用高等数学知识求解初等数学问题

虽然高等数学与初等数学无论是在思维方式还是在教学内容上都有极大的差别,但是高等数学的相关概念和问题对初等数学的发展产生了一定的影响。文章将从多个方面阐述利用高等数学知识处理初等数学问题,从而使我们可以站在一个更高的角度看待初等数学问题。     

运用高等数学知识证明不等式的探讨

探讨灵活运用函数的单调性、极值、凸函数、中值定理、柯西一施瓦兹不等式等高等数学知识对不等式问题进行分析、构造与转化,通过实例给出了用高等数学知识证明有关不等式的方法.     

浅谈几个不等式在中学数学解题中的应用 ——供给侧改革模式下教学方式变革初探

高等数学中的许多知识抽象,不易理解,同学们在学习过程中总认为其应用性不强,对中小学数学教育没有实质性帮助.本文主要介绍数学分析中几个抽象不等式,即哥西-施瓦兹不等式,赫尔德不等式,闵可夫斯基不等式在中学数学解题中的应用,以期对广大数学专业学生有所帮助,从而改变他们对高等数学的认识.     

浅谈高等数学在初等数学中的应用

本文主要阐述高等数学与初等数学之间联系的意义,高等数学在初等数学中的应用,并撷取几例,借助高等数学的手段处理初等问题。     

论高等数学在初等数学中的作用

初等数学是学习高等数学不可缺少的基础,高等数学是初等数学的继续和提高,它不但解释了许多初等数学未能说清楚的问题,并使许多初等数学束手无策的问题,至此迎刃而解了。本文就几个方面探讨一下高等数学在初等数学中的作用。     

谈高等数学对中小学数学教学的作用

本文从高等数学与初等数学的关系上分析了高等数学对初等数学的指导作用和对提高教师教学素质的潜在作用。     

略谈高等数学在初等数学教学中的应用

本文把初等数学与高等数学联系起来，理论联系实际地谈了高等数学在初等数学教学中的作用问题。     

高等数学思想在初等数学中的渗透

本文通过笔者的教学实践,对高等数学方法在初等数学的渗透作系统总结,突出高观点下的数学教学的理念。     

初等数学与高等数学在教学中的衔接问题研究

初等数学教学与高等数学教学之间存在着较大的差别,在衔接过程中很容易导致学生出现两极分化的现象。面对这种情形,教师需要处理好初等数学与高等数学在教学过程中的衔接问题,引导学生顺利地完成过渡,将初等数学作为基础,更好地学习高等数学。文章主要探究初等数学与高等数学在教学中的衔接问题,旨在为新时期数学教学改革提供参考。     

数学中的构造方法——兼谈初等数学和高等数学方法的一致性

初等数学与高等数学中的构造方法在本质上是一样的,常见的有构造图形（或函数）与构造算法,教学中教师要注意提炼和应用,以提升学生对该方法的领悟和使用能力。     

Does prior mathematics knowledge really lead to variation in elementary statistics performance? Evidence from a developing country

A model incorporating prerequisite mathematics performance and other variables deemed to be associated with learning elementary statistics (ES) is developed. The relationship between ES performance and the explanatory variables is well represented by the logistics form. Aptitude, effort and motivation are the only significant explanatory variables of ES performance. Since prerequisite mathematics is not significant, statistical thinking at the tertiary level may be mostly intuitive and non-mathematical. Students with low aptitude experience increasing returns to effort over the first half of the feasible effort interval, while high-aptitude students experience diminishing returns at all levels of effort. The levels of effort required to achieve a minimum pass are interpreted.     

Relations between mathematics achievement growth and the development of mathematics self-concept in elementary and middle grades

Creating an educational program that results in positive science, technology, engineering, and mathematics or STEM-oriented outcomes for all students is an important education objective and federal policy directive in the United States. In addition to developing strong mathematics foundations in Grades K–8 that are closely associated with successful STEM outcomes, intrapersonal skill development is also critical to academic and postsecondary success. Using nationally representative data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 the current study applied structural equation growth modeling to examine relationships among mathematics achievement in Grades K–1 and Grades 3–8, and mathematics self-concept development across Grades 3–8. Study results revealed that students reported declining levels of mathematics self-concept across the middle grades. Importantly, third grade reports of self-concept were associated with both mathematics achievement at kindergarten entry and third grade mathematics achievement; however, mathematics achievement at kindergarten entry was also associated with the development of mathematics self-concept in third through eighth grade. In addition, after accounting for mathematics achievement in Grades K–1, mathematics achievement growth in Grades 3–8 was directly associated with mathematics self-concept development across the same time period. Implications for future research, mathematics instruction, and curriculum development are discussed.     

