中学课堂渗透数学文化的立足点和侧重点

数学是看不见的文化,数学文化是数学的思想、精神、方法、观点、语言,以及它们的形成和发展,其核心是数学观念。数学文化具有重要的教育价值。数学教育本质上是一种素质教育,是对数学文化的认识与传承,实施数学素质教育就是要充分发挥数学文化的价值。中学数学教育必须在教学过程中有机渗透数学文化,通过在数学史、数学概念的形成与发展、数学的应用、数学美的挖掘、数学的理性思维等方面展开数学教学,达到使学生进一步理解数学、喜欢数学、热爱数学的目的。     

写作——新课程下数学作业的有效尝试

传统的数学作业往往只停留在机械练习这一层面上,而数学写作这种极富创造性的新型作业形式,可以使参与数学写作的学生的创造性得到尽情释放,有利于激发和开发学生的潜能,有利于培养学生阐述数学知识和道理的能力。数学作文体裁可分为数学小论文、数学学习体会、数学日记、数学散文、数学诗歌、数学相声、数学谜语、数学对联、数学诗等等。     

在小学数学教学中引领学生发展

小学数学教学要关注学生数学学习情感、数学学习差异、数学学习过程,要激活学生数学学习兴趣、数学学习思维、数学学习策略,要发展学生数学学习习惯、数学学习能力、数学学习个性,从而实现引领每一个学生的发展。     

数学课应着力培养学生的思维能力与数学能力

<正>数学思维是一个由数学思维材料、数学思维方法、数学思维方式、数学思维观念组成的一个立体结构。前苏联教育家斯托利亚尔认为:数学教学应该是数学思维活动的教学。培养学生的思维能力,学会数学地思维,是当前小学数学教学研究的一个重点,是培养小学生数学能力的根本出路。笔者认为在小学生数学思维训练与数学能力的培养过程中应注重以下方面。一、数学思想观念应成为数学教学活动中的航标。数学是研究现实世界的空间形式和数量关系的科学,数学     

数学文化在小学数学教学中的渗透与融合

数学文化是文化的一种。简单来说,数学文化是指数学的思想、精神、方法、观点以及它们的形成和发展;详尽说,除上述内涵以外,还包括数学家、数学史、数学美、数学教育、数学发展中的人文成分、数学与社会的关系、数学与各种文化的关系。教学过程中,数学与文化结合最大的问题就是“文化是文化,数学是数学”的两层皮现象,其本质还是数学知识的教学。应该将数学与文化融为一体,有机地渗透、融合到数学课堂教学中来。     

成功数学教育研究

成功数学教育是通过数学管理者、数学教学者、数学学习者树立成功数学观念,采用成功运行机制最终使数学学习者数学才能获得成功的数学教育活动。成功数学教育的特征:面向全体数学学习者;数学潜能变成才能,并使之全面发展;数学学习不断成功;全程数学教育;全员数学管理。成功数学教育机制包括系统组织和和软组织穴观念雪,成功数学教育系统组织包括成功数学管理、成功数学教学、成功数学学习三部分,成功数学教育软组织穴观念雪主要是期望——机会——评价机制。     

地方高师院校数学专业师范生数学素养的调查研究

数学专业师范生的数学素养包括三个方面:数学知识、数学能力、数学情意。数学专业师范生具备较强的数学情意,数学能力比较薄弱;数学专业素养在不同年级和性别之间存在不同程度的差异;数学情意、数学知识、数学能力与数学专业素养的相关性依次增加;数学师范生的数学知识、数学能力、数学情意间都存在显著的正相关。     

数学素养背景下小学数学教学中数学文化的融入策略探究

所谓"数学素养"泛指个体在社会实践活动中体现出一定水平的数学能力,能够高质高效地利用数学思维、方法、工具等解决现实问题,且具有一定的反思、改进及创新能力。"数学文化"是影响数学素养的重要因素,它既包含狭义上的数学观点、语言、思想等,也包括广义上的数学历史、数学审美、数学价值观等。文章以小学数学为研究对象,以提升学生数学素养为目的,通过论证数学文化与数学素养之间的关系,探索小学数学教学引入数学文化的策略。     

让学生先“做”后“学”

