Integration of Mathematics History into Junior Middle School Education: A Pedagogical Approach to Enhance Mathematical Literacy

The integration of the history of mathematics into junior middle school mathematics education represents a significant focus of international research in mathematics and education.The mathematics curriculum standards for compulsory education have emphasized the importance of incorporating the history of mathematics,aiming to gradually integrate it into the mathematics classroom.However,in the practical implementation of junior middle school mathematics education,the effective combination of the history of mathematics with teaching methodologies remains largely unexplored.This article explores the integration of junior middle school mathematics education and the history of mathematics,aiming to provide classroom teaching recommendations for teachers and promote the formation of students’mathematical literacy.

Enhancing Learners’Performance in Grade 7 Mathematics Through 50-30-20 Exercise

Assessment exercises constitute a crucial component of the teaching and learning process,serving the purpose of gauging the degree to which learning objectives have been accomplished.This study aims to assess the mathematics performance of Grade 7 learners using the 50-30-20 exercise.Specifically,this study seeks to determine the learners’pre-test and post-test mean scores,identify significant differences between the pre-test and post-test results,evaluate learners’exercises,and propose enhanced exercises.The research employs a quasi-experimental design,with 40 Grade 7 learners in the school year 2023-2024 as participants,selected through purposive non-random sampling.Statistical data analysis involves the use of mean,standard deviation,paired t-test,and Cohen’s D effect size.Ethical considerations were paramount,as evidenced by a letter of authorization from the school head outlining the strict adherence to voluntary participation,informed parental consent,anonymity,confidentiality,risk mitigation,results-sharing protocols,and the commitment to keeping research data confidential.The data yielded a remarkable outcome:the experimental group exhibited improvement in both the pre-test and post-test.This result substantiates the initial objective of the study,showcasing a noteworthy and favorable performance among the participants.Consequently,it suggests that a majority of the participants strongly agree that the 50-30-20 exercises contribute to enhancing their understanding and problem-solving skills,as well as their ability to grasp mathematical concepts and improve their overall performance in mathematics.Therefore,the 50-30-20 exercises not only facilitated students in understanding mathematics lessons but were also aligned with the Department of Education’s development plan.

Measurement Analysis and Evaluation of Twenty-Five Years of Mathematics Education Research in China:Visual Econometric Analysis Based on CiteSpace Knowledge Mapping(1999-2024)

Since the new century,China’s mathematics curriculum reform in basic education has continued to move forward in attempts and explorations,presenting many new changes,trends,movements,and developments.Sorting out,analyzing,and summarizing the achievements,experiences,problems,and challenges in this journey are conducive to providing insights for the reform and development of the Chinese basic education mathematics curriculum in the new era.This paper analyses the research on mathematics education in China(1999-2024)using the visual measurement of CiteSpace knowledge mapping,hoping to provide directions for the future of mathematics education in China.

Discussion on the Skillful Use of Mind Maps in High School Mathematics Teaching

With the continuous development of China’s education,the social requirements for high school teaching are constantly improving.The teaching of high school mathematics is a key point in the high school curriculum,but also a major difficulty.Due to the strong logic and abstraction of the content of high school mathematics,some students find it very difficult to learn.In order to solve this problem,high school mathematics teachers can make use of mind maps to teach,so that students can exercise their thinking ability,and realize the improvement of comprehensive ability in mathematics.This paper analyzes the shortcomings of high school mathematics classrooms under the background of new curriculum reform and discusses the significance and methods of applying mind maps in high school mathematics classrooms,so as to put forward reasonable suggestions for realizing the efficient teaching of high school mathematics.

Curriculum Reform of Higher Vocational Mathematics Under the Background of Digital Transformation

Under the background of digital transformation,the reform of the higher vocational mathematics curriculum faces urgent challenges and opportunities.This article explores the impact of digital transformation on the reform of higher vocational mathematics curriculum and emphasizes the importance of improving teaching methods centered on learners.The article proposes specific reform methods and discusses the practical application of digital technology in the reform process.By combining digital technology with specific reform methods,further conducting innovative practice research,and continuously exploring the path of reform,we can effectively improve the quality of higher vocational mathematics classroom teaching and provide strong support for the cultivation of comprehensive qualities and employment abilities.

