关于几道数学问题解答的再思考

作为一名中学数学教师,一直把<数学通报>当作必读之书.对其中每一期的数学问题也总是尝试着去做一做,而后去和下一期的解答对照一下,做对了,欣欣然,没解答出来的,既惊叹于编题者的高明,也唏嘘于自己知识的欠缺,慢慢地从中学到了不少的知识.     

把课堂还给学生——以一节解三角形习题课为例

如何让我们的数学课堂变得精彩?关键还得从教师做起,从课堂做起,把课堂还给学生,让学生大胆地去尝试,去思考,去表达,面对课堂上学生提出的新问题,教师要给予鼓励与支持,本文以一节解三角形习题课为例进行说明.     

对高中数学课堂教学改革的几点尝试与思考

教师的任务是教书育人，好的数学教师就要力争使自己所教的每一个学生都受到高质量的数学教育．为此，我们对数学课堂教学进行了整体改革的思考与尝试．指导思想是：（１）教育是为学生的持续发展打基础，数学教学应把提高全体学生的数学素质与修养作为中心任务．我们认为...     

来自国外的数学应用题一束

数学课堂上进行双语教学中,常常要接触到国外的数学应用题,学生不仅要能够阅读英语,了解其中的文字含义和数学题意,而且还要能建立简单的数学模型,并求解数学模型,通过这种训练方式来培养中学生的综合素质是我们近几年来的数学教学尝试。下面的内容请读者先阅读英语原题,检测一下自己的英语阅读能力,然后求解数学问题,最后再对照一下翻译稿,找一下差距或发现一点什么。     

125一类复数习题的自然引申——研究性学习的一次尝试

波利亚的“解题表”中有这样两个问句 :“你能用不同的方法得出结果么 ?你能应用这结果或方法到别的问题上去么 ?”其实 ,这完全是基于数学学科的一种特性 :数学的许多材料之间常常有着种种类似性 .本课设计 ,就是利用材料的类似性的研究性学习的一次尝试 :教师引导学生回忆了相关的内容后 ,随即提出了一个开放性问题 ,让学生在一个类似的领域中 ,自己去发现问题 ,提出问题 ,又自己去解决问题 .这是充分利用数学的特殊魅力 ,让学生自己去感受发现的新奇 .是否可以把这种做法 ,适当编辑后将来迁移到数学考试的命题中去呢——出一个有一定范围要求的开放题 ,要学生类似地去作出某些发现 ,并予以解决之——至少是可以设想与试验的吧 !     

对阶梯式累进电价问题的数学思考

《数学课程标准》指出：要培养学生“用数学的眼光去认识自己所生活的环境与社会”，学会“数学地思考”．更为关注是否向学生提供了具有现实背景的数学，包括学生生活中的数学．所以，我们教师在今后的数学教学中，要使学生“领悟”出数学知识源于生活，又服务于生活，引导学生能用数学眼光去观察生活实际，从而培养学生解决实际问题的能力．使学生感到生活中处处有数学，数学就在我们的身边．     

“玩转”两个直角三角形

直角三角形是最简单最常见的几何图形,她一直伴随着我们,但如何利用直角三角形作一些数学探究,恐怕并没有多少同学去尝试过.现在就让我们利用中心对称来探究两个全等或者相似的直角三角形的组合图形问题,探索以几个点为顶点的三角形的形状问题.     

放任乘法 收获成功

<正>乘法是数学最基本的运算,数、向量、式子都可以进行乘法运算．乘法运算就像是一眼活水,只要我们做一个有心人,放任乘法,大胆尝试,勇于探索,常可从中攫取新的解法,提升自己的数学素养．兹举数例,以飨读者．     

数学奇观

数学奇观黔西南民族师专王耀富自然界有许许多多的奇妙景观，也有形形色色的解不开的谜团。可是，小朋友们可知道，在人类自己创造的数学世界里，这样的奇观也不少。当然，光用眼是看不到。还要用心去想，去琢磨才行。下面我们就去看一看数学奇观吧！记注，要用脑子才看得...     

类比推理思想应用一例

在数学发现活动中,类比推理在提出猜想、确定研究方向、提供解题思路等方面发挥着重大作用.著名数学家、教育家波利亚说过:"在尝试去解一道题时,如果我们能成功地想到一道更为简单的类比题目,那么可以说我们是幸运的."     

“Playing the game” of story problems: Coordinating situation-based reasoning with algebraic representation

This study critically examines a key justification used by educational stakeholders for placing mathematics in context –the idea that contextualization provides students with access to mathematical ideas. We present interviews of 24 ninth grade students from a low-performing urban school solving algebra story problems, some of which were personalized to their experiences. Using a situated cognition framework, we discuss how students use informal strategies and situational knowledge when solving story problems, as well how they engage in non-coordinative reasoning where situation-based reasoning is disconnected from symbol-based reasoning and other problem-solving actions. Results suggest that if contextualization is going to provide students with access to algebraic ideas, supports need to be put in place for students to make connections between formal algebraic representation, informal arithmetic-based reasoning, and situational knowledge.     

