常微分方程课程分层教学的探索与实践

随着高校扩招,高等教育由精英教育转化为大众教育,由于学生的基础和水平参差不齐,传统的"一刀切"教学模式很难适应现在的高等教育.尝试将分层教学的理论应用到常微分方程课程的教学实践中,提高了学生学习的兴趣和自主学习的能力,使不同层次的学生在学习的有效性、数学应用能力等方面都有不同程度的提高.     

分层教学中的“三个注重”

学生的个体是有差异的,表现为认知方式与思维策略的不同,以及认知水平和学习能力的差异.教师要及时了解并尊重学生的个体差异,满足多样化的学习需要,让不同的人在数学上得到不同的发展.这就需要在日常教学中实行分层次教学.要想达到高效的分层教学目的,必须做到“三注重”才能达到使不同程度的学生在同一课堂中,获得不同程度知识吸收的目的,促进学生学习水平的提高和学习能力的发展.     

分层递进教学的理论与实践研究

素质教育要求面向全体学生 ,实现全体学生的全面发展 ,分层递进教学是落实这一基本精神的有效途径 .所谓分层递进教学 ,就是针对班内不同学习水平的学生 ,提出不同的教学目标 ,创设不同的教学情景 ,使各层次的学生都能经过努力得到最优发展 .它不仅克服了传统教学因教学内容、要求、方法都同步划一所带来的种种弊端 ,而且保证了教师主导作用 ,学生主体作用的发挥 ,提高了学生参与教学活动的积极性 ,使不同层次的学生都能找到自己的主攻方向 ,制定自己的学习进程 ,学会学习 .下面来探讨它的理论依据和实施策略 .1　理论依据分层递进教学以最…     

带动学生学习初中数学的几点尝试

教师的教育思想和教学方法的不同将直接影响着课堂教学效果.在课堂上利用科学的方法带动学生主动参与教学过程,使教学课堂持续活跃,促进学生思维持续发展,将有助于学生的成长.探索带动学生的学习方法优化课堂教学是非常重要的.     

多元情境在初中数学教学中的有效创设

新课标多次强调,当代教育背景下,必须创造学生喜欢的课堂,让学生能够主动、积极地参与到学习中,提高学生的学习效果与质量.教师需要立足实际,合理设计教学情境,使学生形成逻辑思维,提高综合能力.当然,很多时候教师教学中更倾向于使用灌输的教学方式.教师所用的单调、枯燥方法,很难激发学生学习的兴趣,无法保障数学教育的质量和效果.教学中,教师必须以课程标准作为参考,打造多元、有趣的教学课堂、情境.有了不同情境的引导,学生才能进入深度学习状态,从而获得更好的教学质量.多样化的情境能够深化核心素养教育,对学生未来的成长有积极影响.     

分层教学在高中数学课堂上的应用

<正>在“学为中心”的教学理念下,促进不同层次学生在数学学习上的不同发展是十分重要的,这样,才能为提升他们的数学核心素养奠定基础.当前,我国高中教学实施的是大班化教学模式,由于学生基础知识水平、对知识的理解和认知都存在差异,教师在课堂上很难兼顾所有学生,久而久之就会造成学生成绩呈现出差异,尤其是数学学科,差异性会表现得更为明显.分层教学是兼顾学生差异性的教学方式,是指教师通过寻找不同层次学生学习中的平衡点,为各种学情的学生提供更好的指导.     

对《高等数学》教材建设的一点看法

在高等教育进入到大众化教育时期,建设《高等数学》教材,必须以学生为本.要编写有利于提高学生学习兴趣、启发学生思考和培养学生的能力、适合不同层次学生需要和以后实际需要的教材.     

赏识教育理论在高职院校数学教学中的应用

高职数学虽然不是职业院校的专业课程,但却是高职院校非常重要的专业基础课和必修课,能否学好高职数学直接影响学生相关专业课程的学习,与学生的终生教育密不可分.赏识教育强调对学生以欣赏为主,主动不断发现学生的优点和长处,并对这些优点和长处进行针对性表扬和鼓励,使学生处于较好的学习认知状态,产生较好的学习动机和学习欲望,取得较好的学习效果.将赏识教育运用于高职数学教学的实践中,不仅可以改变高职学生在数学学习上的自卑感,而且在学生的主观幸福感、学习动机和学业成绩等方面具有十分重要的作用,对于提升高职数学的教学效果具有非常积极的意义.     

浅谈Dirchlet积分的教学

在高等数学的教学中,有一些很重要的结论对不同专业的学生来说,由于数学知识水准不一,在推导它的结果时,需要用不同的处理方法,以便不同层次的学生接受.     

分层教学——有效课堂教学的研究和实践

1问题的提出在中学数学教学中,由于学生对数学的兴趣、对知识的接受能力存在着客观差异,导致不同学生对知识的领悟与掌握能力有很大的差异.若按同一标准要求学生,必然不能发挥某些学生的才能和特长,在以素质教育为核心的教育改革的今天,更应当注重学生的个性发展.针对上述情况,笔者对“面向全体,正视差异,分层推进”的课堂教学策略进行了初步研究和实践.2理论依据美国著名教育家布卢姆提出的“掌握学习”理论,强调每个学生都有能力学习和理解任何教学内容,达到掌握水平.笔者也认为,绝大多数学生之间的差异更多在于对知识接受速度的差异,只要给予足够的时间和有针对性的指导,学生们都能达到掌握水平.而分层教学正是根据学生个体间存在的差异性,将全班学生分为若干层次,并针对不同层次学生的特点和基础,采用个别指导、分组教学和集体讲授三种形式的组合,使教学目标、教学内容、教学速度以及教学方法更符合学生的知识水平和接受能力,符合学生实际学习的可能性.避免不分对象“一刀切”的弊端,把因材施教提升到可操作水平,大大提高了教学效率,是班级授课制条件下实施个别化教学的有效模式.3具体实施分层教学是在学生分层的基础上,有针对性地进行教学目标分层、授课分层、作业...     

