Combining reinforcement learning with mathematical programming:An approach for optimal design of heat exchanger networks

Heat integration is important for energy-saving in the process industry.It is linked to the persistently challenging task of optimal design of heat exchanger networks(HEN).Due to the inherent highly nonconvex nonlinear and combinatorial nature of the HEN problem,it is not easy to find solutions of high quality for large-scale problems.The reinforcement learning(RL)method,which learns strategies through ongoing exploration and exploitation,reveals advantages in such area.However,due to the complexity of the HEN design problem,the RL method for HEN should be dedicated and designed.A hybrid strategy combining RL with mathematical programming is proposed to take better advantage of both methods.An insightful state representation of the HEN structure as well as a customized reward function is introduced.A Q-learning algorithm is applied to update the HEN structure using theε-greedy strategy.Better results are obtained from three literature cases of different scales.

The Effects of Cooperative Learning in Enhancing the Performance Level of Grade-10 Mathematics Students in Talavera National High School in the Philippines

Mathematics is considered by many students as a difficult academic subject. To improve their performance, various learning strategies are employed by teachers abandoning the conventional method. This study focused on the cooperative learning as a method to enhance level of performance of grade 10 mathematics students in the Philippines. It looked into the method and how it influenced students’ performance. By using a quasi-experimental research method, the following results are generated: 1) the method positively improved the performance in mathematics of the control and experimental groups;2) while effectiveness assessment showed a highly effective result;and 3) the application of the method showed a positive impact on the participants as shown by their positive perception of the subject mathematics.

Learning Mathematics Online Using Information Technology Tools during COVID-19 in Kosove

The COVID-19 pandemic has brought significant challenges to higher education worldwide. Due to the COVID-19 pandemic, e-learning has begun to be widely used and applied in the teaching and learning processes. However, learning under technological circumstances has proven not always to be a proper solution in education. A highlight challenge, in this regard, is considered to be learning Mathematics online. While some support its positive impact, others greatly oppose it by arguing that neither teaching nor learning has proven successful. Thus, this study examines Kosovo selected universities to see the effectiveness of learning Mathematics online as a case study. Further, it compares the online and traditional learning methods and explores how teachers in higher education in Kosova Universities apply and integrate technology into learning mathematics. This study employed a methodology encompassing questionnaires for students. The results show that students are not overall satisfied with learning Mathematics online leading to the conclusion that online learning is not an effective educational method for learning Mathematics.

Analysis and Strategy Research on the Mathematics Learning Situation of the Postgraduate Candidates

This study takes the students who intend to study for graduate students as the research object,and makes a questionnaire survey on the mathematics learning situation and learning platform of the postgraduate candidates.Questionnaires were distributed online and offline,and a total of 326 valid questionnaires were collected.Based on 326 questionnaires,this paper analyzes the current learning situation of mathematics in the postgraduate entrance examination and studies the strategies based on the present situation,which points out the direction for the construction of mathematics learning and communication platform based on the needs of postgraduate entrance examination.

Comparison of Students Academic Performance in Mathematics Between Online and Offline Learning

The coronavirus has affected many areas of life,especially in the field of education.With the beginning of the Pandemic,the transition to online learning began,which affected the development of students and teachers in terms of using innovative technologies and programs,such as Zoom,Webex,Discord,Google Meet,Moodle,EDX,Coursera,www.examus.network,etc.In this regard,many teachers are wondering whether the online method of teaching is as effective as the offline method.In this article,we focused on finding out whether there is a significant difference in student performance between online and offline modes of learning in the study of mathematics.58 students were in a group where they studied online and 58 students were in a group where they studied offline.The study involved first-year college students of Jambyl Innovative Higher College(JICH)in Taraz,Kazakhstan.The final control work was carried out at the end of week 18,which tested all areas covered by the topic in both groups.The average scores of students studying offline were compared with the average of students studying online.To avoid confusion,the researchers also conducted and analyzed an independent t-test.The results showed that there is a significant difference in the academic performance of students who study online and offline.The offline teaching method has proven to be more effective for improving students’understanding and comprehension of mathematics topics.

Problem-based Learning Combining Seminar Teaching Method for the Practice of Mathematical Modeling Course's Teaching Reform for Computer Discipline

Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult since it requires students to have a strong mathematical foundation,good ability to design algorithms,and programming skills.Besides,limited class hours and lack of interest in learning are the other reasons.To address these problems,according to the outcome-based education,we adopt the problem-based learning combined with a seminar mode in teaching.We customize cases related to computer and software engineering,start from simple problems in daily life,step by step deepen the difficulty,and finally refer to the professional application in computer and software engineering.Also,we focus on ability training rather than mathematical theory or programming language learning.Initially,we prepare the problem,related mathematic theory,and core code for students.Furtherly,we train them how to find the problem,and how to search the related mathematic theory and software tools by references for modeling and analysis.Moreover,we solve the problem of limited class hours by constructing an online resource learning library.After a semester of practical teaching,it has been shown that the interest and learning effectiveness of students have been increased and our reform plan has achieved good results.