Effects of QD2R Numeracy Enhancement Strategy on the Mathematics Performance of Grade 10 Students

Learning mathematics requires an effective and strategic teaching approach.This study aimed to assess the mathematics performance of the learners with the implementation of the numeracy enhancement strategy QD2R(Questions,Drills,Repetition,and Recitation)and to propose a strategy implementation plan to elevate their performances.This study employed the use of a quasi-experimental research design,purposive sampling with 70 Grade 10 students of Lian National High School who were distributed equally to control and treatment groups.The pre-test and post-test results were statistically analyzed using independent and paired sample t-tests,and a survey questionnaire was examined by getting the mean and standard deviation.The results indicated that better performance was achieved by the students from the treatment group compared to the students from the control group,as revealed by the Mean Percentage Score(MPS)results,mean scores,and P values of their pre-test and post-test scores.The learners’perception of the implementation of this strategy was to a great extent,wherein it was perceived to be more helpful in concepts related to understanding the lesson compared to concepts related to developing their attitude and skills.Moreover,the proposed implementation plan of numeracy enhancement strategy QD2R had three expected outcomes:elevated understanding and performance in mathematics lessons;modified strategy to focus on the development of attitude and skills towards mathematics;and refined and well-implemented QD2R strategy in teaching mathematics.Relative to these expected outcomes,appropriate measures,timeframe,and resources of each were comprehensively formulated.

“算学”、“数学”和“Mathematics”——学科名称的古今演绎和中西对接

"算学"和"数学"是中国古代已有的语汇,在对译西方"Mathematics"这一学科概念的过程中,出现了二者混用的局面。"算学"和"数学"的演变和发展,以及"Mathematics"译名的确立,经历了复杂的语义变迁和中外对接过程。

Microsoft Mathematics软件在高等数学辅助教学中的案例探究

计算机辅助教学是利用计算机作为主要教学载体进行的教学活动。通过对Microsoft Mathematics软件简介、简单计算、图像绘制等方面的应用及其在高等数学中求极限、求导数、求积分等方面具体案例的探究,探究了Microsoft Mathematics在高等数学辅助教学中的应用,以帮助学生更好地学习高等数学课程,激发学生的学习兴趣。

基于联系数投影的三角模糊数组合预测模型及其应用

在模糊预测中,三角模糊数比区间数更能准确刻画不确定信息。针对三角模糊数组合预测,本文首先引入集对分析中联系数,找出三角模糊数与三元联系数的转换关系,巧妙回避三角模糊数组合预测运算的模糊性和复杂性。其次定义三元联系数运算规则,构建联系数投影作为最优准则,建立联系数投影的定权系数三角模糊数组合预测模型。然后依据高精度预测方法应赋予较大权系数的原则,构建联系数广义诱导有序加权平均(CNGIOWA)算子,研究其性质定理,再结合联系数投影的最优准则,建立基于联系数投影和CNGIOWA算子的变权系数三角模糊数组合预测模型。最后将两类三角模糊数组合预测模型应用到模糊预测实证分析中,结果显示两类组合预测模型都能有效提高预测准确性。

数智赋能推进敏捷化应急情报体系研究

[目的/意义]为有效提高应急情报的流转效率,本研究提出敏捷化应急情报体系。[方法/过程]本文从物理世界、信息空间、社会系统3个层面分析敏捷化应急情报体系现实困境,阐明数智赋能对于推进敏捷化应急情报体系建设的重要性,基于敏捷治理理论剖析敏捷化应急情报体系的理论内涵,提出敏捷化应急情报体系架构。[结果/结论]敏捷化应急情报体系主要面临聚集性、融合性、即时性困境。数智赋能通过制定全流程应急数据吸纳机制、建立联动的应急情报共同体、运用多元化应急情报技术推进应急情报体系敏捷化。敏捷化应急情报体系具有灵敏和迅捷、联通和共识、双向反馈的三大核心理念,并基于三大交互系统实现即时风险感知、快速信息生成和科学情报提供的运行机制,从而提升应急管理效能。

