What is 'Mastery' in mathematics?

The most significant progress in mathematics teaching in recent years has occurred in Singapore and Shanghai, whose consistent success in international comparisons of learners’ progress and attainment, measured by the OECD’s Programme for International Student Assessment (PISA) provoked interest from education ministries in many other countries, including the DfE in England.

Independently of one another, both Singapore and Shanghai completely overhauled their teaching of mathematics, in order to gain a more highly educated population to compete in the global marketplace of the 21st Century. New curricula, school structures and teaching methods were adopted in the two states, similar in some ways, yet different in others.

The key similarity was that both states implemented a ‘Mastery’ approach to learning.

Mastery was first defined by the educationalist Bloom in Learning for Mastery (1968), in which he proposed that all learners should have a confident foundational understanding of any concept at an appropriate level before teachers introduced them to the next stage of progression in that area of learning.

Singapore and Shanghai also drew upon work by other respected educationalists, including learning through a ‘concrete-pictorial-abstract’ (CPA) progression, based on Bruner’s ideas, Freudenthal’s  ‘Realistic mathematics education’, the UK’s Cockcroft report (1982), and Lo’s ‘Variation Theory(2012)’.

In Singapore, a significant visual image primary children are taught to use to represent problems is the bar model.

The English National Centre for Excellence in Teaching Mathematics (NCETM) has written an expanded summary, which has also been cited by Ofsted:  www.ncetm.org.uk/public/files/19990433/Developing_mastery_in_mathematics_october_2014.pdf