美国数学家哈莫斯指出：“学习数学的唯一方法是做数学。”数学新课标积极倡导“做数学”,将过去的说数学、听数学、课堂中的数学,转变为做数学、生活中的数学。如何“将数学作为一种活动来解释和分析”,“将现成的数学转化成做出来的数学”呢？     

数学教学怎样体现“文化味”

小学数学教科书中的数学文化是数学文化的启蒙,主要包括数学史、数学家的故事、数学趣闻和数学趣题、数学应用、数学思想和方法。通过这些知识的了解,可以丰富学生所学的知识,激发学生学习数学的兴趣,拓展学生的视野,形成良好的文化氛围,坚定学生学好数学的信心。所以小学数学的数学文化的教学是非常重要的,也是应该重点关注的一个问题。那么怎样在小学数学教学过程中强化数学文化的教学呢?     

Alternaria toxin-induced resistance against rose aphids and olfactory response of aphids to toxin-induced volatiles of rose plants

The search for active toxins for managing weeds or plant diseases is believed to be a promising avenue of investigation. However, the effects of Alternaria toxins on insects have just begun to be investigated. Bioactivities of toxins from four strains of Alternaria alternata on Rosa chinensis and rose aphid Macrosiphum rosivorum were tested in the present study. At a concentration of 50.0 μg/ml, the crude extract (toxin) of strain 7484 was found not to be harmful to rose plants with excised leaf-puncture method (P≥0.079), and rose plants showed enhanced resistance to rose aphids when this Alternaria toxin was sprayed on the plants (P≤0.001). However, this toxin caused no detrimental effects on aphids in insecticidal bioassay at a concentration of 10.0 to 160.0 μg/ml (P≥0.096). Therefore, the Alternaria toxin had significantly induced the resistance of rose plants against rose aphids, demonstrating that the resistance mechanism triggered by the Alternaria toxin in the rose plant may also be used by the plant to defend itself against insects. Further bioassays aimed to discover the olfactory responses of aphids to the toxin-induced volatiles of host plants. The aphids were significantly more attracted to both volatiles emitted and collected from control rose plants than to both volatiles emitted and collected from the toxin-treated rose plants (P≤0.014). This result showed that the toxin-induced resistance related to the volatile changes of host plants.     

Formative assessment strategies for students' conceptions—The potential of learning analytics

Formative assessment is considered to be helpful in students' learning support and teaching design. Following Aufschnaiter's and Alonzo's framework, formative assessment practices of teachers can be subdivided into three practices: eliciting evidence, interpreting evidence and responding. Since students' conceptions are judged to be important for meaningful learning across disciplines, teachers are required to assess their students' conceptions. The focus of this article lies on the discussion of learning analytics for supporting the assessment of students' conceptions in class. The existing and potential contributions of learning analytics are discussed related to the named formative assessment framework in order to enhance the teachers' options to consider individual students' conceptions. We refer to findings from biology and computer science education on existing assessment tools and identify limitations and potentials with respect to the assessment of students' conceptions.

Practitioner notes

What is already known about this topic

• Students' conceptions are considered to be important for learning processes, but interpreting evidence for learning with respect to students' conceptions is challenging for teachers.
• Assessment tools have been developed in different educational domains for teaching practice.
• Techniques from artificial intelligence and machine learning have been applied for automated assessment of specific aspects of learning.

What does the paper add

• Findings on existing assessment tools from two educational domains are summarised and limitations with respect to assessment of students' conceptions are identified.
• Relevent data that needs to be analysed for insights into students' conceptions is identified from an educational perspective.
• Potential contributions of learning analytics to support the challenging task to elicit students' conceptions are discussed.

Implications for practice and/or policy

• Learning analytics can enhance the eliciting of students' conceptions.
• Based on the analysis of existing works, further exploration and developments of analysis techniques for unstructured text and multimodal data are desirable to support the eliciting of students' conceptions.

     

Fostering children's acceptance of educational apps: The importance of designing enjoyable learning activities

Educational applications (apps) offer opportunities for designing learning activities children enjoy and benefit from. We redesigned a typical mobile learning activity to make it more enjoyable and useful for children. Relying on the technology acceptance model, we investigated whether and how implementing this activity in an app can increase children's intention to use. During the 27-day study, children (N = 103, 9–14 years) used the app to memorize one-sentence learning plans each day. Children used three different app-based learning activities throughout the study. In two standard activities, children reread or reassembled the words of the plan. In the redesigned activity, children represented the meaning of the plan with emojis. Children repeatedly reported on their attitude towards each activity. Subsequently, children reported perceived enjoyment and intention to use the app. Results showed children found the emoji activity most enjoyable, and enjoyment of the emoji activity contributed uniquely towards intention to use. Additionally, children's enjoyment of the app mediated their intention to use the app in the future. Overall, the study suggests that children's enjoyment of an app is crucial in predicting their subsequent intention to use, and it provides a concrete example of how emojis can be used to boost enjoyment.

