试论数学教学中数学思维的培养

在进行高等数学的具体授课过程中切实转变教育观念,将培养学生的创新精神和探索精神作为重点来抓,是实现学生数学素养全面提高的重要方法。高等数学作为现今大学科目设置的一门基础课程,授课教师在进行教学活动理应通过有意识的引导,培养学生尽快形成并熟练运用逆向思维能力、类比思维能力、归纳思维能力进行高等数学学习,为学生实现数学素质的全面提高奠定坚实基础。     

Preparing beginning teachers to elicit and interpret students' mathematical thinking

This study investigated how teacher education assignments can be designed to support beginning teachers in learning to do the work of teaching. We examined beginners' formative assessment practices—in particular, their eliciting and interpreting of students' mathematical thinking—in the context of an elementary mathematics methods assignment, and the ways in which the scaffolds provided shaped their practice. We found that the scaffolds differentially supported their practice and suggest strategic improvement of the focus and organization of different types of scaffolds. Findings from the study contribute to the conceptualization and design of scaffolds for practice-based learning opportunities in teacher education.     

英语议论文写作教学中学生批判性思维能力的培养

目前学生的写作能力不是很理想。原因是教师在教学中过多的注重语法,阅读等能力的培养,而忽略了学生思维能力的提升。写作作为思维输出能力的重要体现。议论文作为重要的写作题材之一,教师可以从选材,同伴互评,教师评价,反馈日记等多样形式来培养学生的批判性思维能力。     

从生态视角看英语写作课上学生思辨能力的培养

我国传统的大学英语写作过于重视语言知识能力训练而忽视了学生思辨能力的培养,忽视了学生分析问题、创新求异、以及对问题独立提出见解等思维能力的培养。因此,本研究从生态的视角探讨大学英语写作课的设计,尝试将生态学原理和写作课相互融合,提出从生态学视角看待写作课堂,探寻能促进学生思辨能力发展的写作课,促进英语写作课生态、平衡、动态、开放的发展,从而促进语言学习者的全面发展。生态视角下英语写作中学生思辨能力培养对学生的思辨能力产生了显著的积极影响,尤其是在激起学生写作热情以及思辨意识方面,同时,学生整体写作水平以及相关思辨技能也会有所提高。此外,本研究也提出对英语写作教学的改革建议,这对于学生思辨发展和写作教学等都有重要的启示意义。     

Making sense of student mathematical thinking: the role of teacher mathematical thinking

Educational Studies in Mathematics - In mathematical whole-class discussions, teachers can build on various student ideas and develop these ideas toward mathematical goals. This requires teachers...     

Professional noticing of coordinated mathematical thinking

Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.     

Inversion in mathematical thinking and learning

Inversion is a fundamental relational building block both within mathematics as the study of structures and within people’s physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and subtraction, and multiplication and division, have important implications in relation to flexible and efficient computation, and for the assessment of students’ conceptual understanding. It is suggested that the extensive research on arithmetic should be extended to take account of numerical domains beyond the natural numbers and of the difficulties students have in extending the meanings of operations to those of more general domains. When the range of situations modelled by the arithmetical operations is considered, the complexity of inverse relationships between operations, and the variability in the forms that these relationships take, become much greater. Finally, some comments are offered on the divergent goals and preoccupations of cognitive psychologists and mathematics educators as illuminated by research in this area.     

用数学思想方法探求函数最值

最值问题是在生产、科学研究和日常生活中常会遇到的一类特殊的数学问题 ,尽管其严格的理论指导需借助高等数学知识 ,但由于它与中学数学中许多的知识以及蕴含在这些知识中的数学思想方法紧密相关 ,训练思维能力效果显著 ,所以在高考和数学竞赛中占有相当重要的地位 ,成为近几年高考的热点内容之一。因此在高考数学总复习中 ,对解决最值问题的常用方法进行系统总结 ,并进行深化训练 ,从而提高学生解决综合问题的能力很有必要。本文就利用数学思想方法探求函数最值的常用方法进行归纳整理并举例说明之。一、利用巡数与方程的思想函数的思想 ,…     

论数学思维能力中的分类思想

数学思想是数学知识和方法在更高层次上的抽象与概括,分类是一种重要的数学思想,分类思想是根据数学本质属性的相同点和不同点,将数学研究对象分为不同种类的一种数学思想。分类以比较为基础,比较是分类的前提,分类是比较的结果。分类应在同一标准下具有完备性和互斥性,不同的类之间的逻辑关系是＂或＂,因此,分类的结果是集合运算的＂并＂,通过分类思想的学习,培养学生思维的条理性,缜密性,提高学生的思维能力。初中数学中,分类问题总体归结为两类,涉及数与代数、空间与图形,因此,分类思想是安徽省中考每年必考的核心思想方法。     

