Parent Workshop

What can you expect from this evening? An overview of what your child will be learning in Mathematics throughout their time at the Boswells school. Answer to some questions you may already have. A change of Mindset

The Mathematics Mastery partnership approach exceptional achievement exemplary teaching specialist training and in-school support collaboration in partnership integrated professional development

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

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 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

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 = 14 years 39 years 33 years Lucy is 11 years Pete is = 16 years Problem solving Jake is 3 years older than Lucy and 2 years younger than Pete. The total of their ages is 41 years old.

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?

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: , , 177 = 4,665 Problem solving – a pictorial approach

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

If children hear ‘I can’t do maths’ from parents, teachers, friends they begin to believe it isn’t important People become less embarrassed about maths skills as it is acceptable to be ‘rubbish at maths’

Fixed mindset praise I am amazed that you have finished the task already - you are such a fast worker! I enjoyed marking your work. You got all the questions right! You are destined to be a mathematician when you grow up! You scored 90% on your exam which is an ‘A’ grade! You are excellent at Maths!

Growth mindset praise I like the way you tried to work that out. Your answer is very close – try again! I am impressed by how hard you have tried to work this out. Great! You persevered and did well in your subtracting equations! Well done on your maths test, you have learnt from the feedback I gave you last week and have improved.

The mindset of pupils A fixed mindset A growth mindset The main thing I want when I do my school work is show how good I am at it! It is more important for me to learn new things in my classes! The harder you work at something, the better you will be at it. When I have to work hard at something, it makes me feel like I am not very clever.

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”

A typical Mastery Lesson

Do Now Arrange the digits above to make: a) the smallest number possible b) the greatest number possible c) a number with a zero in the hundreds place d) a number with a two in the tens place Write your numbers in words and figures Three rabbits had 15 carrots between them. Each rabbit had an odd number of carrots. How many carrots did each rabbit have? How many solutions can you find? What is the greatest odd number you can make? What is the smallest even number you can make?

Comparing Numbers Which one of the bees is right? How could you show this? 14 is less than 23. No, no, no. 23 is less than 14.

Comparing Numbers TensOnes 14 TensOnes is less than 23. No, no, no. 23 is less than 14.

Comparing Numbers Which pairs of numbers have a difference of more than 20 tens? Which pairs of numbers have a difference of less than 30 tens plus 150 ones? Can you show this with manipulatives? Put these numbers in ascending order. Can you think of a sentence to explain how you know where to put them? 3671

is greater than No way! Is greater than Place Value Ten ThousandsThousandsHundredsTensOnes

is greater than No way! is greater than Place Value I know this because ___________________________ Ten ThousandsThousandsHundredsTensOnes

How many comparison sentences can you write? Example is greater than > I know this because is greater than Comparison Cloud Put the numbers in order starting from the smallest. What number is 20 thousands, 800 hundreds and 550 tens? What number is 12 ten thousands, 610 hundreds, 85 tens and 40 ones?

A writing frame

Comparison Cloud Fill in the gaps with > or < Can you think of a number that would go between each pair?

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

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

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?

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 £ 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?