To celebrate World Maths Day, Jennifer Shearman shares her thoughts on Mathematics Mastery:
Mastery Learning
Mastery learning, like most ideas in education, is not new.  Benjamin S. Bloom and Thomas Guskey wrote about Mastery and its application to mathematics learning in the 1960s, 70s and 80s.  More recently Mathematics Mastery has had a resurgence, largely due to the increased interest in the teaching of mathematics in countries which perform well in international tests, such as Singapore and Shanghai.  An early trial of a specific Maths Mastery programme in a group of primary and secondary schools by the Educational Endowment Foundation reported small, statistically significant learning gains in pupils who had been on the programme for one year.
Mathematical Mastery is currently an all-encompassing term that includes

• A set of beliefs about how children learn mathematics
• an approach to teaching
• a curriculum
• something to be achieved by pupils.

Spotting mastery learning, to the experienced teacher, is not new, nor particularly difficult.  Pupils demonstrate mastery of a topic, concept or skill if they can

• Represent it in multiple ways
• Communicate it to others using mathematical language
• Apply the knowledge learnt in different ways
• Apply the knowledge to unfamiliar problems

This is why examinations at higher levels require much more that ‘getting to the answer’ (and showing the units!); the emphasis is much more on choosing an appropriate method where the solution is not obvious, being efficient and accurate in calculation, and providing justification.
Less easy to spot is the type of teaching that best leads to mastery learning.  How do teachers help our students become masters of their mathematics?  Is there a best way to ‘teach for mastery?’ And why might this involve a change to the way many classrooms operate in the UK at the moment?
Teaching for Mastery
Firstly, teaching for mastery is built on the assumption that all children are capable of learning mathematics to a high level.  There is no ‘maths gene’, and teachers need to realise this.  The implication for classroom teaching, in the UK at least, is therefore that the current widely-instigated practice of setting, streaming and providing different work for different pupils is the wrong approach, and children should be taught as a whole group as much as possible.  All pupils should be working on the same content at the same time.
Secondly, teaching for mastery approaches place a lot of emphasis on careful, collaborative lesson planning.  All lessons must explicitly identify the new mathematics that is to be taught, the key points, the difficult points, and be very carefully sequenced.  Each question that the pupils will answer is very carefully thought out and linked with one before, and the one afterwards, so connections can be made.  The design of every lesson should be discussed within planning groups.  In the UK many teachers currently plan their lessons on their own; although there is a common curriculum and scheme of work, teachers are expected to adapt their planning to meet the individual needs of their class.
Thirdly, teachers are very clear leaders of the mathematics in mastery lessons.  Pupils sit facing the teacher who leads the episodes of demonstration, explanation, questioning, short tasks and discussion.  Teachers, and pupils will be expected to use mathematical vocabulary accurately, this includes episodes where pupils listen and repeat mathematical sentences led by the teachers. Surprise is not a feature of a mastery lesson.  There is an acknowledgement that part of mathematics learning involves learning, recall and practise of key facts and procedures such as number bonds and times tables.  Currently, teachers have a lot of autonomy in their teaching style; some advocate a high level of direct instruction, others prefer a much more pupil-led, discovery approach to learning.  Some teachers strongly believe in rote learning of key facts; some are very opposed to it.
Fourthly, teaching for mastery advocates curriculum design which is linear rather than spiral.  The National Curriculum stipulates ‘what’ is to be learnt (and broadly ‘when’) but not ‘how’.  Many curricular cover all broad areas of school mathematics (number, algebra, geometry and statistics in most secondary schools) equally each year, revisiting topics such as ‘fractions’ two or three times annually, building upon what happened last time.  In a mastery curriculum the pace is slower, and a single topic is explored in much more depth, much less often.  Adopting this in the UK clearly has implications for curriculum and lesson planning, readiness for external assessments and transition between educational phases.
Future developments
The Department for Education has committed millions of pounds to the development of Teaching for Mastery approaches in both Primary and Secondary schools across the UK.  Much of this funding is being distributed through the national Maths Hub programme, co-ordinated by the National Centre of Excellence in Teaching Mathematics (NCETM).  Hubs are running a range of local and national projects aimed to implement and evaluate different elements of Mastery teaching within schools.  There is also a growing output of research, publication and teacher development.  The current knowledge and uptake of Teaching for Mastery approaches in schools is growing fast and new entrants to the mathematics teaching profession will find that a working knowledge of Mastery, and its implications for teaching and learning, very useful.  Key to instilling Mastery learning in classrooms is a high level of mathematical knowledge; IMA scholars are an important part of this.
References, websites and further reading
Drury, H. (2015) Mastering Mathematics. 1st edn. Oxford: Oxford University Press.
Guskey, T. (1987) ‘The essential elements of Mastery Learning’, The Journal of Classroom Interaction, 22(2), pp. 19-22.
Guskey, T.R. (2007) ‘Closing Achievement Gaps: Revisiting Benjamin S. Bloom’s “Learning for Mastery”’, Journal of Advanced Academics, 19(1), pp. 8-31.
Jerrim, J. and Vignoles, A. (2016) ‘The Link between East Asian ‘Mastery’ Teaching Methods and English Children’s Mathematics Skills’, Economics of Education Review, 50, pp. 29-44.
Kent and Medway Maths Hub (2016) ‘Elements of Mastery, available at http://www.elementsofmastery.org/ (Accessed 20^th April 2018)
National Centre for Excellence in Teaching Mathematics (2016) ‘Mastery Explained’, available at https://www.ncetm.org.uk/resources/49450 (accessed 20th April 2018)
About the author
Jennifer Shearman is a senior lecturer in secondary mathematics education at Canterbury Christ Church University.  She currently teaches on various PGCE programmes including the INSPIRE PGCE with Imperial College London, and has trained many IMA scholars (including the featured Daniel Portelli).  Jennifer is a Teach First Ambassador and an active member of the Kent and Medway Maths Hub.  She currently studying for an Education Doctorate, researching secondary mastery, and is the Lead Evaluator for the NCETM’s secondary mastery project.
Jennifer can be contacted at Jennifer.shearman@canterbury.ac.uk or via Twitter @jenshearman.