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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]

The importance of integrating history into mathematics education is widely recognised in the literature and advocated in curricula worldwide, including in China. However, under the influence of the long-standing centrally designed curricula, teachers in China are accustomed to content- and teacher-centred examination-driven teaching practices. Adopting a life story approach, this paper reports the case of a mathematics teacher who integrated history into her mathematics teaching during the initial two years of her teaching in a Shanghai high school. The agentic perspective adopted in the study allows us to focus on how the teacher's agency was enacted and achieved when engaging in teaching practices. Our findings reveal the roles played by personal qualities, prior experiences, and the structure and culture of schooling in the teacher's agency in integrating history into teaching under a dominant performance-driven context. Implications of the results for integrating history into teaching in restricted contexts are then discussed. [ABSTRACT FROM AUTHOR]

In this paper, characteristics of mathematics classrooms in the East Asian countries1 of Hong Kong and Japan are discussed based on an analysis of the data of the TIMSS 1999 Video Study. The data shows that although students in these East Asian countries did not talk a lot in the classroom, they were exposed to more instructional content. The mathematics problems they worked on were set up mainly using mathematical language, and compared with the problems solved by students in other countries, the problems took a longer duration to solve and more proof was involved. According to the judgement of an expert panel on the Hong Kong lessons (Japan did not participate in this part of the study), more advanced contents were covered and the lessons were more coherent. The mathematics presentations were more developed, and the students were more likely to be engaged in the lessons. In sum, the overall quality of the teaching in this East Asian country was judged to be high. The findings show that high quality teaching and learning can take place even in a teacher directed classroom. It is argued that these East Asian classroom practices are deeply rooted in the underlying cultural values of the classroom and the wider society. The paper ends by drawing some implications of the study for the mathematics education community in other cultures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper introduces the current situation of the popular Chinese university education, points out the impact of popularized Chinese higher education on its university mathematics education, and presents the actualities and existing problems of university mathematics education research in China. [ABSTRACT FROM AUTHOR]

This paper explores the perceived parental influence (PPI) on mathematics learning among over 700 students across three year levels (Years 5, 7, 9) in China and Australia. It was found that the PPI of students was less strong as year levels increased in both countries. Students in China had stronger perceived parental encouragement and higher perceived parental educational expectation than students in Australia. The PPI of students from different home language backgrounds was also investigated. Students in China demonstrated stronger perceived parental encouragement and parental expectation than English speaking students and other language speaking students in Australia, and they also demonstrated stronger perceived parental expectation than Chinese speaking students in Australia, and similar perceived parental encouragement. Within the three groups of students in Australia, Chinese speaking students and other language speaking students demonstrated similar levels of perceived parental encouragement and expectation, but they both demonstrated a higher level of perceived parental encouragement and expectation than English speaking students. Possible reasons for the similarities and differences between the different groups of students were discussed. [ABSTRACT FROM AUTHOR]

Due to the COVID-19 pandemic in Shanghai, China, all school classes were delivered through an online environment from February 24 to May 22, 2020. To support this transition, the Shanghai Education Commission led expert teachers and specialists to develop a series of online video lessons based on the Shanghai unified curriculum, and suggested students watch the online video lessons individually from home, followed by an online synchronous lesson supported by class teachers. This study investigated what primary mathematics teachers learned from addressing these challenges through a case study. By following two purposefully selected teachers over 2 weeks during the transition, multiple data sets including online video lessons, online synchronous lessons, daily reflections, and post-online teacher interviews were collected. A fine-grained analysis of the data from the lens of the documentational approach to didactics found that teachers adaptively used online video lessons as important resources for their online synchronous lessons and virtual Teaching Research Groups as a teachers' collaboration mechanism supported them to develop online video lessons and address various technological constraints. Finally, implications of this case study for mathematics education globally are discussed. [ABSTRACT FROM AUTHOR]

In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in mathematics by analyzing their problem-posing abilities in geometric scenarios. The participants in this study were from one location in the USA and two locations in China. All participants were enrolled in advanced mathematical courses in the local high school. Differences in the problems posed by the three groups are discussed in terms of quality (novelty/elaboration) as well as quantity (fluency). The analysis of the data indicated that even mathematically advanced high school students had trouble posing good quality and/or novel mathematical problems. We discuss our findings in terms of the culture and curricula of the respective school systems and suggest implications for future directions in problem-posing research within mathematics education. [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]

Most studies of children's attitudes to mathematics have dealt with children in second grade or later, and have suggested that attitudes deteriorate, and anxiety increases with age. The present study investigated attitudes to mathematics in 67 English and 49 Chinese children at the end of their first year of school. The participants were given Thomas and Dowker's (2000) Mathematics Attitude Questionnaire, which uses pictorial rating scales to assess primary school children's mathematics anxiety, liking for mathematics, unhappiness at poor performance in mathematics, and self-rating in mathematics. They were also given the British Abilities Scales Basic Number Skills test. Attitudes were generally positive, though not more so than previously found for older primary school children. The Chinese children performed better in the arithmetic test and also rated themselves higher than the English children, but did not differ in other attitudes. Self-rating in mathematics and lack of unhappiness at poor performance were associated with better performance in the English group. There were no significant relationships between attitudes and performance in the Chinese group. Implications of the findings are discussed. [ABSTRACT FROM AUTHOR]

The purpose of this cross-national study is to understand teachers' views about the meaning of instructional coherence and the ways to achieve instructional coherence. With respect to the meaning of instructional coherence, whereas the majority of U.S. teachers paid attention to connections between teaching activities, lessons, or topics, the majority of Chinese teachers emphasized the interconnected nature of mathematical knowledge beyond the teaching flow. U.S. teachers expressed their views about ways to achieve instructional coherence through managing a complete lesson structure. In contrast, Chinese teachers emphasized pre-design of teaching sequences, transitional language and questioning based on the study of textbooks and students beforehand. Moreover, they emphasized addressing student thinking and dealing with emerging events in order to achieve 'real' coherence. The findings of the study contribute to our understanding about the meaning of instructional coherence and ways to achieve instructional coherence in different cultural contexts. [ABSTRACT FROM AUTHOR]