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This paper aims to investigate whether online private supplementary education, also known as shadow education, can alleviate educational inequality and what types of mechanisms can help alleviate it. We investigate this using an online learning platform dataset (3,603 anonymous students from China) with additional data from multiple sources and employ geospatial analyses to measure students' socioeconomic, regional and rural/urban inequalities. We find that taking part in online education narrows the performance gap in mathematics between privileged and unprivileged students in terms of school status and regional disparity in China. Theoretically, two micro-level mechanisms explain the alleviating differences: (1) equal access mechanism: students from lower city tiers and low-status schools show greater score improvement when having equal access to online education; (2) equal quality mechanism: students from rural regions improve their in-class rankings more substantially if they receive equal quality online education with the same tutoring and learning environment alongside urban students. This study comprehensively looks at the different effects of two mechanisms of online education--equal access and equal quality--for alleviating various types of inequality. Thus we speak to both educational inequality and digital inequality theory, finding that equal access to online education is not enough for rural students, as they also need access to classes of equal educational quality with their urban counterparts.

The teachers of mathematics education in China have gradually demonstrated the need for the systematic theory about mathematics education. However, the philosophy of mathematics education is biased towards the academic level, and there are few "readable materials" for direct application in practice. This paper prepares a curriculum system for the philosophy of mathematics education for normal students (the students of teaching universities). The purpose is to stimulate the discussion of the philosophy of mathematics education among the (future) mathematics teachers for practical guidance, to implant the necessary "genetic genes" for the benign development of mathematics education.

Mathematical modelling has been included in many mathematics curricula worldwide, and China's curricula are no exception. The development of modelling competencies has recently been listed among the Chinese mathematics curriculum's six key objectives. However, the manner in which nationwide learning and teaching of modelling should be conducted presents a key challenge to China's schools, most of which are wholly lacking in experience of this practice. In this study we present a thematic analysis of the conceptions of four mathematicians, five mathematics educators and seven mathematics teachers, with regard to the learning and teaching of modelling. The results show that the participants' views of modelling can be categorised and linked to the following theoretical perspectives of modelling: applied, epistemological, educational, pedagogical and conceptual perspectives. Interestingly, the mathematicians and mathematics educators tended towards the atomistic approach to the learning and teaching of modelling, while the mathematics teachers placed greater emphasis on the holistic approach. The mathematicians and mathematics educators stressed student autonomy, while the teachers emphasised teacher demonstration. All participants considered group work to be an appropriate means of conducting modelling learning and teaching. Additionally, some teachers were concerned that modelling could not be incorporated into mathematical teaching and learning if it could not be included in high-stakes examinations. The paper concludes with a discussion on the rationale behind the existence of the various conceptions and the potential insights that may be drawn from these conceptions.

The level of difficulty of mathematical test items is a critical aspect for evaluating test quality and educational outcomes. Accurately predicting item difficulty during test creation is thus significantly important for producing effective test papers. This study used more than ten years of content and score data from China's Henan Provincial College Entrance Examination in Mathematics as an evaluation criterion for test difficulty, and all data were obtained from the Henan Provincial Department of Education. Based on the framework established by the National Center for Education Statistics (NCES) for test item assessment methodology, this paper proposes a new framework containing eight features considering the uniqueness of mathematics. Next, this paper proposes an XGBoost-based SHAP model for analyzing the difficulty of mathematics tests. By coupling the XGBoost method with the SHAP method, the model not only evaluates the difficulty of mathematics tests but also analyzes the contribution of specific features to item difficulty, thereby increasing transparency and mitigating the "black box" nature of machine learning models. The model has a high prediction accuracy of 0.99 for the training set and 0.806 for the test set. With the model, we found that parameter-level features and reasoning-level features are significant factors influencing the difficulty of subjective items in the exam. In addition, we divided senior secondary mathematics knowledge into nine units based on Chinese curriculum standards and found significant differences in the distribution of the eight features across these different knowledge units, which can help teachers place different emphasis on different units during the teaching process. In summary, our proposed approach significantly improves the accuracy of item difficulty prediction, which is crucial for intelligent educational applications such as knowledge tracking, automatic test item generation, and intelligent paper generation. These results provide tools that are better aligned with and responsive to students' learning needs, thus effectively informing educational practice. [ABSTRACT FROM AUTHOR]

This paper aims to trace the origins of dual entry beyond a Eurocentric boundary. The aim can be refined further by asking: did the Chinese use dual entry and how did dual entry appear in Europe. Double entry is more advanced as it includes the location of the account in which the contra entry is made. Dual entry approaches accounting, like mathematics, as a tautology, whereby an equation is constructed from a simple axiom. Defined as such, this paper argues that the concept of dual entry had its earliest origins in China. [ABSTRACT FROM AUTHOR]

Purpose — The aims of this article are to describe the current status, usage, and acceptance of domestic preprint servers in mainland China by investigating three integrated preprint servers in mainland China. These are the Qiji e-print archive (Qiji), the Chinese Preprint Server (CPS), Chinese Science Papers Online (CSPO)., Design/methodology/approach — This research gives a quantitative analysis of the submission numbers to three preprint servers, the subject distribution and citations. An investigation of university websites and their policies was also carried out. Findings — Preprint submissions have a strong correlation with official promotion and policies. The preprints communication pattern in mainland China concentrates on the disciplines of physics, mathematics and computer science which reflects international preprint communication behaviour. As yet the domestic preprint servers in mainland China attract little attention from excellent scholars and have a low impact on scientific communication. Research limitations/implications — No author survey was conducted. Originality/value — This is the first paper to characterize the usage and acceptance of domestic preprint servers in mainland China using a quantitative method. [ABSTRACT FROM AUTHOR]

This paper proposes a cloud multi-criteria group decision-making model for teacher evaluation in higher education which is involving subjectivity, imprecision and fuzziness. First, selecting the appropriate evaluation index depending on the evaluation objectives, indicating a clear structural relationship between the evaluation index and objectives and establishing a proper evaluation system are all critical and fundamental tasks. Then, collect expert evaluation data, process data, establish training set to build the decision trees, extract evaluation rules, simplify evaluation process, while reducing the cost of evaluation in real applications. Third, establish the interval cloud evaluation matrix through the decision cloud, transforming the evaluation value through the cloud model, determining the order of importance of the decision program, and make the decision. Finally, an addressing linguistic decision-making problem for college teacher evaluation is provided to illustrate the effectiveness of the proposed model.

