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

2. 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

3. 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.

4. 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

5. 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

6. 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

7. 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:

8. 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)

9. 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

10. How Shanghai Does the Research Teacher Group(RTG)?

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

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

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

14. 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

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

16. 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.