Practitioner notes

What is already known about this topic

• Educational applications provide children with unrestricted access to mobile learning resources.
• Positive attitudes towards educational applications predict behavioural intention to use these applications, at least in young adults.
• There is a need for more research examining the relevance of enjoyable learning activities in fostering children's sustained usage of an educational application.

What this paper adds

• Positive attitude towards the use of emojis during learning activities uniquely contributed to children's behavioural intention to use the application.
• Perceived enjoyment predicted behavioural intention to use the application.
• Perceived enjoyment mediated the effect of attitude towards using learning activities on the behavioural intention to use the mobile educational application.

Implications for practice and/or policy

• These findings highlight the importance of enjoyment for children's' acceptance of educational applications.
• Enjoyable learning activities are necessary to ensure sustained usage of educational applications.
• The paper provides a concrete example of how emojis can be used to boost enjoyment of a typical mobile learning activity.

     

Trust and improvement in schools

This paper examines how trust affects teachers’ willingness to work with innovations introduced by central office administrators. Interview and focus group data collected over a three-year period in five schools are used to analyze the centrality of trust to teachers’ willingness to work with administrators to implement continuous improvement and quality management practices for their schools and classrooms. A qualitative data analysis software package was used to code interviews and focus groups for spontaneous comments that addressed trust. Two schools were characterized by high trust, and high willingness to change; high levels of distrust distinguished three others. This emphasis of the analysis is on the association of spontaneously expressed sentiments of trust or distrust and the association of those sentiments with willingness to participate in change initiated from outside the school building. Pre-existing patterns of relational and institutional trust will enhance or limit the ability of leaders to initiate large-scale change. More needs to be known about how to change coherently distrustful school settings in order for systemic change to occur.

What’s in a name? Preschoolers’ noun learning performance in relation to their risk for reading disability

This paper reports the findings of an investigation aimed at gaining a clearer understanding of the nature of vocabulary difficulties associated with dyslexia and associated risk status. Three studies were conducted to examine preschoolers’ access and mastery of syntactic- and phonological-based processes believed to support word learning. Results are reported for 82 participants whose (reading) risk status was assessed from a composite of measures known to be related to reading development. As expected, risk status correlated positively with participants’ ability to recall the phonological form of novel nouns. No relationship was found between risk status and participants’ use of syntactic form-class cues in interpreting the noun class of novel names in isolation. However, the ability to use form-class cues was impaired for at-risk participants on a task that required them to learn both the phonological form and noun class. Findings are discussed in relation to the suggestion that limitations in processing resources such as working memory rather than in the availability of language structures may be at the root of the reported poor performance by at-risk children on vocabulary and other linguistic measures.

On ‘developing a framework for critical science agency through case study in a conceptual physics context’

This paper provides a review of research that examines the development and expression of agency in and through high-school physics. The interchange offers realizations and questions brought to mind by the reading of the research and provides written comments connected to specific sections of the paper germane to my own theoretical perspective. Within the context of this commentary, raised issues are discussed in a dialogic manner in order to elucidate deeper understanding concerning the empirical investigation presented in the study. As a final point, a brief synopsis is put forward regarding some of the contributions that studies such as the one reviewed have to offer for providing equitable access to science for all students.

Professional Responsibility – An Issue for Higher Education?

The aim of this article is to shed light on some aspects of professional responsibility by investigating students’ visions of future work and notions of professional responsibility. The data is based on interviews with samples of freshmen in three educational programmes at the University of Oslo in Norway. The data has been analysed in relation to two thesis claimed by Steven Brint: “The rise of a utilitarian ethos” in higher education and the movement from “social trustee professionalism” to “expert professionalism”. The findings show that the students in our sample do not think of higher education primarily as a means to get credentials that will be useful in the labour marked. An intellectual interest in the discipline is the most prevalent reason for the students’ educational choices. Furthermore our findings support an orientation towards “expert professionalism” rather than “social trustee professionalism”. But, embedded in the perspective of an expert there is an emphasis on ethical knowledge, moral and/or societal responsibility and the wish to do good for others. However, the students’ sense of responsibility seems to be restricted to certain “localism” of their specific occupation. Based on the findings we argue that the students reveal a moral awareness that should be taken seriously by the educational institution in order to foster critical rationality and professional commitments.     

