As a tool for quantifying individuals’visual attention and information processing,eye-tracking technology is gradually being applied in the reform of higher education.This paper focuses on issues in university mathem...As a tool for quantifying individuals’visual attention and information processing,eye-tracking technology is gradually being applied in the reform of higher education.This paper focuses on issues in university mathematics teaching,such as heavy cognitive load,delayed feedback,and insufficient adaptability.Based on theories of cognitive psychology,the study explores application pathways of this technology in cognitive diagnosis,instructional optimization,classroom regulation,personalized support,and teaching assessment.Research shows that eye-tracking data can reveal key cognitive features during the learning process,enhance the visualization of instructional feedback,and improve the scientific basis of decision-making.This provides both theoretical support and practical reference for data-driven and precise transformation in university mathematics education.展开更多
In the context of the new era of education,advanced mathematics not only undertakes the function of knowledge transmission but also plays a vital role in cultivating logical thinking,scientific spirit,and value orient...In the context of the new era of education,advanced mathematics not only undertakes the function of knowledge transmission but also plays a vital role in cultivating logical thinking,scientific spirit,and value orientation.However,traditional teaching has overemphasized knowledge instillation while neglecting value guidance,making it difficult to meet the demands of cultivating interdisciplinary talents.This study introduces the OBE concept and constructs a“knowledge–ability–value”teaching framework,integrating outcome orientation,backward design,and diversified evaluation to promote the systematic incorporation of ideological and political education into the curriculum.Taking limits,definite integrals,and series as representative knowledge points,the paper designs case-based pathways to foster dialectical thinking,patriotism,and scientific spirit.Practice has shown that this model effectively unifies knowledge education and value education,enhancing students’logical reasoning,sense of responsibility,and scientific literacy.The study provides an operational pathway for the reform of ideological and political education in advanced mathematics courses and carries practical significance for implementing the goal of“all-round education.”展开更多
Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high scho...Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.展开更多
In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment a...In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment among teaching,learning,and assessment.To counter these challenges,we propose an Inquiry-Construction Double-Helix model that uses a domain-specific knowledge graph as its cognitive spine.The model interweaves two mutually reinforcing strands-student-driven inquiry and systematic knowledge construction-into a double-helix trajectory analogous to DNA replication.The Inquiry Strand is launched by authentic,situation-based tasks that shepherd students through the complete cycle:question→hypothesis→verification→reflection.The Construction Strand simultaneously externalizes,restructures,and internalizes core disciplinary concepts via visual,hierarchical knowledge graphs.Within the flow of a lesson,the two strands alternately dominate and scaffold each other,securing the co-development of conceptual understanding,procedural fluency,and mathematical literacy.Empirical evidence demonstrates that this model significantly enhances students’systematic knowledge integration,problem-solving transfer ability,and core mathematical competencies,offering a replicable and operable teaching paradigm and practical pathway for deepening high school mathematics classroom reform.展开更多
Under the strategy of building an educational power country,the reform of higher mathematics teaching should take into account both value guidance and digital innovation.This study,guided by the“educationalist spirit...Under the strategy of building an educational power country,the reform of higher mathematics teaching should take into account both value guidance and digital innovation.This study,guided by the“educationalist spirit”,explores the integration of course ideological education into teaching and leverages digital innovation for empowerment.Analyzing the literature reveals that there is a gap in the connection between the“educationalist spirit”theory and the“digital and intelligent technology”practice.Therefore,a“spiritual guidance–technological empowerment”dual-wheel driving model is proposed,along with the corresponding framework and path.Research shows that this model can enhance teaching effectiveness and educational quality,providing an integrated path for cultivating top-notch innovative talents.展开更多
