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Primary students' learning about citizenship through data science. 小学生通过数据科学学习公民意识。
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-02 DOI: 10.1007/s11858-022-01450-7
Katie Makar, Kym Fry, Lyn English

Much of the mathematics that children experience in school neglect the skills increasingly needed for citizenship, particularly the power of complex data to investigate and make sense of the world. We draw on the relatively new field of data science as a multi-disciplinary approach to investigate problems through analysis of massive, non-standard, incongruous and/or messy data. Our exploratory qualitative study had as its research question: What can children learn about citizenship when they engage with data science? The case study in this paper illustrated ways that children's learning about citizenship were enriched through an age-appropriate data science investigation. The study analysed classroom video from a Year 4 classroom (aged 9-10) over six lessons that integrated curricula in digital technologies, health, and mathematics. In these lessons, the children generated and analysed non-standard data and debated social, well-being and privacy issues as they considered their activities in cyberspace. The video data were analysed using a framework based on critical citizenship education literature that examined dimensions of power, collective engagement, individual responsibility and action. Three key findings emerged. First, the case study highlighted skills in citizenship education developed through data science, positioning children as agents and advocates. Second, the study showed how a complex data investigation in citizenship education was achievable with primary children through meaningful curriculum integration. This is important given that problems that citizens address are typically interdisciplinary. Finally, the findings revealed a gap between data science skills and those developed in the mathematics curriculum, and recommend ways that the maths curriculum could be updated.

孩子们在学校学习的数学知识,大多忽视了公民日益需要的技能,特别是利用复杂数据调查和理解世界的能力。我们借鉴了数据科学这一相对较新的领域,将其作为一种多学科方法,通过分析大量、非标准、不协调和/或混乱的数据来研究问题。我们的探索性定性研究的研究问题是儿童在参与数据科学时能学到哪些公民知识?本文中的案例研究说明了儿童通过适合其年龄的数据科学调查学习公民意识的方式。该研究分析了一个四年级(9-10 岁)班级的课堂视频,共六节课,整合了数字技术、健康和数学课程。在这些课程中,孩子们生成并分析了非标准数据,并在考虑他们在网络空间的活动时就社会、福祉和隐私问题展开了辩论。在分析视频数据时,使用了一个基于批判性公民教育文献的框架,该框架考察了权力、集体参与、个人责任和行动等方面。得出了三个主要结论。首先,案例研究强调了通过数据科学发展的公民教育技能,将儿童定位为推动者和倡导者。其次,研究表明,通过有意义的课程整合,小学生可以在公民教育中进行复杂的数据调查。这一点非常重要,因为公民要解决的问题通常是跨学科的。最后,研究结果揭示了数据科学技能与数学课程中培养的技能之间的差距,并提出了更新数学课程的方法。
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引用次数: 0
Using enaction to evolve from pre-Covid to post-Covid pedagogy: a case study with South African mathematics teachers. 利用行动从疫情前教学法向疫情后教学法演变:对南非数学教师的案例研究
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01416-9
Ronel Callaghan, Jody Joubert, Johann Engelbrecht

The Covid-19 pandemic and subsequent national lockdown in South Africa induced a rapid, albeit challenging, implementation of blended learning (with a strong online focus) at all educational levels. During this time, a group of teachers were involved in a specialised computer integrated education course, preparing them for the design and implementation of technologically enhanced modes of teaching. In this research we considered the positive impact of the situation during the pandemic on these mathematics teachers' practice, as well as their conceptualisation of the way forward for technology enhanced mathematics education. We conducted an explorative survey study, employing an enactivist approach, to investigate their experiences of addressing procedural and conceptual aspects of mathematics education, as well as their observations of learners' reactions to these changed practices. Our findings show that participants experienced their exposure to technology as creating an environment they foresee will have a lasting impact on their teaching practice. Participants emphasised the importance of using educational technology meaningfully as a cognitive tool that allows for learners to learn with the technology and not from the technology, which impacts on the importance of learner-centred teaching strategies and the development of high cognitive level interactive learning activities.

