Inquiry and mastery - part 2

Since my post about Mathematics Mastery in January 2014, the UK’s National Centre for Excellence in the Teaching of Mathematics (NCETM) has converted wholesale to mastery or, at least, to a variant it claims to have observed in China. This swing to Shanghai is the inevitable outcome of having a national centre funded by governments with ideologically-fuelled visions of education. Nevertheless, the NCETM’s definition of mastery brings two features, which were not addressed in the original post, into sharper focus: firstly, all students move through and ‘master’ the curriculum content at the same time; and, secondly, mastery is achieved by ‘intelligent practice’.

Charlie Stripp, the NCETM’s director, feels his organisation is justified in promoting mastery because the new National Curriculum in England is “explicitly a mastery curriculum”1. However, in requiring teachers to teach “a detailed, structured curriculum” in “a precise way”2, the NCETM’s mastery allows students no space to explore and inquire. Moreover, in his characterisation of the new curriculum, Stripp ignores the mention of 'enquiry' in the second of its three aims.

Ensuring students move through the curriculum at the same pace sounds like a good idea. Indeed, Stripp links the idea to the development of a growth mindset because students will no longer be labelled as ‘mathematically weak’3. An individual who understands a concept ahead of her peers will spend time deepening her knowledge instead of moving on; and, just as happens in Shanghai, students who have difficulty understanding a concept will have their issues diagnosed and remedied on the same day to ensure they keep pace.

Leaving aside the obvious practical problem of UK teachers having a vastly greater teaching load than their colleagues in Shanghai (see Inquiry and Shanghai maths), there is also a theoretical problem with the NCETM’s prescription. Mastery is driven by the teacher’s skills to pose “precise” (that word again) questions and choose tasks that are “sequenced carefully”2. This level of ‘scientific’ exactitude denies students any agency. It is the teacher who defines the pace and level of challenge; there is no opportunity for students to set their own. Such passivity, in which students have no responsibility for their own learning, is the opposite of a growth mindset.

To achieve mastery, asserts the NCETM, students need to be involved in ‘intelligent practice’. As if to foresee the danger in this term, the NCETM immediately warns against “repeating a mechanical activity” in favour of students being “taken down a path where the thinking process is practised with increasing creativity”4. Unfortunately, when it comes to the students, mechanical repetition is exactly their experience of mastery (see Debra Kidd’s Mastery Overload).