In the context of the continuous deepening of the“Double Reduction”policy and the growing demand for quality education,leveled mathematics readers,as an emerging form of publishing that integrates subject education ...In the context of the continuous deepening of the“Double Reduction”policy and the growing demand for quality education,leveled mathematics readers,as an emerging form of publishing that integrates subject education and reading experience,face challenges such as unclear leveling logic,insufficient functional support,and weak user engagement.This paper introduces the 4V marketing theory and constructs an analytical framework from four dimensions:differentiation,functionality,added value,and resonance.Two representative products,“Climbing Mathematics”and“Spark Mathematics,”are selected for a typical case comparison to identify their strengths and weaknesses in content design,service systems,and brand operation,and to extract transferable strategic elements.The study finds that the user-value-oriented strategy based on the 4V model can effectively address the core issues in the market promotion and user relationship building of leveled mathematics readers,providing practical paths and theoretical support for educational publishing institutions to achieve product innovation and brand upgrading in this niche field.展开更多
As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Int...As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.展开更多
This paper examines the grain of content in junior high mathematics digital textbooks from People’s Education Press(PEP)using Cognitive Load Theory(CLT)in a sequential explanatory mixed-methods design:(1)bibliometric...This paper examines the grain of content in junior high mathematics digital textbooks from People’s Education Press(PEP)using Cognitive Load Theory(CLT)in a sequential explanatory mixed-methods design:(1)bibliometric analysis of 2008–2023142 publications found substantial gaps in cognitive-aligned pedagogical design;then,(2)large-scale surveys of 231 teachers and 102 students found critical gaps in navigation intuitiveness(71.3%),interactive affordance deficiency(68.9%),and personal pathway rigidity(76.5%).(3)Interviews with 6 teachers and 3 developers further revealed these deficiencies lay in:(1)content fragmentation serving procedural skills at the expense of conceptual integration;(2)sequence disruption violating CLT’s intrinsic load tenets;and(3)passive multimodal serving static text/images(82%of resources)limiting germane processing.We thus innovated a CLT-driven framework to reduce intrinsic load by animating schema builders chunking complex concepts,minimize extraneous load by Gestalt-principled UI redesign serving spatial consistency,and enhance germane load by adaptive analytics serving personal pathways.Empirical results showed 34%more knowledge retention(p<0.01,d=1.87)and 28%less perceived cognitive load(NASA-TLX)relative to conventional textbooks.Our work contributed both a theoretically grounded resource optimization model and an advancement of CLT in technology-enhanced mathematics instruction.展开更多
In recent years,the rapid development of artificial intelligence(AI)technology has been driving profound transformations in higher education.As a fundamental course in science and engineering disciplines,Advanced Math...In recent years,the rapid development of artificial intelligence(AI)technology has been driving profound transformations in higher education.As a fundamental course in science and engineering disciplines,Advanced Mathematics plays a crucial role in cultivating students’logical thinking and innovative capabilities.However,the current teaching models exhibit significant shortcomings in fostering students’ability to identify and solve problems,primarily reflected in the monotony of teaching content,the limitations of students’thinking,and the constraints of instructional methods.In response to these issues,this paper proposes an AI-based teaching approach for Advanced Mathematics.By utilizing scenario simulations to guide students in discovering problems and employing modeling tools to assist them in solving problems in real time,the study constructs a comprehensive teaching model that spans the entire process from problem identification to problem resolution.Research findings indicate that the application of AI technology can effectively enhance students’abilities in problem awareness,logical reasoning,and creative thinking.This study provides both theoretical support and practical reference for the reform of Advanced Mathematics education and the innovation of higher-level talent cultivation models.展开更多
To meet the demands of higher education reform and innovative talent cultivation,the teaching team of Tarim University,with ability cultivation as the core,has established a new“331”university mathematics teaching s...To meet the demands of higher education reform and innovative talent cultivation,the teaching team of Tarim University,with ability cultivation as the core,has established a new“331”university mathematics teaching system.Through the multi-dimensional linkage of master teachers’guidance,course optimization,stratified teaching,practical reinforcement,and competition-driven,it has significantly improved students’mathematical application ability and innovative quality.展开更多
Mathematics is a basic course for cultivating advanced technical talents,a core course for students in the basic education stage,mathematical knowledge content is the foundation of professional courses,mathematical th...Mathematics is a basic course for cultivating advanced technical talents,a core course for students in the basic education stage,mathematical knowledge content is the foundation of professional courses,mathematical thinking ability is one of the abilities for students’sustainable development,mathematical literacy is a basic quality that students should possess,and it carries the function of implementing the fundamental task of fostering virtue and nurturing talent and developing quality-oriented education.It has the characteristics of being fundamental,developmental,applied,and vocational.In today’s era of rapid development of artificial intelligence and big data,mathematics plays a huge role in production and life.This paper briefly expounds and analyzes the current situation of mathematics teaching,explores the significance of information-based teaching for mathematics teaching,and on this basis,proposes relevant strategies for information-based mathematics teaching,including knowledge visualization,the use of information technology to create mathematics teaching scenarios,the realization of efficient mathematics teaching through micro-lessons,and the realization of teaching interaction through network platforms.展开更多
