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Background: Previous studies indicated that working memory (WM) updating and WM capacity play essential roles in mathematical ability. However, it is unclear whether WM capacity mediates the effect of WM updating on mathematics, and whether the cascading effects vary with different mathematical domains. Aims: The current study aims to explore the longitudinal mediating role of WM capacity between WM updating and mathematical performance, and how the relations change with the age and domains. Sample: A total of 131 Chinese first-graders participated the study. Methods: Participants were required to complete tasks on WM updating and WM capacity in Grade 1 and Grade 2, as well as paper-and-pencil tests on mathematics achievement in Grade 3. The role of WM updating and capacity in the development of pupil's mathematical achievement was examined. Results: Results revealed that verbal WM updating in Grade 1 predicted basic arithmetic and logical-visuospatial ability in Grade 3 via its cascading effect on verbal WM capacity in Grade 2. Moreover, visuospatial WM updating in Grade 1 predicted visuospatial WM capacity in Grade 2. Visuospatial WM capacity in Grade 1 predicted logical-visuospatial ability in Grade 3 instead of basic arithmetic ability in Grade 3. Conclusions: The findings suggested that WM updating exerts effect on pupil's mathematical performance via WM capacity, meanwhile, this effect depends on children's mathematics domain.

Rational numbers can be represented in multiple formats (e.g., fractions, decimals, and percentages), and a rational number notation can be used to express different concepts in different contexts. The present study investigated the distribution of the multiple concepts expressed by these different rational number notations in real-world contexts as well as the semantic alignment between entity type (discrete vs. continuous) and rational number format (decimal vs. fraction) in the Chinese context. Textbook analysis and two paper-and-pencil experiments yielded the following four major findings: (1) Decimals were more likely used to represent numerical magnitudes, while fractions were more likely used to represent relations between two numerical magnitudes. (2) Decimals were more often used to represent continuous entities while fractions were preferred to represent discrete entities. (3) The strength of the association between different formats of rational numbers and their preferred conceptual meanings seemed more pronounced than the semantic alignment between number type and entity type. (4) Percentages were used in a way more similar to fractions than decimals in terms of the concepts they express. These findings indicate that different formats of rational numbers differ dramatically in their use in real-world contexts both in terms of the conceptual meanings they express and the entities they model. Educational implications of this study are discussed.

A central issue in the mathematics curriculum is that we want students to make connections. This issue has been analysed in a series of curricula and instruction design and analysis studies. Moving towards mathematics connections--and away from treating mathematics as a body of isolated concepts and procedures--is an important goal of mathematics education. Although many studies identify "whole number bias" in learning fractions, few studies have examined how this bias may be overcome. In this paper, I aim to clarify how problem variation in Chinese textbooks helps to make concept connections between fractions and whole numbers. To the best of my knowledge, this study systematically addresses the central issue of using the unity of four fraction operations and whole number arithmetic to overcome long-standing whole number bias for the first time. The lack of such methods represents a significant gap in curriculum practice. This study's framework for understanding variation practice to make connections, with an emphasis on the invariant concepts, also is helpful for the analysis of textbook or instructional design, which represents another significant gap in curriculum development theory.

Background: This paper reports on the use of classroom assessment techniques (CATs) by primary school mathematics teachers in China. CATs are short, focused assessment activities that can reveal students' understanding of specific mathematical subjects. The study involved six female third-grade mathematics teachers from Nanjing, China. The focus was on assessing division. Data were collected by teacher interviews, feedback forms and final reports, lesson observations, and student work. Results: The study revealed that the teachers could easily include CATs in their daily practice. By conducting the CATs, the teachers got new information about their students' learning. Most teachers liked using the CATs, especially those with the red/green cards, which is a whole-classroom immediate response format, providing quick information of the students' learning. The teachers also found the CATs feasible to conduct and helpful to engage their students during the lesson. However, no evidence was found that they used the information gained from the CATs for adapting their instruction to meet the students' needs in subsequent lessons. In fact, the teachers only used the teacher guide of the CATs to adapt their instruction beforehand. The CATs, instead of being implemented as assessment activities, were often included as extra exercises in the pre-arranged lesson plans of the teachers. If necessary, the teachers provided their students with instant help in order to assist them to get the correct answers. Conclusions: In general, the teachers were positive about the CATs as a way to reveal their students' understanding of division in an effective and efficient fashion. The teachers recognized that it can be very revealing to challenge their students with questions that are not completely prepared by the content of their textbooks. The results of this study suggest that on the one hand CATs can be helpful for Chinese mathematics teachers' formative assessment practice in primary education. On the other hand, our study also provides some evidence that using CATs, as an approach to formative assessment, to make informed and adequate decisions about further teaching, can be a real challenge for teachers.