Academic dishonesty is recognised as a serious problem in Australia, and educators have been searching for ways to prevent its escalation. It is important to understand what factors influence cheating. This study used a sample of 446 grade 7 to 9 students, 160 from Macao and 286 from Zhuhai in China, to examine the personal and contextual aspects of academic dishonesty. The findings suggest that involvement and task orientation in the classroom environment (contextual aspects) and intrinsic value and utility value (personal aspects) are associated with students' attitudes toward the acceptability of cheating and cheating behaviour in mathematics. Some suggestions for reducing academic dishonesty are included in the paper.

This paper describes the development of BOLE, a MATLAB-based interactive learning environment, that facilitates the process of learning bio-inspired optimization algorithms, and that is dedicated exclusively to unmanned aerial vehicle path planning. As a complement to conventional teaching methods, BOLE is designed to help students consolidate the concepts taught in the course and motivate them to explore relevant issues of bio-inspired optimization algorithms through interactive and collaborative learning processes. BOLE differs from other similar tools in that it places greater emphasis on fundamental concepts than on complex mathematical equations. The learning tasks using BOLE can be classified into four steps: introduction, recognition, practice, and collaboration, according to task complexity. It complements traditional classroom teaching, enhancing learning efficiency and facilitating the assessment of student achievement, as verified by its practical application in an undergraduate course "Bio-Inspired Computing." Both objective and subjective measures were evaluated to assess the learning effectiveness.

This paper reports findings from a survey of how rural junior secondary school students in the western part of China perceive their mathematics classroom learning environments and associations of learning environment with their attitudes toward mathematics and mathematics achievement. Using adaptations of the widely-used What Is Happening In this Class? questionnaire and a mathematics attitude scale, the study involved data from 749 Grade 7, 842 Grade 8 and 864 Grade 9 students from 12 coeducational schools and 52 classrooms in three provinces. Data were analysed through factor analysis, descriptive statistics, two-way ANOVA, simple correlation analysis and multiple regression analysis. It was found that rural junior secondary students generally did not perceive their mathematics classroom environment very favourably, and they did not hold very positive attitudes towards mathematics. There existed significant gender and grade differences in the perceptions of mathematics classroom learning environments and attitudes towards mathematics. Positive correlation between mathematics classroom learning environment and students' attitudes towards mathematics and their mathematics achievement were identified.

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students' mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students' mathematical content knowledge and their problem-posing abilities in mathematics.

This paper aims to demonstrate the impact of coal enterprises’ vertical integration on the performance of innovation corporate social responsibility (ICSR) and to elaborate its specific transmission path through financing structure and market power. This paper takes the data of A-share listed coal company from 2008 to 2017 as samples, uses input-output table method to measure the degree of vertical integration, and explores the relationship between the four factors through multiple linear regression and Bootstrap method. We found that: (1) the vertical integration of coal enterprises has positive incentives for the promotion of ICSR. (2) Financing structure and market power play a chain intermediary role in this process of incentive. (3) In areas with high marketization process, vertical integration has more significant incentive effect on ICSR. The paper extends the research on the relationship between vertical integration and innovation, which provides a reference for the improvement of China’s supply-side reform and corporate social responsibility (CSR) fulfillment policy. It is helpful to promote the sustainable development of the coal industry, stimulate the innovation vitality of enterprises, and improve the fulfillment of CSR. [ABSTRACT FROM AUTHOR]

The Ministry of Industry and Information Technology (MIIT) universities are important bases for science and technology research and play a critical role in China’s National Innovation System. Based on the Web of Science (WoS), this article analyzes the statistics of paper published by MIIT universities and universities from across China including MIIT universities. The results are as follows: (1) Both the MIIT universities and universities nationwide in China have increased their international academic publications, and MIIT have shown a greater increase for the past decade. (2) In terms of U-I-G interaction, for UG relations, the Tug value of MIIT universities has remained stable, while that of universities in China has become declined. For UI relations, the Tui value of both MIIT universities and universities in China has shown steady growth. For UIG relations, MIIT universities have a greater synergistic effect of Triple Helix relationship than universities in China. (3) For more details in seven MIIT universities, universities elected into “Project 985”, including HIT, BUAA, BIT and NPU, have published more papers, and been more synergistic with government and industry (UIG relations) than other three universities, including NUAA, NUST and HEU. Based on the empirical results, we discuss our findings, and make certain suggestions regarding policy incentives, reasonable administrative system and U-I-G interaction mode, which is significant not only for Chinese universities but also for universities in other developing countries. [ABSTRACT FROM AUTHOR]

Anemia is a global public health problem, especially common among children in developing countries, which affects their physical and mental health development. However, there is currently a lack of research on the relationship between anemia and academic performance. The objective of this study was to explore the association between anemia and academic performance, and the possible factors mediating this association among Chinese children. The data for this study came from the baseline survey of the Chinese Education Panel Survey Elementary School Cohort. The cohort was conducted from September 2018 to June 2019 in 160 elementary schools, covering 20 provinces and 40 counties/districts throughout China. Paper-based questionnaires were used, completed by 4th grade students, parents, head teachers, main teachers, and principals. The data used included questionnaire responses, physical measurements, and academic performance of 17,695 students. Based on students' hemoglobin levels and school altitude data, we grouped them into anemia and nonanemia categories using WHO criteria. The anemia group had 1,154 individuals, while the nonanemia group had 16,541 individuals. An ordinary least squares regression and mediation effect analysis were conducted. Our findings found the prevalence of anemia was 6.52% among Chinese Grade 4 students. Students without anemia had a higher average test score for three academic subjects than students with anemia (P < 0.001); their test scores for Chinese, Mathematics, and English were also higher (P < 0.05). Multivariate regression analysis showed a negative association between anemia and average test scores as well as individual test scores for the three subjects. Mediation analysis found that anemia affected academic performance directly (P < 0.05), and indirectly by decreasing the cognition score (P < 0.05). The indirect effect was 19.9% of the total effect. Findings highlighted anemia affected academic performance both directly and indirectly. Nutrition-related interventions should be implemented to prevent a decrease in academic performance among students with anemia. [ABSTRACT FROM AUTHOR]