International student enrollment has rapidly grown in China,positioning transnational education as a significant component of the country’s higher education system.So our study investigates an innovative teaching app...International student enrollment has rapidly grown in China,positioning transnational education as a significant component of the country’s higher education system.So our study investigates an innovative teaching approach that combines the Knowing-Understanding-Doing(KUD)framework with the BOPPPS pedagogical model(which includes the Bridge-in,Objective,Pre-assessment,Participatory Learning,Post-assessment,and Summary components),with specific application to undergraduate mathematics teaching for international students at a Chinese university.Taking Calculus 1 as a case study,our study evaluates the implementation efficacy of this integrated approach.The findings offer valuable insights for those seeking to enhance the quality and effectiveness of their teaching methodologies in culturally diverse undergraduate mathematics classrooms.展开更多
In this paper,the necessity of constructing a golden course for Advanced Mathematics is presented.For teachers,golden courses enhance their teaching ability and job satisfaction.For students,golden courses improve the...In this paper,the necessity of constructing a golden course for Advanced Mathematics is presented.For teachers,golden courses enhance their teaching ability and job satisfaction.For students,golden courses improve their sense of learning value and significance and encourage them to actively learn and participate deeply.Next,the relevant content of course ideological and political construction is provided.Finally,a specific approach was proposed to create a golden course for Advanced Mathematics by integrating ideological and political education into the curriculum.展开更多
The relationship between arts and mathematics is very close, computer graphic design is based on digital methodology. The paper reveals the mathematical backgrounds behind graphic design by the example of computer-aid...The relationship between arts and mathematics is very close, computer graphic design is based on digital methodology. The paper reveals the mathematical backgrounds behind graphic design by the example of computer-aided cubic modeling and mathematical exchange methodology. Furthermore, one can get incredible artistic effects if computer graphic designers pay more attention to the probability and use probable numbers and fractal operation in their design activities.Finally, the author also discusses the bidirections between arts and mathematics.展开更多
基金The 2024 Education and Teaching Reform Project,“Exploration and Practice of University Mathematics Teaching Reform Driven by Eye-Tracking Technology”(Project No.:JG2024047)。
文摘As a tool for quantifying individuals’visual attention and information processing,eye-tracking technology is gradually being applied in the reform of higher education.This paper focuses on issues in university mathematics teaching,such as heavy cognitive load,delayed feedback,and insufficient adaptability.Based on theories of cognitive psychology,the study explores application pathways of this technology in cognitive diagnosis,instructional optimization,classroom regulation,personalized support,and teaching assessment.Research shows that eye-tracking data can reveal key cognitive features during the learning process,enhance the visualization of instructional feedback,and improve the scientific basis of decision-making.This provides both theoretical support and practical reference for data-driven and precise transformation in university mathematics education.
基金2024 Education and Teaching Reform Project(Project No.:JG2024047)Basic Scientific Research Funding of the Xinjiang Uygur Autonomous Region(Project No.:XQZX20250005)。
文摘In the context of the new era of education,advanced mathematics not only undertakes the function of knowledge transmission but also plays a vital role in cultivating logical thinking,scientific spirit,and value orientation.However,traditional teaching has overemphasized knowledge instillation while neglecting value guidance,making it difficult to meet the demands of cultivating interdisciplinary talents.This study introduces the OBE concept and constructs a“knowledge–ability–value”teaching framework,integrating outcome orientation,backward design,and diversified evaluation to promote the systematic incorporation of ideological and political education into the curriculum.Taking limits,definite integrals,and series as representative knowledge points,the paper designs case-based pathways to foster dialectical thinking,patriotism,and scientific spirit.Practice has shown that this model effectively unifies knowledge education and value education,enhancing students’logical reasoning,sense of responsibility,and scientific literacy.The study provides an operational pathway for the reform of ideological and political education in advanced mathematics courses and carries practical significance for implementing the goal of“all-round education.”
文摘Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.