The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade but that difference in addition, subtraction and division skills between the groups decreased as grade increased. Secondly, the levels of mastery of the four skills varied between Chinese and Flemish students. Multiplication was relatively easier for Chinese students than for their Flemish peers as compared to the other skills (that is, the gap was larger). Third, low achievers experienced comparable learning difficulties in both countries, and higher achievers demonstrated their greater ability early on.

In mathematics education, there has been tension between deep learning and repetitive learning. Western educators often emphasize the need for students to construct a conceptual understanding of mathematical symbols and rules before they practise the rules (Li, 2006). On the other hand, Chinese learners tend to be oriented towards rote learning and memorization (Marton, Watkins & Tang, 1997). One aspect of the criticism is that rote learning is known to lead to poor learning outcomes (Watkins & Biggs, 2001). However, Chinese students consistently outperform their Western counterparts in many international comparative studies on mathematics achievement such as TIMSS (Beaton, Mullis, Martin, Gonzalez, Kelly & Smith, 1997; Mullis, Martin, & Foy, 2008) and PISA (OECD, 2004; OECD, 2010). This paper aims to contribute to an understanding of the "paradox of the Chinese learners" (Marton, Dall' Alba & Lai, 1993) by exploring the procedural variation and its place in the development of mathematical understanding. (Contains 4 figures.)

This paper presents the results obtained from a study comparing the strategies used by 1,070 Chinese students and 1,002 Singaporean students from primary grade 6 to secondary year 2 in solving three fraction-related problems. It is part of the author's Ph.D. study, which involves more word problems on speed. The Chinese students performed better than the Singaporean students on two of the three problems, while the Singaporean students performed better than the Chinese students on the other. The strategy analyses reveal that the Chinese students used the traditional methods like arithmetic and algebraic strategies more frequently than the Singaporean students, whereas the Singaporean students used the model and unitary methods more frequently than the Chinese students. Implications for the teaching and learning of word problems on speed, as well as problem solving, are also provided.

Academia is fascinated by the process of how Western science and mathematical knowledge converged with the Chinese mathematical tradition. This topic not only reflects East–West interaction, but also turns upon the philosophical question of whether the Chinese have the scientific or cognitive ability to comprehend critical, logical, and abstract thinking. Fundamental to mathematical knowledge is arithmetic, which deals with numbers and their operations. This paper re-evaluates the significance of Alexander Wylie's (1815–1887) pioneering role in translating Western arithmetical knowledge in China, through (1) unearthing a mathematician-missionary, Edward Moncrieff (1824–1857), who compiled a textbook of arithmetic and translated associated mathematical knowledge, in particular Euclidian geometry, one year earlier than Wylie, and (2) critically analyzing the concept of arithmetic in their textbooks by means of the method of Begriffsgeschichte. [ABSTRACT FROM AUTHOR]

Background: This study aimed to investigate the cognitive and affective factors associated with cross-cultural differences in arithmetic tasks. Methods: A total of 404 third- and fourth- graders were recruited from China and Italy to complete exact arithmetic, arithmetic estimation and cognitive tasks (i.e., short-term memory, executive functions, and fluid reasoning). Their mathematical anxiety was also measured. Results: The results showed that Chinese children performed better than Italian children in both arithmetic tasks and in shifting task. Italian children performed better in visuospatial updating task and reported higher levels of mathematical anxiety than their Chinese peers. Multi-group path analyses showed that the patterns of relations among cognitive factors (i.e., short-term memory, inhibition and shifting), mathematical anxiety, and arithmetic performance were similar across groups. The only exception was that visuospatial updating uniquely predicted arithmetic estimation for Chinese but not for Italian children. Conclusions: Chinese children outperformed their Italian peers in the exact arithmetic task, likely due to the greater emphasis on arithmetic fluency in Chinese mathematics education, both in schools and at home. They also had a slight advantage than Italian peers in the arithmetic estimation task. The unique link between updating and arithmetic estimation found in Chinese children but not Italian children suggests that, although arithmetic estimation is not emphasized in the curricula of either country, instruction and practice in exact arithmetic may enhance Chinese children's efficiency in solving arithmetic estimation problems. [ABSTRACT FROM AUTHOR]

