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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]

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. [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]

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]

Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted, activity-enriched lessons. It argues that creative mathematics teaching in the Chinese context is reference-based. There is a standard on what good teaching should look like and there is a greater emphasis on appropriateness in addition to novelty. Chinese mathematics classrooms are also mostly teacher-led, and Chinese teachers often spend a great deal of time to harness their creative teaching methods through various levels of professional development. The mechanism of exemplary mathematics lesson contest fosters collaborations among teachers on course preparation to achieve more effective mathematics teaching. Both features are consistent with the Chinese view of creativity. Implications are discussed. [ABSTRACT FROM AUTHOR]

It is commonly recognized that the second wave of transmission of Western science and mathematics into China took place in the second half of the nineteenth century, thereby starting a process of modernization which has become synonymous with 'westernization' of the country. In this context mathematics education in China also went through a process of modernization. During this period of great change reformers faced serious challenge and went through a 'mental struggle'. This paper discusses this challenge and mental struggle by taking a close look at the controversy over the establishment of Tianwen Suanxue Guan (School of Astronomy and Mathematics) in Tongwen Guan (School of Combined Learning), one of the schools of Western learning at the time. The attempt to integrate Western mathematics with Chinese traditional mathematics is also discussed through the study of some questions sampled from examinations and students' homework assignments of this school. [ABSTRACT FROM AUTHOR]

We consider divergence form, second-order strongly parabolic systems in a cylindrical domain with a finite number of subdomains under the assumption that the interfacial boundaries are C 1 , Dini and C γ 0 in the spatial variables and the time variable, respectively. Gradient estimates and piecewise C 1 / 2 , 1 -regularity are established when the leading coefficients and data are assumed to be of piecewise Dini mean oscillation or piecewise Hölder continuous. Our results improve the previous results in Fan et al. (Electron J Differ Equ 2013:1–24, 2013) and Li and Li (Sci China Math 60(11):2011–2052, 2017) to a large extent, and appear to be the first of its kind for time-dependent subdomains. As a byproduct, we obtain optimal regularity of weak solutions to parabolic transmission problems with C 1 , μ or C 1 , Dini interfaces. This gives an extension of a recent result in Caffarelli et al. (Regularity for C 1 , α interface transmission problems. arXiv:2004.07322 [math.AP]) to parabolic systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

There were numerous records of solar eclipse in China from the eighth century BC to the fifteenth century AD. Because these records are concise and formalized, I have arranged 938 items into a computer-readable table called ‘‘The table of historic Chinese regular records of solar eclipse’’. In this paper, I explain the structure of the table with a preliminary analysis and statistics of the historical records. To receive the table itself, please request it at liucy@ntsc.ac.cn. [ABSTRACT FROM AUTHOR]

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The major objectives of our study were (a) to identify student profiles according to five homework characteristics (homework time, frequency, quality, interest, and favorability) and (b) to examine their relationship with three critical variables in the homework process—homework effort, completion, and math achievement. Latent profile analysis (LPA) was used to examine a data set with 3018 8th graders in China. Based on these characteristics, five distinct profiles were identified: Profile 1 (Low), Profile 2 (Moderate Time/High With Others), Profile 3 (Low Frequency/Moderate With Others), Profile 4 (Moderate Time/High Frequency/Low With Others), and Profile 5 (High Time and Frequency/Moderate With Others). Parent education was positively associated with the two healthiest profiles (Profile 2 and Profile 5). Finally, profile membership was a significant predictor of homework effort, completion, and math achievement. Specifically, our study suggests that students can work about 30 min on math homework and achieve the same results, if they work often, with high quality, fueled by interest and favorability (compared with students who spend about 110 min on math homework). Taken together, our study provided novel insights into the combination of homework characteristics that could have significant implications for homework practice and research. [ABSTRACT FROM AUTHOR]