智慧课堂环境下指向数学学科能力的学情分析研究:理论框架与实践进路

数学学科能力培养是落实数学核心素养的关键路径,指向学科能力的学情分析成为实现因材施教的关键所在。如何科学表征指向数学学科能力的学情内容、学情数据,并开展学情分析实践,成为亟待研究的问题。该文在探寻形成数学学科能力的内隐认知与外显行为机制的基础上,深入剖析学科能力、学情内容、学情数据三者间的具象、量化、关联表征关系。将观察、判断、类比、解释、验证、质疑等数学学科能力外显行为与数学概念、性质、关系、规律相结合,以智慧课堂环境为培养数学学科能力提供的技术支撑为依托,构建了指向数学学科能力的学情分析框架,其中包含识别表达数学概念、表达数学关系、发现数学规律等学情内容,及测评数据、评价数据、在线学习数据、知识网络数据等学情数据。最后,基于指向数学学科能力的学情分析框架,以学科能力行为表现、学情分析工具设计、学情数据智能采集、学生学情深入剖析作为四大实践环节,将实时互评、自动批阅、在线测评、任务打卡、学情报告等功能作为技术辅助,提出智慧课堂环境下指向数学学科能力的学情分析实践路径。

The Role of Mathematics in STEAM Education under the“Double Reduction”Policy

This essay delves into the pivotal role of mathematics within the context of STEAM(science,technology,engineering,arts,and mathematics)education under China’s“Double Reduction”policy.Amidst a shifting global education landscape that emphasizes holistic growth,policies such as the“Double Reduction”strategy underscore the significance of well-rounded development alongside academic excellence.By advocating for a balanced approach to education,the policy resonates with the principles of STEAM education,which seeks to cultivate versatile and innovative individuals.Mathematics,acting as a unifying force,connects disparate STEAM disciplines,fostering interdisciplinary collaboration and preparing students to thrive in a rapidly evolving,technology-driven world.This essay provides an in-depth exploration of the multifaceted role of mathematics in STEAM education,drawing on specific cases and scholarly references to highlight its contributions to creativity,critical thinking,and holistic development.

高校图书馆数学阅读推广研究

数学阅读是认识和学习数学的主要方法,也是提高数学素养和养成阅读习惯的重要途径。高校图书馆在学科阅读理念下开展数学阅读推广体现了阅读推广的细分化和精准化,对于创新阅读推广主题、丰富阅读推广资源、拓展阅读推广渠道具有重要意义。问卷调查发现,大学生数学阅读存在阅读质量不高、阅读能力薄弱、阅读指导欠缺和宣传推广乏力等问题。基于调查结果,提出建设分众书目、多元主体联动、嵌入课堂教学和借力实践活动等数学阅读推广策略。

混合式教学下高等数学课程思政建设的优化路径

课程思政理念融入大学数学教育,对培养合格的社会主义接班人起到重要作用。基于大学边界理论的视角,在CSCL为基础的协助学习环境中优化高等数学课程与思政课程之间的边界。在具体的课堂教学情境中,将知识学习、价值凸显与能力培养进行有机结合。在大学数学类课堂教学中强调辨析社会系统中的数学、复杂性问题解决、工程伦理以及数学价值观的塑造。

深度学习视角下应用型大学课堂教学策略——以高等数学为例

基于应用型大学人才培养目标,以高等数学课程为例,分析应用型大学课堂教学现状。研究深度学习的意涵和特征,及其对应用型大学课堂教学改革的实际意义。提出在高等数学教学实践中实现深度学习的5个策略,优化传统课堂教学模式,为应用型大学高素质人才培养助力。

属性偏序形式结构的数学形式化

属性偏序形式结构,作为一种基于人类认知原理和粒计算思想的知识发现和知识表示新理论,目前已有广泛的应用,但其理论基础缺乏抽象化数学化,这势必影响该理论的系统发展。针对上述问题,研究了属性偏序形式结构的数学形式化描述问题。首先,基于粒计算的思想提出了知识表示的形式化框架。在此基础上,通过定义对象集合的覆盖和最简覆盖,给出属性偏序形式结构的粒和粒群的概念,进而通过对粒衍生出粒群的充要条件的讨论,给出了属性偏序形式结构中的知识结构,从而完成属性偏序形式结构的数学形式化描述。最后,通过具体实例展示了利用数学形式化描述构造属性偏序形式结构的过程,并揭示了该过程所体现的人类认知规律。