基于相对联系数的区域水利高质量发展评价指标体系筛选方法

为综合判断在区域水利高质量发展目标、发展途径、发展条件相互作用下区域水资源-经济社会-生态环境复合系统不断协同优化的系统高质量发展水平状态,构建了由发展目标、发展途径和发展条件3个子系统组成的区域水利高质量发展初步评价指标体系。为定量分析初步评价指标体系的专家咨询信息,根据专家指标排序合理性模糊关系的取值区间特点提出了相对联系数,用相对联系数的平均集对势估计各专家指标排序合理性的权重,进而可得各指标重要性的专家综合排序值,据此筛选初步评价指标体系,构建了基于相对联系数的区域水利高质量发展评价指标体系筛选方法(SM-RCN)。SM-RCN在陕西省的应用结果表明:筛选后的指标体系汇聚了各专家对区域水利高质量发展主要影响指标的综合评判;SM-RCN可克服评价指标体系构建过程缺乏定量分析依据的不足,可识别不同专家、同一专家对不同评价方面的指标排序合理性的程度。该筛选方法在区域水利现代化、水资源空间均衡、水资源承载力等评价指标体系构建过程中具有应用前景。

数智赋能信息资源管理新路径:指令工程的概念、内涵和发展

新一轮科技革命和产业变革方兴未艾,大数据、人工智能等系列数智技术对信息资源管理学科产生了深远影响。在大模型背景下,指令工程通过高质量、体系化、流程化的指令设计引导模型生成结果,是高效发挥大模型能力的重要途径,可以用于解决学科相关重要问题。本文首先介绍了指令工程的概念,然后详细梳理了指令的构成要素、设计模式以及指令工程的特点和意义,并探讨了指令工程赋能信息资源管理的建设路径。未来,指令工程的研究和发展还需要关注通用及领域指令工程建设、指令工程标准化、知识产权保护、安全性和体系化测试评估等问题,以期能够在各行业复杂的应用场景中更好地发挥指令的效能。

财务数智化环境下的大数据与财务管理专业课程体系改革

近年来,国家深化教育改革的政策接力出台,形成了多元化产教融合教育新格局。财务数智化体现为提升财务处理和管理工作的智能化程度。数字化平台的搭建和人工智能的迅猛发展,给予财务领域转型的条件,助推财务管理变革,同时深刻影响人才培养的走向。大数据与财务管理专业作为财务人才培养的重要专业,其重要性不言而喻。同时在新时期,高职院校大数据与财务管理专业亟须改变人才培养策略,积极推进课程体系改革。基于此,文章以财务数智化环境为依托,探究大数据与财务管理专业课程体系改革方向,找出现阶段课程体系建设中存在的问题,提出针对性建议,旨在设置与社会需求相符的课程,提升大数据与财务管理专业课程的前瞻性,更好地满足社会对财务管理人才的需求。

大学数学课程思政的“道”与“术”

教书且育人的理念在我国有着深厚的文化基础,教师依托于课程在落实课程思政的过程中发挥着至关重要的作用。通过探讨大学数学课程实施课程思政的立足点和发力点,提出数学课程育人要依托于数学课程自身特点和专业内涵,植根于数学教师的专业知识和专业素养,注重数学史特别是中国数学史的融入,以及数学不同分支知识之间的互通互融,同时也要重视教材建设。

工科类院校高等数学教学改革探索——基于工程案例与数学文化视角

工科类院校高等数学教学存在专业衔接有空缺、教材内容不完善、学生基础不均衡、课堂效果不理想等问题,结合学校特点,融合工程案例、数学文化、数学建模等教学内容,体现高等数学的应用、文化、思维、思想价值,推行应用性考核模式,可以提升专业服务水平。

7—9月登陆华南热带气旋频数异常与大气环流和海温的关系

利用1949—2021年中国气象局上海台风研究所热带气旋资料、NCEP/NCAR再分析资料、NOAA重构的海表温度资料(SST)和大气向外长波辐射(OLR)资料,采用线性趋势分析、Mann-Kendall检验等方法分析了近73年7—9月登陆华南热带气旋频数的变化特征。采用合成分析的方法研究7—9月登陆华南热带气旋频数异常与同期大气环流和海温的关系。结果表明,1949—2021年7—9月,登陆华南热带气旋有243个,年均3.3个,占全年登陆总数的70.2%。登陆华南热带气旋频数具有显著的年际和年代际变化特征。1973年最多(7个),1950年最少(0个);在1990年代中期由前期偏多转为后期偏少,但没有突变发生。近73年7—9月登陆华南热带气旋频数以0.1(10 a)^(-1)的速率减少。7—9月登陆华南热带气旋频数异常与大气环流和海温异常密切相关,在异常多、少年同期:(1)大气环流差值场上,南亚高压偏强、偏东、偏北,副高偏西、偏北、偏强,110°E以东的赤道东风引导气流偏强,季风槽加强,北半球中低纬海平面气压场东高西低,北高南低,同时南海、热带西太平洋对流活动加强。(2)海温差值场上,赤道中东太平洋偏冷,西太平洋暖池偏暖,沃克环流加强。高中低层大气环流和海温这种差异可能是导致登陆华南热带气旋频数异常的原因。

