数学问题解决中的元认知

数学问题解决的复杂性和曲折性决定了解题过程必须有元认知的参与。文章在波利亚解题理论的基础上,阐述了数学问题解决中元认知所起的作用,并且提出了元认知培养的一些途径和方法,要善于活学活用提示语,从而使对自身解题活动的监控达到自我意识的水平。     

发掘元认知实现对波利亚解题思想的超越

近年来，在数学素质教育观下，人们深入研究并实践波利亚的解题思想。教学实践引发人们辨证地认识波利亚的解题观，因此对波利亚解题观需要再认识。要全面理解数学解题中的“元认知”函义：解剖“事例”透视数学解题活动能力差异及其成因，元认知的培训与训练是深化波利亚解题思想的重要手段。     

波利亚解题表在数学公式教学中的应用

波利亚解题表为解决各种数学问题设计了一个清晰、完整的流程,提供了大量的元认知提示语。以"等比数列求和"的教学为例,说明在数学公式教学中,可以结合波利亚解题表的步骤和提示语,预设包含"创设情境,提出问题""弄清题意,明确任务""类比联想,寻找策略""拟定计划,实施解决""回顾反思,评价总结"五个环节的流程,并运用丰富的启发性问题,引导学生自主提出问题、解决问题,经历研究一个数学对象的一般过程,在探索数学知识的过程中感悟数学思维方法。     

阅读 转译 分析——初中数学综合题审题教学例说

波利亚曾经说过,“掌握数学意味着善于解题”,而“善于解题”的关键之一是“善于审题”.     

论波利亚的元认知思想

波利亚是数学解题的思想大家,在讨论解题策略和猜想过程的论述中,轻松自然地描述了丰富的数学元认知知识、数学元认知体验和数学元认知监控.波利亚的元认知思想融入数学认知活动之中,是研究数学元认知的宝库,也是探索法的基本要求.     

专家型教师与熟手教师运用元认知提示语的数学课堂比较研究

运用课堂观察及录像文字记录稿分析的方法,对数学新授课中专家教师与熟手教师运用元认知提示语的状况进行比较研究,发现专家型数学教师善于运用元认知提示语使学生经历“思维和情感”的困惑,感受新学习内容产生的必要性,注重思维过程和思维策略的引导,较好地渗透了启发式教学思想;而元认知提示语运用较少的熟手数学教师“简单告诉”的教学行为较多,学习内容的生成不自然,注重思维结果的获得;元认知提示语的运用与数学教师的教学风格有关.需深化教师对元认知提示语教学价值的认识并合理运用,使数学教学自然而合乎情理.     

应用发散思维的三特征指导解题教学

数学教育家G·波利亚指出:“掌握数学就是意味着于解题,不仅善于解一些标准的题,而且善于解一些要求独立思考,思路合理,见解独到和有发明创造的题”.从波利亚的这段话可以知道,教会学生解题是教师教好数学,学生学好数学的重要目标.会解题、善于解题离不开良好的思维习惯,发散思维具有多端性、变通性和独     

精彩缘于创造性联想，彰显课本习题的魅力——一道习题的解法探索研究

波利亚说过“掌握数学意味着什么呢？就是要善于解题”．从某种意义上讲,学习数学就是在于学会解题．由于初中学生的年龄特征及数学认识结构水平,往往只热衷于做习题,却不对解题思路进行反思、     

点击"模型"的解题策略

波利亚认为：“中学数学首要的任务就是加强解题训练”，“掌握好数学就是意味着善于解题”，本文就如何利用“模型”来思考这一问题，谈一点自己的体会。     

元认知提示语指导下的数学师范生解题教学技能培养

元认知提示语是教师针对学生生动活泼的元认知活动的提问,若将其运用到中学数学解题教学之中,则能有效地改观解题教学重"解"轻"学解"的现状。本文介绍了将元认知提示语运用到数学师范生解题教学技能培养上的具体策略,并结合例题作了解题教学示范。     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.     

Improvement of one-cycle controller by use of proportional integral differential controller

1.IntroductionOne-cyclecontrolmethod,whichwasproposedaboutonedecadeago[1],hasbecomeanattractivemethodinspecialfieldssuchaspowerfactorcorrection[2-6],switchingamplifiers[7,8],etc.Themainideaofthiscontrollerisbasedonintegrationofdiodevoltageinone-cycleandforcesittobeexactlyequaltothereferencevalue.Themainadvantageofthiscontrollerisitsrealtimeabilitytorejectthevariationofinputvoltage[1].Despitethisgreatability,ithasnogoodperformancesinrejectingofloaddisturbanceandfollowingreferencecommands.Espec…     

库克斯顿城堡

城堡, 是欧洲典型的建筑之一, 每个城堡都有一个美丽的传说或是一段历史。从本期开始, 我们将推出“城堡之旅”, 带各位读者去浏览、观赏欧洲各地的城堡, 开始一段文化与历史的旅途!     

胡主席在印度,我却在中国

Today, Sunday morning, I sit thinking and typing at my computer. My thoughts are in my homeland, India and my body is in China. The body is here and mind there for a good reason. Mr. Hu is president and I am resident and both are in each other's countries (what a difference the absence of one small letter makes!). Mr. Hu will return in a few days and I will stay on longer.