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。     

微积分在初等数学教学中的作用分析

运用高等数学方法与原理分析并解决初等数学问题,能够进一步充实初等数学理论知识及内涵,有助于提高解决初等数学问题效率。微积分是高等数学的重要组成内容,具有高等数学与初等数学衔接的作用。因此,可以从微积分的角度解析初等数学问题,发挥微积分对初等数学的指导作用。     

浅析微积分在初等数学中的微妙作用

高等数学与初等数学是密不可分的,初等数学可以看做是高等数学的基础,同时高等数学对于初等数学又具有一定的指导作用。微积分理论是高等数学的基础,借助微积分这个工具来解决一些初等数学问题,往往迎刃而解,显示出了微积分的重要作用。     

初等数学和高等数学的联系与矛盾

本论文由初等数学与高等数学本身的一些特性出发,讨论了初等数学和高等数学的一些联系和矛盾,它们之间联系的意义,以及如何从初等数学过渡到高等数学。     

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。     

本刊征稿简则

《福建中学数学》创刊于1958年,是面向国内公开发行的中学数学教学与研究的学科刊物;秉承"服务中学数学教师的‘教’、服务中学学生的‘学’"的办刊宗旨,积极引导初等数学教育工作者开展初等数学教育教学理论研究,全面展示初等数学教育教学研究的新成果,介绍初等数学教育教学改革的新经验,扎扎实实地为初等数学教育的改革与发展作贡献,被誉为"学生的良师、教     

高等数学思想下的初等数学探讨

探讨高等数学思想下的初等数学,可以启示我们突破初等数学知识的局限性,寻求新的理论工具进行数学学习,提升教师教学专业化素养,培养学生的创新精神和探究性学习能力.现立足于初等数学的案例,融合高等数学的思想方法,探讨新课程理念下的初等数学.     

例谈微积分方法在初等数学教学中的应用

极限方法是研究高等数学的基础与核心方法,同时也对初等数学教学有一定的指导作用。它是从高观点、多角度认识理解初等数学、简捷有效地解决初等数学问题的有力武器。以微积分的概念、原理和方法为指导,使得对初等数学的研究在深度和广度上都有了更大的发展。     

略谈微积分对学生理解初等数学的帮助

本文举例讨论了微积分在帮助学生理解初等数学中常见问题的作用,既为解决初等数学中的某些问题找到了一些新途径,又使微积分对初等数学的指导作用得到一定的说明.     

初等教学与高等数学的融合

本文从高等数学对初等数学的渗透，高观点下的初等教学，高等数学对初等数学的直接指导作用三个方面阐述了初等数学与高等数学的融合。     

微分方程的通积分与初等超越函数公式的推导

利用微分方程的通积分及其积分因子去研究和解决某些初等函数中的公式推导问题的探讨，这是利用高等教学知识研究和解决有关初等数学中的问题的一个范例。     

常微分方程与初等函数

中学数学教学中如何应用高等数学,一直是困扰中学数学教师的一个问题。我们对此作了一些探讨.阐述了常微分方程在中学数学中的一些应用。     

常微分方程与曲线性质

本文讨论了常微分方程在中学数学中的一些应用，给出了一个定理及其导出的曲线。     

微分导数理论在初等数学中的应用探讨

主要介绍微分导数的相关定义理论及性质定理,以此来探讨微分导数理论在初等数学解题中的应用。     

对称性在数学中的应用

本文主要论述了对称性在初等数学的代数、几何、三角等中的应用,并通过例题来验证,同时也通过一些例子介绍了其在高等数学微积分、高等几何等中的价值。     

谈超越不等式的应用

一般地,用微分学的方法可以证明许多超越不等式,这些超越不等式在数学中有许多重要的应用。应用它们来证明一些初等不等式,更显示出导数之重要性。     

The Language Factor in Elementary Mathematics Assessments: Computational Skills and Applied Problem Solving in a Multidimensional IRT Framework

The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and the extent to which students' language level plays a differential role in these abilities. Data from a sample of over 2,000 students from first, second, and third grade in the Netherlands were analyzed in a multidimensional item response theory (IRT) framework. The latent correlation between the two ability dimensions (computational skills and applied mathematics problem solving) ranged from .81 in grade 1 to .87 in grade 3, indicating that the ability dimensions are highly correlated but still distinct. Moreover, students' language level had differential effects on the two mathematical abilities: Effects were larger on applied problem solving than on computational skills. The implications of these findings for measurement practices in the field of elementary mathematics are discussed.     

A Constructive Program in Silent Reading

ABSTRACT

The authors examined whether self-concept, self-efficacy, and self-esteem show differential predictive utility for academic achievement across age groups and domains. More specifically, the relationships of 3 self-constructs with achievement were examined in mathematics for elementary school students and mathematics and language arts for middle school students in Korea. Task value and test anxiety were hypothesized to mediate these relationships. Consistent with previous reports, domain-specific self-constructs such as self-efficacy and self-concept were better predictors of task value and achievement than was general self-esteem. Task value and test anxiety significantly mediated only the relationships of self-efficacy assessed by the Bandura-type scale to achievement. These domain-specific relationships tended to be stronger for middle school than elementary school students and in mathematics than language arts.     

数学思想方法在小学数学教学中的渗透路径

数学课程的精华在于数学思想方法。以下将小学数学教学作为载体,先对小学数学教学中渗透数学思想方法的意义进行分析,随后探讨小学数学教学中渗透数学思想方法的路径,希望提供有利参考。     

Building the wall brick by brick: one prospective teacher’s experiences with mathematics anxiety

Mathematics education researchers have investigated mathematics anxiety in prospective elementary teachers. While many of these studies have focused on the bodily sensations and emotions of mathematics anxiety, particularly those felt in assessment situations, opportunities remain to investigate how prospective elementary teachers interpret their experiences with mathematics anxiety and connect them over time to compose personal histories of mathematics anxiety. Currently, over 90 % of elementary teachers in US schools are women, and women have been shown to suffer more from mathematics anxiety than do men. In this article, I analyze how one woman prospective elementary teacher described, explained, and related her experiences of mathematics anxiety across her personal narratives of learning mathematics as a K-12 student and of learning to teach mathematics as a college student in a teacher preparation program. My research demonstrates that experiences of mathematics anxiety may persist beyond assessment situations to influence women prospective elementary teachers’ larger mathematical histories. I also show that women prospective elementary teachers may interpret mathematics anxiety as specific fears (e.g., loss of opportunities for social participation) and may develop particular coping strategies related to those fears. Finally, I point out that while a coping strategy may be used consistently across K-12 mathematics learning and undergraduate teacher preparation, and may even offer a woman prospective elementary teacher some relief from mathematics anxiety, it may also limit her mathematics learning and professional development. To conclude, I present implications of my research for mathematics teacher educators.