mathematics education, whereas the majority belong to the disciplines of psychology and social sciences (educational science). The main research directions that have been pointed out are adults’ metacognitive abilities, considering gender differences and problem-solving abilities; metacognition and the ability to learn mathematical concepts (more recently arithmetic concepts); control metacognitive processes and students’ academic achievement. Early-career researchers as well as interested scholars can find important scholars, documents, and research directions on this topic to refer to for their research activities.
元认知最初由心理学家提出,在学术界引起了极大的兴趣,并已转变为数学教育领域的一个重要研究焦点,通常被称为 "数学元认知"。本调查是对 Scopus 数据库中与数学教育中的元认知(MiME)相关的所有出版物进行全面研究的主要尝试。这些数据共包含 288 篇文献,由来自 58 个不同国家和地区的 653 位作者撰写,通过 162 个不同来源传播。值得注意的是,这项研究划分了两个截然不同的发展阶段,从 2016 年开始,论文数量出现了特别明显的激增。虽然亚洲有两位代表(中国和印度尼西亚)在发表论文数量方面位居前十,但发达国家的作者也为水教育研究做出了重要贡献,尤其是美国、德国、土耳其和比利时。在 15 种最有影响力的学术期刊中,仅有两种与数学教育领域有关,而大多数属于心理学和社会科学(教育科学)学科。已指出的主要研究方向包括:成人的元认知能力(考虑性别差异和解决问题的能力);元认知和学习数学概念(最近是算术概念)的能力;控制元认知过程和学生的学业成绩。早期研究人员和感兴趣的学者可以从中找到有关这一主题的重要学者、文献和研究方向,为他们的研究活动提供参考。
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引用次数: 0
Spatial visualization skills present in items of the Brazilian high school national exam 巴西高中全国统考项目中的空间可视化技能
Q1 Mathematics Pub Date : 2024-03-03 DOI: 10.29333/ejmste/14322
Carmen Vieira Mathias, Cristian Martins da Silva, Fábio Luiz Borges Simas
This article aims to analyze, categorize, and quantify the Brazilian high school national exam (ENEM) questions that require spatial visualization skills (SVS) for their resolution. This is a documentary research with a qualitative-quantitative approach whose corpus of analysis is ENEM exams carried out from 2009 to 2022, in the subject of mathematics and its technologies. There are four main results of this research: (1) spatial geometry (SG) questions that require SVS for their resolution (39.7%) are proportionally more frequent in ENEM than in four most used textbooks in Brazil (<20.0%), (2) some categories of SVS are much more frequent than others in ENEM questions, (3) the proportion of geometry questions in ENEM mathematics exam (23.0%) is considerably higher than the corresponding proportion of geometry-related skills in ENEM skills framework (13.0%), and (4) approximately half of ENEM geometry questions address SG.
本文旨在对巴西全国高中会考(ENEM)中需要空间可视化技能(SVS)来解决的问题进行分析、分类和量化。这是一项采用定性-定量方法的文献研究,其分析语料库是 2009 年至 2022 年期间进行的 ENEM 考试,涉及数学及其技术科目。这项研究有四个主要结果:(1) 在 ENEM 中,需要用 SVS 来解决的空间几何(SG)问题(39.7%)的比例高于巴西最常用的四本教科书(<20.0%),(2) 在 ENEM 的试题中,某些类别的 SVS 比其他类别的 SVS 更常见,(3) 在 ENEM 数学考试中,几何试题的比例(23.0%)大大高于 ENEM 技能框架中与几何相关的技能的相应比例(13.0%),(4) 大约一半的 ENEM 几何试题涉及 SG。
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引用次数: 0
Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models 几何建模的挑战--比较学生利用实物、照片和三维模型进行数学学习的情况
Q1 Mathematics Pub Date : 2024-03-03 DOI: 10.29333/ejmste/14321
Simone Jablonski
Mathematical modelling aims at contributing to the involvement of reality in mathematics education. As an example, geometric modelling can be implemented by the use of real objects in modelling tasks. Still, (geometric) modelling tasks can be a challenge for students, especially in the transfer from reality to mathematics, which is referred to as mathematization. Since the representation of a real object in tasks might differ, the question arises, which challenges can be observed when working in different task settings. In a study with 19 secondary school students, the task settings (1) outdoors at the real object, (2) indoors with photos of the real object, and (3) indoors with a 3D model of the real object are compared. Based on video recordings, differences concerning the students’ challenges are examined. The results highlight challenges in estimating and measuring when working at the real object, scale and perspective when working with photos and the transfer between representation and object when working with 3D models.
