基于“学生提出问题”的数学教学

数学教学是数学活动的教学,数学活动本质上是数学思维活动,数学思维活动是以数学问题为载体的。数学教学的主体是学生,数学教学的目标是促进学生数学素养的提升,让学生提问题就应该成为数学教学的基本要求。数学教学问题通常分为两类:现实世界中提出的问题和数学内部生成的问题,它们分别在研究实际问题和数学研究中产生。数学教学要为学生提出恰当的数学问题创设合适的条件,让学生经历提出问题、分析问题和解决问题的完整的数学过程,发展思维能力,提升学科素养。     

论数学问题提出和数学活动经验的关系

数学问题提出是数学活动经验的源泉之一,提出的问题作为结果性经验将成为下一数学活动的任务;问题意识、问题解决经验和外部数学活动经验等数学活动经验是数学问题提出的基础.数学问题提出和数学活动经验互为基础、相互引发、相互促进.通过数学"情境--问题"教学案例--"图形面积等分"检验了这种关系.     

提出问题：层次·因素·策略

20世纪80年代,在美国掀起了以问题解决为核心的数学教育改革运动,作为问题解决的一种手段,提出问题也随之成为人们关注的话题．在美国《学校数学课程与评价标准》（1989）和《数学教学的专业标准》（1991）等文件中,已经把提出问题作为数学课程的学习目标．这就是说,数学教学不仅要关注学生解决预先提出的数学问题,还要关注学生提出数学问题的活动,使提出数学问题成为数学活动的有机组成部分．在数学活动中,提出问题是指通过对情境的探索产生新问题,或在解决问题的过程中对问题的再阐述．它是教学活动中师生交往的重要手段,有助于培养学生的数学洞察力和对数学本质的理解．     

在数学课堂教学中要培养学生的问题意识

在数学教学中,数学问题是引发学生思维与探索活动的向导。通过问题,学生主动探究,发现数学的内在规律,认识并理解数学的本质,在活动过程中建构数学。数学问题的提出与解决,就是数学创造或再创造的过程,而要做到这一点,就必须加强学生问题意识的培养。下面,笔者从数学课堂中学生发现问题、提出问题、解决     

联系生活学数学,提高数学应用能力

在数学教学中要紧密联系生活实际学习数学,让学生从数学角度提出、认识和理解问题,培养学生提出问题和解决问题的能力。开展实践活动让学生在接近实际情境的实践性活动中应用数学,解决生活中简单的实际问题,培养创新意识和解决实际问题的能力。     

例谈对数学问题的探究、创新——由椭圆的第二定义想到的

问题是数学的心脏。虽然数学及其教学中的问题大量存在、层出不穷,但数学问题的发现和提出却离不开数学探究．换言之,数学探究活动是数学问题获得与解决的必由之路．因此在数学教学中,我们应大力提倡问题探究式教学,概括的说,即在课堂教学中,教师要不断地引导学生发现、提出问题,探究、     

数学活动教学设计随笔

一、贴近生活的初始问题是数学教学活动的起点数学教学是数学活动的教学 ,从本质上说 ,数学活动是一种思维活动 ,而数学思维活动又集中表现在提出问题和解决问题的过程中 .在“问题解决”的活动中 ,数学思想、思维方式与方法 ,不仅是学生掌握知识与技能的工具 ,而且是学生学习的对象 ,是促进学生逐步学会探索和掌握新知识所必须的科学方法 .从这个意义上讲 ,数学教学设计的中心任务就是要设计出一个或一组问题 ,进而把教学过程组织成为提出问题和解决问题的过程 ,让学生在解决问题的过程中 ,学习数学知识 ,发展数学能力 .基于上述观点 ,我们…     

在实践活动课中渗透数形结合思想

小学数学实践活动是数学学科内的综合实践活动,是在学生已有的生活经验和数学知识背景的基础上,综合运用所学的数学知识进行拓展延伸去解决现实生活中的实际简单问题.数学实践活动过程:即首先根据数学现实找出所要研究的对象,其次是引导学生自己探索、合作交流,最后对活动进行评价小结,进行反思.数学综合实践活动不同于一般的数学活动教学,它是以解决问题为抓手,在这个过程中,培养学生发现问题、提出问题、综合运用数学思想方法去分析解决生活中的问题的能力,激发学生的创新意识,培养学生的数学意识和数学精神.下面笔者谈谈在小学数学实践活动课中如何渗透数学思想方法.     

小议数学课堂中的问题分类

问题是数学课堂学习中的主动力;问题对思维具有定向作用,因此问题是探索活动中的路灯和灯塔。问题性是思维的本质属性,因此思维过程表现为提出问题和解决问题的过程。提出问题是探索活动的关键环节,新的数学问题的出现,既表现为数学思维的进展,同时又为更深入的数学思维活动提供了动力和规划了方向。数学课堂学习动力来自教师,是教师的向导性在发挥作用,     

浅谈数学课堂教学中的问题意识培养

数学问题意识是指人们在进行数学的认识活动中,活动主体对既有的知识经验和一些难以解决的实际或理论问题所产生的怀疑、困惑、焦虑、探究等的心理状态,并在其驱动下,不断提出问题、解决问题.它在数学思维过程乃至整个数学认识活动中占有重要的地位.数学问题意识和问题提出,是对数学"内在理性"的一种突破,指人以质疑索解的态度审视数学这门学科所形成的一种思维方式和文化观念,既是一种叛逆思维习惯,也是一种洞见古今的批判精神.在中学数学教学中,引导提出问题的途径很多,     