The main purpose of this article was to understand the current situation and challenges of the integration of mathematics and science (IMS) in Chinese primary schools. We used a questionnaire responded to by 453 primary school mathematics/science teachers and interviewed 7 teachers among them. Research showed that Chinese primary school teachers had a positive attitude toward IMS, but their beliefs about IMS were not high. Most teachers ever integrated mathematics/science in their class, but they did not have a complete understanding of the form of IMS in their minds. Results revealed that IMS in Chinese primary schools faced some challenges, such as teachers' incomplete perceptions of IMS, lack of resources, and insufficient school support and time. Finally, we proposed some recommendations for better implementation of IMS. This research would help policymakers, curriculum developers, educators, and primary teachers in China have an overall picture of IMS. [ABSTRACT FROM AUTHOR]

Spatial ability has been shown the positive correlations with the mathematics achievement of typically developing children. However, whether there is a relationship between spatial ability and mathematics achievement in deaf children and the mechanisms that underlie the relationship remain unknown. 256 deaf children in Grades 3 to 9 in two special education schools in China performed a series of cognitive and mathematical tests. After controlling for age and gender, we found that spatial ability, processing speed (both accuracy and reaction time), and intelligence were significantly related to mathematics achievement. Moreover, processing speed and intelligence were found to mediate the relationship between spatial ability and mathematics achievement in deaf children. The mediating effect of intelligence was significantly greater than the serial mediating effect of processing speed (accuracy) and then intelligence; both the mediating effect of processing speed (reaction time) and the mediating effect of intelligence were significantly greater than the serial mediating effect of processing speed (reaction time) and then intelligence. These findings suggest a process through which processing speed can decrease intelligence and identify the mediating effects of processing speed (both accuracy and reaction time) and intelligence in the relationship between spatial ability and mathematics achievement in deaf children. [ABSTRACT FROM AUTHOR]

In this study the research was focused on the mechanisms of how Chinese in-service teachers' beliefs about mathematics, together with their professional knowledge, affect their teaching approaches. With a quantitative survey study involving 92 in-service teachers, it identified six types of teachers with three different categories of beliefs (i.e., Instrumentalist, Platonist, and Problem-solving oriented) and two different levels (i.e., strong and limited) of subject knowledge and pedagogical content knowledge on the topic of functions. Six teachers were subsequently selected, for a detailed analysis of how the teachers' beliefs and knowledge influenced their teaching practices. The case study results showed that teachers with different professional knowledge levels about functions and beliefs about mathematics had different teaching focuses and showed different teaching approaches. Three teaching approaches were identified, including the performance-focused content-centered approach, the understanding-focused content-centered approach, and the thinking-focused student-centered approach. [ABSTRACT FROM AUTHOR]

Interest is vital for students' learning in mathematics. Over the course of the Chinese mathematics curriculum reform in the past 30 years, cultivating students' positive emotions, attitudes, and values has gained growing attention. In the current study we examined the trajectory of Chinese mathematics textbook development by analyzing textbook content that stimulated students' mathematics learning interest through the curriculum reform in the past three decades. First, we selected textbooks that represent each phase of the curriculum reform (the Incubation Phase, the Reform Phase, and the Conditioning Phase). Then, taking eighth grade as an example, we used Hidi and Renninger's model to identify content that focus on stimulating students' learning interest. Finally, we explored the trajectory of textbook development in this aspect within the scope of curriculum reform. Results show that attention to strategies developing positive emotions and values towards mathematics has been emerging in recent times. Interest-stimulating strategies directed toward the triggering and maintaining of situational interest have been integrated more frequently into textbooks since the Reform Phase, while text content employing strategies that may lead to rote memorization is generally decreasing. Using Chinese curriculum reform as a context, this study demonstrates how mathematics textbooks have been revisioned and revised with a focus on stimulating students' learning interest. The reform of mathematics education has been successfully implemented in more than thirty provinces in China, despite significant differences in geographical, cultural, and economic development. It is hoped that this study can provide practical evidence of interest stimulation in mathematics for the international education community. [ABSTRACT FROM AUTHOR]

In this study we aimed to capture the characteristics of Chinese high-quality lessons from a lesson structure perspective, specifically addressing the elements of teaching activity and their sequence. Sixteen videotaped middle school mathematics lessons were selected from 224 daily lessons collected from urban districts in five cities located in the east, north, west, south, and center of China, approved by three independent parties (based on the scores of an instruction quality assessment and ratings by two experts). We found the following five common features among most mathematics lessons: (a) most lessons began with a review; (b) pure learning of mathematical knowledge was emphasized; (c) recurrent teaching activities related to mathematics problems ran throughout the lesson; (d) highlighting and summarizing important points during the lesson and summarizing the entire lesson at the end of the class were frequently used; and (e) teaching activities were dense and large in volume. The research findings paint a broad picture of high quality instruction (deepening our understanding of high-quality teaching in different cultures) and provide multiple choices for teachers. [ABSTRACT FROM AUTHOR]