数学建模旨在促进数学教育中的现实参与。例如,几何建模可以通过在建模任务中使用真实物体来实现。然而,(几何)建模任务对学生来说仍然是一个挑战,尤其是在从现实到数学的转换过程中,也就是所谓的数学化。由于真实物体在任务中的表现形式可能会有所不同,因此问题就来了,在不同的任务设置中,可以观察到哪些挑战。在一项以 19 名中学生为对象的研究中,比较了(1)室外真实物体、(2)室内真实物体照片和(3)室内真实物体 3D 模型的任务设置。根据视频记录,研究了学生所面临挑战的差异。结果凸显了在真实物体前进行估算和测量、在照片前进行比例和透视以及在三维模型前进行表象和物体之间的转换时所面临的挑战。
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引用次数: 0
Heutagogy in action: Unveiling the transformative power of virtual “air campus” experiences of mathematics trainee teachers Heutagogy in action:揭示数学实习教师虚拟 "空中校园 "体验的变革力量
Q1 Mathematics Pub Date : 2024-03-03 DOI: 10.29333/ejmste/14320
Jogmol Kalariparampil Alex, Angel Mukuka
The fourth industrial revolution has brought about significant changes in various fields including the education sector. It is increasingly essential for individuals, particularly student teachers, to embrace lifelong learning and acquire the know-how and skills required to grow into autonomous and critical thinkers. In this paper, we examine the virtual “air campus” experiences of 39 first-year student teachers of mathematics at a rural university in South Africa’s Eastern Cape Province. The heutagogical approach served as a lens for trainee teachers’ virtual “air campus” explorations. An exploratory qualitative case study design was employed to provide answers to two main questions that guided the inquiry. Findings of the study show that trainee teachers had varied experiences regarding what they learned from their virtual “air campus” visits. These include what constitutes effective teaching and how students learn as well as correction of common misconceptions regarding specific concepts in school mathematics. Through virtual lesson observations on the “air campus” of their choice, trainee teachers were also able to create their professional identities in terms of their future goals, ideal teacher traits, and desired teaching and learning environments. These findings demonstrate that integrating virtual learning environments into teacher education curricula and assessment has practical implications for enhancing trainee teachers’ self-directed learning, critical thinking, and professional identity development.
