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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.

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]

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]

This study investigated the impact of cognitive strategy instruction (CSI) on mathematical word problem solving of students with mathematics disabilities. A sample of fourth-grade students in a Chinese primary school was divided into a treatment group (75 students) and a comparison group (75 students). The sample consisted of students with mathematics disabilities only, students with both mathematics and reading disabilities, as well as average- and high-achieving students. Results showed that students at all ability levels (except high-achieving students) in the treatment group outperformed significantly their counterparts in the comparison group; the intervention effect was stronger for students with mathematics disabilities only than for those with both mathematics and reading disabilities. The present study indicates that CSI is a contextually and pedagogically appropriate model that has a strong potential to improve mathematical word problem solving. [ABSTRACT FROM AUTHOR]

This study examines the mediating role of homework in the daily practice of a middle-school mathematics teacher and her colleagues in Shanghai. It aims to explore how a system of homework activities mediates and engenders a cultural pedagogy characterized by transforming errors into resources for teaching and learning. The transformation itself embodies teacher learning processes tied up with making sense of errors and providing feedback and pedagogical support to help as many students as possible to 'get it right'. The findings of the study raise important questions about what teaching entails, and how to organize teachers' work so that teacher learning occurs in the process of fostering student learning. This requires a reconceptualization of homework to capitalize on its pedagogical potentials. [ABSTRACT FROM AUTHOR]