2019冠状病毒病大流行和随后南非的全国封锁促使各级教育迅速(尽管具有挑战性)实施混合学习(以在线为重点)。在此期间,一组教师参加了专门的计算机综合教育课程,为设计和实施技术增强的教学模式做好准备。在这项研究中,我们考虑了大流行期间对这些数学教师实践的积极影响,以及他们对技术增强数学教育前进道路的概念化。我们进行了一项探索性调查研究,采用积极的方法,调查他们在处理数学教育的程序和概念方面的经验,以及他们对学习者对这些变化的实践的反应的观察。我们的研究结果表明,参与者认为他们接触技术创造了一个环境,他们预计将对他们的教学实践产生持久的影响。与会者强调了有意义地使用教育技术作为一种认知工具的重要性,这种工具允许学习者通过技术而不是从技术中学习,这影响了以学习者为中心的教学策略的重要性和高认知水平互动学习活动的发展。
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引用次数: 3
Exponential behaviour and variational practices in Chilean newscasts: a socioepistemological view. 指数行为和变分实践在智利新闻广播:社会认识论的观点。
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01458-z
Ricardo Cantoral, Lianggi Espinoza, Claudio Gaete-Peralta

The research on which we report in this paper was framed within the socioepistemological theory and dealt with the fundamental role of variational practices in the understanding of COVID-19 pandemic graphs. Given the proliferation of mathematical graphs related to the pandemic in the media, we proposed to analyse the variational practices in use in the interpretation of graphs of exponential behaviour that a Chilean newscast of high rating used to inform the population about the pandemic in Chile. For this purpose, a thematic analysis intertwined with documentary analysis techniques was carried out, in order to describe the types of graphs shown in the newscast, and a variational reference system was studied to analyse the use of variational practices. To obtain our results, the types of graphs most frequently shown in the newscast at the beginning of the pandemic were identified and the use of the variational practices of comparison, seriation and prediction in such graphs was analysed. In conclusion, the need is discussed for the conceptual evolution of the exponential function to be accompanied by a pragmatic evolution in school that favours the use and development of variational practices in the student body.

我们在本文中报告的研究是在社会认识论理论框架内进行的,并处理了变分实践在理解COVID-19大流行图表中的基本作用。鉴于媒体上与大流行病有关的数学图表的激增,我们建议分析在解释指数行为图表时使用的变分做法,该指数行为图表是智利一档高收视率的新闻广播用来向民众通报智利的大流行病的。为此目的,进行了与文献分析技术交织在一起的专题分析,以描述新闻广播中显示的图表类型,并研究了变分参考系统,以分析变分做法的使用。为了获得我们的结果,确定了大流行开始时新闻广播中最常出现的图表类型,并分析了在这些图表中使用比较、序列化和预测的变分方法。总之,本文讨论了指数函数的概念演变需要伴随着学校的实用主义演变,这种演变有利于学生群体中变分实践的使用和发展。
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引用次数: 0
Mathematical modelling of exponential growth as a rich learning environment for mathematics classrooms. 指数增长的数学建模为数学课堂提供了丰富的学习环境。
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01433-8
Hans-Stefan Siller, Hans-Jürgen Elschenbroich, Gilbert Greefrath, Katrin Vorhölter

Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Our contribution has the aim of showing that basic mental models about exponential growth are important for understanding media reports of Covid-19. Furthermore, we highlight how the coronavirus pandemic can be used as a context in mathematics classrooms to help students understand that they can and should question media reports on their own, using their mathematical knowledge. Therefore, we first present the role of mathematical modelling in achieving these goals in general. The same relevance applies to the necessary basic mental models of exponential growth. Following this description, based on three topics, namely, investigating the type of growth, questioning given course models, and determining exponential factors at different times, we show how the presented theoretical aspects manifest themselves in teaching examples when students are given the task of reflecting critically on existing media reports. Finally, the value of the three topics regarding the intended goals is discussed and conclusions concerning the possibilities and limits of their use in schools are drawn.