第四次工业革命给包括教育部门在内的各个领域带来了重大变化。个人,尤其是学生教师,越来越有必要接受终身学习,掌握成长为自主和批判性思考者所需的知识和技能。在本文中,我们研究了南非东开普省一所农村大学 39 名数学专业一年级学生教师的虚拟 "空中校园 "经历。综合教学法是见习教师探索虚拟 "空中校园 "的透镜。本研究采用了探索性定性案例研究设计,以回答指导调查的两个主要问题。研究结果表明,见习教师从虚拟 "空中校园 "参观中学到了不同的经验。其中包括什么是有效教学、学生如何学习以及纠正学校数学中特定概念的常见误解。通过在自己选择的 "空中校园 "进行虚拟观课,受训教师还能根据自己的未来目标、理想的教师特质和理想的教学环境来创建自己的专业身份。这些研究结果表明,将虚拟学习环境融入师范教育课程和评估中,对提高受训教师的自主学习能力、批判性思维能力和专业身份发展具有实际意义。
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引用次数: 0
A refined framework for qualitative content analysis of mathematics textbooks 数学教科书定性内容分析的改进框架
Q1 Mathematics Pub Date : 2024-03-01 DOI: 10.29333/ejmste/14284
Fereshteh Zeynivandnezhad, İpek Saralar-Aras, A. Halai
Within the realm of mathematics education, the examination of textbooks has emerged as a focal point of scholarly investigation. This endeavor necessitates the development of a comprehensive instrument capable of facilitating both qualitative and quantitative textbook analysis. To address this need, we draw upon a corpus of seminal studies, and supplement our analysis with local research reports that assess the quality of mathematics textbooks through a qualitative content analysis approach. Content analysis was utilized to examine the documents and identify the themes relevant to the analysis of mathematics textbooks. Our data analysis revealed the identification of six overarching themes for the systematic evaluation of mathematics textbooks: (1) language and communication, (2) content analysis, (3) pedagogical approach, (4) cultural sensitivity and inclusivity, (5) assessment and exercises, and (6) visual aids and presentation. Each of these themes is meticulously expounded upon, shedding light on their significance in shaping the intricacies of mathematics textbook authorship. This proposed analytical framework presents an invaluable resource for enhancing the quality of mathematics textbooks at the school level. The themes elucidated herein offer a structured approach to textbook assessment, ultimately fostering the advancement of mathematical education by improving the instructional materials that are integral to the teaching and learning process.
在数学教育领域,教科书研究已成为学术研究的一个焦点。这项工作需要开发一种能够促进对教科书进行定性和定量分析的综合工具。为了满足这一需求,我们借鉴了大量开创性的研究成果,并通过定性内容分析方法,对评估数学教科书质量的本地研究报告进行了补充分析。我们利用内容分析法来研究这些文件,并确定与数学教科书分析相关的主题。通过数据分析,我们确定了系统评估数学教科书的六大主题:(1) 语言与沟通;(2) 内容分析;(3) 教学方法;(4) 文化敏感性与包容性;(5) 评估与练习;(6) 视觉辅助工具与演示。我们对每一个主题都进行了细致的阐述,揭示了它们在塑造数学教科书编写的复杂性方面的重要意义。这一分析框架为提高学校数学教科书的质量提供了宝贵的资源。本文阐释的主题为教科书评估提供了一种结构化的方法,通过改进教学过程中不可或缺的教学材料,最终促进数学教育的发展。
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引用次数: 0
Assessment of scientific literacy levels among secondary school students in Lebanon: Exploring gender-based differences 评估黎巴嫩中学生的科学素养水平:探索性别差异
Q1 Mathematics Pub Date : 2024-03-01 DOI: 10.29333/ejmste/14279
Marina Baltikian, Sirpa Kärkkäinen, J. Kukkonen
In recent years, educational reforms have made scientific literacy a major priority because of its increasing importance in today’s dynamic world. Program for international student assessment 2015 evaluated scientific literacy from 72 countries, and Lebanon ranked 65th. Scientific literacy levels among Lebanese secondary school students and gender differences are unknown. This study fills this research gap. A total of 130 students from Lebanon’s private secondary schools were involved in this research. Scientific literacy levels were assessed using an instrument developed by Gormally et al. (2012), who conceptualized nine science competencies contributing to scientific literacy including understanding research designs, creating and interpreting graphs, and solving quantitative problems. Welch’s ANOVA and Mann-Whitney U tests were used to analyze the data. Lebanese secondary school students have very low scientific literacy levels, and no significant difference was observed between genders. We present recommendations for adding desired skills to the curriculum based on a review of the underlying factors.
