Welcome to St Margaret’s · – growth mindset Innate ability Intelligence can grow Intelligence...
Transcript of Welcome to St Margaret’s · – growth mindset Innate ability Intelligence can grow Intelligence...
Welcome to St Margaret’s
Year 7 Mathematics Mastery
Information Evening
The Importance of Maths (as told by an English teacher…)
Do we have a Mathematics problem in the UK?
“I’m not able to read properly…”
Do we have a Mathematics problem in the UK?
“I’m not able to read properly”
Do we have a Mathematics problem in the UK?
“I’m just not good at maths…”
Do we have a Mathematics problem in the UK?
• Numeracy skills have got worse, not better
• International Top 40 (PISA tests)
• Mathematics:
1. Sigapore
2. Hong Kong (China)
3. Macao (China)
4. Chinese Taipei
5. Japan
Do we have a Mathematics problem in the UK?
27: United Kingdom
(also beaten by Estonia, Slovenia, Ireland, Poland, Vietnam, New Zealand, Australia)
Do we have a Mathematics problem in the UK?
Do we have a Mathematics problem in SMA?
Grade SMA%
9
33 8
7
6
57 5
4
3
10 2
1
And there is always room for improvement…
• Are we getting enough top grades?
• Do our boys have a real confidence with number?
• Are they ready for the world of work?
• Have we taught them to pass an exam at the expense of being mathematically able?
Do the maths – true or false?
Even + Even = Even
Even + Odd = Even
Odd + 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
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 1
Number sense
Half term 2
Multiplication & division
Half term 3
Angle and line properties
Half term 4
Fractions
Half term 5
Algebraic representation
Half term 6
Percentages & pie charts
KEY
Half term topic
Big idea Substantial new knowledge
mastered
Year 7
Place value
Multiplication and division
Using scales
Angle and line properties
Area
Perimeter
Addition and subtraction
Algebraic notation
Calculating with fractions
Fractions, decimals and percentages
Mathematical problem solving
Conceptual understanding
Language and communication
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 - DOING At 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 - SEEING At 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 –SYMBOLIC At 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 communication
Mathematical thinking
Conceptual understanding
Mathematical problem solving
Bar models
Dienes blocks
Cuisenaire rods
Multilink cubes
Fraction towers
Bead strings
Number lines
Shapes
100 grids
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?
4,665
Ceri
Ben
311
Abe
4,665 – 311 = 4,354
4, 354
4, 354 ÷ 7 = 622 Ceri 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 = 33 33/3 = 11 ? = 11 years Jake is 11 + 3 = 14 years
39 years 33 years
Lucy is 11 years Pete 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
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 I D E F G H C G H I A B F
A B C B A C D E F E F D G 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?