高考数学中程序框图的综合题

<正>数学高考中,程序框图的题目,常以选择题或是填空题的形式出现,这也是算法及程序框图的特点所确定的.近几年,算法与程序框图的题目也在发生着变化,不只注重算法与程序框图自身的相关内容,也在逐步与数学知识、方法等进行综合.在考查算法与程序框图知识的同时,也考查学生对数学其它相关知识、方法等掌握程度,提高了此类题目的综合性,使此类题目的考查形式多样,内容丰富,思维灵活,综合性强.     

相似三角形等积式问题证明“三部曲”

等积式证明问题是初中平面几何的重要内容,它涉及的知识内容广泛,有利于培养学生综合运用知识的能力.等积问题综合性强,类型繁多,涉及面广,难度大,加之许多学生由于基础知识不牢,不善于归纳总结,结果在解决等积问题时不能灵活运用,感觉问题的分析困难,甚至是无从下手,望而生畏.为此,     

浅析高考数学中的数列综合问题

在高考试题中,数列是必考内容.数列一般与方程、函数、不等式、导数、圆锥曲线等知识综合.常在知识的交汇点命题,综合考查应用意识和数学思想方法.呈现出综合性强、立意新、角度新、难度大的特点.因此,教师在复习数列时,应对往年的高考题进行精心研究,挑选其中的精品给学生,引导他们对习题归类,有意识、有计划地引导学生对新题的背景知     

《几何画板精品课件大全》(光盘)介绍

<正>几何画板精品课件大全是以中学数学基本内容为依据,以各章节重点难点课题为蓝本进行精心编制和设计,各课件设计理念新,制作方式活,紧扣知识点,信息容量大,知识发掘深,课件具有版面设计新颖.技巧性强,创新多变,可操作性强等特点,是为广大师生设计的精品教学辅导光盘.由于几何画板的开放性和交互性,老师们可根据教学的需要,对课件中参数进行控制或部分内容进行修改即可用在教学中.课件内容重点突出丰寓多彩;课件操作简明快捷易学易用;设汁理念科学求实求新求变;制作技巧灵活多样技术全面;界面设计清晰整洁新颖美观;课件展示动态多变生动形象.是老师的好帮手,是学生的良师益友.     

不同的视角 别样的精彩

<正>解析几何是高中数学的重要内容,也是高考考查的热点与难点.其知识综合性强,对学生的逻辑思维能力与计算能力等要求都较高.特别在计算能力方面,面对许多解析几何题学生常常因为复杂的计算而"知繁而退".所以解题方法的选择就显得特别重要,它体现了思考问题的角度.一、"设点的坐标"还是"设直线方程"     

中考阅读理解型试题简析

近几年来,阅读理解型试题一直活跃在各地的中考数学试卷上,成为广大师生关注的焦点.这类题型具有内容丰富、构思新颖、题样多变、知识覆盖面大、综合性强等特点.它一般是先给出一段材料,让学生通过阅读领会其中的知识内容、方法要领,然后理解实质,把握本质,并能加以应用,解决后面提出的问题.     

解最值问题忽视等号成立致错举例

最值问题往往涉及的知识点多、覆盖面广、综合性强,它是高考考查的一项重要内容.利用不等式中的等号成立求最值是解决最值问题的主要方法.运用这种方法,往往需要对相关对象进行适当的放大、缩小,或不等式之间进行传递、相加、相乘等变形.在此过程中,学生常常因忽视等号成立而导致错误,而且错误不易察觉.下面介绍几例,以引起复习中足够的重视.     

“直线与二次曲线关系问题的运算策略”教学设计与思考

1教学设计1.1教学需要分析适用对象分析:本课内容综合性强,适用于高三二轮专题复习阶段的学生.学习内容分析:直线与二次曲线的有关问题是高考的重点,此内容均出现在江苏2010年、2011年、2012年高考试卷的解答题中.教学目标分析:对直线与二次曲线的关系问题,学生往往有思路而难以算出最后正确结果,究其原因是学生不能根据题目条件,采取有效的运算策略,致使运算繁复.通过本课的教学,让学生获得解决此     

例析求不等式最佳系数的常用策略

不等式是高中数学的重要内容,题型灵活多变,对学生的思维能力要求较高.其中有一类已知含参数的不等式恒成立,求参数的最值(或范围)问题,称为求不等式最佳系数问题.这类问题频频出现于高考、竞赛、质检试题中,综合性强,充分考查学生数形结合、分类与整合、化归与转化等数学思想.本文以几道高考和竞赛试题为例,分析处理这类问题的常用策略,探寻破解之道.     

新型数学试题——掀起你的盖头来

《标准》指出,数学课程基本出发点是促进学生全面、持续、和谐地发展.学生的数学学习内容应当是现实的、有意义的、富有挑战性的,这些内容要有利学生主动地进行观察、实验、猜测、推理与交流等数学活动……动手实践、自主探索与交流合作是学生学习数学的重要方式.近年来,各地中考试卷不断涌现出大量具有探究性、实践性、创新性的试题,题型设计贴近生活、别具匠心.既符合了新课程理念,又适应了素质教育的要求.     

