数学解题反思与学生思维方法的培养

作者通过介绍关注数学解题反思,寻求查缺补漏,确保解题的合理性和正确性;探求一题多解和多题一解,提高综合思维能力;增强解题中思维的系统性、条理性和目的性,让学生逐步养成正确的思维方法和良好的思维习惯。这对于教师的教,比按部就班地传授知识更重要、更有效;对于学生的学,解题能力和思维品质能在更深和更高层次得到有效提高和升华。     

注重解题反思提高数学解题能力

在数学解题教学中，教给学生解题后反思的方法，培养反思习惯，不仅能有效地使学生对知识、技能的深化理解，而且对训练思维、促进知识能力相互转化具有特殊功效。积极反思，能促进学生探求一题多解和多题一解，提高综合解题能力。     

数学解题后的反思

"一题多解"教学法是培养学生从不同角度观察、分析、思考解题方法的重要课题,是高中数学教学的重要内容.本文结合新课标和高考新特点,从一道大家非常熟悉的不等式证明题入手,从解题到反思逐步引导学生发散思维,突出数学思想,知识融会贯通,使学生的思维空间更广阔,解题更富有灵活性.     

一题"多解"不是最终目的

在数学解题训练中,一题多解是训练学生发散性思维,培养学生思维的灵活性和创造性的一种有效方法,是培养学生勇于探索、勇于实践的良好品质的一种有效途径.但是,如何来认识一题"多解",是更好地发挥一题多解的训练作用的有力保证.     

数学解题后的反思

“一题多解”教学法是培养学生从不同角度观察、分析、思考解题方法的重要课题,是高中数学教学的重要内容。本文结合新课标和高考新特点,从一道大家非常熟悉的不等式证明题入手,从解题到反思逐步引导学生发散思维,突出数学思想,知识融会贯通,使学生的思维空间更广阔,解题更富有灵活性。     

解题反思:数学解题中被遗忘的角落

解题反思是对整个解题活动深层次的思考,是再发现、再创造的过程。数学问题的解决后,还应该更深一步挖掘题目隐含的条件,命题的目的,所涉及的知识要点和数学思想方法,进一步探讨解题过程的思维方式是否正确、合理、严谨;解决问题的策略是否巧妙,有无其他解法;本题的解法和结论能否进一步推广。反思解题过程,可以培养学生思维的严谨性;反思解题结果,可以培养学生思维的合理性;反思解题方法,可以培养学生思维的创造性;反思"一题多解、一题多变、一解多题",可以培养学生思维的发散性。     

在解题中发展学生的思维品质

<正>数学教学离不开解题,学生在解题的过程中可以巩固所学知识点,通常教师在讲解时就题论题、逐题讲解,对于一些典型问题还会抓住问题的本质特征进行开放式讲解,比如一题多解、一题多联、一题多变。如果仅仅是这样显然还不够,那么如何才能最大程度地发挥解题的作用呢?解题不是学习数学的终点,比"解"更重要的是"思",因此除了会解,教师     

例谈数学解题反思的收获

解题反思是对解题活动的深层次再思考．通过对错解原因的反思,可以帮助学生提高对数学知识理解的层次性;通过对解题策略的反思,可以帮助学生提高数学思维的变通能力;在解题结束后通过对原题的整体反思可以提高学生数学解题的“境界”,实现数学教学更高层次的目标．     

在解题教学中训练学生的创造性思维

数学教学的目的之一是培养学生的创造性思维能力,创造性思维的训练是提高教学质量、赋予学生丰富知识和高度智慧的关键.本文结合教学实践,就如何在解题教学中训练学生的创造性思维谈两点意见.1 多角度审题,训练学生创造性思维的广阔性 解题本身就是一个创造的过程,在解题教学中通过一些典型例子让学生进行一题多解,能开拓学生的思维广度,训练他们创造性思维的广阔性.     

数学解题与学生反思意识的培养

学生对于学习数学,需进行反思性学习.反思是数学活动的核心和动力,要指导学生反思,培养学生反思意识;通过反思,提高学生解题能力,让学生理清头绪,探求一题多解.     