近年来,由于科学素养在当今这个充满活力的世界中日益重要,教育改革已将科学素养列为主要优先事项。2015 年国际学生评估计划对 72 个国家的科学素养进行了评估,黎巴嫩排名第 65 位。黎巴嫩中学生的科学素养水平和性别差异尚不清楚。本研究填补了这一研究空白。共有 130 名来自黎巴嫩私立中学的学生参与了本研究。Gormally 等人(2012 年)开发了一种工具来评估学生的科学素养水平,他们将有助于提高科学素养的九种科学能力概念化,包括理解研究设计、创建和解释图表以及解决定量问题。数据分析采用了韦尔奇方差分析和曼-惠特尼 U 检验。结果表明,黎巴嫩中学生的科学素养水平很低,男女生之间没有明显差异。根据对基本因素的审查,我们提出了在课程中增加所需技能的建议。
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引用次数: 0
Teaching and learning of physical sciences grade 11 in rural schools through rural blended learning strategy 通过农村混合学习策略在农村学校开展 11 年级物理科学的教与学活动
Q1 Mathematics Pub Date : 2024-03-01 DOI: 10.29333/ejmste/14295
T. Nkanyani, Awelani V. Mudau, Lettah Sikhosana
The aim of this paper was to explore how teaching and learning of physical sciences using rural blended learning strategy (RBLS) in rural schools occurred. A qualitative case study design was used to collect data from a from a rural school. Hence, it was a purposeful sampling strategy with one physical science teacher and his 45 learners. Data was collected through classroom observation, semi-structured, and focus group interviews. The study found that issues such as digital divide, poor training of teacher, incorrect teaching approaches, workloads, poor parental involvement remain challenges in rural areas, even though the teacher experienced effective institutional support and exposure to e-learning. As such, we noted his ability to create Google Classroom (GC) and WhatsApp platforms and their effective use, even though the same could not be said about the use of video conferencing (VC) platforms. Issues like workload were cited as the barriers to the implementation of RBLS. The teacher also carried on with teacher centered methods, which were not effective not only for the learning of science but also for the implementation of blended learning. Therefore, the teacher failed to flip the classroom. Learners on the other hand found RBLS to be inducing their self-directed learning and motivation. We recommend that more prolonged training on the use of RBLS should be provided, not only to teacher but also to the learners. Department of basic education should engage network providers on the provision of zero-rated data for educational applications such as GC and VC platforms while school governing bodies provide institutional support to both learners and teacher.
本文旨在探讨如何在农村学校使用农村混合式学习策略(RBLS)进行物理科学的教与学。本文采用定性案例研究设计,从一所农村学校收集数据。因此,这是一种有目的的抽样策略,对象是一名物理科学教师和他的 45 名学生。通过课堂观察、半结构式访谈和焦点小组访谈收集数据。研究发现,在农村地区,数字鸿沟、教师培训不足、教学方法不正确、工作量大、家长参与度低等问题仍然是挑战,尽管该教师经历了有效的机构支持并接触了电子学习。因此,我们注意到他有能力创建谷歌教室(GC)和 WhatsApp 平台,并能有效使用这些平台,但在使用视频会议(VC)平台方面却并非如此。工作量等问题被认为是实施 RBLS 的障碍。该教师还继续采用以教师为中心的方法,这种方法不仅对科学学习无效,而且对混合式学习的实施也无效。因此,教师未能翻转课堂。另一方面,学习者发现 RBLS 能够激发他们的自主学习和学习动机。我们建议,不仅应为教师,也应为学习者提供更多有关使用 RBLS 的长期培训。基础教育部应与网络供应商合作,为 GC 和 VC 平台等教育应用程序提供零费率数据,同时学校管理机构应为学生和教师提供机构支持。
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引用次数: 0
Characterization of STEM teacher education programs for disciplinary integration: A systematic review 科学、技术、工程与数学(STEM)教师教育项目的学科整合特征:系统回顾
Q1 Mathematics Pub Date : 2024-03-01 DOI: 10.29333/ejmste/14280
Carlos Mauricio Agudelo Rodríguez, Ronald Andrés González-Reyes, Andrés Bernal Ballen, Martha Andrea Merchán Merchán, Ellie Anne López Barrera
STEM education is established as an alternative for developing 21st century skills, with the premise of integrating its component disciplines. Although numerous studies exist on the subject, STEM teacher training programs are not widely discussed. Therefore, a systematic literature review was conducted in Scopus and Web of Science to identify the intentions of the training and the design and implementation of such teacher training programs. Among the 15 articles identified, there are three groups of intentions: Improving knowledge, developing competencies and skills, and changing attitudes and perceptions. Five methodological strategies were identified: project-based learning, problem-based learning, collaborative learning, ODR (observation/discussion/reflection) approach, and design-based learning. Disciplinary integration can be achieved through content or competencies. It is concluded that design-based learning is the most appropriate strategy for disciplinary integration. It is recommended that research be conducted to measure the impact of modality and time of training on the development of STEM competencies.