Toward a model for students’ combinatorial thinking

Combinatorics has many applications in different disciplines, however, only a few studies have explored students’ combinatorial thinking at the upper secondary and tertiary levels concurrently. The present research is a grounded theory study of eight Year 12 and five undergraduate students, who have participated in semi-structured interviews and responded to eight combinatorial tasks. Three types of combinatorial tasks were designed: combinatorial reasoning, evaluating, and problem-posing tasks. In the open coding phase of data analysis, seventy-one codes were identified which categorized into seven main categories at the axial coding phase. At the selective coding phase, five relationships between categories were identified that led to designing a model of students’ combinatorial thinking. The model consists of three movements: Horizontal, vertical downward, and vertical upward movement. It is asserted that this model could be used to improve the quality of teaching combinatorics, and also as a lens to explore students’ combinatorial thinking.     

教学质量评估的定量比较评价模型

依据华南农业大学 2 0 0 2学年第一学期课堂教学质量评估卡的调查数据 ,利用层次分析法建立了学生评价教师教学质量的定量评价模型 P =WR,并应用该模型对担任数学类课程的 1 3位教师的课堂教学质量作了定量比较分析 .分析结果表明 ,近几年来的扩招 ,对教师的教学提出了新的要求 ,在教学内容、教学手段、教学方法等方面 ,应做出相应的调整 ,才能收到好的教学效果 .     

Differentiation of teaching and learning mathematics: an action research study in tertiary education

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.     

Toward a student-centred process of teaching arithmetic

This article describes a way toward a student-centred process of teaching arithmetic, where the content is harmonized with the students’ conceptual levels. At school start, one classroom teacher is guided in recurrent teaching development meetings in order to develop teaching based on the students’ prerequisites and to successively learn the students’ arithmetic. The students are assessed in interviews. Two special teachers participate and their current models of each student's arithmetic are tested when assessing the students. The students’ conceptual diversity and the consequent different content in teaching are shown. Further, the special teachers’ assessments and the class teacher's opinion of the new way of teaching are reported. A wide range both of the students’ conceptual levels and of the kinds of relevant problems was found. The special teachers manage their duties well and the classroom teacher has so far been satisfied with the new teaching process.     

Evaluating and Improving a Learning Trajectory for Linear Measurement in Elementary Grades 2 and 3: A Longitudinal Study

We examined children's development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching. We checked the hierarchical structure of the trajectory by generating formative instructional task loops with each student and examining the consistency between our predictions and students' ways of reasoning. We found that attending to intervals as countable units was not an adequate instructional support for progress into the Consistent Length Measurer level; rather, students must integrate spaces, hash marks, and number labels on rulers all at once. The findings have implications for teaching measure-related topics, delineating a typical developmental transition from inconsistent to consistent counting strategies for length measuring. We present the revised trajectory and recommend steps to extend and validate the trajectory.     

Incorrect but instructive

This note is a possible contribution to the teaching of mathematics. We present a variety of examples of wrong proofs, misinterpreted definitions and the mistaken use of theory. The examples are based on our experience of teaching mathematics to engineering students. They include elementary examples and more advanced ones, and are taken from different subjects. In analysing the mistakes, we try to use them to improve the students' understanding.     

基于电子信息领域创新型人才培养的微积分教学改革探索

电子信息类高校是培养该领域创新人才的重要基地,作为核心基础课程之一的微积分在其中发挥着重要作用.在建设创新型国家的时代背景下,从创新思维、创新能力和创新综合素质等方面讨论了微积分教学改革在电子信息领域创新型人才培养中的积极作用,并从三个不同视角分析了微积分教学改革所面临的诸多机遇和挑战,最后结合教学实践经历对开展微积分教学改革的具体措施浅谈一些思考与尝试.     

Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories

In our research work, we have looked at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical activity. The issues related to the use of tools and technologies in mathematical education are now widely considered. A look to history highlights the different ways in which the same questions have been studied at different times and in different places. This suggests that the contribution of artefacts to mathematics learning should be considered in terms of various contexts. Our “visits” to these contexts will be guided by the coordination of two main theoretical frameworks, the instrumental approach and the semiotic mediation approach from the perspective of mathematics laboratory. This journey through history and schooling represents a good occasion to address some questions: Are there “good” contexts in which to develop mathematical instruments? Are there “good” teaching practices which assist students’ instrumental geneses and construct mathematical meanings? How is it possible to promote such teaching practices? Some study cases are discussed.     

“问题解决”教学模式在高等数学教学中的实践运用与实验结果分析

根据学生学习的实际状况提出"问题解决"教学模式,教师以问题的形式进行教学的同时,创设问题情境,培养学生的各种能力.对试验结果用T检验法进行分析,得出用"问题解决"教学模式进行教学比传统教学模式有显著差异.