Recently, Hattori–Lagha established the global existence and asymptotic behavior of the solutions for a three-dimensional compressible chemotaxis system with chemoattractant and repellent (Hattori and Lagha in Discrete Contin. Dyn. Syst. 41(11):5141–5164, 2021). Motivated by Hattori–Lagha's work, we further investigated the optimal time-decay rates of strong solutions with small perturbation to the three-dimensional Keller–Segel system coupled to the compressible Navier–Stokes equations, which models for the motion of swimming bacteria in a compressible viscous fluid. First, we reformulate the system into a perturbation form. Then we establish a prior estimates of solutions and prove the existence of the global-in-time solutions based on the local existence of unique solutions. Finally, we will establish the optimal time-decay rates of the nonhomogeneous system by the decomposition technique of both low and high frequencies of solutions as in (Wang and Wen in Sci. China Math., 2020, https://doi.org/10.1007/s11425-020-1779-7). Moreover, the decay rate is optimal since it agrees with the solutions of the linearized system. [ABSTRACT FROM AUTHOR]

Asian children, including Chinese children, perform better than their English-speaking peers in cross-national mathematics studies. This superior Asian performance is attributed to several factors including cultural beliefs, educational systems and practices, and the Chinese number naming system. Given the limited empirical evidence on pre-school mathematics learning in Chinese societies, the outcomes of Western studies are often borrowed and adopted in curriculum planning in Asian schools. The study reported in this paper investigated the performance of Hong Kong Chinese pre-school children based on Western studies involving English-speaking children, and examined the relationship between the Chinese number naming system and children's performance in number and operation concepts. Data were collected from 299 pre-school children aged between 3 and 5 years. The learning sequence of the children in mastering number and operation concepts was established using the Rasch Model. This study provides empirical evidence for the feasibility of borrowing lists of mathematics concepts from studies of English-speaking children to serve as a reference for school-based curriculum planning in a Chinese-speaking context. However, it is not enough to establish the relationship between children's performance and the Chinese number naming system. Classroom instruction and cultural beliefs in mathematics learning are also important in explaining children's performance. [ABSTRACT FROM AUTHOR]

This article deals with the roles of variation problems ('one problem multiple solution' and 'one problem multiple changes') as used in Chinese textbooks. It is argued that variation problems as an 'indigenous' Chinese practice aim to discern and to compare the invariant feature of the relationship among concepts and solutions. This practice also aims to provide opportunities for making connections, since comparison is considered the pre-condition to perceive the structures, dependencies, and relationships that may lead to mathematical abstraction. In the first part of the article, the 'indigenous' practice is discussed against its philosophical Daoism and Confucianism backgrounds. To grasp its distinctiveness, a comparison between Chinese and American textbooks is carried out. In the second part of the article, the focus is on the manner in which fraction division is articulated in an important Chinese textbook. A framework to understand variation practice is introduced and some educational implications are suggested. [ABSTRACT FROM AUTHOR]

General cognitive and specific numerical abilities that underlay mathematical performance have been heavily investigated among hearing students; however, the inquiry has rarely been applied to students who are deaf or hard-of-hearing (d/Dhh). We examined whether general cognitive abilities (i.e. nonverbal IQ, processing speed, and spatial ability) and specific numerical abilities (i.e. symbolic and non-symbolic numerical magnitude processing) are related to mathematics achievement in 198 d/Dhh students in Grades 3 to 9. The results of our regression models indicated that, the three general cognitive abilities independently explained the variance in mathematics achievement when entered in one step; and spatial ability and processing speed had an independent contribution to mathematics achievement in the presence of the specific numerical abilities. The specific numerical abilities independently explained the variance in mathematics achievement when entered in one step; however, none of them had an independent contribution to mathematics achievement in the presence of the general cognitive abilities. These findings suggested that mathematics achievement in d/Dhh students depended more on general cognitive abilities, such as spatial ability and processing speed, than on specific numerical abilities. [ABSTRACT FROM AUTHOR]

