如何在高等数学教学中培养学生的创新思维

创新是当今的时代精神.创新能力的培养是实施素质教育的重要目标之一.高等数学作为高等教育的重点基础课程,在训练和培养学生创新能力方面具有重要地位.如何在高等数学教学过程中培养学生的创新思维,提高创新能力是我们高等数学教学改革的重要任务.文章通过对当前教育形势的分析以及创新思维的特点的思考,从教学理念、教学模式以及教学内容三个方面讨论了在高等数学教学过程中学生的创新思维的培养问题.     

从高等数学教学谈学生创新能力的培养

为了得到最佳的教学效果,在教学过程中培养学生创造性的教学活动成为课堂教学的重要组成部分.本文分析了高等数学教学在培养学生创新思维方面存在的问题及原因,并以研究性教学为例,分析了在教学过程中如何实现对学生创新能力的培养.最后提出学生创新思维能力培养在教学实施中的几点思考.     

培养初中生创新思维能力浅述

如何通过课程培养初中生的思维个性,培养初中生的创造思维能力,是值得每位初中教师认真思考的问题,以下是我的一些教学实践和体会感受,与大家交流。一、创设创新思维课堂教学环境,培养学生的数学兴趣宽松、愉快的课堂教学环境是引发学生数学兴趣的重要因素.在课堂教学中,要注意引导学生养成独立思考的习惯;善于捕捉学生创造思维的灵感,保护学生创新思维的积极性,唤起学生探求、创新的欲望,激发学生乐于思考、善于思考、勤于思考的思维习惯,使学生在创新思维的海洋中体验探求数学的奥秘,教师要善于把抽象、枯燥的数学具体化、趣味化.当引进一…     

从失效到高效——再探数学课堂问题的有效设计

一、问题描述问题是创新的开始."看过问题三百个,不会解题也会问",通过恰时恰点地提出问题,提好问题,不仅能提高课堂的教学效率,而且可以使学生领悟发现和提出问题的艺术,逐步培养学生的问题意识,孕育创新精神.然而,现在的课堂教学中,很多问题都未能达到预期的目标,一些肤浅平庸的问题,再加上单调的问法,经常置学生于被动地位,抑制学生的思维活动,     

核心素养视角下高中数学探究式教学——以《等比数列前n项和》为例

当前高中数学课堂教学还存在很多问题,学生缺乏探索知识的能力,缺乏一定的钻研精神,有些数学教师已经采用一些新的方法,不过教师的方式与讲的内容结合的不是很恰当,还有部分教师教学形式老旧,无法有效锻炼学生的思维,不能很好促进学生的发展,没有做到让学生真正学会学习.新课标中提到学生的自主学习能力是要重点培养的,所以教师要一直探索适当的教学形式,以提高课堂教学效率,提高学生的综合能力.探究式教学方式把课堂真正还给学生,使学生积极参与课堂.本文以探究等比数列前n项和的公式推导为例,阐述探究式教学对促进学生思维发展、提高课堂教学效率的重要意义.     

设计各类题组,培养学生思维品质

现代数学教学论认为,数学活动的核心是数学思维活动.在数学教学中,我们应重视培养学生具有良好的思维品质,提高学生数学素质,这对提高中学数学教学质量有着十分重要的意义.在课堂教学中,实施题组教学,是有效培养学生的思维品质的重要手段.     

基于几何直观的微积分教学内容改革探索

探讨一种新的教学理念.以培养好学,善学,勤学的学生为目标,提高学生学习兴趣为出发点,改革教学内容为手段,提出改革微积分教学内容和方法的具体知识点,增加相应知识点的几何直观性,提高学生的课堂思考能力,活跃课堂教学,体验数学美感,培养创新思维,克服微积分抽象难于理解的难题.     

初中生数学解题教学有效追问的实践探索

随着素质教育的推进,培养学生综合能力逐渐成为各阶段学校的目标,而如何整体性的提高课堂教学的效率,则是现阶段亟需解决的问题.在初中数学解题教学中,教师通常通过提问的方式促进学生的思考和探究,但在这过程中也存在一定的问题.本文通过对解题教学与有效追问的概念以及有效追问的原则进行分析,提出三点强化当前解题教学中提问与追问有效性的对策,以促进学生掌握数学知识的本质,形成科学严谨的数学思维,最终实现对学生数学综合能力与素养的培养.     

促进数学高阶思维实现的问题驱动教学——以“函数单调性”一轮复习为例

<正>高阶思维是创新型人才必备的品质.在数学教学中如何培养学生的高阶思维,使课堂教学由知识本位向素养与思维本位转变、由低阶思维向高阶思维转变是当前课堂教学变革面临的重要问题,也是落实核心素养的关键突破口.随着数学核心素养“落地生根”于课堂,其中,蕴含反思、批判、创新、问题解决等高阶思维是核心素养达成的关键.     

高中数学教学中培养学生问题意识的实践与思考

数学的思想方法在社会生活与实践中是非常重要的,其中问题意识更是创新与创造的源头,因此,培养学生的问题意识是笔者始终想要追求的价值目标.这源于笔者对数学教育的理解:从本质而言,数学教育的目的是不断地改善和提高学生的思维品质.其中,笔者把提高学生思维的创造性作为数学教育的重点,即提高学生思维活动的创新程度,在课堂教学中着力培养学生分析、解决问题的能力,特别是培养学生发现、解决并延伸问题的能力.     

