高等数学“情境—问题”的教学实践——“数列的极限”教学案例

极限思想是高等数学中的重要思想,我们在数列的极限教学过程中,通过设置问题情境,加深了学生对极限概念的理解,培养了学生发现问题、分析问题、解决问题的能力。     

0.618的文化内涵

0.618神圣的黄金分割是世界上最美的数字,对0.618的研究可以追溯到古希腊时代。文章扼要阐述了0.618黄金分割的内涵,并介绍了0.618黄金分割在我们生活中的几个应用,使人们对生活、大自然、社会又有了另一层的理解。     

类比推理在高中数学教学实践中的应用研究

类比推理是一种常用且科学的研究方法,长期以来在数学教学中得到普遍应用,他不仅是数学教学中的重要内容,更是高中数学考试中受到命题人热爱的一大考点。类比推理是一种以两个事物的某些相同属性作为判断前提,以试图找出更多其他属性方面的相同点的推理方式,同时也是一种从特殊推向特殊的推理方法。对学生的实际研究能力和判断推理能力以及相关的思维发散都能取得很好的培养作用,在高中数学教学实践中更是起着非常重要的作用,为教学注入新活力的同时又能为学生的解决问题提供新的思维模式。     

初等数学与密码学

在中学里,新学科永远是中学学生感兴趣的一点,特别是现在网络时代,密码学更是中学时代学生想去探究的学科。本文将从中学基础的因子、模、同余、最大最因数介绍起,到深层次的逆元、群、多项式逐一讨论,且立足于中学数学与信息技术两门学科,通过一个个例子把中学数学中所蕴含的密码学基础知识传输给学生,以提高了学生兴趣,并为其它学科的学习打下基础。     

情境教学在小学数学教育中的应用研究

数学新课程的教学设计尤其注重充分发挥学生的主体作用,这就要求教师要在教学中设计合适的教学情境和教学条件,充分调动学生的学习热情和动力,引导学生主动参与到教学之中。本文以情境教学在小学数学教学中作用、实现情境教学的方法和应注意事项为重点,对情境教学在小学数学教育中的应用开展了较为详细的研究。     

Comparing performance: a cross-national investigation into the teaching of mathematics in primary classrooms in England and China

This article presents initial findings from an empirical study of the effectiveness of mathematics teaching (EMT). The article explores the teaching of mathematics in two very different contexts: England and China. Within each country, the target cohort of pupils were those aged 9–10 and overall, 19 teachers, 10 from England and nine from China, participated in the study together with their pupils (n = 562). Two internationally validated instruments were used to collect the data and teacher behaviours were also measured systematically. In addition, structured observation was undertaken in classrooms in both countries. The results show that, on average, Chinese teachers scored higher on effective teaching measures and Chinese pupils outscored their English peers in the tests that were part of the study. This research project is currently collecting qualitative data but its findings, to date, reinforce the findings from previous research studies suggesting that certain teacher behaviours and classroom factors work effectively to improve student learning outcomes.     

Supporting English second-language learners in disadvantaged contexts: learning approaches that promote success in mathematics

In the Australian context, children living in disadvantaged circumstances, whose second language is English, are one of the groups at risk of failing in mathematics. This paper explores the impact purposely developed learning activities (Representations, Oral Language and Engagement in Mathematics Learning activities) have on pupils' mathematics outcomes in the first three years of formal schooling (Foundation, Year 1 and Year 2). The participating group (n = 461) comprised 328 English language learners and 133 mainstream pupils. To ascertain the impact of the learning experience, pre- and post-tests were conducted at the commencement and completion of each school year. The results indicate that all of the children significantly improved, with English as a second language pupils showing the greatest gains, and achieving norm-referenced expectations for their age.     

The Efficacy of Using Diagrams When Solving Probability Word Problems in College

Previous experiments have shown a deleterious effect of visual representations on college students’ ability to solve total- and joint-probability word problems. The present experiments used conditional-probability problems, known to be more difficult than total- and joint-probability problems. The diagram group was instructed in how to use tree diagrams to solve conditional probability problems; the equation-only group was instructed only in the formulation of equations. Results indicated that the diagram group outperformed the equation-only group on a posttest of 10 near- and far-transfer problems given immediately and as long as 1 week later (Experiment 2). In addition, when rating their experience with the training phase the equation-only group reported significantly higher levels of frustration and lower levels of perceived success than the diagram group.     

Improved Appreciation of Mathematics Through an IBL Liberal Arts Mathematics Course

Abstract

The author has taught an inquiry-based liberal arts mathematics class using the text “The Heart of Mathematics: An Invitation to Effective Thinking” by Edward B. Burger and Michael Starbird a total of 20 times since Spring 2001. The students in this class have almost all been in non-technical majors and many started the semester with negative or ambivalent attitudes toward mathematics based on their prior experiences. The author has gathered responses from students in this class that illustrate significant changes in their attitudes towards mathematics during the course. In particular, the responses gathered at the end of the semester are often eloquent about understanding the great ideas of mathematics that students confronted in this course and about seeing many more and varied connections between mathematics and the “real world” than they had previously realized existed.     

类比法在“大学数学”教学中的应用

类比方法是用已有的知识和已掌握的技能去解决新问题,从而加深学生对新知识的理解,促进学生对新规律的认识;找出问题、探究问题、解决问题,有助于思想、方法和技巧的开拓与延伸。类比法对提高教学效果和培养学生的创新意识是十分必要的,也是课程改革所倡导的。介绍类比式教学的基本概念,分别大学数学的基础学科和应用学科两类课程来以类比式教学方法的使用情况。运用好类比式教学法将有助于学生加深对数学课程的认识,形成系统全面的知识体系。