数学研究性学习的教学设计与实施

研究性学习不是脱离课堂的孤立性的学习,它应当灵活地贯穿于教学之中．笔者着重从明确知识与默会知识之间的关系谈数学研究性学习的教学设计与实施．     

如何正确看待经验学习

随着数学教学改革的逐渐深入,不少教师转变过去的传统教学方式,尝试探究性教学,让学生转向经验学习.本文讨论的是这个过程中教师应该注意些什么.首先,并非所有的经验都是有意义的学习,只有那些有一定基础的新经验才有教育意义.而且,从知识分类的角度看,书本知识应该是可以讲授的,但是像解决问题的能力这样的默会知识的确只有通过学生亲自实践才能够掌握.最后一点值得提醒的是,除了在课堂上设计问题之外,布置作业也是一个让学生进行经验学习的很好机会.或许因为担心落入俗套,对这个方面我们的关注太少.总之,在设计探究性教学的同时,教师应该多问问自己：“我们的教学目的到底是什么?这样做是否真的能够对学生的学习有所帮助?”     

基于默会知识的初中数学概念教学路径探寻

<正>默会知识就是一种大家都在用,只可意会不可言传的知识,是相对于明确知识而言的.默会知识的特点包括：一是情境性,是基于情境的一种直观感受;二是实践性,在实践中应用与意会;三是主体性,主体只有参与实践才会领会.学生每学习一个概念,都会启动相应的默会知识,在学习任务下,自觉搜索、联想默会知识,从而让新知在头脑中复活.1 概念引入,启动默会知识默会知识是基于情境的一种直觉感受,具有情境性.因此,创设一定的情境,可以启动学生的默会知识,     

让学生形成连贯一致的知识脉络——初中相似三角形复习课的尝试

数学复习课是数学教学的重要组成部分,在平常的课堂教学中,多数教师把学过的知识再“炒一遍”,或以大量的习题进行题海战术,学生在这种复习中,只会做讲过的习题,知识迁移能力不强,收获不大．因此复习课除了进行专题训练以外,也要尝试帮助学生建立相对系统的知识脉络,探求数学学科的本质．     

数学知识间的相互联系探析

数学知识具有很强的系统性,各知识间有着内在联系.数学的新知识是在人类已有知识的基础上发展的,因此数学知识间结构严谨,系统性强.学生在学习新的数学知识的过程中,理解与掌握数学知识之间的联系,对理解数学概念,培养数学思维,发展数学兴趣有着重要的影响.     

加强策略性知识学习,提升解题瓶颈的突破能力

在数学教学中有一个问题非常值得重视:有时学生对有关数学概念和公式已经了然于心,但遇到具体的题目求解时还会思维受阻,在经人点拨或查阅答案后,发现自己根本没有知识和逻辑推理的障碍,但在独立解题时,就是因为一些关键步骤"没想到",从而导致解题的失败.本文就加强策略性知识教学来提升学生解题瓶颈的突破能力作些探讨.1突破解题瓶颈需要加强策略性知识学习认知心理学理论认为,人脑中对于知识有三种类别的建构,一是描述性知识,主要回答是什么的问题,学生的学习体现在是否记住和理解这些概念和内容.二是程序性知识,主要是一些公式及推理法则,学生的学习体现在是否能利用它们进行推理运     

“兴趣”走进初中数学课堂

“知之者不如好知者,好知者不如乐知者．”由此可见兴趣是推动学生学习的一种内部动力,学生一旦对数学产生了兴趣,就会充分发挥其主观能动性,高效率获取知识．那么,如何增强学生学习数学的兴趣,使学生达到乐学的境界呢？     

学会用整体视角看问题

每一个学科都是一个知识的整体,数学也不例外．因此,在数学学习中,以一种整体的视角来理解所学的知识内容,看待遇到的数学问题,对学好数学至关重要．     

“三会”为数学课堂教学定向明标——以《三角形的中位线》教学为例

数学课程要培养的学生核心素养主要包括：会用数学的眼光观察现实世界、会用数学的思维思考现实世界、会用数学的语言表达现实世界(简称“三会”).如何在初中数学教学中落实“三会”目标,已成为每一位数学教师面临的实践问题.本文以《三角形的中位线》教学为例,谈一谈具体的做法与思考.     

探析立体几何与相关知识的“交汇性”

在“知识网络的交汇点设计试题”是近几年高考数学命题改革的重要理念和方向．这就要求在数学学习中，要善于有效地把握好知识间的纵横联系和综合应用，打破各章节的界限，对所学内容融会贯通，运用自如，形成有序的网络化的知识体系，以开阔视野，形成能力，全面提高数学素养．本文就立体几何与其它知识的“交汇性”，对这方面问题作如下探析，仅供参考．     

基于改进SIR模型的知识密集型企业隐性知识转移研究

通过对比分析传染病传染机制与隐性知识的转移过程,引入SIR模型,根据隐性知识转移的特点对SIR模型进行改进,并在组织遗忘视角下,将员工知识遗忘细分为主动遗忘和被动遗忘,建立知识密集型企业隐性知识转移模型.而后,通过Matlab对该模型的演化函数进行模拟,分析知识接收方占比、知识转移能力、知识遗忘率及核心员工流失率对知识密集型企业隐性知识转移的影响.最后,基于模拟分析结果,为提升知识密集型企业隐性知识转移效益提出相应策略.     