The purpose, design and use of examples in the teaching of elementary mathematics

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.

Combined fluency and cognitive strategies instruction improves mathematics achievement in early elementary school

One hundred and seventy-eight second grade students from two states (Georgia and Massachusetts) participated in an experiment in which they were randomly assigned to either (1) a computer program designed to increase fluency in addition and subtraction, (2) a program designed to improve cognitive strategy use for addition and subtraction, (3) a program that combined the fluency and cognitive strategy instruction programs or (4) a control condition. The intervention consisted of 40 half-hour sessions (2 sessions per week for 20 weeks). Prior to the intervention, and immediately following the intervention, the participants were tested on fluency, cognitive strategy use, and mathematics achievement. ANCOVAs indicated that children in the combined fluency and cognitive strategy use condition significantly improved their mathematics achievement in comparison to the control group. When we examined the impact of the intervention as a function of gender, boys appeared to benefit from the intervention, but girls did not.     

The effects of cooperative learning on Turkish elementary students’ mathematics achievement and attitude towards mathematics using TAI and STAD methods

This study was designed to compare the effects of Team Assisted Individualization (TAI) and Student Teams-Achievement Divisions (STAD) on fourth grade students’ academic achievement in and attitudes towards mathematics. Seven classes of a school were randomly selected for this experimental study. Two of these were given instruction through TAI; two through STAD, and the remaining three were treated as a control group. For the purpose of the data analysis regarding academic achievement, the 3 X 1 covariance analysis was used to compare the groups. As a result of this comparison, both the TAI and STAD methods were found to have positive effects (d = 1.003 for TAI and d = 0.40 for STAD) on students’ academic achievement in mathematics. The pairwise comparisons showed that the TAI method had a more significant effect than the STAD method. The scores for the attitude towards mathematics were analyzed by using non-parametric statistics. As a result of this analysis, no significant difference was observed regarding students’ attitudes towards mathematics.     

Academic mathematics and mathematical knowledge needed in school teaching practice: some conflicting elements

In this article we analyze the relations between academic mathematical knowledge and the mathematical knowledge associated with issues mathematics school teachers face in practice, according to the specialized literature, and restricted to the theme “number systems”. We present examples that illustrate some areas of conflict between those forms of knowledge. We point out some implications of our study for teacher education, such as: 1) the importance of making conflicts explicit and of discussing them with prospective teachers in order to develop a professionally relevant perception of academic mathematics; 2) the relevance of further research in order to better understand the extent of those conflicts and their effects on the process of integrating, in a body of professional knowledge, the different kinds of mathematical knowledge presented to prospective teachers.

高等数学美学探微

本文通过高等数学中某些数学概念之间内在联系，以及某几个数学问题呈现形式及解题策略与技巧，从不同角度阐述了数学美在数学内容、数学语言、数学规律、数学思维、解题方法等方面的体现。让学生欣赏数学美、体验数学美，在美的熏陶中提高数学能力。     

The significance of mathematical knowledge in teaching elementary methods courses: perspectives of mathematics teacher educators

Our study investigates perspectives of mathematics teacher educators related to the usage of their mathematical knowledge in teaching “Methods of Teaching Elementary Mathematics” courses. Five mathematics teacher educators, all with experience in teaching methods courses for prospective elementary school teachers, participated in this study. In a clinical interview setting, the participants described where and how, in their teaching of elementary methods courses, they had an opportunity to use their advanced mathematical knowledge and provided examples of such opportunities or situations. We outline five apparently different viewpoints and then turn to the similar concerns that were expressed by the participants. In conclusion, we connect the individual perspectives by situating them in the context of unifying themes, both theoretical and practical.     

高等代数观点下中学数学问题的新认识两例

利用<高等代数>观点,给出中学数学两问题的新思考:抛物线相似与Cauchy不等式应用.     

高等数学在高职院校专业中的改革与实践

在高职院校中,作为专业基础课的高等数学具有不可代替的专业服务功能和素质培育功能,是学生进一步学习专业基础课、专业课及毕业后继续深造的重要基础和必备工具。但当前高职数学的开设中陷入了困境,面临着教师不愿教和学生不愿学的尴尬局面。因此,基于专业结合的视角,整合课程内容,使之成为系统板块与若干拼盘,提供给各专业选择,以便稳固学校各专业基础,从而提高学生职业能力。