Science, Technology, Engineering, and Math (STEM) education emphasizes solving problems in authentic contexts and developing 21st-century skills. It also helps to cultivate individuals possessing scientific curiosity and innovative abilities. These capacities align with China's core literacy training. Recent years have seen K-12 STEM cases flourish nationally. However, little attention has been paid to the shared characteristics of these practices, and suggestions for implementing STEM in primary and secondary schools are scarce. This paper presents commonalities in STEM practices within China from a curriculum perspective and offers recommendations for implementation based on these attributes. Specifically, this study first constructed analytical metrics via the Delphi method to assess STEM cases. Next, 51 typical STEM teaching cases in different regions of China were analyzed using these metrics. Based upon the statistical results, five characteristics of STEM cases were summarized: China's STEM education has an unbalanced geographical distribution; current practices benchmark the need for innovative talent training; most instructional content is drawn from real-world problems, but interdisciplinary integration deserves closer focus; the cases featured rich teaching activities and were conducted in a project-based learning fashion with insufficient emphasis on mathematical applications; and China seems to be holistically promoting STEM education, especially through new technologies and supplementary materials. Findings should allow instructors to better understand the intricacies of STEM implementation and to promote successful STEM cases. Recommendations are also provided to optimize the localization of STEM education in China in order to cultivate innovative and interdisciplinary talent. [ABSTRACT FROM AUTHOR]

This cross-sectional study looks into how students' perceived teacher support is linked to achievement emotions in mathematics via academic control and value. The data was gathered from 602 secondary students (13-16-year-olds) in 16 mathematics classrooms from three public schools in Jiangsu province, China. Participants were asked to respond to the paper-pencil questionnaire assessing students' perceived teacher support, cognitive appraisals, and achievement emotions in mathematics. Findings showed that cognitive appraisals played complete mediation roles in teacher support and achievement emotions. Intrinsic value and mathematics self-concept were shown to serve a positive role in teacher support and achievement emotions, whereas extrinsic value was found to play a negative one. Besides, teacher support showed the greatest indirect effect on achievement emotions through mathematics self-concept. Lastly, findings indicated the great relevance of teacher support to students' anger, boredom, enjoyment and relaxation in mathematics classrooms. [ABSTRACT FROM AUTHOR]

The small data global well-posedness of the 3D incompressible Navier--Stokes equations in R³ with only one-directional dissipation remains an outstanding open problem. The dissipation in just one direction, say, 2 1u is simply insufficient in controlling the nonlinearity in the whole space R³. The beautiful work of Paicu and Zhang [Sci. China Math., 62 (2019), pp. 1175-1204] solved the case when the spatial domain is bounded in the x1-direction by observing a crucial Poincaré-type inequality. Motivated by this Navier-Stokes open problem and by experimental observations on the stabilizing effects of background magnetic fields, this paper intends to understand the global well-posedness and stability of a special 3D magnetohydrodynamic (MHD) system near a background magnetic field. The spatial domain is R³, and the velocity in this MHD system obeys the 3D Navier-Stokes with only one-directional dissipation. With no Poincaré-type inequality, this problem appears to be impossible. By discovering the mathematical mechanism of the experimentally observed stabilizing effect and introducing several innovative techniques to deal with the derivative loss difficulties, we are able to bound the Navier-Stokes nonlinearity and solve the desired global well-posedness and stability problem. [ABSTRACT FROM AUTHOR]

Background: Digital game‐based learning (DGBL) has the potential to provide a gender inclusive learning environment for children. Objective: The present study aimed to explore gendered differences among primary school learners in grades three, four, and five within the context of game‐based fraction learning from cognitive, motivational and emotional perspectives. Methods: Two hundred and sixty‐nine participants completed a pre‐test and post‐test on fraction conceptual knowledge and surveys in math anxiety, intrinsic motivation and self‐efficacy. In addition, facial expression detection technology was employed to evaluate emotional states. Results: In general, within the DGBL environment, boys and girls exhibited similar performance in both their understanding of fraction concepts and their motivational aspects. However, gender differences were identified and manifested uniquely across different grade levels. Specifically, third‐grade girls exhibited significantly lower self‐efficacy than boys, but after DGBL intervention, the gender gap in self‐efficacy was no longer significant. Additionally, third‐grade girls achieved significant improvements in both the competence and interest dimensions of their intrinsic motivation, while boys did not show significant improvements. In the fourth grade, girls exhibited a significantly higher frequency of angry expressions compared to boys during gameplay. Fifth‐grade girls' cognitive performance appeared to be less correlated with motivational factors compared to boys. Conclusions: The results suggest that DGBL may help narrow the gender difference in math learning, with girls potentially benefiting more from DGBL than boys. Lay Description: What is already known about this topic: Gendered differences in math learning include historical advantages for boys, diminishing achievement gaps, persistent math anxiety with gender variations, and gender‐related disparities in intrinsic motivation and self‐efficacy, highlighting the need for targeted support for girls, particularly in science, technology, engineering, and mathematics fields.Studies on digital game‐based learning (DGBL) indicate varying effects on academic performance, with some showing improvement in girls, minimal gendered differences, and potential differential impacts on emotional states by gender.Fraction knowledge plays a pivotal role in math learning, DGBL emerges as an effective and gender‐inclusive tool to enhance conceptual understanding of fractions. What this paper adds: The game‐based fraction learning could effectively enhance conceptual understanding of fractions for third to fifth‐grade students, revealing consistent positive outcomes for both boys and girls across different grade levels, particularly in tasks related to measurement interpretation.The game‐based fraction learning significantly improves motivational experiences, particularly enhancing competence, interest, and self‐efficacy for third‐grade beginner girls, with less pronounced effects observed in fourth and fifth‐grade students.Fourth‐grade girls displayed a significantly higher proportion of angry faces compared to boys, suggesting potential differences in cognitive load, stress, and emotional engagement in digital game‐based learning.After game‐based intervention, fifth‐grade girls' cognitive outcomes were less influenced by motivational factors, while boys still demonstrated a strong correlation between motivational factors and cognitive scores. Implications for practice: Educational practitioners are encouraged to integrate game‐based learning into early childhood math education, as demonstrated by this study, which highlights the significant contribution of early exposure to game‐based learning in fostering girls' positive attitudes towards mathematics.Game designers should incorporate relevant intelligent technologies for monitoring emotions and different gameplay modes, and when learners experience negative emotions, various strategies should be employed to provide a gender‐inclusive and supportive learning environment.For girls facing challenges in mathematics, their underperformance may be associated with lower motivation levels and emotional states, and game developers can address this issue by offering positive reinforcement, personalized feedback, and challenges tailored to individual learning needs to foster competence in learners. [ABSTRACT FROM AUTHOR]