STEM 教育是培养 21 世纪技能的另一种选择,其前提是整合各组成学科。虽然有关这一主题的研究不胜枚举,但对 STEM 教师培训计划的讨论却并不广泛。因此,我们在 Scopus 和 Web of Science 上进行了系统的文献综述,以确定培训的意图以及此类教师培训计划的设计和实施。在确定的 15 篇文章中,有三组意向:提高知识水平、培养能力和技能、改变态度和观念。确定了五种方法策略:基于项目的学习、基于问题的学习、合作学习、ODR(观察/讨论/反思)方法和基于设计的学习。学科整合可以通过内容或能力来实现。结论是,基于设计的学习是最适合学科整合的策略。建议开展研究,衡量培训方式和时间对培养 STEM 能力的影响。
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引用次数: 0
A bibliometric analysis covering the relevant literature on science anxiety over two decades 对二十多年来有关科学焦虑的相关文献进行文献计量分析
Q1 Mathematics Pub Date : 2024-03-01 DOI: 10.29333/ejmste/14283
Aygul A. Khafizova, Sergei P. Zhdanov, Oksana V. Beltyukova, Natalia I. Lapidus, L.Yu. Grebenshchikova, Irina V. Lushchik
This study aimed to examine publications related to science anxiety to contribute to developing relevant literature. A bibliometric analysis was conducted on 71 articles published between 2003 and 2022 from the Scopus database. The analysis examined the bibliographic links between the sources, authors, countries, and publications through the VOSviewer software. The results regarding keyword analysis showed that the five most frequently used keywords in the selected articles are anxiety, science anxiety, students, self-efficacy, and education. The results also showed that 80% of research papers on science anxiety, among the top 10 highest cited publications, were conducted in the USA. All of the top-10 publications were published in journals that have published articles in education literature for a long time. In addition, the results indicated that half of the publications also used psychology education journals. Furthermore, the bibliographic coupling of the authors showed that research teams from the USA authored the most publications on science anxiety. In light of the results, recommendations for future studies are made in conclusion.
本研究旨在研究与科学焦虑有关的出版物,以促进相关文献的发展。我们对 Scopus 数据库中 2003 年至 2022 年间发表的 71 篇文章进行了文献计量分析。该分析通过 VOSviewer 软件检查了来源、作者、国家和出版物之间的书目联系。关键词分析结果显示,所选文章中最常使用的五个关键词是焦虑、科学焦虑、学生、自我效能感和教育。结果还显示,在引用率最高的前 10 篇论文中,80% 有关科学焦虑的研究论文是在美国发表的。排名前十的论文全部发表在长期发表教育文献文章的期刊上。此外,研究结果表明,半数出版物还使用了心理学教育期刊。此外,作者的书目耦合显示,来自美国的研究团队撰写了最多有关科学焦虑的出版物。最后,根据研究结果对今后的研究提出了建议。
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引用次数: 0
期刊
Eurasia Journal of Mathematics, Science and Technology Education
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