文摘In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment among teaching,learning,and assessment.To counter these challenges,we propose an Inquiry-Construction Double-Helix model that uses a domain-specific knowledge graph as its cognitive spine.The model interweaves two mutually reinforcing strands-student-driven inquiry and systematic knowledge construction-into a double-helix trajectory analogous to DNA replication.The Inquiry Strand is launched by authentic,situation-based tasks that shepherd students through the complete cycle:question→hypothesis→verification→reflection.The Construction Strand simultaneously externalizes,restructures,and internalizes core disciplinary concepts via visual,hierarchical knowledge graphs.Within the flow of a lesson,the two strands alternately dominate and scaffold each other,securing the co-development of conceptual understanding,procedural fluency,and mathematical literacy.Empirical evidence demonstrates that this model significantly enhances students’systematic knowledge integration,problem-solving transfer ability,and core mathematical competencies,offering a replicable and operable teaching paradigm and practical pathway for deepening high school mathematics classroom reform.
基金High-level talent start-up fund project of Gan Dong University,Research on Ideological and Political Education of Higher Mathematics under the Leadership of Educator Spirit(Project No.:12225000408)。
文摘Under the strategy of building an educational power country,the reform of higher mathematics teaching should take into account both value guidance and digital innovation.This study,guided by the“educationalist spirit”,explores the integration of course ideological education into teaching and leverages digital innovation for empowerment.Analyzing the literature reveals that there is a gap in the connection between the“educationalist spirit”theory and the“digital and intelligent technology”practice.Therefore,a“spiritual guidance–technological empowerment”dual-wheel driving model is proposed,along with the corresponding framework and path.Research shows that this model can enhance teaching effectiveness and educational quality,providing an integrated path for cultivating top-notch innovative talents.
文摘In the context of the continuous deepening of the“Double Reduction”policy and the growing demand for quality education,leveled mathematics readers,as an emerging form of publishing that integrates subject education and reading experience,face challenges such as unclear leveling logic,insufficient functional support,and weak user engagement.This paper introduces the 4V marketing theory and constructs an analytical framework from four dimensions:differentiation,functionality,added value,and resonance.Two representative products,“Climbing Mathematics”and“Spark Mathematics,”are selected for a typical case comparison to identify their strengths and weaknesses in content design,service systems,and brand operation,and to extract transferable strategic elements.The study finds that the user-value-oriented strategy based on the 4V model can effectively address the core issues in the market promotion and user relationship building of leveled mathematics readers,providing practical paths and theoretical support for educational publishing institutions to achieve product innovation and brand upgrading in this niche field.
文摘As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.
基金funded by the Macao Science and Technology Development Fund(FDCT)under Grant(No.0071/2023/RIB3&No.0003-2024-AGJ)by the Macao Foundation under Grant(No.MF2342).
文摘This paper examines the grain of content in junior high mathematics digital textbooks from People’s Education Press(PEP)using Cognitive Load Theory(CLT)in a sequential explanatory mixed-methods design:(1)bibliometric analysis of 2008–2023142 publications found substantial gaps in cognitive-aligned pedagogical design;then,(2)large-scale surveys of 231 teachers and 102 students found critical gaps in navigation intuitiveness(71.3%),interactive affordance deficiency(68.9%),and personal pathway rigidity(76.5%).(3)Interviews with 6 teachers and 3 developers further revealed these deficiencies lay in:(1)content fragmentation serving procedural skills at the expense of conceptual integration;(2)sequence disruption violating CLT’s intrinsic load tenets;and(3)passive multimodal serving static text/images(82%of resources)limiting germane processing.We thus innovated a CLT-driven framework to reduce intrinsic load by animating schema builders chunking complex concepts,minimize extraneous load by Gestalt-principled UI redesign serving spatial consistency,and enhance germane load by adaptive analytics serving personal pathways.Empirical results showed 34%more knowledge retention(p<0.01,d=1.87)and 28%less perceived cognitive load(NASA-TLX)relative to conventional textbooks.Our work contributed both a theoretically grounded resource optimization model and an advancement of CLT in technology-enhanced mathematics instruction.
基金supported by the 2023 Teaching Reform and Research Project of China University of Petroleum(Beijing),Karamay Campus(Grant No.JG2023048)the 2024 National Undergraduate Innovation and Entrepreneurship Training Program of China(Project No.202419414009)the 2024 General Program of the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant No.2024D01A160).