The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of different cultural contexts. We discuss the background theoretical issues of this approach and also give an analysis of two examples of cultural transposition experiences carried out in Italy. In particular, by means of qualitative analysis of some excerpts, discussions, and interviews, we show that the contact with different perspectives coming from China and Russia fostered educational practices and reflections on whole number arithmetic education. [ABSTRACT FROM AUTHOR]

The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade but that difference in addition, subtraction and division skills between the groups decreased as grade increased. Secondly, the levels of mastery of the four skills varied between Chinese and Flemish students. Multiplication was relatively easier for Chinese students than for their Flemish peers as compared to the other skills (that is, the gap was larger). Third, low achievers experienced comparable learning difficulties in both countries, and higher achievers demonstrated their greater ability early on. [ABSTRACT FROM PUBLISHER]

This paper presents the results obtained from a study comparing the strategies used by 1,070 Chinese students and 1,002 Singaporean students from primary grade 6 to secondary year 2 in solving three fraction-related problems. It is part of the author's Ph.D. study, which involves more word problems on speed. The Chinese students performed better than the Singaporean students on two of the three problems, while the Singaporean students performed better than the Chinese students on the other. The strategy analyses reveal that the Chinese students used the traditional methods like arithmetic and algebraic strategies more frequently than the Singaporean students, whereas the Singaporean students used the model and unitary methods more frequently than the Chinese students. Implications for the teaching and learning of word problems on speed, as well as problem solving, are also provided. [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]

The study explored the mediating effect of number sense between nonverbal intelligence and children's mathematical performance. The sample consisted of 131 pupils in Shaoxing City of China from grades 1, 3, and 5. The students completed measures of nonverbal intelligence, number sense, basic arithmetic ability, mathematical performance, rapid automatized naming, and working memory. Results show that although all variables significantly relate with each other (all p <.01), only nonverbal intelligence, number sense, and basic arithmetic ability significantly affect children's mathematical performance (all p <.01). According to multiple-mediation model, nonverbal intelligence significantly predicts children's mathematical performance through number sense and basic arithmetic ability. These findings suggest that domain-specific mathematical skills play a prominent role in children's mathematical performance in primary school, rather than domain-general cognitive functions. Educators should pay attention to develop children's number sense in order to improve children's mathematical ability. [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]

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests. [ABSTRACT FROM AUTHOR]

The Bonferroni mean (BM) can portray the inter-relationships among the arguments, which is based on algebraic norm. Archimedean norm is the generalization of algebraic norm. In this work, the intuitionistic fuzzy (IF) BMs on the basis of the Archimedean norm are investigated, including the Archimedean norm-based IF arithmetic BM (AN-IFABM) and the Archimedean norm-based IF geometric BM (AN-IFGBM). Then, we discuss their typical properties and several particular cases of the AN-IFABM and AN-IFGBM in detail. Moreover, we design the Archimedean norm-based IF weighted arithmetic BM (AN-IFWABM) and the Archimedean norm-based IF weighted geometric BM (AN-IFWGBM) to consider the importance of each argument and their interconnections. Applying the proposed extensions, an approach is designed to cope with the multiattribute decision-making (MADM) problems. Finally, an efficiency evaluation problem of some public companies in China is analyzed by the proposed approach to demonstrate its applicability and validity. [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]

Symbolic numerical magnitude processing skills are assumed to be fundamental to arithmetic learning. It is, however, still an open question whether better arithmetic skills are reflected in symbolic numerical magnitude processing skills. To address this issue, Chinese and German third graders were compared regarding their performance in arithmetic tasks and in a symbolic numerical magnitude comparison task. Chinese children performed better in the arithmetic tasks and were faster in deciding which one of two Arabic numbers was numerically larger. The group difference in symbolic numerical magnitude processing was fully mediated by the performance in arithmetic tasks. We assume that a higher degree of familiarity with arithmetic in Chinese compared to German children leads to a higher speed of retrieving symbolic numerical magnitude knowledge. [ABSTRACT FROM AUTHOR]

This study examined the influence of nationality, age and gender on Chinese (N=130) and Finnish (N=203) pre-schoolers' number sense. Two highly correlated aspects of number sense were extracted: one reflecting the children's ability to organise and compare quantities (i.e. relational skills), and another pertaining to their ability to operate with number-word sequence (i.e. counting skills). The results showed a significant age-related gain in both aspects of number sense, whereas no gender differences were found. With respect to counting skills, the Chinese children outperformed the Finnish children irrespective of age, whereas in relation to relational skills, this was true only among the older children. Differences in language, teaching and cultural ethos are considered as alternative explanations for the findings. [ABSTRACT FROM AUTHOR]