Comparing Mathematics Curriculum and Pedagogies in Shanghai and Singapore towards a Better Understanding of East Asian Pedagogy

• In Event: Curriculum and pedagogy

Proposal

Abstract
This paper uses social-cultural perspectives to compare mathematics education, curriculum and teaching in Shanghai and Singapore and views the teachers as agents of activities mediated by various cultural tools, artefacts, discourses, and social, cultural norms. Two teacher cases, an 8th grade math teacher in Shanghai teaching the Unit of Geometry Proofs, and a 6th grade math teacher in Singapore teaching a unit of word problems using the Model Method, are examined in terms of the curriculum, classroom teaching and student learning to portray the unique emphases both place on the mathematical thinking and reasoning in their younger generation, the tools they employ and the common and unique ways in their achieving the desired results. Careful discourse analysis revealed findings that debunk the stereotypical images and a better understanding of East Asian pedagogy.
Three Key words for submission: Cross-national, ethnography, and mathematics education

(961 words not including Abstract)
1. Background and Conceptual Framework:
This paper uses social-cultural perspectives to compare mathematics education, curriculum and teaching in Shanghai and Singapore, the top two performing cities in PISA with Confucian heritage culture and views the teachers as agents of activities mediated by various cultural tools, artefacts, discourses, and social, cultural norms. Though much has been published on Singapore and Shanghai mathematics education separately by local and international scholars in recent years (Fan et al, 2004, 2015; Wang et al, 2009), rarely has any research been conducted to compare their curricular and pedagogical work together. Such comparative inquiry will inform the debate on the controversies incurred in studying educational systems comparatively (Alexander, 2009), such as the so-called East Asia Learner Paradox (Mok, 2006) as well as the good and bad of Singapore education (Hogan 2014) contributing towards a better understanding of East Asian Pedagogy.
Drawing on data from two independent research projects, this study compares the classroom discourses and task mediations of two veteran math teachers, Ms Wang, teaching Geometric Proofs in 8th grade in Shanghai and Mr Tan, teaching math problem solving using the Model method in 6th grade in Singapore. More specifically, it aims to understand the alignment between curriculum, teaching and student learning by focusing on one important pedagogical feature common to both classrooms – the teacher-dominated feedback sharing sessions featured by going over marked student work with careful explanation in large classes proceeded by hours of the teachers’ marking. Alexander’s (2009) conception of pedagogy is used to examine the curriculum translation at the school level and classroom transposition around Lesson in which transformation by the acts of the teacher in engaging students in learning through tasks, activities, interactions and assessment. Such a framing allows the manoeuvre between and across the macro and micro dimensions of the comparative pedagogies and considers the central questions regarding the pedagogical features as well as the cultural values that shape them.
2. Methods
Ethnographic fieldwork with long hours of participant observations of classroom practices and open-ended interviews with the observed teachers and students informed the building of two detailed case studies that offer “a means of investigating complex social units consisting of multiple variables of potential importance in understanding the phenomenon” (Meriam, 1998, p. 41). The cases were built based on a three-level data analysis process guided by Alexander’s framework. First, a coding scheme was built to code the interactive classroom discourses at the activity and task level and grounded analysis let patterns emerge through constant comparison (Creswell, 2014) within and across the cases. These pedagogical features were then triangulated with analysis of documents, such as curriculum materials, lesson transcripts, student work and exam papers to determine the national and school level impact on teaching and learning. Based on the above, the interrelationships between and among the variables as well their relationship to the cultural contexts and values were teased out.
3. Findings
First of all, at the broader level, Shanghai and Singapore imbue deep cultural values in cultivating mathematical thinking through challenging topics, geometric proofs and problem solving. Unique cultural tools have been devised in serving the purpose, such as Shanghai’s writing of rigorous proofs and Singapore’s use of the model method, “a powerful visual method for solving challenging multi-step word problems, and it serves as a link to algebra.” (Foong, 2009, 271) across its elementary schools. Second, the curriculum units and tasks in both places are designed with variation in both form and content to help students discern the mathematics ideas and thinking behind. Thirdand most importantly, at the classroom discourse and activity level, teachers’ meticulous marking of student work followed by immediate feedback to student errors with structured and thorough explaining in the classroom to delve into the embedded mathematics. Teacher-directed teaching practices in both classrooms show that common student misconceptions, procedural inaccuracies, and poor habit of work displayed in student work became shared object of investigation known as culture of errors (Author, 2010); engaged thinking and metacognition were prominent under the teachers’ interrogation and probing; steps of correction or improvement were carefully demonstrated with mathematics thinking justified and made clear. Good attitudes towards learning mathematics, such as perseverance, accuracy, simplicity, were nudged into students through such homework practices. (Author, 2014).

4. Discussion and Conclusion
The findings debunk a few stereotypical images of East Asian teaching and learning. First, as Confucian heritage cultures, both Shanghai and Singapore are known for their pragmatism yet instead of focusing on short-term practical applications, their curriculum and pedagogical practices address long-term goals of logical deductive thinking and problem solving. Both cultures tap into the curriculum task design for pedagogical values rather than seen as simply blind following of the textbook. The discourse patterns in both classrooms apparently reinforce common findings about East Asian classrooms with rows of desks and quiet students behind them listening to teacher-dominated lecturing (Paine, 1990; Stevenson & Stigler, 1992), but the analysis shows co-construction going on in homework practices despite of limited contribution from students who were mostly engaged. Homework checking and feedback giving as formative assessment focusing on errors cultivate values and habit of mind of lifelong learning rather than repetitive drill and practice view of repetitive practice and accumulation of teachers’ PCK. Such pedagogical features could be easily dismissed with attribution to the examination cultures. Our research suggests that there can be much more knowledge work and deep learning going on in preparing students for high-stakes examinations (Author, 2014; Watkins & Biggs, 1996). This kind of inquiry would push beyond quest for success or failure in student performance to inform better understanding of East Asian pedagogy and the controversies revolving around its debate, such as those behind the East Asian Learner Paradox.

Author

• Yanping Fang, National Institute of Education, Singapore