独立学院数学课程体系的探索

为解决独立学院数学教学中能力强的学生"吃不饱",能力欠佳的学生"吃不消"的问题,提出了"基础+提高"统筹优化的数学课程体系."基础"模块的教学坚持为后续专业课服务,并穿插教书中"育人"理念;"提高"模块作为公共选修范畴,具有自主性、多元化特点,并突出人才培养的阶梯式发展.通过近5年的教学改革与实践,新课程体系有效地提高了学生学习数学的兴趣,降低了期末考试的不通过率,并造就一批有创新意识的人才.     

注重数学概念教学 发展问题解决能力

数学概念是中学数学教学中至关重要的内容,是基础知识和基本技能的核心.正确理解概念是学好数学的基础.数学的问题解决是学好数学的具体体现,是学生有兴趣学习数学的动力源泉.在平常的教学中,可以通过解题训练,提高学生问题解决的能力.当下普遍的是重解题训练,轻概念教学.这样虽可短期内提高学生平时数学成绩,但其淡化了对知识本质的理解,不利于可持续发展.笔者结合自身的教学实践,以"离散型随机变量的分布列"为课例(下文简称为"课例"),分析如何通过概念教学提高学生数学问题     

与线性规划交汇题例析

重视在"知识的交汇处命题"是高考数学命题的原则,知识的交汇处体现了知识的内在联系,是高考考查学生数学综合能力的命题点.线性规划是新教材新增加的内容,随着教学的深入,线性规划不断地成为各知识模块的交汇点,成为求范围或最值问题的工具.……     

数学教学中建模能力的培养——化“冰冷的美丽”为“火热的思考”

以提高学生数学能力为目标,加强数学教学中对学生建模能力的培养,要端正学生学习态度、培养数学兴趣,倡导开放式的数学建模教学形式,以应用为驱动、采用案例教学,并注重学生软件应用能力的培养,在建模竞赛中提高学生建模能力.     

反思问题的分析与解题思路的形成

从近年的高考数学试题来看,对能力的要求逐年提高,"题海战术"的功效明显下降,在教学中如何摆脱"题海战术",提高数学素质,培养数学能力呢?这就要求在教学中教师应引导学生学会分析问题和解决问题,并从中发现问题解决的规律.本人试从一道试题的标准答案的分析来谈谈如何通过解题分析来获得问题解决的新视角,并从中提高学生的数学解题能力.     

数学建模教学模块:认识与示例

阐述了对数学建模教学模块的认识,给出了一个数学建模教学模块示例——卷轴的最佳直径.     

高职高专学生数学建模能力的调查与分析

培养学生应用数学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,提出有效的教学方法.为此,通过问卷调查和访谈,分析存在问题的原因,目的是提高老师的思想认识,把握教学的主动权,为下一步纠正问题,提高教学水平准备理论基础.通过调查发现高职学生数学建模能力总体水平不高;建模过程中缺乏灵活性和应用数学的能力;大部分学生将建模能力归因于专门培训.在分析研究调查结果的基础上,提出了适合于高职高专院校培养学生数学建模能力初步途径.     

对工科高等数学的研究性教学的一些认识

当前"研究性教学"是比较提倡的教学方式,它有利于培养学生的数学思想和数学素养.为了更好地进行"研究性教学",教师应研究数学史培养学生数学思想,应研究数学教学的认知规律培养学生"研究性学习"习惯,以及进行应用数学知识能力的研究,完美的逻辑体系与学生接受能力的研究,支持这种教学方式的考核方式的研究.     

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.     

"生物数学"本、硕一体化系列课程的研究与探索 ——兼谈数学建模能力培养之途径

以东北林业大学本、硕两阶段"生物数学"系列课程的整体改革实践为例,针对数学本科专业和数学硕士点学科拔尖人才创新能力培养问题,通过构建"理论学习—专题研究—课外研讨班"一体化教学体系的教学法实践,探讨了如何以生物问题为背景,构建"问题—建模—求解"的研究型教学模式、搭建培养数学建模能力平台的问题,以实现培养学生数学建模能力的一体化教学体系和研究型教学模式的目标.     

高师数学专业学生实验能力培养的理论研究与实践

数学实验活动是提高学生数学素养,提高学生应用能力和创造能力的有效途径.高师院校学生肩负着未来培养中小学生的数学探究能力和创造能力的重大使命.因此,高师院校数学实验的教学改革研究具有双重的意义.本文通过对高师院校数学实验课程体系改革的理论研究与教学实践,探讨了高师院校数学实验教学的一条新路,提供了适合高师院校学生数学实验能力培养的新教学模式和新途径.     