How to effectively solve traffic congestion and transportation pollution in urban development is a main research emphasis for transportation management agencies. A carbon emissions tax can affect travelers’ generalized costs and will lead to changes in passenger demand, mode choice and traffic flow equilibrium in road networks, which are of significance in green travel and low-carbon transportation management. This paper first established a mesoscopic model to calculate the carbon emissions tax and determined the value of this charge in China, which was based on road traffic flow, vehicle speed, and carbon emissions. Referring to existing research results to calibrate the value of time, this paper modified the traveler’s generalized cost function, including the carbon emissions tax, fuel surcharge and travel time cost, which can be used in the travel impedance model with the consideration of the carbon emissions tax. Then, a method for analyzing urban road network traffic flow distribution was put forward, and a joint traffic distribution model was established, which considered the relationship between private cars and taxis. Finally, this paper took the city of Panjin as an example to analyze the road traffic carbon emissions tax’s impact. The results illustrated that the carbon emissions tax has a positive effect on road network flow equilibrium and carbon emission reduction. This paper will have good reference value and practical significance for the calculation and implementation of urban traffic carbon emissions taxes in China. [ABSTRACT FROM AUTHOR]

In order to supplement and improve the landscape evaluation system of traditional villages and play a positive guiding role in the specific protection and development of village landscape, this paper proposes the ecological landscape environment evaluation of traditional villages in Guanzhong from the perspective of rural revitalization. First of all, the relevant national and provincial evaluation standards are deeply studied, and the comprehensive evaluation system of the traditional village landscape in the Guanzhong region is constructed by using expert scoring and an analytic hierarchy process, which includes 6 criteria and 25 indicators. Three typical villages of different types and different development stages, namely, village A, village B, and Village C, were selected for landscape investigation and comprehensive evaluation. The results show that the weight of village location and landscape pattern is the largest, that is, the most important. The second is architectural landscape, with a weight of 0.236, accounting for a high proportion. Then, it is the natural landscape and street landscape, with a weight of 0.1-0.2. Finally, it is the intangible cultural landscape and landscape style protection, with a weight of less than 0.1. The alpha value of the comprehensive evaluation questionnaire of the village A is 0.984. The alpha value of the comprehensive evaluation questionnaire of village B is 0.941. The alpha value of the comprehensive evaluation questionnaire for the landscape of village C is 0.986, which is greater than 0.8. Conclusion. This study makes a comprehensive evaluation of the landscape of typical traditional villages. [ABSTRACT FROM AUTHOR]

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Background Study: The effects of the flipped classroom (FC) on students' academic performance remain ambiguous, and the use of pre‐class videos may be one of the main factors hindering students' progress. A software package called GeoGebra has been proposed as a substitute for pre‐class videos to aid students' learning. Objective: This study investigates the effect of the FC using GeoGebra (FCG) on mathematical performance and memory among senior secondary students. Methods: One hundred and sixty students of a senior high school in China were selected. A quasi‐experimental design was implemented in which the classes were split into the intervention group (FCG), control group A (FCV) and control group B (TL) by random assignment. Pretest, Post‐test 1 and Post‐test 2 were introduced. Results and Conclusion: The results indicate that both the FCG and the FC with pre‐class videos (FCV) were more effective than traditional lectures in enhancing students' academic test scores, and that the effect of the FCG was comparable to its video counterpart, F(2, 136) = 3.752, ρ = 0.026, η2 = 0.052. Although their effects were similar, the qualitative results revealed some hidden benefits associated with the replacement of pre‐class video with GeoGebra. Furthermore, although they were equally effective in promoting students' performance in the short‐term, the long‐term effects on academic performance of both forms of FC were non‐significant when compared with traditional lectures. Lay Description: What is already known about this topic: Flipped classroom is an effective strategy in teaching mathematics.Among those challenges, video may be one of the main factors hindering the effect of flipped classroom. What this paper adds: GeoGebra could be an effective alternative to video.Effect between the flipped classroom using GeoGebra and the flipped classroom using video were similar.Both the flipped classroom with GeoGebra and the flipped classroom with videos were more effective than traditional lectures. Implications for practice and/or policy: Students' short‐term performance could be enhanced by visualisation provided by flipped classroom.To enhance students' long‐term performance, an appropriate amount of homework is suggested. [ABSTRACT FROM AUTHOR]

China’s fast economic growth contributes to the rapid development of its urbanization process, and also renders a series of industrial accidents, which often cause loss of life, damage to property and environment, thus requiring the associated risk analysis and safety control measures to be implemented in advance. However, incompleteness of historical failure data before the occurrence of accidents makes it difficult to use traditional risk analysis approaches such as probabilistic risk analysis in many cases. This paper aims to develop a new methodology capable of assessing regional industrial safety (RIS) in an uncertain environment. A hierarchical structure for modelling the risks influencing RIS is first constructed. The hybrid of evidential reasoning (ER) and Analytical Hierarchy Process (AHP) is then used to assess the risks in a complementary way, in which AHP is hired to evaluate the weight of each risk factor and ER is employed to synthesise the safety evaluations of the investigated region(s) against the risk factors from the bottom to the top level in the hierarchy. The successful application of the hybrid approach in a real case analysis of RIS in several major districts of Beijing (capital of China) demonstrates its feasibility as well as provides risk analysts and safety engineers with useful insights on effective solutions to comprehensive risk assessment of RIS in metropolitan cities. The contribution of this paper is made by the findings on the comparison of risk levels of RIS at different regions against various risk factors so that best practices from the good performer(s) can be used to improve the safety of the others. [ABSTRACT FROM AUTHOR]

