Understanding the Pedagogical Implication of Teaching Higher Level mathematics through Peer Learning Pedagogical Application of New Developments and Approaches (PANDA) Phase 1 (2015-2016) Dr. Linda (Yuqian) Wang

Background: How Shanghai does it? Our aims 1. Culture, 2. View of Maths knowledge, 3. Curriculum, 4. Differences of England and Shanghai, 5. Model of learning, 6. View of good teacher, 7. Classroom How Shanghai does it? Teacher Research Group (TRG), Mastery in Shanghai Our aims

Six distinctive characteristics of Maths education in East Asia Background 1: Culture Six distinctive characteristics of Maths education in East Asia (Leung, 1997) (1) the content, including two basics, is fundamental; (2) meaningful learning including memorization; (3) enjoying studying hard; (4) students’ extrinsic motivations, such as familial and communal expectations; (5) whole class teaching rather than individualised learning; (6) teachers’ subject matter knowledge prior to pedagogy.

Different views towards Mathematics itself (Wang, 2015) Background 2: Different views towards Mathematics itself (Wang, 2015) Pure Mathematics Applied Mathematics Absolutist view: Isolated and discrete from human knowledge Fallibilist View: models of system abstracted from real world objects Objective and value-free or, at least, not imbued with human values Corrigible and perpetually open to revision Discover the already existing truths of formal logic The paradigm of a certain knowledge The product of a taken-as-shared or human activity learning mathematics is to master a set of mathematical facts and procedural knowledge domain-specific, context-bound and procedurally rooted as well as influenced by culture

Different emphasis on the national curriculum (Wang, 2015) Background 3: Different emphasis on the national curriculum (Wang, 2015) Visual method in England VS algebraic method in Shanghai Different ways to presenting knowledge – in case of gradient at linear function/graph  

Differences between England and Shanghai, China(Wang, 2015) Background 4: Differences between England and Shanghai, China(Wang, 2015) England Shanghai Approach to understanding Bottom-up (mathematising) Top-down (transfer) Teaching approach Student-centred Content-centred View of maths Applied mathematics Pure mathematics

Background 5: Model for Learning: Technique & Insight Beech & Macintosh (2012) Social zone where, models and theories are sourced & tested Social zone where the technique need is contextualised Dialogical zone where the technique is developed through questioning and experimentation Dialogical zone where “reflective thinking meets practical doing” Personal zone where the technique is internalised and integrated with existing skills Personal zone of reflection and sense-making Source:

Background 6: The image of good teacher (Jin & Cortazzi, 1998) British university students: Be able to arouse their interest, explain clearly, use effective instruction. Chinese university students: Have a deep knowledge, be able to answer questions, and be a good moral model. Teachers’ subject knowledge can provide ‘an effective structure’ for setting up activities to facilitate learning (Hodgen & Marshall, 2005, p. 169) Pedagogy and the quality of instruction are proven to have a strong impact on students’ performance. (Coe, Aloisi, Higgins, & Major, 2014)

What classroom looks like Students are passive, obedient, and uncritical? A more collaborative type of negotiation rather than teacher’s overt dominance. What classroom looks like

How Shanghai Does the Research Teacher Group(RTG)?

Mastery in Shanghai – problem-solving New Higher Tier GCSE Content Course 2015 Camel College (17th June 2015) Problem-Solving Strategy: England

Problem-solving Strategy in Shanghai Creating middle questions Procedural variation for problem-solving (Gu et. al., 2004, p.322)

Four Basics in China: Mastery approach Basic knowledge, Basic skills, Basic method, and Basic experience (Wang, Wang, & Wang, 2008)

Basic method – mastery approach Conceptual understanding of mathematics: Link concepts with each other – web of knowledge In case of division, fraction, and ratio Fraction Ratio Procedural knowledge understanding: Prime factor, Highest common factor (HCF), Least common multiples (LCM) HCF LCM

Our aims – The depth: three curricula The Tripartite Model of curricula classification (Valverde et al., 2002, p. 13)

Three aims: the width to establish a professional learning community for teaching (PLC4T) and pioneer collaborative lesson planning involving the local schools, regional Archimedes Maths Hub, Durham University School of Education, Education Durham, and the Further Mathematics Support Programme (FMSP) across the North East; to enhance teachers’ decision-making for effective evidence-based teaching to promote (i) students’ learning with understanding of Maths, and (ii) deepening of teachers’ understanding and application of the Mastery Approach; to make recommendations to policy makers on specific actions to support PLC4T. The project will be a trial to establish PLC4T, including further research into topics which are ‘dropping down’ to Key Stages, i.e. from Key Stage 3 to Key Stage 2, Key Stage 5 to Key Stage 4.