Parent Workshop
The Mathematics Mastery partnership approach
exceptional achievement
exemplary teaching
specialist training and
in-school support
collaboration in
partnership
integrated professional development
Do the maths – true or false?
Even + Even = EvenEven + Odd = EvenOdd + Odd = Even
• Can you explain why?
• Can you prove why…– Using algebra?– Without using algebra?
m
m
n
n
2m 2n
2m + 1 2n + 1
2m + 1 + 2n + 1
2m + 1 + 2n + 1
2m + 2n + 2
2(m + n + 1)
Our shared vision
• Every school leaver to achieve a strong foundation in mathematics, with no child left behind
• A significant proportion of pupils to be in a position to choose to study A-level and degree level mathematics and mathematics-related sciences
A belief and a frustration
• Success in mathematics for every child is possible• Mathematical ability is not innate, and is increased
through effort
Mastery member schools wanted to ensure that their aspirations for every child’s mathematics success
become reality
Effort-based ability – growth mindset
Innate ability
Intelligence can grow
Intelligence is fixed
Effort leads to success
Ability leads to success
When the going gets tough ... I get smarter
When the going gets
tough ... I get found out
When the going gets
tough ... dig in and persist
When the going gets
tough ... give up, it’s
hopeless
I only need to
believe in myself
I need to be
viewed as able
Success is the
making of
targets
Success is doing better than
others
Our approach
Language and communicatio
n
Mathematical thinking
Conceptual understandin
g
Mathematical
problemsolving
NC 2014
“Decisions about progression should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on”
• Fewer topics in greater depth
• Mastery for all pupils
• Number sense and place value come first
• Problem solving is central
Curricular principles
Y7 differentiation through depth
Half term 1Number sense
Half term 2Multiplication &
division
Half term 3Angle and line
properties
Half term 4Fractions
Half term 5Algebraic
representation
Half term 6Percentages & pie
charts
KEYHalf term topicBig ideaSubstantial new knowledge mastered
Year 7
Place value
Multiplication and division
Using scalesAngle and line properties
Area
Perimeter
Addition and subtraction
Algebraic notation
Calculating with fractions
Fractions, decimals and percentages
Mathematical problem
solving
Conceptual understandin
g
Language and communicatio
n
Mathematical thinking
Conceptual understanding Pupils deepen their understanding by representing concepts using objects and pictures, making connections between different representations and thinking about what different representations stress and ignore.
Language and communication Pupils deepen their understanding by explaining, creating problems, justifying and proving using mathematical language. This acts as a scaffold for their thinking deepening their understanding further.
Mathematical thinking Pupils deepen their understanding by giving an examples, by sorting or comparing, or by looking for patterns and rules in the representations they are exploring problems with.
Mathematics Mastery key principles
Mastering mathematical understanding
Concrete - DOINGAt the concrete level, tangible objects are used to approach and solve problems. Almost anything students can touch and manipulate to help approach and solve a problem is used at the concrete level. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding.
Pictorial - SEEINGAt the pictorial level, representations are used to approach and solve problems. These can include drawings (e.g., circles to represent coins, tally marks, number lines), diagrams, charts, and graphs. These are visual representations of the concrete manipulatives. It is important for the teacher to explain this connection.
Abstract –SYMBOLICAt the abstract level, symbolic representations are used to approach and solve problems. These representations can include numbers or letters. It is important for teachers to explain how symbols can provide a shorter and efficient way to represent numerical operations.
Concrete-Pictorial-Abstract (C+P+A) approach
What are manipulatives?
Language and communicatio
n
Mathematical thinking
Conceptual understandin
g
Mathematical
problemsolving
Bar models
Dienes blocks
Cuisenaire rods
Multilink cubes
Fraction towers
Bead strings
Number lines
Shapes
100 grids
Ben is 5 years older than Ceri. Their total age is 67.How older Ben?How old is Ceri?
Ceri
Ben
5
67 – 5 = 62
67
62 ÷ 2 = 31Ceri is 31, Ben is 36 Check: 31+36=67
Problem solving – a pictorial approach
Abe, Ben and Ceri scored a total of 4,665 points playing a computer game. Ben scored 311 points fewer than Abe. Ben scored 3 times as many points as Ceri.
How many points did Ceri score?
4,665Ceri
Ben
311
Abe
4,665 – 311 = 4,354
4, 354
4, 354 ÷ 7 = 622Ceri scored 622 Check: 622 + 1,866 + 2, 177 =
4,665
Problem solving – a pictorial approach
• Jake is 3 years older than Lucy and 2 years younger than Pete.
• The total of their ages is 41 years old.
Find Jake’s age.What else can you find?
Do the maths!
41 years
3 years
2 years
Jake ?
Lucy ?
Pete ?
41 – 8 = 3333/3 = 11? = 11 yearsJake is 11 + 3 = 14 years
39 years33 years
Lucy is 11 yearsPete is 11 + 5 = 16 years
Problem solving
Mastering mathematical thinking
“Mathematics can be terrific fun; knowing that you can enjoy it is psychologically and intellectually empowering.” (Watson, 2006)
We believe that pupils should:• explore, wonder, question and conjecture• compare, classify, sort• experiment, play with possibilities, modify an
aspect and see what happens• make theories and predictions and act
purposefully to see what happens, generalise
Mathematical problem
solving
Conceptual understandin
g
Language and communicatio
n
Mathematical thinking
Conceptual understanding Pupils deepen their understanding by representing concepts using objects and pictures, making connections between different representations and thinking about what different representations stress and ignore.
Language and communication Pupils deepen their understanding by explaining, creating problems, justifying and proving using mathematical language. This acts as a scaffold for their thinking deepening their understanding further.
Mathematical thinking Pupils deepen their understanding by giving an examples, by sorting or comparing, or by looking for patterns and rules in the representations they are exploring problems with.
Mathematics Mastery Key Principles
Vocabulary – Multiple Meanings
What number is half of 6?
6 is half of what number?
What number is half of 6?
6 is half of what number?
What comes next…?
• Thousands• Hundreds• Tens• Ones!!!!!!!
Why is this important?
Consider:
• One Hundred = Ten Tens• Ten Tens = One Hundred Similarly:
• One Ten = Ten Ones• Ten Ones = One Ten
Fractions – a “talk task”
Challenging high attainers
• What number is 70 hundreds, 35 tens and 76 ones?
• Which is bigger, 201 hundreds or 21 thousands?
• How many bags each containing £10 000 do you need to have £3 billion?
• How many ways can you find to show/prove your answers?
True or False?A B C D E ID E F G H CG H I A B FA B C B A CD E F E F DG H I I G H
Can you make your own true or false statements like these?
=
=
Does it work?
Evidence from successful schools:• Pupil collaboration and discussion of work• Mixture of group tasks, exploratory activities and
independent tasks• Focus on concepts, not on teaching rules• All pupils tackled a wide variety of problems• Use of hands on resources and visual images• Consistent approaches and use of visual images and
models• Importance of good teacher subject-knowledge and
subject-specific skills• Collaborative discussion of tasks amongst teachers
What would OfSTED think?