Mathematics courses in higher education (advanced mathematics, linear algebra, etc.) are characterized by abstract concepts, many easily confused concepts, many nature theorems, and large amount of calculation of many difficulties. In most cases, due to the knowledge level, knowledge structure, and requirements of the teaching process, the traditional mathematics teaching adopts the straight-to-point approach to the introduction of mathematical concepts, and the explanation of property theorems mostly adopts the method of giving the theorems first and then analyzing and proving them for the calculation problems are mostly manual calculation. Educators are mainly concerned with how to organize teaching so that the trainees can acquire more knowledge, while ignoring the subject status of the trainees, and it is often related to the talents of higher education. The training goals are consistent. The traditional mathematics teaching only reflects a function of knowledge inheritance, but lacks the function of knowledge innovation. The lack of concept generation process in teaching makes the abstraction stronger; the lack of case analysis process makes the applicability weaken; and the serious separation of engineering problem solving and computer operation makes it lack of practicability. The current mathematics knowledge and curriculum make students in a passive position in the process of mastering basic knowledge. From the study about the present condition of the math education and the real requirement, the thesis will talk about content, characteristics, and the relationships for the practical education along with interactive teaching process. What is more, the ways of education and online education is able to be presented. At the same time, this paper also obtains the maximum weight value of each teaching quality evaluation index through analytic hierarchy process, introduces the quadratic fuzzy comprehensive calculation method of fuzzy operator, and determines the maximum component of the evaluation level as the final evaluation level according to the most subordinate degree criterion of fuzzy comprehensive evaluation. Especially in the formulation of teaching quality evaluation model in China, the qualitative description is processed quantitatively by the method of fuzzy mathematics and statistics, so that the qualitative index and the quantitative index are organically combined. [ABSTRACT FROM AUTHOR]

Competitions and related activities are an essential part of mathematics education for gifted students. China has been one of the most successful countries in recent decades in the International Mathematical Olympiad. To illustrate the Chinese experience of mathematics competitions, in this paper we first present a historical sketch of Chinese mathematics competitions, then provide a comprehensive description of its pyramidal selection and training systems, including the introduction of main competitions for high school students, some examples of competition problems, and the training of students and tutors. Furthermore, to investigate the influence of mathematics competitions on contestants, an empirical study of 372 former contestants was conducted and is reported. The results showed that most of the contestants majored in mathematics or areas closely related to mathematics. Nearly half of the contestants intended to do mathematics research or work highly related to mathematics. A majority of the contestants held positive attitudes toward their mathematics competition experiences and affirmed the value of these experiences in cultivating personal interests and developing mathematics abilities. Some negative influences of competition experiences on contestants are also identified. Finally, problems existing in the development of Chinese mathematics competitions and future research directions are discussed. [ABSTRACT FROM AUTHOR]

For any n\in \mathbb {N}=\{0,1,2,\ldots \} and b,c\in \mathbb {Z}, the generalized central trinomial coefficient T_n(b,c) denotes the coefficient of x^n in the expansion of (x^2+bx+c)^n. Let p be an odd prime. In this paper, we determine the summations \sum _{k=0}^{p-1}T_k(b,c)^2/m^k modulo p^2 for integers m with certain restrictions. As applications, we confirm some conjectural congruences of Sun [Sci. China Math. 57 (2014), pp. 1375–1400]. [ABSTRACT FROM AUTHOR]

This study examined the perceptions and experiences of a teacher and students in a Shanghai public primary school when digital games were used in a second‐grade math class. The participants included one teacher and 45 students. Data collection methods included classroom observation, focus‐group and individual interviews, and document analysis. Digital gameplay, when used once daily over a 6‐day period, was found to enhance student engagement and interest in learning; many students, however, were concerned about its effect on academic achievement and eyesight. The teacher employed a "making thinking visible" approach using pencil and paper and problem‐solving strategies to help students understand the game's mathematical principles and master mathematical knowledge. Obstacles included large class size, difficulty evaluating learning outcomes, balancing fun and learning, and effective game–classroom integration. This study found that exam‐oriented education and traditional teacher‐centred teaching in China influenced participants' perceptions and experiences of digital game‐based learning. Lay Description: What is already known about this topic: Digital game‐based learning is effective and leads to a more relaxed learning environment that promotes students' engagement, interest, motivation, and confidence.Learning with digital games helps students acquire mathematics knowledge more effectively than traditional classroom lectures.Digital game‐based learning is helpful in math class as it makes students feel challenged and more capable, thereby improving self‐efficacy and task persistence. What this paper adds: Mathematics teachers and students have a contradictory attitude that shows both approval and concern towards game‐based learning.In the Chinese context, exam‐oriented culture is an important factor that influences the teacher's and students' perceptions and experiences of digital game‐based learning.While digital game‐based learning helps students' engagement and interest in math, it also faces numerous challenges such as large class size, balancing fun and learning, and effective game–classroom integration. Implications for practice and/or policy: Digital game‐based learning may be more effective when combined with pencil and paper to write down the process and make thinking visible.Fun and learning should be balanced in digital game‐based learning.Teachers need training and support for digital game‐centred programmes to succeed. [ABSTRACT FROM AUTHOR]

With the advent of mobile technologies, well‐designed fraction apps can be used to help children gain fraction knowledge, a challenging topic for both teachers and students. The present pilot study adopted a quasi‐experimental design to investigate whether children can learn fraction concepts equally well if half of the lesson time (20 min) is replaced with game‐based learning. Keeping the total lesson time (40 min) identical, the control group (N = 33) received traditional instruction, and the experimental group (N = 32) was presented with a blended learning approach spending half of the class time (20 min) playing tablet‐based fraction games, where each of the learners had their own tablet. The results suggested that in the posttest, the experimental group achieved similar learning gains to the control group and appear to have achieved better performance in the transfer test than the control group. This paper also discusses the efficiency of game‐based learning, the mechanism of how fraction games might enhance learning, and the potential of integrating game‐based learning in educational settings. Lay Description: What is already known about this topicAs a significant mathematical concept in daily life, fractions are crucial for later success in math learning.As a promising new technology, educational games show a great potential for improving learning.Well‐designed fraction apps can be used to help children gain fraction knowledge.What this paper addsGame‐based fraction learning can be combined with formal learning in school education.Game‐based fraction learning might provide a more efficient approach to increasing students' conceptual knowledge of fractions.The result showed that the experimental group achieved a similar cognitive level as the control group although they spent half of the time playing a game, suggesting that children can gain knowledge from the experiences of playing games.What are the implications for practice and/or policyThe result suggests that the proper use of educational games in teaching fractions can make learning more efficient.Further research needs to be done to determine whether the fraction understanding gained through playing these games will have an impact on students' future learning of more complicated fraction concepts. [ABSTRACT FROM AUTHOR]