高等数学教学方法的改革实践与回顾

高等数学在高校的课程体系中占有十分特殊的地位.高等数学的知识和方法,业已成为当代大学生知识、能力结构中不可或缺的重要组成部分.开展高等数学的教学改革,特别是开展教学内容、教学方法与学习方法的整合研究,是提高高等数学教学质量,实现高校人才培养战略目标的需要.     

高等数学课程分层次教学理念的思考和举措

高等数学课程是高校所有专业的基础课程之一,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,科学设计了分层次教学模式,对于开展分层次教学的意义和理论依据作了阐述,提出了分层次教学模式的组织与实施,并就教学内容、教学方法、考核模式的改革给出相应的实施方案.     

独立学院高等数学课程的几种分层次教学方案探讨

独立学院办学规模的快速扩张导致学生的数学素质参差不齐,给高等数学的教学带来新的挑战.在已有的分层次教学法的基础上,结合独立学院的实际情况,探讨了适合独立学院的按教学对象分层次、教学内容分层次和教学模式分层次的几种分层次教学方案.     

The design of tasks that address applications to teaching secondary mathematics for use in undergraduate mathematics courses

This paper describes theoretical design principles emerging from the development of tasks for standard undergraduate mathematics courses that address applications to teaching secondary mathematics. While researchers recognize that mathematical knowledge for teaching is a form of applied mathematics, applications to teaching remain largely absent from curriculum resources for courses for mathematics majors. We developed various materials that contain applications to teaching that have been integrated into four standard undergraduate mathematics courses. Three primary principles influenced the design of the tasks that prepare future teachers to learn and apply mathematics in a manner central to their future work. Additionally, this paper provides guidance for instructors desiring to develop or implement similar applications. The process of developing these tasks underscores the importance of key features regarding the roles of human beings in the tasks, the intentional focus on advanced content connected to school mathematics, and the integration of active engagement strategies.     

Undergraduate mathematics majors’ writing performance producing proofs and counterexamples about continuous functions

In advanced mathematical thinking, proving and refuting are crucial abilities to demonstrate whether and why a proposition is true or false. Learning proofs and counterexamples within the domain of continuous functions is important because students encounter continuous functions in many mathematics courses. Recently, a growing number of studies have provided evidence that students have difficulty with mathematical proofs. Few of these research studies, however, have focused on undergraduates’ abilities to produce proofs and counterexamples in the domain of continuous functions. The goal of this study is to contribute to research on student productions of proofs and counterexamples and to identify their abilities and mathematical understandings. The findings suggest more attention should be paid to teaching and learning proofs and counterexamples, as participants showed difficulty in writing these statements. More importantly, the analysis provides insight into the design of curriculum and instruction that may improve undergraduates’ learning in advanced mathematics courses.     

Pre-service science teachers’ perceptions of mathematics courses in a science teacher education programme1

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers’ opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were ‘difficult’ because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers’ lack of knowledge in terms of teaching mathematics.     

工科微分方程课程的实践教学改革初探

国家中长期教育改革和发展规划纲要（2010—2020）在论述“提高人才培养质量”中明确提出：支持学生参与科学研究,强化实践教学环节．如何在本科数学公共课程中开展实践教学以适应创新型人才培养的需要,是数学教育教学改革中迫切需要解决的问题．微分方程是联系数学理论与实际问题的桥梁,本文以工科微分方程课程的实践教学为例,阐述实践教学的内容模块设计、教学方法等改革实践．     

Factors affecting student success in a first-year mathematics course: a South African experience

In spite of sustained efforts tertiary institutions implement to try and improve student academic performance, the number of students succeeding in first-year mathematics courses remains disturbingly low. For most students, the gap between their mathematical capability and the competencies they are expected and need to develop to function effectively in these courses persists even after course instruction. In this study, an instrument for identifying and examining factors affecting student performance and success in a first-year Mathematics university course was developed and administered to 86 students. The overall Cronbach's Alpha coefficient for the questionnaire was found to be 0.916. Having identified variables from prior research known to affect student performance, factor analysis was used to identify variables exhibiting the greatest impact on student performance. The variables included prior academic knowledge, workload, student approaches to learning, assessment, student support teaching quality, methods and resources. From the analysis, students' perceptions of their workload emerged as the factor having the greatest impact on student's performance, followed by the matriculation examination score. The findings are discussed and strategies that can be used to improve teaching and contribute to student success in a first-year mathematics course in a South African context are presented.