Exploring The Role of Long-term Student-centred Pedagogy in Mathematical Problem-solving Skills, Mathematical Creativity, and Mathematical Creative Self-efficacy: A Comparative Case Study Methodology in Chinese Schools

Abstract

Although researchers proposed that student-centred pedagogy (SCP) has potential in improving mathematical problem-solving skills and creativity compared to teacher-centred pedagogy (TCP), the relationship between pedagogy and these two constructs remains either contested or underexplored, particularly within the Chinese context. Furthermore, most studies examining the effectiveness of SCP on learning outcomes are relatively short in duration, leaving the benefits of its long-term implementation largely unexplored. Additionally, mathematical creative self-efficacy, that refers to students’ beliefs in their ability to generate creative ideas in mathematics, has yet to be investigated in relation to SCP. To address these gaps, this study explored the relationship between long-term use of SCP and the constructs of mathematical problem-solving skills, mathematical creativity, and mathematical creative self-efficacy through a comparative case study of two Chinese secondary schools (Grades 7-9), where this PhD study found differ significantly in their delivered pedagogy: one is more student centred and the other more teacher centred. The significant difference in student-centredness between the two schools’ pedagogies was identified using both classroom observations and teachers’ perceptions. Afterwards, the three constructs of students from the two schools were investigated after they had experienced their respective pedagogical environments for nearly one and three consecutive academic years, respectively. Specifically, the Grade 7 and Grade 9 final mathematics examinations, both standardised assessments, were used to compare students’ mathematical problem-solving skills across the two schools. Multiple-solution tasks (MST) were used to evaluate the mathematical creativity of Grade 8 and Grade 9 students across the two schools via fluency, flexibility, and originality. Questionnaires were designed and conducted within- and between schools to measure students’ creative self-efficacy at four time points: the beginning of Grade 7, two weeks into Grade 7, seven months into Grades 7 and Grade 9, using a combined cross-sectional and longitudinal design. Notable findings include the following: 1) By the end of Grade 7 and Grade 9, the two schools differed significantly in the quartile containing the lowest performers, with SCP School’s low-performing students achieved higher scores. 2) The Grade 8 students in the SCP school exhibited significantly higher creativity in a geometric task compared to the respective students in the TCP group. 3) Both schools’ Grade 9 students showed significantly higher mathematical creativity in an algebraic task compared to the Grade 8 students, and such significance is regardless of the pedagogies they received. 4) Grade 7 students in the SCP school were more likely to have higher mathematical creative self-efficacy compared to the respective students in the TCP school. However, this advantage of the students in the SCP school was not present in Grade 9. The findings of this PhD study have several implications. The problem-solving data implies that, in the long term, SCP has more advantages in improving the mathematical problem-solving skills of low achievers. Regarding the creativity data, the significantly higher creativity in a geometric task of the Grade 8 participants at the SCP school compared to the respective ones in the TCP school suggests that SCP may have a potential in improving students’ geometric creativity. Moreover, the significantly higher creativity performance of the Grade 9 participants than the Grade 8 participants in the given algebraic task suggests that mathematical creativity may require sufficient familiarity with content. Regarding the creative self-efficacy data, the fact that the two schools differed significantly at all three time points following the start of secondary education suggest a likely relationship between pedagogy and mathematical creative self-efficacy. The fluctuations in creative self-efficacy across different times suggest that the duration of exposure is an important factor influencing the relationship between pedagogy and creative self-efficacy. I discussed different aspects of mathematical problem solving, creativity, and creative self-efficacy, as well as propose future research directions to potentially broaden and deepen research in the field of mathematics education.