Slides rEd23

1. MASTER MATHEMATICS
TEACHERS: WHAT DO CHINESE
PRIMARY SCHOOLS LOOK LIKE?
ResearchEd
9 September 2023
Zhenzhen Miao
Christian Bokhove
David Reynolds

2. Prof Christian Bokhove
Dr Zhenzhen Miao Prof David Reynolds

3. We will present for
around 30 minutes and
will then leave 10
minutes for comments,
questions and
discussion.
The project is incredibly
rich, so we are going to
cover many points, but
hope to wrap up with a
focussed message.

4. Why this MasterMT project?
• Misconceptions about East Asian education.
• Still very much a ‘black box’.
• Focus on Master Teachers:
• The cluster of teachers who demonstrate best practice in
mathematics teaching;
• Are well regarded by their professional peers locally or nationally;
• Play a leading role in their peer’ PD within and across schools.
• Teacher ranks: Third Level—>Second Level—>First
Level—>Senior—>Professoriate-Senior
• Teacher honorary titles (at district, municipal or provincial
levels): Super Teachers, Subject Leaders, Backbone
Teachers.

5. The policy context in China
• Modernisation agenda since the 1980’s from low skill, based on
simple manufacturing to higher skill.
• Pressure to increase the output of the education sector to feed
manufacturing - high expectations of students/children, belief in
hard work, respect for teachers and an exam system that
opens up education with data.
• Then emphasis in education on improvement, planning,
openness to ideas from outside China, tackling low performing
schools, CPD, moving money from wealthy areas to poor
areas, quotas of top students in poor areas, curriculum reform.
• Very basic agenda of valid policies much used around the
planet - but a difference is a reliable and valid system for
continuous teaching improvement and teacher growth.

6. The MasterMT project (ch 3)
https://www.youtube.com/watch?v=Y5hVYQHaxOE
Green=student
Yellow=teacher
We try to look at
the phenomenon
from as many
sides as possible.

7. Who were involved?
• 70 Master teachers and their pupils in cities or
socioeconomically equivalent cities from five Chinese
provinces/municipalities: Anhui, Beijing, Jiangsu, Jiangxi,
and Tianjin.
• 3,178 pupils in Grades 2-6.

8. Mathematics teaching
1) Structured observation using three instruments, the OTL, the
ISTOF and the MQI;
2) Student-perceived teaching engagement collected as part of
the student questionnaire;
3) Teacher self-comments on the observed lesson and maths
teaching in general during the post-lesson interview;
4) Teachers’ teaching beliefs collected through the teacher
questionnaire;
5) Teacher’s and colleagues’ comments on the lessons delivered
during the teaching research meetings/conferences;
6) Our unstructured observation of the lessons as researchers.
7) In-depth case study of a master teacher’s teaching over 40
school days;

9. 40 days in Ms Q’s class… (ch 2)

10. Timetable for fifth graders in Ms Q’s class

11. Percentages whole-class and student work

12. Learning
1) Affective learning outcomes as measured with the
TIMSS 2015 items;
2) Metacognitive learning outcomes as measured with the
Jr MAI questionnaire;
3) Cognitive learning outcomes in mathematics as
measured with the test;
4) Multicategories of learning-in-action captured by our
lesson observations.

13. Teaching-learning mechanisms
1) Multilevel modelling of teaching effects on three types of learning
outcomes;
2) Multilevel structural equation modelling of the direct and indirect
effects of teaching on learning;
3) Teacher beliefs on what works and how teaching works on learning
(interview);
4) The interaction of teaching and learning during the teaching
research sessions and teachers’ individual and collective
interpretation of teaching and learning just observed;
5) Our unstructured observation of interaction between teaching and
learning.
In addition, analyses of PD-trajectories and PD-in-action data

14. It would be impossible to report on all of these.
So, we report on a few aspects
and then formulate some
overall conclusions.

