Elements of Teaching for Mastery
Elements of Teaching for Mastery

Classroom Practice

Good use of concrete, pictorial and abstract (CPA) representations are provided and pupils are encouraged to connect and see relations between these different representations.


The CPA approach is based on Jerome Bruner’s stages of representation.


Using technical and precise language.





Source Guidance/Examples/Links/Stimuli
Strategy Shanghai         A blog by Tim Brogan (@brogan_mr) about his improving classroom practice.
Bruner's Stages of Representation Jerome Bruner is a psychologist who focused much of his research on the cognitive development of children and how it relates to education.
Concrete-Pictorial-Abstract: Surveying its origins and charting its future An article by Leong Yew Hoong, Ho Weng Kin, Cheng Lu Pien of the National Institute of Education, Nanyang Technological University, Singapore.
Importance of Concrete        CPD Video and resources from White Rose Maths Hub about using concrete apparatus.
Mr Barton podcast A podcast by Mr Craig Barton and Bernie Westacott about using manipulatives to support mathematics.
Improving Learning in Mathematics - Challenges and Strategies Standards Unit by Malcolm Swam, University of Nottingham.
The Bar Model An overview from NCETM of use of the Bar Model for visualisations.

Fractions Bar Model
Multiplcation and Division

Addition and Subtraction

[Full Folder]

A series of powerpoint shows developed from a workgroup in Kent and Medway. Designed to be used as a self study guide. Download each show and view.
Bar Method A collection of resources by Dawn Denyer about using the Bar Model
Mastery Moments - Video 1 A video 'Moment' from NCETM on answering in full sentences.
www.thesingaporemaths.com Links from their website to modelling problems.
Thinking Blocks Interactive tutorials for use with the Bar model.
Numicon Youtube video about using Numicon.
Cuisenaire Cuisenaire website.
MathsBot A great website with interactive demonstrations and manipulatves.
Nrich Directed Numbers A nice page from Nrich about adding and subtracting postive and negative numbers. Includes some nice use of double sides counters.
Manipulatives in Secondary A case study, with accompanying lesson slides, in the mastery section of the NCETM website, which profiles a secondary school where the use of representations and physical materials is now routine in Key Stage 3 maths lessons.
Primary Shanghai Exchange Feedback Mid Exchange report from the NCETM Shanghai Primary Exchange.
Nrich Manipulatives Report by Jenni Back on the use of manipulatives in the classroom.
NRICH Use of Cuisenaire List of resources by NRICH on using Cuisenaire.
CPA Approach Video by Maths no Problem by Dr. Yeap Ban Har on the concrete, pictorial, abstract approach.
CPA Article by mathteachingstrategies.wordpress.com in the CPA approach.
Multiplicative Reasoning Resources for CPD by NCETM on developing multiplicative reasoning within the curriculum aimed at KS3.
Instructional Guidance An article by Jinfa Cai et al (2013) looking at coherence, in particular instructional coherence in the classroom.
Visual Support Visual prompts by iseemaths
Maths Visuals A website by @BerkeleyEverett containing some nice visuals for representing different concepts.
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