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MODIFICATION OF ALGORITHM FOR SELECTED TERM OF THE INTEGER EXTENDED EUCLIDEAN MATRIX SEQUENCE
整数扩展欧几里得矩阵序列的选择项算法的修正
DING Xiuhuan,ZHANG Shugong,TAN Chang,
丁秀欢,张树功,谭畅
系统科学与数学 , 2010,
Abstract: Wang and Pan proposed an algorithm for computing a selected term of the integer extended Euclidean matrix sequence, and use it for the modular rational number reconstruction problems. The algorithm only spent nearly linear time, matching the known complexity bound for the integer gcd, which is a special case of the algorithm. In this paper, by analyzing the algorithm, we point out an error in relevant reference, then complement the properties of the matrix sequence, finally modify the algorithm.
初中有理数加减法运算教材对比分析——以人教版和苏教版为例
Comparative Analysis of Textbooks on Addition and Subtraction of Rational Numbers in Junior High School—Taking the PPE Version and the Jiangsu Education Press as an Example  [PDF]
钦珊珊, 刘淼
Advances in Education (AE) , 2022, DOI: 10.12677/AE.2022.129545
Abstract: 有理数的加减法运算是有理数运算的基础。本文采用了内容分析法，以人教版初中数学教材和苏教版初中数学教材为例，对“有理数加减法运算”的相关内容进行分析对比研究。研究发现：人教版教材与苏教版教材在有理数加减法运算内容的呈现方面均以问题为主线，重视知识的形成过程。
The addition and subtraction of rational numbers is the basis of rational number operations. This paper adopts the content analysis method to analyze and compare the relevant content of “addition and subtraction of rational numbers” by taking the PPE version of the junior high school mathematics textbook and the Jiangsu Education Press of the junior high school mathematics textbook as examples. The research found that both the teaching materials of the People’s Education Edition and the textbook of the Jiangsu Education Press are based on the problem in the presentation of the content of the addition and subtraction of rational numbers, and pay attention to the formation process of knowledge.
新旧版本数学教材有理数内容的比较和教学思考——以人教版和苏科版为例
Comparison and Teaching Reflection on Rational Number Content in Old and New Editions of Mathematics Textbooks—Taking the People’s Education Edition and Jiangsu Science and Technology Edition as Examples  [PDF]
杨敏, 董玉成
Vocational Education (VE) , 2025, DOI: 10.12677/ve.2025.144185
Abstract: 2024年教材是落实核心素养的最新教材，新教材在实施课程上有哪些变化是一个值得关注的问题。比较人教版和苏科版新旧教材有理数主题在定义、习题设置及课外阅读材料方面的变化，发现人教版在有理数定义上从归纳分类模式变成了形式定义，而苏科版恰恰相反；在习题配置上，人教版强化了有理数的分类和集合意识的渗透；在阅读材料上，新版人教版教材从中国历史中对负数的认识，进一步扩充至人类对负数的认识历程。苏科版新教材删除了“循环小数可以化为分数”的课外阅读内容，保留了有理数在日常应用的阅读材料。建议在具体教学中教师应该参考多个版本的教材，取长补短，适当淡化形式，加强应用和整数、小数化分数的练习。
The 2024 textbook is the latest textbook for implementing core competencies. What changes will be made in the new textbook in the curriculum implementation is a question worthy of attention. This study compares the changes in the rational number content of the old and new editions of the People’s Education Edition and the Jiangsu Science and Technology Edition, focusing on definitions, exercise arrangements, and extracurricular reading materials. The findings reveal that the People’s Education Edition has transitioned from an inductive classification model to a formal definition in terms of the definition of rational numbers, whereas the Jiangsu Science and Technology Edition has taken the opposite approach. In terms of exercise configuration, the People’s Education Edition strengthened the classification of rational numbers and the infiltration of collective consciousness. Regarding reading materials, the new People’s Education Edition has expanded the historical context of negative numbers from a focus on Chinese history to a broader exploration of their development in human civilization. Meanwhile, the new Jiangsu Science and Technology Edition has removed the extracurricular reading material on converting repeating decimals into fractions while retaining the practical applications of rational numbers. In practical teaching, educators should consult multiple textbook editions to integrate their strengths, appropriately downplay the form, and strengthen applications as well as exercises on converting integers and decimals into fractions.