基于纹理特征与深度学习的小麦图像中的穗粒分割与计数

穗粒数是小麦产量构成的重要因素和估测产量的参数之一,传统的人工计数方法耗时费力,人为因素影响大。为了实现对小麦穗粒数的智能、快速监测,以百农307、新麦26、稷麦336这3个小麦品种为试验材料,利用智能手机于小麦灌浆后期拍摄麦穗图像,随后对麦穗图像进行预处理并归一化为480×480像素大小,结合深度学习和迁移学习机制,构建基于冻结-解冻机制的HRNet模型的小麦小穗图像分割计数深度学习模型,利用图像处理算法、小麦小穗图像纹理特征确定小穗像素数与穗粒数之间的关系阈值,构建小穗粒数预测模型,实现对小麦穗粒的预测计数。结果表明,对比同样采用冻结-解冻机制的PSPNet模型、DeeplabV3+分割模型、U-Net模型及无冻结解冻机制的HRNet模型,采用基于冻结-解冻机制的HRNet模型对小麦小穗的分割效果更优,且具有更好的鲁棒性,分割精确度为0.9594,平均交并比(mIoU)为0.9119,类别平均像素准确率(mPA)为0.9419,召回率为0.9419;通过3个不同品种小麦的麦穗图像对小穗进行计数,所得决定系数(R2)为0.92,平均绝对误差为0.73,平均相对误差为2.89%;籽粒计数的R2为0.92,平均绝对误差为0.43,平均相对误差为5.51%。由研究结果可知,基于冻结-解冻机制得出的HRNet模型的小麦小穗图像分割算法能够有效分割小麦图像中的小穗,并获得更加丰富的语义信息,可用于解决小目标图像分割困难及训练欠拟合问题,通过粒数预测模型可以快速、精确地对小麦的籽粒数进行预测,从而为小麦高效、智能化估产提供算法支撑。

新文科数学课程体系的构建与实施路径

在新文科建设与人才培养视域下,培养新型社会所需优秀文科人才的关键在于不同学科之间的交叉融合,而数学与文科的交叉融合尤为重要。随着社会的发展,文科专业对学生数学能力的要求不断提升,原有的文科数学课程在教学目标、教学内容和教学模式等方面已不能满足新文科专业建设与人才培养的需要。新文科数学课程体系要在融合与守正的平衡中建立新的目标,深入挖掘数学在新文科建设中的价值。在内容上进行更新或重构,在教学模式上紧跟教育数字化转型的步伐,重视数学技术的应用,构建适应新文科建设与发展要求的大学数学课程体系,发挥数学类优质课程与教材在培养高素质文科人才方面的积极作用。因此,在对新文科数学课程体系的构建依据和课程体系的构建理念、体系结构和课程设置进行深入分析的基础上,文章从教学目标、课程内容、新形态文科数学教材开发、数字化资源建设、考核评价模式和保障制度几个方面探讨了新文科大学数学课程体系的实施路径,并在吉林大学进行教学实践,取得了较好的效果。

加权核范数最小化和改进小波阈值函数的图像去噪算法

针对加权核范数最小化算法存在结构残余噪声以及无法较好地保持图像边缘结构的问题,提出基于加权核范数最小化和改进小波阈值函数的图像去噪算法。利用全变分模型对噪声图像进行初步去噪,使用噪声图像与初步去噪后的图像进行差分运算,对差分后得到的噪声残差图像使用改进的小波阈值函数去噪,将小波去噪后的残差图像与初步去噪图像叠加,将叠加后的图像使用基于残余噪声水平迭代的加权核范数最小化算法进行二次去噪。相较于当下主流去噪算法,经该算法处理后的图像的PSNR和SSIM值均有所提升,能够更好地保持图像的纹理结构,且在高噪声环境下效果更佳。