培养学生独立思考能力

前人对学生独立思考能力的研究侧重于从学校教育的角度进行阐述,提出建议,忽略了家庭教育、社会教育和自我教育在培养独立思考能力方面应承担的责任和所起的作用。本文指出要培养学生的独立思考能力,不能仅仅依靠学校一己之力,必须全民参与,并分别给出了相应的建议。     

利用"缺陷"来培养学生思维的严密性

在学习过程中,无论是掌握科学原理与概念,还是解决各种难题与应用,都离不开思维活动。从高中阶段学生的生理和心理特点来看,他们已经具备了较高的感知能力,且逻辑思维能力也有了很大的发展,并且喜欢独立思考问题及解决问题。但他们也存在明显不足,主要表现在思维方式欠科学性,准确性也有待于进一步的培养。笔者认为提高学生思维的严密性是解决上述不足的具体方法之一。所以就这一点而言对高中生思维严密性的培养就显得非常重要了。     

试析数学思想方法的迁移

论述了将数学思想方法迁移到数学之外领域的必要性和具体做法.     

Facilitating Asian students' critical thinking in online discussions

The purpose of the study reported here is to illustrate how an approach based on a culturally appropriate 'shepherd metaphor' has helped Asian students to cross cultural boundaries and to engage in critical thinking online. Asian students are under different levels of influence from the Confucian Heritage Culture, which cultivates students to revere authority, maintain harmony and avoid conflicts in public. This has a significant impact on Asian students' cultural readiness to verbalise critical thinking. This paper partially reports research undertaken in a large English as a Foreign Language reading class in Taiwan, in which 'shepherd leadership' was practised. Shepherd leadership involves knowing students individually, offering cognitive modelling, exercising leadership and discipleship, encouraging student leadership and calling on silent students personally to get them to participate. This approach, concentrating on Asian students' affective needs, cognitive modelling, passing leadership to students and reaching out to silent ones, was found effective.     

在英语阅读课中培养学生批判性思维能力

在我国的传统教学过程中,对批判性思维能力在教学中的运用和培养不够重视,在英语阅读教学中更是如此。由于英语阅读中对学生的语言结构和信息处理的要求比较高,需要学生对阅读文本进行深层次的理解,因此,就需要学生充分发挥出主体性批判性的阅读技能。大多数学生批判性思维能力不够强,所以,教师需要注意在英语阅读教学中培养学生的批判性思维能力。本文就批判性思维的含义和重要性进行研究,并探讨在英语阅读中培养学生批判性思维能力的对策,以便有效的提高学生的批判性思维能力,提高英语阅读效率。     

把数学思想渗透到解题方法之中

从数学教育的目的出发 ,阐述了数学思想和解题方法以及它们之间的关系。指出了当前在数学思想和解题方法教学上的一些不足之处 ,并结合实例提出了在解题教学中如何运用数学思想和解题方法的一些观点和做法。     

化学新课改中思维能力的培养

比较了学生思维能力培养与思维品质形成的显性知识形成过程和思考过程的不同.分析了学生学会认识探究事物变化的一般规律,介绍了培养学生思维能力与形成思维品质的方法,最终目的是达到培养学生具有创新精神、实践能力和终身可持续发展的能力.     

在半开放生物实验中培养学生的创造性思维

快速发展的社会需要具有独立思考和创新能力的人才,而创新人才的培养又是高校人才培养的重要目标之一,因此,如何培养学生的创造性思维成为了教学研究中的热点问题。以"叶绿体色素的分离和吸收光谱曲线"实验为例,采用半开放性的实验教学法,阐述了如何在生物实验教学中培养学生的创造性思维。     

Emergent mathematical thinking in the context of play

In the attempt to improve mathematical thinking for safeguarding our future societal needs, there is a worldwide tendency in schools to start training mathematical and arithmetical operations at an earlier age in children’s development. Recent theoretical developments and empirical research have pointed to alternative ways of approaching early mathematical thinking. In these latter approaches, mathematical development in the early developmental stages is seen as an emerging process in the context of children’s own activities that contributes to meaningful learning and stimulation of children’s cultural identity (Bildung approach). The discussion between the training approach versus the ‘Bildung’ approach is still intemperately going on. In this article, some outcomes of a research programme (based at the Free University Amsterdam) are discussed that present empirical studies and their theoretical background (cultural–historical theory, elaborated in an educational concept called ‘Developmental Education’) that demonstrates the promising potentials of promoting mathematical thinking through supporting young children’s appropriation of schematic representations and notations in the context of play.     

论数学教学中学生思维品质的培养

综合教育理论与教学实践 ,论述了在数学教学中培养学生思维品质的新思想和新方法 ,提出了培养学生思维品质的具体措施。