“循源而学”理论视域下的小学数学教学:看见数学、理解数学、学通数学、用好数学

如何提高小学生数学学习兴趣、提升学生数学学习力、体悟数学的价值是当前小学数学教育三大待解难题。解决之道在于让学生看见数学、理解数学、学通数学、学好数学、用好数学、爱上数学,“循源而学”应运而生。它倡导顺着数学产生、发展、应用的“源”与“流”而学,其核心内容包括循数学发展之源而学、循人生成长之源而学、循生存生活之源而学,体现为从数学学习走向人生成长、从人生成长走向完整生活,这是一切学科学习的基本“源”与“流”,是系列内化与外化、专与博、立己与达人、出发与归宿、基础与发展的自然生长、生发、生态过程。“情境与问题、体验与实践、关联与综合、拓展与长程、创造与成长”是“循源而学”的五大设计与实施要义。

混合式教学模式下新形态大学数学教材建设研究

随着新一代信息技术的快速发展以及混合式教学模式的普及,大学数学教材的建设迎来新的挑战和机遇。该文基于常州大学数学课程的混合式教学实践,探讨新形态大学数学教材的特点、建设原则和具体策略。重点阐述如何将线上线下资源有机融合,构建以学生为中心的教材体系,并通过具体案例分析,阐述新形态教材的应用成效。研究表明,新形态教材能够有效提升学生的学习兴趣、促进个性化学习,提高大学数学教学质量。

转换性数学学习:内涵与价值

转换性数学学习表征了数学学习活动中主体的主动性、意义的建构性和常识的转化性,关联着数学学习中多个维度的转换性,但并不是转换性学习理论在数学学习活动中的简单推演,也不能被视为数学学习理论现代发展的主要方向或者唯一的研究范式,而是要将数学的学科特质和学习思维等属性嵌入到那些看似相同或相似的转换性过程中,需要重视数学活动中意义的视角和图式,在变化、变换和变式中建构与完善数学知识结构,将数学知识转化为数学能力和核心素养。好的转换性数学学习不仅能引导数学教与学关系的转变,而且能助推学生数学学习力提升和涵养核心素养教育的全面落实。

论数学教与学中的“知新温故”

在“双减”背景下,为使学生掌握有效的数学学习方式,教师需要思考如何提升课堂教学的质量和效率。知识的对偶性、知识的层进与拓展、知识的传承与进化,使数学学习“知新温故”。知识产生的动力方式、知识运行的自然脉络、知识形式的逐级抽象、知识内涵的理解表征和知识本质的模式凝练,使得数学教学“知新温故”。这一发现启示教师基于知识分析和心理分析以学定教,在数学教学中实现“减负增效”,从而提升学生的数学素养。基于循证研究的实践也表明这种做法是行之有效的。

基于体验学习的中职数学体验式教学改革实践探索

基于体验学习理论,依据《中等职业学校数学课程标准》,拓展了中职数学体验学习的内容,结合专业人才培养方案和职业学校的具体学情,提出了中职数学体验式教学的“三回归”策略,以建构主义教学观为指导,构建了中职数学体验式教学体系,通过对教学设计、内容处理、教学实施、思维培养等方面的改革创新,建立起数学与专业、过程与方法、素养与思维之间的联系,实现了教与学的统一,在体现中职数学职教特色的同时,达到培养学生学科核心素养的目标。

“以学生为中心”的离散数学课内外协同教学模式研究

离散数学是计算机大类专业核心课程,通过离散事务与状态的表示与分析,旨在培养学生的抽象思维、缜密概括和逻辑推理能力。然而,离散数学的知识体系各自独立,知识点相互孤立,课程缺少计算机领域的具体应用案例,课程教师往往以传授知识讲解课程内容为主,导致学生无法掌握离散数学的内涵。基于此,在分析离散数学学习者心理特征的基础上,遵循“以学生为中心”的教学理念,引入建构主义教学理论和协作学习理论,从课内教学和课外学习两个层面,设计课堂教学策略和课外小组协作学习策略,并通过案例展示课程教学的呈现形式,设计学习目标、组织策略及实施案例。通过对比实验分析可知,该教学方法能够有效提高学习者兴趣,教学效果较好。

初中生数学核心素养的影响因素研究——基于多层线性模型的分析

采用多层线性模型探索初中生数学核心素养的影响机制。研究发现:样本学校初中生数学核心素养存在显著差异;从个体层次来看,学生的数学学习投入、数学学习习惯显著正向预测其数学核心素养;从组织层次来看,教师对学生数学认知的激发能显著正向预测其数学核心素养;从跨层交互作用来看,教师对学生数学认知的激发程度,显著影响学生数学学习投入对数学核心素养的解释力,但其影响学生数学学习习惯对数学核心素养的解释力不显著。建议提高教师对学生数学认知的激发程度,引导学生养成良好的数学学习习惯,同时激发学生的学习热情,增加他们的数学学习投入。

混合式教学新常态背景下大学生学习投入及学习满意度提升策略研究——以大学数学课程为例

该文以大学数学课程为例,研究混合式教学新常态背景下大学生学习投入及学习满意度提升策略。首先对学生在大学数学课程中的混合式学习投入与学习满意度现状进行了分析,然后从创新课程教学内容、建设优质数字化资源、优化混合教学实施方案、开展数据驱动的评价创新四个方面提出了混合式学习投入及满意度提升策略。