线性代数课堂中的“教”与“学”

结合教学实践经验,从人才培养的角度阐述线性代数课堂教学中的思维培养问题.指出课堂教学中要善于创设和营造和谐民主、积极向上、与学生心理相融的良好的课堂氛围;设置有利于学生参与认知的教学环节,通过采用灵活的教学方式,激发学生思考;尊重学生主体地位,让他们在教学活动中获得最大的情感体验;充分利用直观形象思维,教学中贯穿直观的几何形象,激发学生学习的兴趣,激发他们的求知欲.     

Comparing the use of number sense strategies based on student achievement levels

The aim of this study is to compare students’ use of number sense strategies based on their mathematics success levels. Participants were 129 seventh graders from three elite secondary schools in Trabzon. Data were collected through a written examination with 10 problems and semi-structured interviews. Interview data were analyzed by considering students’ mathematics success and the differences and similarities among responses. Interviews were held with six students from two schools with different levels of mathematics success. The findings showed that students rarely used number sense strategies and mostly solved problems by using rules and algorithms. Even successful students seemed to have adopted the rule- and algorithm-based solution approach, making it necessary to investigate teacher criteria of mathematical competence. Another noteworthy finding from the interviews with students was teachers’ embrace of rule- and algorithm-based solutions when solving problems. The study finishes with an evaluation of the inclusion of number sense dimensions in secondary school mathematics textbooks in Turkey and recommendations for improving students’ number sense.     

Challenges students identified with a learning disability and as high-achieving experience when using diagrams as a visualization tool to solve mathematics word problems

This article addresses a much understudied topic and concern regarding how students of varying ability levels employ visualization as a strategy in mathematics learning. The importance of this topic can be found in its connection to students’ ability to solve mathematical word problems. Many students, particularly students with learning disabilities, often struggle to use visualization as a strategy and this impacts their mathematics performance. The purpose of this article is to present findings from a study that examined the challenges that students—those identified as learning disabled and high-achieving—displayed when using one visualization form, a diagram, to solve mathematics problems. Overall, nine challenges related to the use of diagram proficiency to solve problems were identified. Further, students with learning disabilities were found to be more likely than their high achieving peers to experience these challenges. Implications for practice are provided.     

高等数学教学现状调查分析

高等学校扩大招生后,非数学专业的数学教育面临很多问题,大部分人把这些问题归结为学生质量的下降造成的,这是不公正的.教学过程是一个系统的过程,从对1995级和2005级同一份高等数学(下册)试卷的考试情况进行分析,虽然可以显现出学生的差异,但这些差异不全是学生的质量的问题,应该与教学环境、教学要求、教学方法、师资条件以及社会发展环境等相关联,同时与学生的学习兴趣、学习能力是密不可分的.调查分析这些因素对当代学生的学习和数学教学的影响程度到底有多大,是有效提高大学数学教学质量的前提.     

A case study of pedagogy of mathematics support tutors without a background in mathematics education

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors’ provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.     

Improper Use of Physics‐Related Context in High School Mathematics Problems: Implications for Learning and Teaching

This article discusses potential pedagogical difficulties arising from using physics‐related contexts in high‐school mathematics problems. It is suggested that such problems should not require any external knowledge of physics by the students; meanwhile, the problems should not contradict the physics knowledge that the students may already have. Several examples of recently published textbook problems are presented along with the discussion of the context pitfalls. A simple technique (SCAN list) is proposed for evaluating the physics‐related mathematics problems.     

Students' attitude towards computer algebra systems (CAS) and their choice of using CAS in problem-solving

We explore students choice of using computer algebra systems (CAS) in problem-solving relative to their self-reported attitude towards learning mathematics with CAS. Our research design is a case study of nine Norwegian upper-secondary mathematics students with a wide range of attitude towards CAS. Our findings on routine problems indicate that (1) students use CAS whenever students perceive the problem as time-consuming regardless of their attitude towards CAS, and (2) students attitude affects their use of CAS whenever students perceive the problem as non-time-consuming. Norway, among other countries, has implemented CAS as an essential digital resource towards learning mathematics in upper-secondary school. Our discussion focuses on the implications of our findings have on local mathematics educators and national policy-makers.     

数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

高等本科院校学生数学建模能力的调查与分析

培养学生数学建模能力是数学教育界共同关注的热点问题.只有了解学生的现状才能做到有的放矢,提出有效的提升方法.本文通过问卷调查,收集数据,进行统计分析存在问题的原因,目的是了解学生的建模能力和其问题的根源,为下一步纠正问题,对症下药以及提出解决的方法准备理论基础.通过调查发现,高等本科院校的学生数学建模能力总体水平不高,学校对此的宣传度和重视度不足.本文在分析研究调查结果的基础上,提出对高等本科院校培养学生建模能力的几点启示.