2012和2024版人教版初中数学教材中有理数内容的对比研究
A Comparative Study on the Content of Rational Numbers in the 2012 and 2024 Editions of Junior High School Mathematics Textbooks Published by People’s Education Press  [PDF]
孔荣, 杨红梅, 刘鹏
Vocational Education (VE) , 2025, DOI: 10.12677/ve.2025.148376
Abstract: 数学作为基础学科，其核心是数量关系与空间形式的研究。教材是知识的重要载体，是教师进行授课传播知识以及学生学习新知识的重要媒介。鉴于此，本研究以2012年和2024年出版的人教版初中数学教材中为研究对象，聚焦于有理数内容，结合《义务教育数学课程标准(2011年版)》与《义务教育数学课程标准(2022年版)》，从课程标准、章节排版、体系结构、知识导入及题目设置等方面进行对比分析。对两版课程标准研究发现，2022年版课程标准新增数学核心素养具体要求，强调“三会”目标，将负数内容从小学调整至初中，并将课程内容进一步细化为内容要求、学业要求和教学提示。对于两版教材，2024年版教材在章节排版上更注重概念与运算的分层设计，将有理数内容拆分为“有理数的基本概念”和“有理数的运算及运算律”两章，并且强化有理数大小比较的重要性；体系结构中新增“图说数学史”“探究与发现”等板块，融入数学史文化以及数系扩充思想；题目设置在总体数量上有所增加，更侧重基础巩固与综合应用。
Mathematics, as a fundamental discipline, centers on the study of quantitative relationships and spatial forms. Textbooks serve as crucial carriers of knowledge, acting as essential media for teachers to deliver instruction and students to acquire new knowledge. In light of this, this study takes the 2012 and 2024 editions of the People’s Education Press (PEP) junior high school mathematics textbooks as its research subjects. Focusing on the content related to rational numbers, it conducts a comparative analysis against the Compulsory Education Mathematics Curriculum Standards (2011 Edition) and the Compulsory Education Mathematics Curriculum Standards (2022 Edition). The analysis encompasses aspects such as curriculum standards, chapter layout, structural organization, knowledge introduction methods, and exercise design. Research on the two editions of curriculum standards reveals that the 2022 edition introduces specific requirements for mathematics core competencies, emphasizing the “three competencies” goals. It relocates the content on negative numbers from primary to junior high school and further refines the curriculum content into content requirements, academic achievement requirements, and teaching suggestions. Regarding the textbooks, the 2024 edition demonstrates a greater emphasis on hierarchical design for concepts and operations in its chapter layout. It divides the rational numbers content into two distinct chapters: “Basic Concepts of Rational Numbers” and “Operations and Laws of Operations for Rational Numbers”, while also enhancing the importance of comparing rational numbers in magnitude. Structurally, new sections such as “Illustrated History of Mathematics” and “Exploration and Discovery” have been added, integrating mathematical history, culture, and the concept of number system expansion. The quantity of exercises has increased overall, with a greater
初中数学教材改版的逻辑思路探讨——以有理数部分为例
Discussion on the Logical Thinking of the Revision of Junior High School Mathematics Teaching Material—Taking the Rational Number Part as an Example  [PDF]
王镁淇, 靳曼莉
Advances in Education (AE) , 2025, DOI: 10.12677/ae.2025.15101797
Abstract: 本文以2024年人教版七年级数学教材《有理数》章节的修订为例，基于《义务教育数学课程标准(2022年版)》的核心素养要求和认知负荷理论，探讨了新教材改版的逻辑思路。研究分析了教材在章节拆分(将“概念”与“运算”分离)、定义更新、情境重构和文化融入等方面的具体改革措施。作者认为，这些改革通过降低认知门槛、强化符号意识、贯通知识网络和渗透数学文化等方式，优化了学生的认知路径。最后，文章从知识本质、学生认知、文化渗透和教学评价四个维度，为一线教师提出了相应的教学实践策略。文章将课程标准、认知理论与具体的教材内容(如定义变化、栏目新增)紧密结合，并最终落脚于可操作的教学策略，兼具理论深度与应用价值。
This study examines the structural revisions in the “Rational Numbers” chapter of the 2024 People’s Education Press seventh-grade mathematics textbook, grounded in the core competency requirements outlined in the “Compulsory Education Mathematics Curriculum Standards (2022 Edition)”. Through the lens of cognitive load theory, it provides an in-depth analysis of the textbook’s reforms in chapter reorganization, definition updates, contextual reconstruction, and cultural integration. The research demonstrates that the new edition effectively optimizes students’ cognitive pathways by: 1) lowering cognitive barriers through “separation of concepts and operations”; 2) enhancing symbolic awareness via “integration of graphical representations and logical derivation”; 3) connecting knowledge networks through “interdisciplinary contexts”; and 4) embedding mathematical culture with “newly added pedagogical features”. Accordingly, this paper proposes practical instructional strategies from four dimensions-mathematical essence, student cognition, cultural permeation, and teaching evaluation-to support frontline educators in comprehending the revised textbook and implementing the updated curriculum standards.
用未确知数学方法确定某坝址岩体变形参数
宋彦辉,聂德新
地质与勘探 , 2004,
Abstract: 首先介绍了未确知信息理论的概念及其应用领域,指出了传统均值法处理数据存在的问题,对未确知信息数学处理方法和过程进行了简要说明.运用这一处理方法对黄河上游某电站坝址岩体变形模量的取值进行了论证,并对两种方法得到的结果进行了对比.结果表明这一方法在不确定性信息处理中比传统方法具有更多的优点,能够给出不同保证率下的岩体变形模量值,表明其处理数据更精细、更科学,值得在地质工程相关数据处理中进一步探讨和应用.