供应链节点企业隐性知识转化的博弈分析

供应链隐性知识与显性知识的相互转化形成螺旋上升的价值创造过程,其中隐性知识是核心.在由多个制造商和多个零售商组成的两级复杂供应链中,考虑知识的含量与成本是负线性相关的情况下,制造商和零售商依照自身利益的最大化进行隐性知识转化决策,使得其存在背离隐性知识显性化的行为.但是在多阶段中,其它节点企业会采取一定的惩罚措施,最终使得其重新回归到隐性知识显性化的行为上.     

面向电力虚拟社区的隐性知识云处理模型

当前电力虚拟社区中非结构化的隐性知识资源数量与日俱增,然而由于其中自由的问答交流模式,导致解决具体问题的隐性知识淹没于大量的无效信息中,电力相关从业人员难以快速从中获取适用性好的隐性知识;同时,随着电力虚拟社区的大规模扩张,激增的数据量将带来存储扩展性和快速检索的问题.为此提出一种面向电力虚拟社区的隐性知识云处理模型MPTKKM.模型以模式匹配算法为核心,设计了可以自动建立电力隐性知识应用情景描述关键词序列的隐性知识收集算法,采用分布式键值对的存储模式,并基于云计算技术实现了电力隐性知识检索.实验结果表明,提出的模型不但能自动收集适用性好的电力隐性知识,而且云检索算法表现出了良好的可扩展性.     

创意团队隐性知识转移绩效影响因素的实证研究

文章采用问卷调研获取一手数据,运用PLS—SEM方法测度了各类因素对创意团队隐性知识转移绩效的影响。研究发现,PLS—SEM方法对观测数据拟合精度较高,在样本数据非正态分布、共线性等情况下仍然稳定。实证结果表明:团队情境、吸收能力、转移意愿、转化能力、媒介丰富度由大到小对创意团队隐性知识转移绩效产生正向影响,而隐性知识特性必须通过对知识源转化能力的显著负影响才能间接影响知识转移绩效。     

Using the Knowledge Quartet to develop mathematics content knowledge: the role of reflection on professional development

In this paper I report findings from a four year study of beginning elementary school teachers which investigated development in their mathematical knowledge for teaching (MKT). The study took a developmental research approach, in that the teachers and the researcher collaborated to develop the mathematics teaching of the teachers, while also trying to understand how such development occurred and might be facilitated. The Knowledge Quartet (KQ) framework was used as a tool to support focused reflection on the mathematical content of teaching, with the aim of promoting development in mathematical content knowledge. Although I focused primarily on whether and how focused reflection using the KQ would promote development, it was impossible to separate this from other influences, and in this paper I discuss the ways in which reflection was found to interrelate with other areas of influence. I suggest that by helping the teachers to focus on the content of their mathematics teaching, within the context of their experience in classrooms and of working with others, the KQ framework supported development in the MKT of teachers in the study.     

一个数学建模问题的简单解法

银行利率给出了一个简单计算方法 ,这种方法更符合中学生思维的习惯 .     

The missing link in teachers’ knowledge about common fractions division

The current study explored the difficulties teachers encounter when teaching common fractions division, focusing on teachers’ knowledge concerning this issue. Nine teachers who study towards a M.Ed. degree in mathematics education demonstrated the algorithms they apply in order to solve fractions division problems, described how they teach the subject, and attempted to explain a student's mistake, in understanding a word problem involving dividing by fraction. The findings indicate there is a missing link in the teachers’ pedagogical capability, stemming from insufficient content knowledge. They presented different solution algorithms and reported using constructivist teaching methods, yet the methods they described couldn't lead a student to understand the logic behind the algorithm they teach (invert-and-multiply – multiplication by an inverse number, in accordance with the requirements of the curriculum). Furthermore, the participating teachers did not possess specialized mathematics content knowledge (SCK) and knowledge of content and students (KCS), enabling them to identify the source of a student's misconception.     

An in-service primary teacher’s implementation of mathematical tasks: the case of length measurement and perimeter instruction

The purpose of this paper is to examine the cognitive demand levels of tasks used by an in-service primary teacher during length measurement and perimeter instruction and to examine a possible link between these tasks and the teacher’s mathematical knowledge in teaching. For this purpose, a case study approach was used and the data was drawn from classroom observations, semi-structured interviews, and field notes. Specific tasks from length measurement and perimeter instruction were presented and analyzed according to the Mathematical Tasks Framework. Then, how these tasks gave information about the teacher’s mathematical knowledge in teaching in the length measurement and perimeter topics was examined according to the Knowledge Quartet model. According to the findings of the study, the tasks used during length measurement and perimeter instruction were mostly categorized as low-level tasks. In addition, teacher’s mathematical knowledge in teaching affected the implementation of the tasks.     

Mathematics teachers’ views about the limited utility of real analysis: A transport model hypothesis

In the United States and elsewhere, prospective teachers of secondary mathematics are usually required to complete numerous advanced mathematics courses before obtaining certification. However, several research studies suggest that teachers’ experiences in these advanced mathematics courses have little influence on their pedagogical practice and efficacy. To understand this phenomenon, we presented 14 secondary mathematics teachers with four statements and proofs in real analysis that related to secondary content and asked the participants to discuss whether these proofs could inform their teaching of secondary mathematics. In analyzing participants’ remarks, we propose that many teachers view the utility of real analysis in secondary school mathematics teaching using a transport model, where the perceived importance of a real analysis explanation is dependent upon the teacher’s ability to transport that explanation directly into their instruction in a secondary mathematics classroom. Consequently, their perceived value of a real analysis course in their teacher preparation is inherently limited. We discuss implications of the transport model on secondary mathematics teacher education.