关于Covid-19大流行的媒体报道经常使用数学概念。其中包括增长模型,它试图解释或预测干预措施和发展的有效性,以及生殖因素。我们的贡献旨在表明,关于指数增长的基本思维模型对于理解媒体对Covid-19的报道很重要。此外,我们强调如何将冠状病毒大流行作为数学课堂的背景,帮助学生理解他们可以而且应该利用自己的数学知识对媒体报道提出质疑。因此,我们首先介绍数学建模在实现这些目标中的作用。同样的关联也适用于指数增长的必要基本心智模型。根据这一描述,基于三个主题,即调查增长类型,质疑给定的课程模型,以及确定不同时期的指数因子,我们展示了当学生被赋予批判性反思现有媒体报道的任务时,所提出的理论方面如何在教学实例中体现出来。最后,讨论了关于预期目标的三个主题的价值,并得出了关于它们在学校使用的可能性和局限性的结论。
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引用次数: 1
Will we ever teach mathematics again in the way we used to before the pandemic? 我们还能像大流行之前那样教授数学吗?
IF 2 2区 教育学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-01-01 Epub Date: 2023-01-13 DOI: 10.1007/s11858-022-01460-5
Johann Engelbrecht, Marcelo C Borba, Gabriele Kaiser

After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) normal. However, after the period of mostly teaching online, there is uncertainty about the extent to which we will return to the way we were teaching before. In this survey paper we attempt to give some background to the impact that emergency remote teaching may have had on teaching mathematics. We examine the possible social implications and then focus on the changing mathematics classroom, focusing on the actual mathematics curriculum, learning design and assessment, the role of collaborative activities and social media, educational videos, and the role of family and parents in future. There are indicators from the literature that educators may not return to the traditional way of teaching entirely, especially in secondary and higher education. We conclude with describing some possible new research areas that have developed through emergency remote teaching, including online education for younger learners, local learning ecosystems, the role of family and parents, instructional design, and the mathematics content of curricula.

经过大流行病期间约两年的紧急远程教学,数学教学正在慢慢恢复(过去所谓的)正常状态。然而,在经历了大部分时间的在线教学之后,我们在多大程度上能恢复到以前的教学方式还存在不确定性。在这篇调查报告中,我们试图就紧急远程教学可能对数学教学产生的影响提供一些背景资料。我们研究了可能产生的社会影响,然后聚焦于不断变化的数学课堂,重点关注实际的数学课程、学习设计和评估、协作活动和社交媒体的作用、教育视频以及家庭和家长在未来的作用。有文献表明,教育工作者可能不会完全回归传统的教学方式,尤其是在中等和高等教育中。最后,我们将介绍一些通过紧急远程教学发展起来的可能的新研究领域,包括针对低年级学生的在线教育、本地学习生态系统、家庭和父母的作用、教学设计以及课程的数学内容。
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引用次数: 0
Intelligent tutoring systems for word problem solving in COVID-19 days: could they have been (part of) the solution? 2019冠状病毒病疫情期间解决文字问题的智能辅导系统:它们能成为解决方案的(一部分)吗?
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01396-w
Javier Del Olmo-Muñoz, José Antonio González-Calero, Pascual D Diago, David Arnau, Miguel Arevalillo-Herráez