Although the educational potential of social media has been widely acknowledged, it remains unclear whether social media use might present opportunities for the development of math identity. This study drew on the socialization framework of math identity to examine the relationships between social media use for math learning, bicultural identity integration, ethnic‐math beliefs and math identity among ethnic minority high school students in China. Structural equation modelling results showed that (a) social media use was positively related to math identity; (b) high bicultural identity integration was positively associated with math identity, while biased ethnic‐math beliefs were negatively related to math identity and (c) social media use suppressed the socialization process of math identity, weakening the maladaptive roles of low bicultural identity integration and biased ethnic‐math beliefs in shaping math identity. Our findings highlight the beneficial role of social media use in student math learning. Theoretical and practical implications are discussed. Practitioner notesWhat is already known about this topicSocial media use for learning is associated with students' academic motivation, engagement and academic achievement.Social media use may have affordances for identity development, especially for ethnic minorities.The formation of ethnic minority students' math identity is intertwined with their math and ethnic socialization.What this paper addsSocial media use for math learning was directly and positively related to ethnic minorities' math identity.This study quantitatively confirmed the associations of bicultural identity integration and ethnic‐math beliefs with math identity.Social media use suppressed the relations of bicultural identity integration and ethnic‐math beliefs with math identity.Implications for practice and/or policyPromoting social media use for math learning benefits ethnic minority students' math identity.Social media use for math learning could alleviate the maladaptive role of low bicultural identity integration and biased ethnic‐math beliefs in math identity development.Ethnic minority students' math identity socialization processes merit attention. [ABSTRACT FROM AUTHOR]

Previous studies have emphasised that play can promote children's learning of mathematics. However, little research has been directed towards understanding how collective imaginary play motivates children's mathematical learning. Informed by the cultural-historical conception of play and motives, this paper examines how Conceptual PlayWorld (CPW) creates conditions for Chinese children's meaningful mathematical learning using the concept of repeating patterns as an example. Video observations of teachers interacting with children (4–5 years) during the CPW implementation (8.54 h), as well as children's interviews (5.75 h), were gathered and analysed. Following the focus child Zeng's motives and intentions but all children's experiences in the CPW, the findings show CPW appears to create mathematical conditions that promote thinking, imagining and play. Zeng's motives for mathematical learning are stimulated by his play motives which are amplified through his active participation and problem-solving in a CPW, and this creates conditions for his personally meaningful learning of mathematics in the Chinese kindergarten context. [ABSTRACT FROM AUTHOR]

This paper aims to optimize a desirable fare structure for the public transit service along a bus-subway corridor with the consideration of those factors related to equity in trip, including travel distance and comfort level. The travel distance factor is represented by the distance-based fare strategy, which is an existing differential strategy. The comfort level one is considered in the area-based fare strategy which is a new differential strategy defined in this paper. Both factors are referred to by the combined fare strategy which is composed of distance-based and area-based fare strategies. The flat fare strategy is applied to determine a reference level of social welfare and obtain the general passenger flow along transit lines, which is used to divide areas or zones along the corridor. This problem is formulated as a bi-level program, of which the upper level maximizes the social welfare and the lower level capturing traveler choice behavior is a variable-demand stochastic user equilibrium assignment model. A genetic algorithm is applied to solve the bi-level program while the method of successive averages is adopted to solve the lower-level model. A series of numerical experiments are carried out to illustrate the performance of the models and solution methods. Numerical results indicate that all three differential fare strategies play a better role in enhancing the social welfare than the flat fare strategy and that the fare structure under the combined fare strategy generates the highest social welfare and the largest resulting passenger demand, which implies that the more equity factors a differential fare strategy involves the more desirable fare structure the strategy has. [ABSTRACT FROM AUTHOR]

The annual exam questions in China National College Entrance Examination (CNCEE, commonly known as Gaokao) have attracted wide attention from the entire society in China. This paper analyzes an important math exam question related to always holding inequalities with an unknown parameter from the 2020 CNCEE and builds different solutions via parameter separation or classified discussion, and then gives a systematic and effective design framework for questions related to problems of always holding inequalities and zeros of functions with an unknown parameter for the CNCEE. The framework reveals the internal mechanism of designing the math exam questions in the CNCEE. According to the design framework, two simulated math exam questions with reference solutions will be proposed. [ABSTRACT FROM AUTHOR]

This paper studies the heterogeneous effects of exchange rate and stock market on carbon emission allowance price in four emissions trading scheme pilots in China. We employ a panel quantile regression model, which can describe both individual and distributional heterogeneity. The empirical results illustrate that the effects of explanatory variables on carbon emission allowance price is heterogeneous along the whole quantiles. Specifically, exchange rate has a negative effect on carbon emission allowance price at lower quantiles, while becomes a positive effect at higher quantiles. In addition, a negative effect exists between domestic stock market and carbon emission allowance price, and the intensity decreasing along with the increase of quantile. By contrast, an increasing positive effect is discovered between European stock market and domestic carbon emission allowance prices. Finally, heterogeneous effects on carbon emission allowance price can also be proved in European Union Emission Trading Scheme (EU-ETS). [ABSTRACT FROM AUTHOR]

In recent years, with the rapid development of China's air transport industry and the change in market consumption structure, service quality has become one of the important factors affecting airline revenue. How to formulate a reasonable pricing strategy and maintain competitiveness in the fierce market competition has become an urgent problem for airlines. First, the impact factor of service quality level in the traditional pricing model is introduced and a static price competition model for multi-oligopoly airlines based on service quality is established in this paper. And then, a dynamic pricing model based on service quality of the multi-oligopoly airlines is established. The model incorporates the weight factor of service quality impact, which is used to indicate the weight of the service quality level in the process of airline dynamic pricing. The research results show that the service quality level of airlines has an indispensable influence on its development. Airlines should improve service quality as soon as possible to enhance market competitiveness and achieve sustainable development. [ABSTRACT FROM AUTHOR]

The changing population age structure has a significant influence on the economy, society, and numerous other aspects of a country. This paper has innovatively applied the method of compositional data forecasting for the prediction of population age changes of the young (aged 0–14), the middle-aged (aged 15–64), and the elderly (aged older than 65) in China, India, and Vietnam by 2030 based on data from 1960 to 2016. To select the best-suited forecasting model, an array of data transformation approaches and forecasting models have been extensively employed, and a large number of comparisons have been made between the aforementioned methods. The best-suited model for each country is identified considering the root mean squared error and mean absolute percent error values from the compositional data. As noted in this study, first and foremost, it is predicted that by the year 2030, China will witness the disappearance of population dividend and get mired in an aging problem far more severe than that of India or Vietnam. Second, Vietnam’s trend of change in population age structure resembles that of China, but the country will sustain its good health as a whole. Finally, the working population of India demonstrates a strong rising trend, indicating that the age structure of the Indian population still remains relatively “young”. Meanwhile, the continuous rise in the proportion of elderly population and the gradual leveling off growth of the young population have nevertheless become serious problems in the world. The present paper attempts to offer crucial insights into the Asian population size, labor market and urbanization, and, moreover, provides suggestions for a sustainable global demographic development. [ABSTRACT FROM AUTHOR]

Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open and often underdetermined real-world problems, we propose to enrich the current conceptualisation of mathematical modelling competencies by including creativity, which plays an important role in numerous phases of the mathematical modelling process but has scarcely been considered in modelling discourse. In the study described in this paper, a new instrument for the evaluation of this enriched construct has been developed and implemented. The modelling competencies incorporating creativity of the students were evaluated based on the adequacy of the models and the modelling processes proposed, and the appropriateness and completeness of the approaches were evaluated in detail. Adapting measurement approaches for creativity that have been developed in the problem-solving discourse, certain criteria of creativity were selected to evaluate the creativity of the students' approaches in tackling modelling problems—namely, usefulness, fluency, and originality. The empirical study was conducted among 107 Chinese students at the upper secondary school level, who attended a modelling camp and independently solved three complex modelling problems. The results reveal significant correlations between fluency and originality in students' performances across all tasks; however, the relationships between usefulness and the other two creativity aspects were not consistent. Overall, the results of the study support the importance of the inclusion of creativity in the construct of modelling competencies. [ABSTRACT FROM AUTHOR]

Tourist satisfaction has always been a crucial research issue in the tourism economy. This paper utilizes the Spatial Durbin Model (SDM) to analyze the impact of urban tourism satisfaction on urban macroeconomics from a macro perspective, using quarterly data on tourist satisfaction in 35 large and medium-sized cities along with major urban macroeconomic variables. This study is quite distinct from previous research that focused on constructing a tourist satisfaction index and analyzing the influence factors of tourism satisfaction from the perspective of the micro-level internal composition of tourism. The empirical results show: Firstly, in respect of the impact of urban tourists' satisfaction on the GDP income of cities, the SDM and the SDM with a lagged first-order dependent variable (SDM_dlag) show that the short-term and long-term indirect effects of log-tourist satisfaction are significantly positive, indicating that city satisfaction has a significant positive spatial spillover effect on GDP growth in other cities; Secondly, in respect of the influence of urban tourist satisfaction on the cost of urban life in the SDM, the long-term direct and indirect effects of logarithmic satisfaction are significantly positive, implying, in the long run, that tourist satisfaction has a positive intraregional spillover effect and spatial spillover effect on urban living costs; Finally, the SDM_dlag for the regression of urban tourist satisfaction on the cost of urban daily life shows that the short-run direct and indirect effects of city tourist satisfaction are significantly negative, indicating that tourist satisfaction has intra-regional and spatial spillover effects, and its rise will reduce the cost of living expenses in local and other cities in the short term. Overall, we have further elucidated the role of different levels of urban tourist satisfaction in city macroeconomics from the spatial dimension, thereby enriching the existing research on tourist satisfaction to some certain extent. [ABSTRACT FROM AUTHOR]

Accidents, bad weathers, traffic congestions, etc. led to the uncertainties of travel times in real-life road networks, which greatly affected the quality of individual’s life and the reliability of transportation system. This paper addressed the school bus routing problem in such a stochastic and time-dependent road environment. Firstly, the problem was set based on a single-school configuration, and the students were picked up at their homes, which was in line with the current situation of school bus systems in China. Thus, it could be regarded as an independent problem of school bus route generation in random dynamic networks, which could be solved as a variant of extended Vehicle Routing Problem. However, due to the fluctuation and uncertainty of link travel times, the arrival time at each stop including the destination was varying. Therefore, the selection of optimal path connecting the current service node with the next one was treated as a sub-problem in this study, where the reliability of travel times in the stochastic and time-varying network was highly concerned by such time-rigid commuters. To this end, a Robust Optimal Schedule Times model with a hard time windows constraint was built to generate a most cost-reliable route for school buses. By the use of Robust Optimization method, it was intended to minimize the worst-case total cost which combined the cost of earlier schedule delays with the disutility of travel times. It was also proved that the proposed model could be converted into solving a conventional problem in deterministic dynamic networks for a reduction of computation complexity, which provided the potential of applying to the practical problems. Finally, the validity of the proposed model and its performance evaluation was analyzed through a small-scale computational instance, where all the link travel times in the simulated network were attributed to both time-varying and stochastic. Then, a mathematical programming solver was used to find the exact optimal solution. The results indicated that the model was valid, and the necessity of considering the stochastic and time-dependent nature of transportation networks was also confirmed in the case study. [ABSTRACT FROM AUTHOR]

Aiming to solve the safety problems of high-speed railway operation and management, one new method is urgently needed to construct on the basis of the rough set theory and the uncertainty measurement theory. The method should carefully consider every factor of high-speed railway operation that realizes the measurement indexes of its safety operation. After analyzing the factors that influence high-speed railway safety operation in detail, a rough measurement model is finally constructed to describe the operation process. Based on the above considerations, this paper redistricts the safety influence factors of high-speed railway operation as 16 measurement indexes which include staff index, vehicle index, equipment index and environment. And the paper also provides another reasonable and effective theoretical method to solve the safety problems of multiple attribute measurement in high-speed railway operation. As while as analyzing the operation data of 10 pivotal railway lines in China, this paper respectively uses the rough set-based measurement model and value function model (one model for calculating the safety value) for calculating the operation safety value. The calculation result shows that the curve of safety value with the proposed method has smaller error and greater stability than the value function method’s, which verifies the feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper we discuss students' opportunities to learn to pose mathematical problems, based on a historical analysis of problem posing in the area of number and algebra in six series of Chinese primary school mathematics textbooks published since the 1950s. We examine changes in the proportion and distribution of the problem-posing tasks, and in the presentation of the problem-posing tasks. Our results show a decreasing number of problem-posing tasks as grade level increases, even though problem posing has become more important in mathematics education in China during the last 70 years. This study also provides a variety of examples of problem-posing tasks which could serve as a reference for teachers in other countries in designing and employing problem-posing tasks in the classroom. [ABSTRACT FROM AUTHOR]