基于UbD理论的单元教学设计——“有理数的加减法”为例
Unit Instructional Design Based on UbD Theory—Taking “Addition and Subtraction of Rational Numbers” as an Example  [PDF]
那扎克提·多力坤
Vocational Education (VE) , 2025, DOI: 10.12677/ve.2025.144182
Abstract: 新课程改革要求以学生为本，注重培养学生的学科核心素养。UbD理论坚持“以终为始”的理念，首先明确预期学习结果，然后确定合适评估依据，最后设计学习体验和教学三个阶段。以人教版七年级上册内容“有理数的加减法”的教学为例进行具体阐述。对学生来说掌握有理数加法法则是一种挑战，没有合适的解决方法，本文基于UbD理论提供了单元教学设计的整体过程，提供了克服有理数加法法则的教学方法和一个模型。
The new curriculum reform requires students to be student-oriented and pay attention to cultivating students’ core quality. UbD theory adheres to the concept of “beginning with the end”, which first defines the expected learning outcome, then determines the appropriate assessment basis, and finally designs the learning experience and teaching in three stages. Take the teaching of “addition and subtraction of rational numbers” as an example. It is a challenge for students to master the law of addition of rational numbers, and there is no suitable solution. Based on UbD theory, this paper provides the whole process of unit teaching design, and provides a teaching method and a model to overcome the law of addition of rational numbers.
单元整体视角下的课时教学设计与实施——以人教版“有理数的加法”为例
Curriculum Teaching Design and Implementation from the Unit Integrated Perspective—Taking the “Addition of Rational Numbers” in the People’s Education Press Edition as an Example  [PDF]
田晋
Advances in Education (AE) , 2025, DOI: 10.12677/ae.2025.1591650
Abstract: 本研究以人教版七年级数学“有理数的加法”为例，探讨单元整体视角下的课时教学设计及其对学生核心素养发展的影响。基于Lynn Erickson和Perkins的理论框架，结合国内崔允漷的学科大单元设计模型，构建了以“宏观概念统摄微观知识”为特征的教学路径。通过行动研究法，从课标分析、教材整合、学情诊断出发，设计并实施强调知识结构化、探究性活动及逻辑关联的课时教学。实证数据显示，单元整体教学提升了学生对有理数加法法则的理解，增强了课堂参与度和知识整合能力。研究揭示了单元整体教学设计通过强化知识关联与思想方法渗透，促进深度学习的机制，为数学核心素养的落地提供了实践范式，并指出未来需进一步优化语言表述规范性及分层教学策略。
This study takes the unit of “Addition of Rational Numbers” in the seventh-grade mathematics curriculum of the People’s Education Press as an example, and explores the lesson-by-lesson teaching design from the perspective of unit integration and its impact on the development of students’ core qualities. Based on the theoretical framework of Lynn Erickson and Perkins, combined with the model of large unit design by Cui Yunhuo, a teaching path characterized by “macro concepts encompassing knowledge” was constructed. Through the method of action research, starting from the analysis of curriculum standards, the integration of textbooks, and the diagnosis of students’ conditions, the lesson-by-lesson teaching that emphasizes the structuralization of knowledge, exploratory activities, and logical correlations was designed and implemented. The empirical data show that unit integrated teaching has improved students’ understanding of the addition rules of rational numbers, enhanced classroom participation and knowledge integration ability. The study reveals the mechanism of unit integrated teaching design to promote deep learning by the correlation of knowledge and the infiltration of ideas and methods, provides a practical paradigm for the implementation of core mathematical qualities, and indicates the need for further optimization of the standard of language expression and hierarchical teaching strategies in the future.
考生填报志愿咨询系统(ISE)的分析与设计
褚东升,安世虎
计算机系统应用 , 1998,
Abstract: 本文主要以高考填报志愿为例介绍该咨询系统的分析与设计过程，给出相关的数学模型。考生使用本文给出的分析与设计结果和数学模型开发的软件，可以得到所需要的信息，使考生填报志愿更有针对性和科学性。
CLUSTER-ADAPTED ITERATIVE FORMULA AND A CLASS IRREDUCIBLE POLYNOIMIAL EQUATION ROOTS-FINDING ON RATIONAL NUMBER FIELDS
Cluster-Adapted迭代公式与在有理数域上一类既约多项式方程的近似求根
陈天机,郭锡伯
计算数学 , 1993,
Abstract: In this paper, the cubic convergence of the cluster-adapted iterative method isproved its applications are discussed. Especially, the approximate roots of twoimportant equations given by Hua and wang are analyzed, and some intere stingproperties about these roots are shown.
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