15. Key features of masterly teaching (ch 4)
Key features of masterly teaching emerge in in-depth
observations and interpretations of all lessons. These key
features include, but are not limited to:
1. Modelling the way for a shared discourse;
2. Multiple representations for one mathematical fact;

16. Multiple representations of fraction addition created by students

17. Key features of masterly teaching (ch 4)
Key features of masterly teaching emerge in in-depth
observations and interpretations of all lessons. These key
features include, but are not limited to:
1. Modelling the way for a shared discourse;
2. Multiple representations for one mathematical fact;
3. Not moving on until the class have reasoned in-depth the very
essence of the task/topic;
4. Variation as scaffolds for fundamental understanding,

18. Variation
Developing the concept of the height of a triangle through variation.

19. Key features of masterly teaching (ch 4)
Key features of masterly teaching emerge in in-depth
observations and interpretations of all lessons. These key
features include, but are not limited to:
1. Modelling the way for a shared discourse;
2. Multiple representations for one mathematical fact;
3. Not moving on until the class have reasoned in-depth the very
essence of the task/topic;
4. Variation as scaffolds for fundamental understanding,
5. Lessons built on a variety of student contribution in an optimal
sequence;

20. Student contributions

21. Key features of masterly teaching (ch 4)
Key features of masterly teaching emerge in in-depth
observations and interpretations of all lessons. These key
features include, but are not limited to:
1. Modelling the way for a shared discourse;
2. Multiple representations for one mathematical fact;
3. Not moving on until the class have reasoned in-depth the very
essence of the task/topic;
4. Variation as scaffolds for fundamental understanding,
5. Lessons built on a variety of student contribution in an optimal
sequence;
6. Constant abstracting and generalising;
7. Key structure of mathematics as the core of each lesson;
8. Teacher gradually unfolding the essence of knowledge on the
board;
and more…

22. Outcomes (ch 5-7)
• Affective outcomes: A general pattern is that the students
from master mathematics teachers’ classrooms give quite
high ratings about school belonging, teaching
engagement and the enjoyment of mathematics learning.
• Metacognitive outcomes: Our findings indicate that in
general the master maths teachers’ students demonstrate
quite good performance in metacognition (MC), having
good knowledge (KC) and regulation (RC) of their own
cognition during the process of mathematics learning.
• Achievement outcomes: Grade 6 >> 5, generally better
than English counterparts (although historical figures).
Age, gender and SES significantly affect cognitive
outcomes.

23. Master mind (ch 8)
Eight common themes emerge amidst teachers’ reflections
upon the specific lessons they just delivered and
mathematics teaching and learning in a broader sense. The
themes include:
1. Teachers as living synthesised textbooks;
2. Scaffolding the learning process;
3. Demonstrating a connected open system of knowledge and
knowledge about knowledge;
4. Cultivating thorough understanding amongst students;
5. Facilitating transition from hands-on to heads-on, from
manipulation to mathematisation;
6. Aiming for deeper and higher-order thinking and reasoning;
7. Teaching towards ‘learning to learn’ with good habits;
8. Cultivating positive attitudes towards mathematics and peers.

24. Growing into master teachers (ch 9)
• Professional development!
• Polishing lessons for public demonstrations and competitions
• Learning from and with peers in Teaching Research Group and
Professional Development events
• Reading, reflecting, writing and publishing
• Learning from expert teachers and renowned master teachers

25. Teacher delivering a demonstration lesson on the stage with a class of unknown students

27. Growing into master teachers (ch 9)
• Professional development!
• Polishing lessons for public demonstrations and competitions
• Learning from and with peers in Teaching Research Group and
Professional Development events
• Reading, reflecting, writing and publishing
• Learning from expert teachers and renowned master teachers
• Support from peers, school leaders and teaching research
officials
• Studying the curriculum and textbooks in depth with great
attention to lesson planning
• Researching as practitioners: a different kind of research
• Keep practising, keep changing
• Leading the way as a way of continuing learning and growing
• Master Teacher Studios: a cross-school professional learning
community

28. Overall conclusions
• ‘Masterly mathematics teaching’ is a whole-class approach with
interaction, modelling, and peer review.
• Master mathematics teachers have strong knowledge and
beliefs.
• Master mathematics teachers pay attention to cognitive,
metacognitive and affective learning outcomes in their
students. They can be developed concurrently – false dilemma.
• Master mathematics teachers grow collectively and practice
independently in their teaching – professional development.
• Master mathematics teachers develop professionally by seeing
development as a shared value that teaching is a public activity
– professional development.
• Master mathematics teachers keep reflecting, keep writing,
keep improving.

29. https://mastermt.org/
This website will be expanded and include
accessible summaries of the book.

30. THANK YOU
QUESTIONS AND DISCUSSION
Prof Christian Bokhove
Dr Zhenzhen Miao Prof David Reynolds