While many studies of monitoring accuracy have been conducted with college students, less is known about middle school students' monitoring accuracy, especially in Asian countries. Prior research also found discrepancies in students' monitoring accuracy between Western and Asian cultures. To understand and support Chinese middle school students' monitoring accuracy in mathematics, we implemented a three-week long monitoring intervention with 7th grade students in Southwestern China. Students were divided into three conditions: a control condition, a confidence rating condition (CR), and a confidence rating combined with monitoring instructions condition (CR + MI). Findings indicated that Chinese middle school students were slightly underconfident, yet quite accurate when monitoring during task completion in mathematics. Specifically, although students in the CR and CR + MI conditions did not show significant increases in mathematics performance, students in the control condition significantly decreased their performance overtime. In terms of monitoring, students' confidence bias increased overtime in the CR + MI and control conditions while students in the CR condition did not show significant change. Students also demonstrated increased self-reported metacognitive awareness across the three conditions. We also asked students to provide justifications for their confidence judgments. Findings indicated that students tended to consider a single factor when judging their performance during a mathematics task. Regression models of students' justifications indicated potential suggestions for future interventions. Implications and future directions are discussed. [ABSTRACT FROM AUTHOR]

Here we report the results of a speeded relative quantity task with Chinese participants. On each trial a single numeral (the probe) was presented and the instructions were to respond as to whether it signified a quantity less than or greater than five (the standard). In separate blocks of trials, the numerals were presented either in Mandarin or in Arabic number formats. In addition to the standard influence of numerical distance, a significant predictor of performance was the degree of physical similarity between the probe and the standard as depicted in Mandarin. Additionally, competing effects of physical similarity, defined in terms of the Arabic number format, were also found. Critically the size of these different effects of physical similarity varied systematically across individuals such that larger effects of one compensated for smaller effects of the other. It is argued that the data favor accounts of processing that assume that different number formats access different format-specific representations of quantities. Moreover, for Chinese participants the default is to translate numerals into a Mandarin format prior to accessing quantity information. The efficacy of this translation process is itself influenced by a competing tendency to carry out a translation into Arabic format. [ABSTRACT FROM AUTHOR]

This study examines the gender gaps in mathematics and physics in Chinese middle schools. The data is from the Education Bureau management database which includes all middle school students who took high school entrance exam in a district of Beijing from 2006-2013. The ordinary least square model and quantile regression model are applied. This study consistently shows that the gender gap is unfavorable toward female students in mathematics and physics while favorable toward female students in Chinese and English. Gender gaps favoring males in math and physics become more noticeable among the students who receive the top tier scores in math and physics testing. However, females' students' advantage in Chinese and English decreases along the distribution from the bottom to the top percentiles. There are significant intersections between rural residency and gender. Rural students (regardless of gender) perform less well than urban students in all subjects and rural female student show the worst testing scores compared with the other subgroups in mathematics and physics. [ABSTRACT FROM AUTHOR]

In this study, we aim to examine and discuss approaches and practices in developing mathematics textbooks in China, with a special focus on the development of secondary school mathematics textbook in the context of recent school mathematics reform. Textbook development in China has its own history. This study reveals some common practices and approaches developed and used in selecting, presenting and organizing content in mathematics textbooks over the years. With the recent curriculum reform taking place in China, we also discuss some new developments in compiling and publishing high school mathematics textbooks. Implications obtained from Chinese practices in textbook development are then discussed in a broad context. [ABSTRACT FROM AUTHOR]

This article uses a multilevel approach to study the Chinese numeral classifiers. It argues that although shape categories constitute a major cognitive base for numeral classification, lexical taxonomy, linguistic convention, and stylistic creativity also play a role in determining the use of Chinese classifiers. It cautions that in general the relationship between noun and classifier is explicable from the semantic/cognitive stance, but the relationship is not always transparent and consistent. At times the choice of a classifier can be entirely arbitrary and subject to linguistic innovation. [ABSTRACT FROM AUTHOR]