文摘In recent years,the rapid development of artificial intelligence(AI)technology has been driving profound transformations in higher education.As a fundamental course in science and engineering disciplines,Advanced Mathematics plays a crucial role in cultivating students’logical thinking and innovative capabilities.However,the current teaching models exhibit significant shortcomings in fostering students’ability to identify and solve problems,primarily reflected in the monotony of teaching content,the limitations of students’thinking,and the constraints of instructional methods.In response to these issues,this paper proposes an AI-based teaching approach for Advanced Mathematics.By utilizing scenario simulations to guide students in discovering problems and employing modeling tools to assist them in solving problems in real time,the study constructs a comprehensive teaching model that spans the entire process from problem identification to problem resolution.Research findings indicate that the application of AI technology can effectively enhance students’abilities in problem awareness,logical reasoning,and creative thinking.This study provides both theoretical support and practical reference for the reform of Advanced Mathematics education and the innovation of higher-level talent cultivation models.
基金Advanced Mathematics A1 First-Class Course of Tarim University(TDYLKC202428)Educational Reform Project of Xinjiang Production and Construction Corps(BTBKXM-2024-Y41)。
文摘To meet the demands of higher education reform and innovative talent cultivation,the teaching team of Tarim University,with ability cultivation as the core,has established a new“331”university mathematics teaching system.Through the multi-dimensional linkage of master teachers’guidance,course optimization,stratified teaching,practical reinforcement,and competition-driven,it has significantly improved students’mathematical application ability and innovative quality.
文摘Mathematics is a basic course for cultivating advanced technical talents,a core course for students in the basic education stage,mathematical knowledge content is the foundation of professional courses,mathematical thinking ability is one of the abilities for students’sustainable development,mathematical literacy is a basic quality that students should possess,and it carries the function of implementing the fundamental task of fostering virtue and nurturing talent and developing quality-oriented education.It has the characteristics of being fundamental,developmental,applied,and vocational.In today’s era of rapid development of artificial intelligence and big data,mathematics plays a huge role in production and life.This paper briefly expounds and analyzes the current situation of mathematics teaching,explores the significance of information-based teaching for mathematics teaching,and on this basis,proposes relevant strategies for information-based mathematics teaching,including knowledge visualization,the use of information technology to create mathematics teaching scenarios,the realization of efficient mathematics teaching through micro-lessons,and the realization of teaching interaction through network platforms.
基金Zhejiang Provincial First-Class Undergraduate Internationalized Course of‘Calculus 1’Teaching Reform Project of the Research and Development Center for University Mathematics Teaching in Higher Education Institutions(Project No.:CMC20240641)Provincial-level undergraduate teaching reform projects in Zhejiang province(Project No.:JGBA2024350)。
文摘International student enrollment has rapidly grown in China,positioning transnational education as a significant component of the country’s higher education system.So our study investigates an innovative teaching approach that combines the Knowing-Understanding-Doing(KUD)framework with the BOPPPS pedagogical model(which includes the Bridge-in,Objective,Pre-assessment,Participatory Learning,Post-assessment,and Summary components),with specific application to undergraduate mathematics teaching for international students at a Chinese university.Taking Calculus 1 as a case study,our study evaluates the implementation efficacy of this integrated approach.The findings offer valuable insights for those seeking to enhance the quality and effectiveness of their teaching methodologies in culturally diverse undergraduate mathematics classrooms.
基金Project of Heilongjiang University of Finance and Economics(XJYB2024056)Project of Heilongjiang University of Finance and Economics(XJYB2024057)。
文摘In this paper,the necessity of constructing a golden course for Advanced Mathematics is presented.For teachers,golden courses enhance their teaching ability and job satisfaction.For students,golden courses improve their sense of learning value and significance and encourage them to actively learn and participate deeply.Next,the relevant content of course ideological and political construction is provided.Finally,a specific approach was proposed to create a golden course for Advanced Mathematics by integrating ideological and political education into the curriculum.
文摘The relationship between arts and mathematics is very close, computer graphic design is based on digital methodology. The paper reveals the mathematical backgrounds behind graphic design by the example of computer-aided cubic modeling and mathematical exchange methodology. Furthermore, one can get incredible artistic effects if computer graphic designers pay more attention to the probability and use probable numbers and fractal operation in their design activities.Finally, the author also discusses the bidirections between arts and mathematics.