Using causal models to bridge the divide between big data and educational theory

An extraordinary amount of data is becoming available in educational settings, collected from a wide range of Educational Technology tools and services. This creates opportunities for using methods from Artificial Intelligence and Learning Analytics (LA) to improve learning and the environments in which it occurs. And yet, analytics results produced using these methods often fail to link to theoretical concepts from the learning sciences, making them difficult for educators to trust, interpret and act upon. At the same time, many of our educational theories are difficult to formalise into testable models that link to educational data. New methodologies are required to formalise the bridge between big data and educational theory. This paper demonstrates how causal modelling can help to close this gap. It introduces the apparatus of causal modelling, and shows how it can be applied to well-known problems in LA to yield new insights. We conclude with a consideration of what causal modelling adds to the theory-versus-data debate in education, and extend an invitation to other investigators to join this exciting programme of research.

Practitioner notes

What is already known about this topic

• ‘Correlation does not equal causation’ is a familiar claim in many fields of research but increasingly we see the need for a causal understanding of our educational systems.
• Big data bring many opportunities for analysis in education, but also a risk that results will fail to replicate in new contexts.
• Causal inference is a well-developed approach for extracting causal relationships from data, but is yet to become widely used in the learning sciences.

What this paper adds

• An overview of causal modelling to support educational data scientists interested in adopting this promising approach.
• A demonstration of how constructing causal models forces us to more explicitly specify the claims of educational theories.
• An understanding of how we can link educational datasets to theoretical constructs represented as causal models so formulating empirical tests of the educational theories that they represent.

Implications for practice and/or policy

• Causal models can help us to explicitly specify educational theories in a testable format.
• It is sometimes possible to make causal inferences from educational data if we understand our system well enough to construct a sufficiently explicit theoretical model.
• Learning Analysts should work to specify more causal models and test their predictions, as this would advance our theoretical understanding of many educational systems.

     

Navigating privacy tensions when responding to online aggression at postsecondary institutions

Postsecondary institutions have a legal responsibility to ensure that students have access to a safe learning environment. While institutions adopt policies and hire administrators to protect students from harm, many are underprepared to support students when these harmful incidents happen online. This is of increased concern now that online aggression is pervasive across universities worldwide. While faculty, administrators and students agree that online aggression is a significant issue and that institutions ought to provide prevention and response services, there is concern that these efforts might violate privacy norms. We used the theory of privacy as contextual integrity (CI) to explore the tensions that postsecondary students and staff perceive regarding student privacy when responding to incidents of online aggression. To do so, we conducted focus groups with undergraduate students and student affairs administrators from a Historically Black College and University (HBCU) in the Mid-Atlantic USA. Our analysis surfaced three considerations that inform students' and staff's decision to report an incident of online aggression: their closeness to the person making the post, their perception of the online post content as a real threat and their knowledge of an authority figure who could help resolve the situation. We used CI theory to explain how these considerations can inform institutional policy, practice and future research.

Practitioner notes

What is already known about this topic

• Online aggression is a pervasive issue at postsecondary institutions worldwide that can contribute to psychological, academic and developmental issues.
• Postsecondary students and staff are unsure of how to respond to incidents of online aggression.
• There is a gap in policies and procedures for responding to online aggression at postsecondary institutions.

What this paper adds

• A novel use of Nissenbaum's (2010) theory of contextual integrity to understand students' and staff's perceptions of privacy.
• Students' and staff's decisions to intervene or report an online aggression incident are determined by their relationship to the perpetrator, the severity of the social media post and their knowledge of who to tell on campus.
• Students and staff are reluctant to inform the police out of fear of violence against the perpetrator.

Implications for practice and/or policy

• Raise awareness about responding to online aggression incidents.
• Implement online bystander intervention training programs to increase awareness and self-efficacy to intervene in unclear situations.
• Develop clear policies regarding online aggression, as well as a trustworthy procedure for how to respond.