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关于数学课标修订变化情况解读(转载)

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关于数学课标修订变化情况解读

作者:重庆师范大学    黄翔教授

 

重庆师范大学黄翔教授是国家课标修订小组核心成员,下面是黄翔教授关于《数学课程标准修订与小学数学课堂教学》的培训讲座整理稿

新修订课标主要呈现以下九大变化:

1. 基本理念“三句”变“两句”, “6条”改“5条”:

原来的“三句话”:

   人人学有价值的数学

   人人都能获得必需的数学

    不同的人在数学上得到不同的发展

现在的“两句话”:

    人人都能获得良好的数学教育

    不同的人在数学上得到不同的发展

(修订后与过去的提法相比:有更深的意义和更广的内涵,落脚点是数学教育而不是数学内容,有更强的时代精神和要求(公平的、优质的、均衡的、和谐的教育。)

6条”改“5条”:

在结构上由原来的6条改为5条,将原《标准》第2条关于对数学的认识整合到理念之前的文字之中,新增了对课程内容的认识,此外,将“数学教学”与“数学学习”合并为数学“教学活动”。

    原课标: 数学课程——数学——数学学习——数学教学——评价——信息技术

     修改后:数学课程——课程内容——教学活动——学习评价——信息技术

2.理念中新增加的提法:

     要处理好四个关系

     有效的教学活动是什么

     数学课程基本理念(两句话)

     数学教学活动的本质要求

     培养良好的数学学习习惯

     注重启发式

     正确看待教师的主导作用

    处理好评价中的关系

    注意信息技术与课程内容的整合

3.关于数学观的修改:

原课标:

   数学是人们对客观世界定性把握和定量刻画、逐渐抽象概括、形成方法和理论,并进行广泛应用的过程。

  数学作为一种普遍适用的技术,有助于人们收集、整理、描述信息,建立数学模型,进而解决问题,直接为社会创造价值。

   数学是人们生活、劳动和学习必不可少的工具,能够帮助人们处理数据、进行计算、推理和证明,数学模型可以有效地描述自然现象和社会现象;数学为其他科学提供了语言、思想和方法,是一切重大技术发展的基础;数学在提高人的推理能力、抽象能力、想像力和创造力等方面有着独特的作用;数学是人类的一种文化,它的内容、思想、方法和语言是现代文明的重要组成部分。

·     课标修改稿:

   数学是研究数量关系和空间形式的科学。

   数学作为对于客观现象抽象概括而逐渐形成的科学语言与工具 ……

   数学是人类文化的重要组成部分,数学素养是现代社会每一个公民应该具备的基本素养。

   要发挥数学在培养人的理性思维和创新能力方面的不可替代的作用

树立正确的数学教学观:教学活动是师生积极参与、交往互动、共同发展的过程。有效的教学活动是学生学与教师教的统一,学生是学习的主体,教师是学习的组织者、引导者与合作者。

数学教学中最需要考虑的是什么?数学教学活动应激发学生兴趣,调动学生积极性,引发学生的数学思考,鼓励学生的创造性思维;要注重培养学生良好的数学学习习惯,使学生掌握恰当的数学学习方法。

4.“双基”变“四基”。

“双基”:基础知识、基本技能;

“四基”:基础知识、基本技能、基本思想、基本活动经验

“四基”与数学素养:

       掌握数学基础知识

       训练数学基本技能

       领悟数学基本思想

       积累数学基本活动经验

《国家数学课程标准》制定组组长、东北师大校长史宁中教授提出了“数学教学的四基”,引起了数学教育界的广泛关注。以前强调的双基是指基础知识、基本技能,双基教学重视基础知识、基本技能的传授,讲究精讲多练,主张‘练中学’,相信‘熟能生巧’,追求基础知识的记忆和掌握、基本技能的操演和熟练,以使学生获得扎实的基础知识、熟练的基本技能和较高的学科能力为其主要的教学目标。现在提出的四基不但包括了基础知识、基本技能、还增加了基本思想、基本活动经验。