Building coherence in research on mathematics teacher characteristics by developing practice-based approaches

Scholars have debated which teacher characteristics are primary in determining teachers’ practice. Some claim that identity is at the core of teachers’ ways of being and acting; others argue that teachers’ actions depend principally on their knowledge or beliefs. We argue that, whichever is examined, it is important to study how teachers use specific characteristics in their work, and how the work of teaching is shaped by that use. We claim that this can be done by addressing research questions about teacher characteristics in ways that provide insight into how they contribute to shaping interactions in classrooms—what we call a practice-based approach. To develop and illustrate our argument, we discuss studies that exemplify what we mean by a practice-based approach to the study of a teacher characteristic and we unpack ways in which these studies distinctively contribute to understanding and improving practice. Further, we explore ways in which the development of practice-based approaches might support coherence across efforts to study different characteristics and innovation in studies that consider the interplay of different teacher characteristics in teaching.     

完善数学建模课程体系，提高学生自主创新能力

随着大学生数学建模竞赛的快速发展,全国大部分高校越来越认识到数学建模教学在大学生创新意识和实践能力培养中的重要作用,如何提高数学建模活动的成效成为普遍关注的问题。从数学建模课程的本质出发,尝试构建了较为完善的数学建模教学体系,达到数学建模教学贯穿大学生培养的全过程的教学理念。同时讨论了拓宽数学建模活动形式的途径和尚存在亟待解决的几个问题。     

Talking mathematically: An analysis of discourse communities

Discourse has always been at the heart of teaching. In more recent years, the mathematics education community has also turned its attention towards understanding the role of discourse in mathematics teaching and learning. Using earlier classifications of discourse, in this paper, we looked at three types of classrooms: classrooms that engage in high discourse, low discourse and a hybrid of the two. We aimed to understand how the elements of each discourse affected classroom learning, relationships between teachers and students, and participatory structures for students. Overall, our findings highlight the important relationship between cognitively demanding tasks and mathematical talk, and the power of discourse as a “thinking device” as opposed to mere conduit of knowledge. Our work also points to the under-theorized nature of hybrid discourse in mathematics classrooms, thereby providing some directions for pedagogy and further research.     

Developing shift problems to foster geometrical proof and understanding

Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students’ learning in experimental classrooms. However, these sequences involve often carefully constructed reinvention route, which do not fit the needs of teachers and students working from conventional curriculum materials. To help to narrow this gap, we developed an intervention—‘shift problem lessons’. The aim of this article is to discuss the design of shift problems and to analyze learning processes occurring when students are working on the tasks. Specifically, we discuss three paradigmatic episodes based on data from a teaching experiment in geometrical proof. The episodes show that is possible to create a micro-learning ecology where regular students are seriously involved in mathematical discussions, ground their mathematical understanding and strengthen their relational framework.     

Teaching and learning of inclusive and transitive properties among quadrilaterals by deductive reasoning with the aid of SmartBoard

Learning to identify Euclidean figures is an essential content of many elementary school geometry curricula. Students often learn to distinguish among quadrilaterals, for example, by categorizing their geometric properties according to two attributes, namely the length of the edges and the size of the interior angles. But knowing how to differentiate them based on their geometric properties does not necessarily help students to develop the abstract concepts of the inclusive and transitive properties among the quadrilaterals. With the aid of dynamic geometry multimedia software in SmartBoard (SB), a kind of digital whiteboard (DWB), we enhanced the teaching and learning effectiveness by the effect of “animation-on-demand” in classrooms. This is basically a dual delivery of geometric concepts by texts, narrations and words accompanied by pictures, illustrations and animations. The preliminary results of our study on 9-year-old students’ performance in tests given after three such lessons show that those students could differentiate with reasons why a square is a rhombus (inclusion) as well as a parallelogram (transitivity).     

思维定势在大学数学课堂创新教育中的迁移作用

从当今教育教学改革研究和创新人才培养的要求出发,结合大学数学课堂教学实践,阐述了思维定势在创新教育过程中的重要性,论述了思维定势在大学数学课堂教学中的正、负迁移作用,最后指出了消除思维定势的负迁移作用、培养学生的创新能力的方法.     

高等数学课堂教学的思考与探索

从问题驱动教学,数学建模实践,多媒体与网络教学三个方面论述高等数学教学方法和手段改革的必要性.以强化数学应用实践,提高学生创新能力为目标,结合实践中的一些具体做法,提出以"课堂+电脑+网络课堂+Internet"的多元化教学模式.     

浅谈高等数学习题课教学

探讨习题课教学应注意的问题．首先明确指出习题课的目的和意义,之后从重视对数学概念的理解运用、习题的选择、课堂互动等方面阐述如何提高课堂教学效率,以达到不断渗透数学思想、数学方法的目的,从而培养学生良好的思维品质．     

Inventing Creativity: An Exploration of the Pedagogy of Ingenuity in Science Classrooms

Concerns with the ability of U.S. classrooms to develop learners who will become the next generation of innovators, particularly given the present climate of standardized testing, warrants a closer look at creativity in science classrooms. The present study explored these concerns associated with teachers' classroom practice by addressing the following research question: What pedagogical factors, and related teacher conceptions, are potentially related to the demonstration of creativity among science students? Seventeen middle‐level, high school, and introductory‐level college science teachers from a variety of school contexts participated in the study. A questionnaire developed for this study, interviews, and classroom observations were used in order to explore potential areas of relatedness between pedagogical factors and manifestations of student creativity in science. Five categories ultimately emerged and described potential areas in which teachers would have to explicitly plan for creativity. These areas could inform the pedagogical considerations that teachers would have to make within their lesson plans and activities in order to support its manifestation among students. These provide a starting point for science teachers and science teacher educators to consider how to develop supportive environments for student creative thinking.