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Teaching Mathematics Mastery and ITE
Claire Morse and Laura Clarke
A shifting landscape of vocabularymasterydepthmultiple representationscumulative curriculumcomplete and connected perspectivesconceptual understandingvariationintelligent practicefluencyprocedural fluencybar modellingpractice, 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
Developing Mathematical Subject
Knowledge
Developing Mathematics
Specific Pedagogy
Developing a personal identity
PrimaryMathematics
Teacher
Positive Attitudes to Mathematics
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 byLim, 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 SpecialismAt 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