史宁中教授指出:“‘基本思想’主要是指演绎和归纳,这应当是整个数学教学的主线,是最上位的思想。”关于基本思想方法,陈老师为我们分析了数学思想方法的四大育人功能:一是有利于完善学生的数学认知结构;二是可以提升学生的元认知水平;三是可以发展学生的思维能力;四是有利于培养学生解决问题的能力。陈老师结合小学数学现有的课标教材重点给我们介绍了小学阶段涉及到的数学思想方法,比如分类、转化、归纳、数形结合、数学建模、猜想、符号化、方程与函数、极限等数学思想方法。他系统地为我们解读了这些数学思想方法的意义、在小学数学教学中的作用和价值以及应用时的注意事项,陈老师的分析让我认识到在教学中关注数学思想方法的重要性,在教学中渗透数学思想方法的必要性。

“双基”变“四基”,为数学教师提出了更高的要求,要求数学教师必须为儿童的学习和个人发展提供了最基本的数学基础、数学准备和发展方向,促进儿童的健康成长,使人人获得良好的数学素养,不同的人在数学得到不同的发展。“双基”变“四基”,任重而道远。

常用的小学数学思想方法:对应思想方法、假设思想方法、比较思想方法、符号化思想方法、类比思想方法、转化思想方法、分类思想方法、集合思想方法、数形结合思想方法、统计思想方法、极限思想方法、代换思想方法、可逆思想方法、化归思维方法、变中抓不变的思想方法、数学模型思想方法、整体思想方法等等。

·5.关于设计思路的修改:

   学段划分保持不变;

   对课程目标动词及水平要求的设计基本保持不变,增加了目标动词的同义词;

 

  对四个学习领域的名称作适当调整;

   对学习内容中的若干关键词作适当调整对其意义作更明确的阐释。

6.四个领域名称的变化:

原课标:数与代数、空间与图形、统计与概率、实践与综合应用

修改后:数与代数、图形与几何、统计与概率、综合与实践

7.主要的关键词的变化:

     原课标:数感、符号感、空间观念、统计观念、应用意识、推理能力

    修改后:数感、符号意识、运算能力、模型思想、空间观念、几何直观、推理能力、数据分析观念

最近一次修改又加上了:应用意识、创新意识。

符号感为何改为符号意识?

     符号感(Symbol Sense

     原课标:

“符号感”主要表现在:能从具体情境中抽象出数量关系和变化规律,并用符号来表示;理解符号所代表的数量关系和变化规律;会进行符号间的转换;能选择适当的程序和方法解决用符号所表达的问题。”

     修改稿:

“符号意识”主要是指能够理解并且运用符号表示数、数量关系和变化规律;知道使用符号可以进行一般性的运算和推理。建立符号意识有助于学生理解符号的使用是数学表达和进行数学思考的重要形式。”

     符号感与数感都用“感”,“感”的表述过多。符号感主要的不是潜意识、直觉。符号感最重要的内涵是运用符号进行数学思考和表达,进行数学活动。“意识”有两个意思:第一,用符号可以进行运算,可以进行推理;第二,用符号进行的运算和推理得到的结果具有一般性。所以这是一个“意识”问题,而不是“感”的问题。数学的本质是概念和符号,并通过概念和符号进行运算和推理。所以只能用“意识”。

8.关于课程目标的修改:

在总体目标中突出了“培养学生创新精神和实践能力”的改革方向和目标价值取向。

课程目标提法上的一些变化:

——明确了使学生获得数学的基础知识、基本技能、基本思想、基本活动经验(数学“四基)。

——提出了培养学生发现问题、提出问题、分析问题和解决问题能力。

——目标具体从“知识技能”“数学思考”“问题解决”“情感态度”四个方面阐述。

——学段目标的表述方式有所改变

9.关于内容标准的修改

结构上的变化:

数与代数的变化:(在内容结构上没有变化。)

第一学段:

①增加“能进行简单的整数四则混合运算(两步)”

②使一些目标的表述更加准确。例如将“能灵活运用不同的方法解决生活中的简单问题,并能对结果的合理性进行判断”,修改为“能运用数及数的运算解决生活中的简单问题,并能对结果的实际意义作出解释”。

第二学段:

①增加的内容:

● 增加“经历与他人交流各自算法的过程,并能表达自己的想法”。

● 增加“了解公倍数和最小公倍数;了解公因数和最大公因数”。

● 增加“在具体情境中,了解常见的数量关系:总价=单价×数量、路程=

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