深入开展数学建模活动，培养学生的综合应用素质

数学建模时大学生综合应用素质培养的一种有效途径。本文首先分析数学建模在大学生实践创新能力和综合应用素质培养中的作用,在此基础上从数学建模的数学理念更新、数学模式和教学内容设计,教学方法运用等多个方面,研究了以培养学生综合应用素质为牵引的多焊接、全方位的数学建模教学模式,提出了一些创新性的实践做法,为教学建模数学与组织竞赛活动的开展提供参考。     

如何在高等数学教学中培养学生的创新思维

创新是当今的时代精神.创新能力的培养是实施素质教育的重要目标之一.高等数学作为高等教育的重点基础课程,在训练和培养学生创新能力方面具有重要地位.如何在高等数学教学过程中培养学生的创新思维,提高创新能力是我们高等数学教学改革的重要任务.文章通过对当前教育形势的分析以及创新思维的特点的思考,从教学理念、教学模式以及教学内容三个方面讨论了在高等数学教学过程中学生的创新思维的培养问题.     

普通高校公共数学课程分类分层模式优化研究

公共数学课程对实现高校的人才培养目标起着十分重要的作用.本文遵循因材施教的原则,科学设计了公共数学课程体系,采用一种新的教学模式———分类分层教学.提出了分层教学方法、教学内容、考核模式、分层教学管理的改革实施方案,使基础课程更加具有针对性.     

Mathematics classroom instruction excellence through the platform of teaching contests

In this study, we aimed to examine features of mathematics classroom instruction excellence identified and valued through teaching contests in the Chinese mainland. By taking a case study approach, we focused on a prize-winning lesson as an exemplary lesson that was awarded the top prize in teaching contests at both the district and the city level. The analyses of the exemplary lesson itself revealed important features on the lesson’s content treatment, students’ engagement, and the use of multiple methods to facilitate students’ learning. These features are consistent with what the contest evaluation committees valued and what seven other mathematics expert teachers focused in their comments. The Chinese teaching culture in identifying and promoting classroom instruction excellence is then discussed in a broader context.     

《数学实验》课程建设及分层次教学与实践

主要介绍在本科一年级讲授《高等数学》课程时同步分层次开展《数学实验》课程教学的教学模式、教学内容、教学方法与改革、课程考核办法,以及我们对《数学实验》课程的认识和建设过程.     

How well prepared are the teachers of tomorrow? An examination of prospective mathematics teachers' pedagogical content knowledge

There is a growing emphasis in the teaching profession on pedagogical content knowledge (PCK) as an important knowledge component. The study reported in this article investigates Turkish prospective mathematics teachers’ mathematics teaching knowledge in the numbers content domain. A series of 10 open-ended scenario-type questions were adopted to challenge 83 prospective mathematics teachers’ knowledge of the learner and presentation of content in the context of PCK. The participants’ responses were analysed by means of rubrics and scoring guides developed by the researchers. The results showed that many of the future teachers performed well in determining what misconceptions students might express in the given scenarios. However, a majority of the participants performed poorly on presentation of content in terms of instructional strategies. In line with these results, the authors offer some suggestions for teacher training programmes.     

Similarities and differences in teachers’ questioning in German and Japanese mathematics classrooms

This study aims to capture similarities and differences in teachers’ questioning in German and Japanese mathematics classrooms, specifically focusing on the stage of introducing new mathematical content. The author analyzed consecutive mathematics classes taught by experienced teachers in Germany and Japan, who were recruited based on their locally defined “teaching competence” in the Learner’s Perspective Study. The results revealed that even questions that required students to recall previously learned content or provide the results of a calculation, which were regarded as lower cognitive questions in previous studies, played key roles at the stage of introducing new mathematical content in both German and Japanese classrooms. Further, distinctive patterns in the sequences of teachers’ questioning were identified. These differences suggest what is valued as quality mathematics teaching in each educational system.     

大学一年级学生创新能力培养探索与实践

详细介绍了我们在主讲《工科数学分析》课程中以问题驱动的研究性微积分教学模式和培养学生创新能力的探索与实践.     

Adult learners' criteria for explanations

This article explores adult learners’ preferences for explanations of mathematical statements in terms of kinds of reasoning and formats of presentation. Based on data from questionnaires and interviews it is concluded thatfamiliarity andclarity influenced students’ preferences more than the format or reasoning used. A contrast between the factors influencing students’ choices and those of instructors is also reported. Implications for teaching and research are drawn from the study.     

Analyzing connections between teacher and student topic-specific knowledge of lower secondary mathematics

The interpretive cross-case study focused on the examination of connections between teacher and student topic-specific knowledge of lower secondary mathematics. Two teachers were selected for the study using non-probability purposive sampling technique. Teachers completed the Teacher Content Knowledge Survey before teaching a topic on the division of fractions. The survey consisted of multiple-choice items measuring teachers’ knowledge of facts and procedures, knowledge of concepts and connections, and knowledge of models and generalizations. Teachers were also interviewed on the topic of fraction division using questions addressing their content and pedagogical content knowledge. After teaching the topic on the division of fractions, two groups of 6th-grade students of the participating teachers were tested using similar items measuring students’ topic-specific knowledge at the level of procedures, concepts, and generalizations. The cross-case examination using meaning coding and linguistic analysis revealed topic-specific connections between teacher and student knowledge of fraction division. Results of the study suggest that students’ knowledge could be associated with the teacher knowledge in the context of topic-specific teaching and learning of mathematics at the lower secondary school.