Helping students to achieve mastery in Mathematics
By Clive Davies
Sharing Good Practice
For a child to have reached that ‘ effortless ’ level , they should :
“ If people knew how hard I worked to get my mastery , it wouldn ’ t seem so wonderful at all .” – Michelangelo
We are in the midst of a great change to classroom practice , particularly in mathematics . The method of ‘ racing ’ learning through the sub levels is being abandoned to ensure a deeper understanding of each objective .
‘ Mastery ’ is now at the heart of the curriculum , and teachers must ‘ come to terms ’ with what that means and how to identify and achieve it with pupils .
Perhaps the above quotation from Michelangelo illustrates it best - the ‘ mastery ’ level can only be achieved with work and time . With limited time to achieve this in each school year , we ’ re forced to cut the curriculum down in order to teach fewer things in greater depth .
Mastery has no single definition , but it may be linked with the concepts of ‘ shallow ’ and ‘ deep learning ’. If shallow learning is superficial and temporary , then deep learning can be recalled and used appropriately . Mastery takes this one level further , where learning can be transferred and applied to different contexts .
CONSCIOUSNESS
The Four Stages of Competence is a useful model for illustrating mastery :
1
2
3
4
STAGE 1 UNCONSCIOUS INCOMPETENCE You don ’ t know that you don ’ t know
STAGE 2 CONSCIOUS INCOMPETENCE You know that you don ’ t know
STAGE 3 CONSCIOUS COMPETENCE Competent , but takes a lot of conscious effort
STAGE 4 UNCONSCIOUS COMPETENCE Second nature Habit Mastery
COMPETENCE
Class Time
• Be fluent in the fundamentals of mathematics . This includes varied , frequent practice with increasingly complex problems .
• Reason mathematically by following a line of enquiry , conjecturing relationships and generalisations , and developing an argument , justification or proof using mathematical language .
• Solve problems by applying mathematics to a variety of routine and non-routine problems with increasing sophistication .
Mastery boils down to independent , consistent working and an ability to explain one ’ s own understanding . Some practical indicators of when a child has reached the mastery level could be : being able to describe the concept to somebody else , recognising real-life instances of problems ( i . e . noticing that triangles are used in the environment for their strength , such as in pylons ) or making up their own examples of the problem .
How can we ensure a child is able to complete the above ?
We must be wary of defaulting to accelerating able pupils through new material once a concept appears to be grasped . We should also recognise that a child ’ s ability to answer questions with more difficult numbers does not necessarily equate to mastery . The increase in challenge should come from thinking harder about the concept or topic being taught .
An indicative question to judge a Year 6 pupil ’ s mastery of times tables might be ; “ My age this year is a multiple of 8 . Next year it will be a multiple of 7 . How old am I ?”
Essentially , we need to build into our maths curriculum the important stage of checking if pupils have ‘ got it ’ through formative assessment , rather than testing . This can be accomplished by using well thought out activities related to the actual objective being taught . If we do this regularly , then it may be more reliable than testing . We may also see an end to the worrying feature of pupils struggling with greater depth questions due to insecurity or lack of fluency with basic mathematical skills .
| | Nov - Dec 2016 |
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