The COVID-19 pandemic led to the lockdown of schools in many countries, forcing teachers and students to carry out educational activities remotely. In the case of mathematics, developing remote instruction based on both synchronous and asynchronous technological solutions has proven to be an extremely complex challenge. Specifically, this was the case in topics such as word problem solving, as this domain requires intensive supervision and feedback from the teacher. In this piece of research, we present an evaluation of how technology is employed in the teaching of mathematics, with particular relevance to learning during the pandemic. For that purpose, we conducted a systematic review, revealing the almost complete absence of experiments in which the use of technology is not mediated by the teacher. These results reflect a pessimistic vision within the field of mathematics education about the possibilities of learning when the student uses technology autonomously. Bringing good outcomes out of a bad situation, the pandemic crisis may represent a turning point from which to start directing the research gaze towards technological environments such as those mediated by artificial intelligence. As an example, we provide a study illustrating to what extent intelligent tutoring systems can be cost-effective compared to one-to-one human tutoring and mathematic learning-oriented solutions for intensive supervision in the teaching of word problem solving, especially appropriate for remote settings. Despite the potential of these technologies, the experience also showed that student socioeconomic level was a determining factor in the participation rate with an intelligent tutoring system, regardless of whether or not the administration guaranteed students' access to technological resources during the COVID-19 situation.

新冠肺炎大流行导致许多国家的学校被封锁,教师和学生被迫远程开展教育活动。以数学为例,开发基于同步和异步技术解决方案的远程教学已被证明是一项极其复杂的挑战。具体来说,在诸如解决文字问题之类的主题中就是这种情况,因为这个领域需要老师的密切监督和反馈。在这项研究中,我们评估了技术如何应用于数学教学,特别是与大流行期间的学习有关。为此,我们进行了一次系统的回顾,发现几乎完全没有实验,在这些实验中,技术的使用不是由老师来调节的。这些结果反映了数学教育领域对学生自主使用技术时学习可能性的悲观看法。大流行危机带来了坏的结果,它可能是一个转折点,从这个转折点开始,研究的目光将转向人工智能等技术环境。作为一个例子,我们提供了一项研究,说明与一对一的人工辅导和以数学学习为导向的解决方案相比,智能辅导系统在多大程度上具有成本效益,以加强对单词问题解决教学的监督,特别是适用于远程设置。尽管这些技术具有潜力,但经验也表明,无论管理部门是否保证学生在新冠肺炎疫情期间获得技术资源,学生的社会经济水平是智能辅导系统参与率的决定因素。
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引用次数: 4
Can flipped classroom pedagogy offer promising perspectives for mathematics education on pandemic-related issues? A systematic literature review. 翻转课堂教学法能否为流行病相关问题的数学教育提供有希望的前景?系统的文献综述。
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01388-w
Mustafa Cevikbas, Gabriele Kaiser

Educators sometimes effect changes in education through the implementation of new ideas, and sometimes extraordinary circumstances force them to change their educational approaches, as during the COVID-19 crisis. Although we live in a digital age, the limited use of technology in education, particularly prior to the COVID-19 pandemic, and teachers' insufficient experience with online or hybrid learning and teaching approaches resulted in several countries being unprepared for education during the pandemic. The flipped classroom (FC) is an innovative pedagogy with the potential to engage students in mathematics education using hybrid education combined with online and face-to-face learning, which is especially important during a pandemic. However, despite the high expectations surrounding this innovative approach, to date, no systematic literature review has discussed the opportunities and pitfalls of FCs in mathematics education regarding pandemic-related issues. In the present systematic review, we aim to bridge this gap and highlight the importance of flipping mathematics instruction during the pandemic and beyond. The results, which are based on textual analysis of 97 eligible articles, demonstrate that FC is a promising pedagogy that has numerous benefits for mathematics teaching and learning, although it is not a panacea for pandemic-related issues, as it also has several significant pitfalls. Overall, if the mechanism of mathematics education is to be crisis-ready, we should learn from experiences during the pandemic. In this regard, the current review contributes to research in mathematics education with the aim of gaining insight into successful implementations of FC pedagogy, not only during the pandemic but also beyond the crisis era of a pandemic.

Supplementary information: The online version contains supplementary material available at 10.1007/s11858-022-01388-w.