如何随时随地和别人交谈

I never wanted to be anything but a broadcaster, a talker. And for 40 years, I＇ve been doing just that. To me, the ability to talk well is one of the great pleasures in life and can bring with it some of life＇s greatest rewards, I＇m not saying it＇s always easy. The vast majority of people would rather jump out of an airplane without a parachute than sit next to someone they＇ve never met at a dinner party. But the more you work at it, the easier it will be. To get you started, here are my five basic ingredients for learning how to talk to anyone, anytime, anywhere.     

通"情"达"理"--对新时期思想政治工作的思考

根据江泽民总书记“三个代表”的重要思想,阐述新时期如何发挥思想政治教育的优势,使这项工作做到入情入理,情理融合,达到良好效果。思考与探究的要点是情与理的同一性、差异性与辩证性。     

Early to Bed,Early to Rise

公鸡来报晓，催人起得早。谁要睡懒觉，脑子不开窍。早睡又早起，有个好身体。早起又早睡，     

统一认识明确目标狠抓落实促进职教发展

我省是一个科技教育大省,我省经济社会发展战略一是科教兴省战略,二是人才强省战略,三是工业强省战略,四是可持续发展战略.从我省发展战略来看教育问题,教育如何为这些战略服务?前两个战略要求教育为全省经济社会发展做出贡献,后两个战略也是以教育为基础的.高水平大学、农村基础教育、职业教育是三大教育战略.我省职业教育和我省发达的高等教育来比,和我们重视的基础教育来比,是一条短腿.全省整个教育结构是不合理的,是严重失衡的.陕西的职业教育到了非抓不可的时候了,我们应该加大力气,把职业教育推上去.     

转变观念,让历史课堂轻松愉快,努力推进素质教育

就如何改进历史课堂教学,如何培养提高学生的历史素质进行了论述,认为应先从教师自身进行改革、历史课教学在加强历史素质教育的同时应教出历史学科的学科特点,尤其应大力加强历史人文素质的教育,以提高学生人文素养.     

Exploratory Analysis to Identify Concepts,Skills, Knowledge,and Tools to Educate Business Analytics Practitioners

Recent technological advancements in data storage and processing have changed how companies conduct their business. An increasing number of firms have started putting their efforts in extracting information from their databases to improve profitability and reduce costs using quantitative approaches. Thus, the job market has been experiencing a rapidly growing demand for business analytics (BA) practitioners, and universities across the globe are increasingly responding to this newly emerged field by offering both undergraduate and graduate level degrees as well as certificate programs. Thus, this research aims to provide a framework for academic institutions to develop a state‐of‐the‐art master's in business analytics (MSBA) curriculum by identifying concepts, skills, knowledge, and tools (CSKT) that industry seeks in BA practitioners. Our data‐driven methodology utilizes peer institution analysis, indeed.com web scraping, and focus group analysis with mid‐ and senior‐level analytics leaders from major companies. Our contribution to the literature and recommendations to institutions developing MSBA programs are offered at the end.     

Reply to Stigler, Nusbaum, and Chalip

In this article, I show that many of Stigler et al.'s criticisms of my 1986 article are incorrect or based on assumptions that are implausible. I agree with their conclusion, however, that theories of cognitive development must include both domain-specific and general processes.     

Reply to Yen,Burket, and Fitzpatrick

In their response to my article, "Item Response Theory, Vertical Scaling, and Something's Awry in the State of Test Mark," Yen, Burket, and Fitzpatrick (this issue) question the validity of my field observations. I present evidence that validates those observations. They claim that my simulation was unrealistic. I present evidence (convincing, I believe) that they are simply misinformed. They argue that Thurstone scaling has several weaknesses. I present information that should enable them to understand the procedure better and that reveals that the supposed weaknesses do not, in fact, exist. They say they are very "up front" about not being able to measure students at the extremes accurately but claim the vast majority of students are assessed well, thus implying that my use of data for students at the 2nd and 98th percentiles led to conclusions that would not be found if other segments of the score distribution were examined. I duplicated the analyses at the 15th and 85th percentile points and demonstrated that they were wrong. Yen et al. seem to be convinced that the variance of performance decreases (they use the term "homogenization") as learning progresses. Using their published data for 7 on-grade tests administered at the beginning and end of each school year, when the same on-grade test form was used-thus eliminating any confounding introduced by scaling—I show that in 67 of 77 instances the variance increased. This should serve as convincing evidence to the most doubtful person that the variance of performance increases as learning progresses. Given that there is a serious problem, as clearly illustrated in Figure 2, I suggest some avenues that research could take to address it.