# 7 THINGS YOU MIGHT NOT KNOW ABOUT MATHS MASTERY…

**7 THINGS YOU MIGHT NOT KNOW ABOUT MATHS MASTERY…**

1. Mastery is used to mean multiple different things in research, practice and policy.

2. The concept of Mastery was first proposed by Benjamin Bloom in 1968. At this time ‘learning for mastery’ was used instead. Bloom believed students must achieve mastery in prerequisite knowledge before moving forward to learn subsequent information.

Bloom suggested that if learners don’t get something the first time, then they should be taught again and in different ways until they do.

Bloom’s “mastery learning”, referred to cycles of teaching, learning and assessment. Bloom developed his ideas in the 1960s, introducing what was then a radical idea that if material had not been learnt then it could and should be represented using different materials or examples, and if this process was repeated then learning would take place. Arguably, many of Bloom’s principles have been adopted and integrated into mathematics teaching and have become the norm.

3. In England, the term 'mastery' has recently become associated with East Asian mathematics and is often referred to as **‘Shangapore’** maths as it appears to be something of a remix or mash up of the Shanghai and Singapore approaches to teach maths. ‘Teaching for mastery’ (TfM) is promoted by the NCETM and adopted as a term by the National Centre for Excellence in the Teaching of Mathematics (NCETM) since 2014.

“There is a mirage of marketisation and variety of initiatives around mastery… The government in England retains a strong influence on what is promoted to teachers and schools, even down to approval of detailed formulation of what will and will not be supported by government resources for materials or professional development. It’s important to carefully sift evidence and ask challenging questions. For example, in the selective filtering of shanghai practices, it is often overlooked that children in Shanghai do not start formal schooling until the age of 6 years old. Thus the notion of Shanghai teaching methods applied to reception or Year 1 is problematic.”

4. The Westminister government, aside from giving England the most detailed and prescriptive National Curriculum for Primary Maths poured 11 million pounds into bringing Shanghai teachers over to England to show us all how to use Chinese textbooks and teach in a Shanghai way. Why at a time of austerity, one would want to spend money in quite this way is a mystery, particularly when we reflect that one country’s favourite recipe book is another nation’s indigestible fare.

5. The research evidence is varied both in terms of the amount of quality of evidence for different schemes, textbooks, materials and practices that are referred to by the word ‘mastery’. It's yet to be rigorously evaluated.

6. Although Singapore and Shanghai are ranked highly in PISA in mathematics it is not clear how attributable this is to teaching methods alone. “For example, Chinese Pupils who are educated in other countries also do better in maths on average than other pupils and research suggests this is because of family and cultural factors. It is important to recognise that there are Western Education systems that are very successful in international tests – for example, Finland, Ontario in Canada, and Massachusetts in the US.”

7. Although complicated to define, many would argue Maths Mastery is still persuasive as an idea and potentially supportive to both primary and secondary school practitioners. For me, despite its potentially divisive label, there is something positive and pedagogically persuasive in the intentions of the idea of ‘mastery’. Its emphasis on depth of understanding, over breadth of knowledge. There are things we can learn from the way others, including those in Shanghai and Singapore, teach maths. However, I hope it does not come to be regarded as some kind of perfect ‘recipe’ for teaching mathematics.

Here are some **LINKS** to other **REFERENCES** which may add value to your thinking :

Bloom, B. S. (1968). Learning for Mastery. Instruction and Curriculum. Regional Education Laboratory for the Carolinas and Virginia, Topical Papers and Reprints, Number 1. Evaluation comment, 1(2), n2

Boylan, M., Wolstenholme, C., Demack, S., Maxwell, B., Jay, T., Adams, G. & Reaney, S (2019). Longitudinal evaluation of the Mathematics Teacher Exchange: China-England - Final report. https://assets.

Boylan, M. & Rycroft-Smith, L. (2019). Mastery in mathematics, Cambridge Mathematics Espresso

Boylan, M. & Townsend, V. (2018) Understanding mastery in primary mathematics. In Cremin, T and Burnett, C. (eds.) Learning to Teaching in the Primary School 4th edition (pp.456-469). London: Routledge

Drury, H. (2014). Mastering mathematics. Oxford: Oxford University Press

Higgins, S., Katsipataki, M., Kokotsaki, D., Coleman, R., Major, L.E., & Coe, R. (2014). The Sutton Trust- Education Endowment Foundation Teaching and learning toolkit. Sutton Trust: London.

McCourt, M. (2019). Teaching mathematics for mastery. In press.

NCETM (2016). The essence of mathematics teaching for mastery.

NCETM (2014). Mastery approaches to mathematics and the new national curriculum

NRICH. Mastering Mathematics: The Role of mastery in nurturing young mathematicians

NEL Portal:

https://www.nel.moe.edu.sg/resources/frameworks-and-guideline