教育工作者有时通过实施新思想来改变教育,有时特殊情况迫使他们改变教育方法,例如在2019冠状病毒病危机期间。尽管我们生活在数字时代,但技术在教育中的使用有限,特别是在2019冠状病毒病大流行之前,教师在在线或混合学习和教学方法方面的经验不足,导致一些国家在大流行期间没有做好教育准备。翻转课堂(FC)是一种创新教学法,有可能通过在线和面对面学习相结合的混合教育让学生参与数学教育,这在大流行期间尤为重要。然而,尽管人们对这种创新方法抱有很高的期望,但迄今为止,还没有系统的文献综述讨论过流行病相关问题数学教育中FCs的机会和陷阱。在目前的系统综述中,我们的目标是弥合这一差距,并强调在大流行期间和以后翻转数学教学的重要性。基于对97篇合格文章的文本分析的结果表明,FC是一种很有前途的教学法,对数学教学和学习有许多好处,尽管它不是解决与流行病相关问题的灵丹妙药,因为它也有几个重大缺陷。总的来说,如果要使数学教育机制做好危机准备,我们应该从大流行期间的经验中吸取教训。在这方面,本综述有助于数学教育的研究,目的是深入了解不仅在大流行期间而且在大流行危机时期之后成功实施FC教学法的情况。补充信息:在线版本包含补充资料,下载地址:10.1007/s11858-022-01388-w。
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引用次数: 7
Strategies implemented by South African teachers to ensure continuing mathematics education during COVID-19. 南非教师为确保在2019冠状病毒病期间继续进行数学教育而实施的战略。
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01408-9
Pamela Vale, Mellony Graven

The COVID-19 pandemic continues to present severe challenges to the education sector more than 2 years after the first case was detected. We explore the strategies South African teachers used to support continued mathematics learning at home during the COVID-19 pandemic across different stages of the response to it and across different contexts. We explore these strategies, first, in relation to the initial shift to emergency remote teaching when learners needed to be reached in their homes under severe lockdown regulations, then through the gradual reopening of schools later as regulations were relaxed. Activity theory informs our perspective on the way in which teachers worked to mediate learning across school and home activity systems. Twenty-five Grade 4-7 mathematics teachers from the Eastern Cape responded to two questionnaires given at the start of the COVID-19 lockdown period and during the phased return to school. Questions focused on the strategies used to support mathematics learning. The results show that strategies focused on engaging caregivers through various technologies and getting resources into the home. WhatsApp, a free internet-based messaging service, was the most frequently used communication app across all types of schools for both messaging parents and sending instructional material and support in the form of videos, pictures and text messages. Department issued workbooks and teacher designed work packs were key resources sent to homes. Differences are evident in the range of use of different technologies across wealthier and poorer schools. Primary teachers' voices inform possible ways forward for the purpose of managing young student mathematical learning gaps and meeting ongoing learning needs.

在发现首例病例两年多后,2019冠状病毒病大流行继续给教育部门带来严峻挑战。我们探讨了在2019冠状病毒病大流行的不同应对阶段和不同背景下,南非教师用于支持在家继续学习数学的策略。我们首先探讨了这些策略,首先是在严格的封锁规定下,当学习者需要在家中接触时,最初转向紧急远程教学,然后随着法规的放松,逐步重新开放学校。活动理论告诉我们教师在学校和家庭活动系统中调解学习的方式。来自东开普省的25名4-7年级数学教师回答了在COVID-19封锁期开始和分阶段返校期间发放的两份问卷。问题集中在支持数学学习的策略上。结果表明,策略的重点是通过各种技术吸引照顾者,并将资源纳入家庭。WhatsApp是一款免费的基于互联网的即时通讯服务,是所有类型学校中使用频率最高的通讯应用,既可以给家长发短信,也可以发送视频、图片和短信形式的教学材料和支持。学校发放的工作手册和教师设计的工作包是送到家庭的主要资源。在较富裕和较贫穷的学校中,不同技术的使用范围存在明显差异。小学教师的声音为管理年轻学生的数学学习差距和满足持续的学习需求提供了可能的方法。
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引用次数: 2
Roles of technologies for future teaching in a pandemic: activity, agency, and humans-with-media. 技术在流行病中未来教学中的作用:活动、机构和媒介中的人。
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01429-4
Jhony Alexander Villa-Ochoa, Juan Fernando Molina-Toro, Marcelo C Borba