高中数学课程改革的现状及对策

高中数学课程改革是在剖析我国数学教育发展的历史与现状的基础上,综合世界各国课程改革的成果,进行的有益探索。改革的宗旨是力求减轻学生负担、提高学习兴趣、改善教学方式,但在如何处理数学推理证明、学生学业负担、教师业务培训、民族教学传统等方面仍有争议。高中数学教师要主动更新教学理念,转换教学角色;加强课程研究,提升教学能力;关注教学过程,改善教学方式,努力适应并积极参与课程改革。     

Do it this way! Metacognitive strategies in collaborative mathematical problem solving

Recent years have seen increasing interest in the role of metacognition in mathematical problem solving, and in the use of small group work in classroom settings. However, little is known about the nature of secondary students' metacognitive strategy use, and how these strategies are applied when students work together on problems. The study described in this paper investigated the monitoring behaviour of a pair of senior secondary school students as they worked collaboratively on problems in applied mathematics. Analysis of verbal protocols from think aloud problem solving sessions showed that, although the students generally benefited from adopting complementary metacognitive roles, unhelpful social interactions sometimes impeded progress. The findings shed some light on the nature of individual and interactive metacognitive strategy use during collaborative activity.     

Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs are a good place to start the process of redesigning mathematics curricula so that school mathematics will pay more than lip service to problem posing. Data are presented and analyzed showing that teacher education students can recognize the need for problem posing both in their own programs and in school mathematics curricula. Examples of problems posed by teacher education students are presented and discussed. An active learning framework for interpreting the role of problem posing in mathematics classrooms is presented.     

我国中小学数学课程中“问题提出”的演变——基于课程标准(教学大纲)的分析

中小学数学课程标准(教学大纲)中对“问题提出”的相关要求影响教科书的编写、教师的教和学生的学。采用内容分析法,对10份涉及“问题提出”的中小学数学课程标准(教学大纲)进行编码,通过定量、定性统计分析发现,中小学数学课程文件中对“问题提出”重视程度逐渐提高,建构起了从宏观到微观的“问题提出”体系;内容表述由单一逐步转向综合;目标要求由模糊笼统趋向于明确具体。未来还需要提高数学课程标准中“问题提出”的实践性;增强课程标准和教科书中“问题提出”的一致性;促进教师成为好的“问题提出”者。     

Mathematical problem posing as a measure of curricular effect on students' learning

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students' responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed.     

A Voyage of Mathematical and Cultural Awareness for Students of Upper Secondary School

Many papers have emphasized the need for and importance of particular examples and the underlying rationale for introducing a historical dimension in mathematics education. This article presents the development and implementation of a project, based on original sources, in a situation where the existing curriculum does not include history. The subject was conic sections and the motivating problems and original work which eventually found resolution in modern concepts. The project was carried out during the school year 2006–2007 with 18 students of a Greek experimental high school 2nd class (11th degree). It was devised as a series of worksheets, separate readings and oral presentations and written essays so that students might appreciate that mathematics evolves under the influence of factors intrinsic and extrinsic to it. Both epistemological and disciplinary issues are taken into account. Even though this work is just one case study, we have found that exposing students directly to primary sources in mathematics contributes greatly to motivation and understanding, and illustrates the nature of mathematics as a discipline and as a human endeavour.     

Effects of Instruction on Verbal Interactions During Collaborative Problem Solving

During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional activities were based on scaffolding instruction and included modelling problem solving, stimulating reflection, and giving feedback on the process of collaboration. These activities were gradually developed and implemented in collaboration with teachers who participated in the study. The main research question in this study was whether student collaboration while working in small groups creates a learning context where students work on open-ended problems and where instructional activities are aimed at stimulating collaborative problem solving in mathematics.To answer the research question, an experiment was undertaken in two classes in different schools. Two groups of students were videotaped while they tried to solve mathematics problems collaboratively. Observational data were analysed with a schema that was developed as part of this research. Analyses of the data showed that, in both groups, collaboration-oriented patterns increased during the school year. It is argued that the approach of gradual implementation of instructional activities that are designed in cooperation with participating teachers is effective in stimulating collaborative problem solving.     

数学教学中游戏运用策略探讨

在数学教学中,游戏能激发学生学习兴趣,调动学生学习的积极性,改变传统课堂教学模式,提高教学效果。然而在实际教学过程中,游戏运用还存在许多误区,只有走出这些误区,才能提高游戏运用的有效性,才能将教学效果最大化地呈现出来。文章分析数学教学中游戏运用存在的误区,对游戏运用策略进行探讨。     

高中生数学焦虑与其学业成绩的关系

分析高中生数学焦虑的现状,探究数学焦虑对高中生数学成绩的影响,为缓解高中生数学焦虑的心理辅导提供实证依据.采用自编的《高中生数学焦虑问卷》评估了207名高中生的数学焦虑水平,运用相关分析和回归分析探究高中生数学焦虑与学业成绩的关系.结果显示：高中生数学焦虑的平均得分为2.65;高中生的数学焦虑总体得分与其数学成绩呈显著性负相关（r=-0.322,P＜0.01）;高中生数学焦虑中的课堂学习过程焦虑和应考情景焦虑对其数学成绩具有显著的预测作用.     

Protocol Analysis as a Fruitful Tool for a Problem Posing Teacher Education

With respect to European science teacher education, a growing interest can be noticed in the idea that teachers should not be confronted with solutions to teaching problems but be given real teaching problems which are open to different interpretations. This ‘problem posing’ course strategy should pay attention to school students’ conceptions as well as existing and new (student) teachers’ conceptions. The present article deals with classroom protocol analysis as a tool for a problem posing teacher education. Some methodological aspects of the production and interpretation of this type of protocol are described. Experiences with classroom protocol analysis in the context of inservice courses in teaching and learning electrochemistry and in problem solving in chemistry are reported. The impact of the analysis method on chemistry teachers’ thinking is investigated by analysing protocols of teacher meetings. Implications for innovating science teacher education are discussed.