The effectiveness of rapid rail transit system is analyzed using tools of complex network for the first time. We evaluated the effectiveness of the system in Beijing quantitatively from different perspectives, including descriptive statistics analysis, bridging property, centrality property, ability of connecting different part of the system and ability of disease spreading. The results showed that the public transport of Beijing does benefit from the rapid rail transit lines, and the benefit of different regions from RRTS is gradually decreased from the north to the south. The paper concluded with some policy suggestions regarding how to promote the system. This study offered significant insight that can help understand the public transportation better. The methodology can be easily applied to analyze other urban public systems, such as electricity grid, water system, to develop more livable cities. [ABSTRACT FROM AUTHOR]

Although studies have increasingly linked air pollution to specific health outcomes, less well understood is how public perceptions of air quality respond to changing pollutant levels. The growing availability of air pollution measurements and the proliferation of social media provide an opportunity to gauge public discussion of air quality conditions. In this paper, we consider particulate matter (PM) measurements from four Chinese megacities (Beijing, Shanghai, Guangzhou, and Chengdu) together with 112 million posts on Weibo (a popular Chinese microblogging system) from corresponding days in 2011–2013 to identify terms whose frequency was most correlated with PM levels. These correlations are used to construct an Air Discussion Index (ADI) for estimating daily PM based on the content of Weibo posts. In Beijing, the Chinese city with the most PM as measured by U.S. Embassy monitor stations, we found a strong correlation (R = 0.88) between the ADI and measured PM. In other Chinese cities with lower pollution levels, the correlation was weaker. Nonetheless, our results show that social media may be a useful proxy measurement for pollution, particularly when traditional measurement stations are unavailable, censored or misreported. [ABSTRACT FROM AUTHOR]

Colorectal Cancer (CRC) is becoming a major threat to people’s life in China. Screening methods adopted by many other countries as effective counter-cancer methods have not been explicitly explored for people there. Thus, we present a Markov model with detailed precancerous adenoma states and then evaluate various screening strategies in this paper. Different from current researches, our model considers the population’s heterogeneous risk of developing adenomas and observation-based screening strategies. Furthermore, we also give a new cost-effectiveness metric. After calibrating, the model is simulated using the Monte Carlo method. Numerical results show that there are threshold values of compliance rates below which strategy with every ten-year colonoscopy becomes the most cost-effective method; otherwise, an observation-based screening strategy is the most cost-effective. We also find that strategy with single colonoscopy for adenoma-free individuals and every three-year colonoscopy for those with adenoma is recommended when the observation-based strategy is not considered. Our findings give an explicit and complete instruction in CRC screening protocol in average-risk Chinese. [ABSTRACT FROM AUTHOR]

Background: Hypochondriac symptoms are commonly reported in health science students. With their incomplete medical knowledge, they may compare their own bodily symptoms with disease symptoms during the process of learning, which can lead to mental distress and the need for repeated medical reassurance. Objective: To estimate the prevalence of hypochondriac symptoms in Chinese health science students. Methods: A systematic literature search was conducted on PubMed, Web of Science, Embase, China National Knowledge Infrastructure, China Biology Medicine disc, and Wanfang Data on July 1, 2018. Additionally, the references of the retrieved papers were searched. Cross-sectional studies published in either English or Chinese that reported the prevalence of hypochondriac symptoms in health science students were included. The selection process was executed based on the Preferred Reporting Items for Systematic Reviews and Meta-Analysis, and study quality was assessed with the checklist recommended by the Agency for Healthcare Research and Quality for cross-sectional studies. A random-effects model according to the DerSimonian-Laird method was used to calculate the pooled prevalence. Results: Seven cross-sectional studies involving 6,217 Chinese health science students were included. The pooled prevalence of hypochondriac symptoms among health science students was 28.0% (95% CI = 19.0%–38.0%). The symptoms were a little more common in females (30.0%, 95% CI = 19.0%–42.0%) than in males (29.0%, 95% CI = 16.0%–42.0%), but the difference was not significant. No significant differences were found between participants grouped by study year. Only three studies explored the coping styles of students with hypochondriasis, and these revealed a high tendency toward help-seeking behaviors. Conclusion: Our systematic review and meta-analysis showed a high prevalence of hypochondriac symptoms among health science students, indicating that it is a noteworthy phenomenon. We suggest that counseling and other support services are necessary for health science students. [ABSTRACT FROM AUTHOR]

To balance the supply and demand in China's beef market, beef consumption must be scientifically and effectively forecasted. Beef consumption is affected by many factors and is characterized by gray uncertainty. Therefore, gray theory can be used to forecast the beef consumption, In this paper, the structural defects and unreasonable parameter design of the traditional gray model are analyzed. Then, a new gray model termed, EGM(1,1,r), is built, and the modeling conditions and error checking methods of EGM(1,1,r) are studied. Then, EGM(1,1,r) is used to simulate and forecast China’s beef consumption. The results show that both the simulation and prediction precisions of the new model are better than those of other gray models. Finally, the new model is used to forecast China’s beef consumption for the period from 2019–2025. The findings will serve as an important reference for the Chinese government in formulating policies to ensure the balance between the supply and demand for Chinese beef. [ABSTRACT FROM AUTHOR]

With green development becoming a global movement, environmental tax has been adopted by many governments to promote green development. This study analyzes the impact of environmental tax on green development by using a four-dimension dynamical system. The establishment of the system is based on the complex and dynamic interactions among economic development, pollution emissions, resources consumption, and environmental tax, where roles of environmental tax are reflected by the linear parameters. A theoretic analysis shows the complexity of the behavior of the system. Mainly, the existence of chaos is inferred by Lyapunov exponent spectrum and bifurcation diagram, then verified by the presence of a chaotic attractor. An empirical study of the green development dynamical system in China demonstrates the particular evolution paths of economic growth, pollution intensity, and resource intensity under different environmental tax parameters. Results indicate a robust beneficial role of environmental tax on green development. Furthermore, when an environmental tax is imposed, a firm government control, an active consumer awareness, an advanced technology level can stimulate economic growth, decrease pollution intensity, and control the resource intensity. But the government control has a stronger effect. This study provides a viable and promising approach to analyze the role of imposing an environmental tax on green development and may have potential application in other areas and countries. [ABSTRACT FROM AUTHOR]