Research literature on the role of mathematics teachers during the COVID-19 crisis shows that teacher preparation for emergency situations is required. In reporting on this exploratory study, we present and analyse lesson plans created by seven future teachers for mathematics classes during the pandemic. Data were collected between April and October 2021 from 16 four-hour class sessions in a Mathematics Degree Program at a public university in Medellín, Colombia. The notion of Humans-with-Media and the Learning by Expanding theory were used as frameworks to understand what roles prospective mathematics teacher (PMTs) assign to technologies for teaching in pandemic conditions. The PMTs' uses of technology for teaching mathematics during a pandemic were categorized. The results show that technology was used to reorganize and reproduce mathematics teaching practices. This report addresses the impact of technology on the activity system, and we conclude with a discussion of opportunities and limitations of students' conceptions about teaching and technology during a pandemic.

关于数学教师在2019冠状病毒病危机中的作用的研究文献表明,教师需要为紧急情况做好准备。在报告这一探索性研究时,我们提出并分析了7位未来教师在大流行期间为数学课制定的教案。数据收集于2021年4月至10月期间,来自哥伦比亚Medellín一所公立大学数学学位课程的16节四小时课程。使用“人与媒体”的概念和“通过扩展学习”理论作为框架,了解未来的数学教师(pmt)在流行病条件下为教学技术分配的角色。PMTs在大流行期间对数学教学技术的使用情况进行了分类。结果表明,利用技术手段对数学教学实践进行了重组和再现。本报告讨论了技术对活动系统的影响,最后讨论了大流行期间学生对教学和技术概念的机会和限制。
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引用次数: 1
The impact of COVID-19 on the format and nature of academic conferences in mathematics education. 2019冠状病毒病对数学教育学术会议形式和性质的影响。
IF 3 2区 教育学 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s11858-022-01421-y
Johann Engelbrecht, Oh Nam Kwon, Marcelo C Borba, Hyunkyoung Yoon, Younggon Bae, Kyungwon Lee

The global COVID-19 pandemic has provided an opportunity to re-examine the possibility of organising virtual conferences in mathematics education, in which the social needs of participants can also be addressed. In this study we investigated the future impact that this change may have on the format and nature of mathematics education conferences. The study was conducted in two phases. We used an online questionnaire in which we asked participants to give us some input on the issues above. In the second phase of the project, focus group interviews were conducted with international mathematics education researchers. This study is an exploratory study, in which the sample was not developed in a way that could generate comparisons. The aim of the study was to raise possibilities about what may be the future of mathematics education conferences. Findings indicate that although academics are pro-actively thinking about alternative conference formats, the proven value of face-to-face conferences is still very real, showing that it is too early for us to have a clear vision of the future format of academic conferences.

2019冠状病毒病全球大流行为重新审视在数学教育领域组织虚拟会议的可能性提供了机会,与会者的社会需求也可以在其中得到解决。在这项研究中,我们调查了这一变化可能对数学教育会议的形式和性质产生的未来影响。这项研究分两个阶段进行。我们使用了一份在线问卷,要求参与者就上述问题提供一些意见。在项目的第二阶段,对国际数学教育研究人员进行了焦点小组访谈。这项研究是一项探索性研究,其中样本没有以一种可以产生比较的方式开发。这项研究的目的是提高未来数学教育会议的可能性。研究结果表明,尽管学术界正在积极考虑替代会议形式,但面对面会议的价值仍然非常真实,这表明我们对学术会议的未来形式有一个清晰的愿景还为时过早。
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引用次数: 2
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