Download Mastery Forum – Specialist Teachers

Mastery Specialist Teachers
Katie Crozier
Claire Gerrard
Jo Harbour
Luke Rolls
What do we mean by Mastery?
• Deep and sustainable learning – for all
Depth is the key to avoiding the need to repeat teaching.
It doesn’t feel like we’re starting again each term.
• The ability to build on something that has already been
sufficiently mastered
…for this stage of learning - Mastery is a continuum
What do we mean by Mastery?
• The ability to reason about a concept and make
connections
• Cuts down on the amount I need to learn
eg relating concepts of division, fractions and ratio
• Deepens conceptual understanding.
•Conceptual and procedural fluency
• Move maths from one context to another. Recognise concepts in
unfamiliar situations.
• Know number facts and tables, have efficient procedures
What do we mean by Mastery?
• A mastery approach: a set of principles and beliefs. This
includes a belief that all pupils are capable of
understanding and doing mathematics, given sufficient
time. Pupils are neither ‘born with the maths gene’ nor
‘just no good at maths’. With good teaching,
appropriate resources, effort and a ‘can do’ attitude all
children can achieve in and enjoy mathematics.
NCETM
https://www.ncetm.org.uk/resources/46689
Teaching for Mastery
• Access
• Pattern
• Making
Connections
• Chains of
Reasoning
• Making
Connections
Representation
& Structure
Mathematical
Thinking
Small connected steps
are easier to take
Coherence
Variation
• Procedural
• Conceptual
• Making
Connections
Fluency
• Number Facts
• Table Facts
• Making
Connections
What examples of
the five big ideas
can you spot during
this session?
Use of stem sentences.
5
5 is the whole.
2 is a part.
3 is a part.
2
3
Use of stem sentences.
5
5 is the whole.
4 is a part.
1 is a part.
4
1
Also use zero.
5
0
5
5
1
?
?
5
?
?
?
4 is a part.
2 is a part.
6 is the whole
4
2
1
1 is a part.
7 is a part.
8 is the whole
7
?
6
3
Use of stem sentences.
3
3 is a part.
3 is a part.
6 is the whole
6
6
?
Use of stem sentences.
?
6 is the whole
1 is a part.
5 is a part.
6
Move from pictorial/ symbolic to abstract.
6
6
1
5
Mastery of the part part whole model!
10
10
10
1
5
2
8
3
9
5
2
3
2
3
4
8
10
Subtraction within a context
?
What does the 6
represent?
What does the 2
represent?
What does the 4
represent?
Before
Next
Now
6-2=4
What does the 6
represent?
What does the 5
represent?
Before
What does the 1
represent?
?
Next
Now
6-5=1
Year 2
停车场
7+5
7+5
7+5
3 2
7+5
2 5
2+2+2=6
What if there were 9 explorers?
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18
What if there were 9 explorers?
2 × 9 = 18
What if there were 8 explorers?
2 × 8 = 16
What if there were 5 explorers?
2 × 5 = 10
What if there were 0 explorers?
2×0=0
Procedural variation is used to support deeper
understanding of a mathematical procedure or
process.
By asking pupils to compare two successive
procedures, where the first is linked to a second,
relationships can be observed. Opportunity is
given to observe the variant and invariant
properties of the procedure - i.e. what stays the
same and what changes? (depending on the
numbers/ conditions) leading to generalising
about the procedure.
What is the variation within the questions and
between the questions
49
Variation
43 X 3
Which number is the multiplicand?
Which number is the multiplier?
STEM SENTENCES:
The multiplicand is …
The multiplier is …
43 X 3 = 129
43 X 3 = 129
44 X 3
What’s the same and
what’s different about
these two calculations?
Can you use your answer from 43 x 3 to work out 44 x 3?
43
43
+ 1
44
+ 1
44
43
43 X 3 = 129
+ 1
44
44 X 3 = 43 x 3 + ?
44 X 3 = ?
A full jar of beads holds 58 beads. How many
beads are there in 6 full jars?
58 X 6
STEM SENTENCES:
58
The multiplicand is …
The multiplier is …
58
58 X 6 = 348
58
58
58
58
A full jar of beads holds 58 beads. In 6 full jars there are 348 beads.
58 X 6 = 348
58
58
58
58
58
58
We’re going to use this answer to find out how many beads there are in 7 full
jars.
Draw a bar picture to show
58 x 6
Draw a bar picture to show
58 x 7
What’s the same and what’s different about them?
58
58
58
58
58
58
58
58
58
58
58
58
58 X 7 = 58 x 6 + ?
58
58 X 7 = 348 + 58 = 406
Use column multiplication to work out the first multiplication calculation.
Adjust your answer from a) to work out the product of b).
Think about whether the multiplicand or the multiplier has changed.
You could draw bar picture to help you see what is the same about the calculations and what has changed.
1a)
A book has 37 pages. How many pages are in 7 books?
1b)
How many pages are there in 8 of these books?
2a)
2b)
A concert ticket costs £38. How much do 6 tickets cost?
The cost of a ticket goes up to £41. How much do 6 tickets cost now?
Teaching for Mastery
• Access
• Pattern
• Making
Connections
• Chains of
Reasoning
• Making
Connections
Representation
& Structure
Mathematical
Thinking
Small connected steps
are easier to take
Coherence
Variation
• Procedural
• Conceptual
• Making
Connections
Fluency
• Number Facts
• Table Facts
• Making
Connections
Katie Crozier – Eynesbury Primary School
[email protected]
Jo Harbour - Mayfield Primary School
[email protected]
@joharbour
Claire Gerrard – Thorndown Primary School
[email protected]
Luke Rolls – University Primary School
[email protected]