Teaching Mathematics
Mastery and ITE
Claire Morse and Laura Clarke
[email protected]
[email protected]
A shifting landscape of vocabulary
mastery
depth
multiple representations
cumulative curriculum
complete and connected perspectives
conceptual understanding
variation
intelligent practice
fluency
procedural fluency
bar modelling
practice, apply, clarify and explore
A return to established literature
• Dienes (1960)
• Bruner (1966)
• Gattegno
(1967)
• Skemp (1976)
• Piaget (1952)
• Liebeck (1984)
• Askew (1997)
•
•
•
•
Lim (2007)
Yu (2008)
Lai (2012)
Hodgen et al
(2014)
• Stobart (2014)
Stobart, G. (2014)The Expert Learner: Challenging the
myth of ability. McGraw Hill: Maidenhead
‘How experts learn’ (chapter 2)
Opportunity
Motivation
Extensive and long term deliberate
practice
Deep knowledge
Extensive memory and skills
Reflection
Positive Attitudes to Mathematics
Developing
Mathematics
Specific
Pedagogy
Developing
Mathematical
Subject Knowledge
Primary
Mathematics
Teacher
Developing a
personal
identity
Andrews, P. and Rowland, T. (2014) Master class in Mathematics Education: International Perspectives on
Teaching and Learning. Bloomsbury: London
Chap, S. L. (2007) Characteristics of Mathematics Teaching in Shanghai, China: through the Lens of a
Malaysian. Mathematics Education Research Journal, 19, (1) 77-89
Fan, L. (2004) How Chinese learn mathematics: perspectives from insiders. Singapore: World Scientific
Hodgen, J., Monahagn, J., Shen, F. and Staneff, T. (2014) Shanghai Mathematics exchange – views, plans
and discussion. Proceedings of the British Society for Research into Learning Mathematics 34(3), November
2014. Available at: http://www.bsrlm.org.uk/IPs/ip34-3/BSRLM-IP-34-3-04.pdf
Huiying, Y. (2008) A comparison of mathematical teachers’ beliefs between England and China. Proceedings
of the British Society for Research into Learning Mathematics 28(2), June 2008. Available at:
http://www.bsrlm.org.uk/IPs/ip28-2/BSRLM-IP-28-2-21.pdf
Rongjin, H. and Leung, F., K., S. (20005) Deconstructing Teacher Centeredness and Student Centeredness
Dichotomy: A Case Study of a Shanghai Mathematics Lesson. The Mathematics Educator, 15, (2) 35-41
Lai, M. Y (undated) Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of
Mathematics. Available at: http://www.cimt.plymouth.ac.uk/journal/lai.pdf
NCETM (2014) Mastery approaches to mathematics and the new national curriculum . Available at:
https://www.ncetm.org.uk/public/files/19990433/Developing_mastery_in_mathematics_october_2014.pdf
NCETM (2015) NCETM Mathematics Textbook Guidance. Available at:
https://www.ncetm.org.uk/files/21383193/NCETM+Textbook+Guidance.pdf
Lesson content is influenced by
Lim, C. S. (2007) Characteristics of Mathematics Teaching in Shanghai, China: through
the Lens of a Malaysian Mathematics Education Research Journal 19(1) 77-89
Within our control
• Teachers depth of SCK
• Teachers depth of PCK
• Teachers beliefs and
attitudes
• Learners beliefs and
attitudes
Beyond our control
•
•
•
•
•
Curriculum demands
External assessment
Cultural context
Expectations of society
Parental demands
Year 2: Children Learning
Mathematics
By the conclusion of this module, a student will be expected to be
able to :
• Understand how children develop conceptual understanding
and mastery of mathematics and explore appropriate
intervention
• Trace progression in key ideas and identify equivalent ideas in
different forms
• Evaluate ways in which subject knowledge can be transformed
to made accessible to all learners
• Justify specific classroom practices with reference to research
and relevant statutory and non-statutory curriculum
documentation
• Articulate developing priorities for mathematics teaching.
Year 3:The Development and Leadership of
Primary Mathematics
By the conclusion of this module, a student will be
expected to be able to:
• understand the role and responsibilities of the
curriculum leader in mathematics;
• articulate and communicate their vision and
philosophy for primary mathematics education;
• engage with current debates and thinking relating to
good practice in primary mathematics learning and
teaching;
• develop mathematically rich tasks and experiences
for primary children.
Year 4: Enhancing Practice through
a Specialism
At Level 6:
• Critically examine an aspect of personal professional practice
• Demonstrate knowledge, conceptual understanding and skills, which
underpin the specialist curriculum area under enquiry
• Use literature (including research, current national policy documents
and inspection findings as appropriate) critically to inform and
evaluate aspects of professional practice & values
• Formulate and undertake an enquiry into an aspect of learning and
teaching in the specified area in the primary context.
And in addition at Level 7:
• Raise issues, pose questions and identify problems and concerns
related to the professional area under review
• Synthesise information in a manner that may be innovative
Tensions, questions and next steps
• National Curriculum and mastery
• Student and tutor ‘buy in’
• Cross department understanding of
mastery
• Definitions of mastery – sources?
• Working in partnership
• Teacher Standards (what is
differentiation? Expectations for subject
knowledge)
In conclusion
• 18 month journey
• Not easily packaged
• Not just methodology (changed how we teach as well as what
we teach, mastery is an embedded pedagogy)
• Transforming the programme … working with PS teams, other
subject teams, Link Tutors, School Direct clusters
• Keeping up to date with latest initiatives whilst maintaining the
academic integrity of the programme
• Developing students’ sense of being change agents