Transcript MaST Mathematics Specialist Teacher

MaST
Mathematics Specialist Teacher
What is MaST?
• Recommended by the Williams Review
2008.
• “My key recommendation is the presence
of a Mathematics specialist in every
primary school, who will champion this
challenging subject and act as the nucleus
for achieving best pedagogical practice.”
(Williams 2008:1)
3 Main Aims
• To develop deep subject knowledge and
understanding of the curriculum and progression
from EYFS up to KS3.
• To develop a fit-for purpose pedagogy so that
they can draw on a wide repertoire of teaching
approaches to support children’s learning of
mathematics.
• To develop skills needed to work with
colleagues providing effective professional
development through classroom based
collaborative activities.
What does the course consist of?
• 1 Higher Education Day each term.
• 1 Local authority meeting each term.
• A Residential Easter School run over two days.
In addition to these other tasks include:
• Readings on subject knowledge and pedagogy.
• Reflective learning logs
• An end of unit essay based on the focus of the
over lying theme of the year.
• The course runs over 2 years awarding 30
credits per yearly module.
• After successful completion
recommendation is made to the DFE for
award of Mathematics Specialist Teacher
Status.
MaST
Content of HEI days 1 and 2
Content of LMs 1 and 2
HEI Day 1
Using and applying Maths
• Puzzle wall
Discuss the key aspects of Maths covered.
Not just ‘problem solvers’ but ‘problem
posers’
http://nrich.maths.org/public/
Excellent website
‘People Mathematics’
1. Reverse Order …
A group of people are given the numbers
1 - N and stand in order in a line.
•
•
•
They can swap adjacent pairs
The number of swaps is counted until the initial
order has been reversed
What is the number of swaps required to
reverse a line of N people?
Looking for Patterns
Nth Term
(the number in this
pattern)
1st (1 2)
2nd (1 2 3)
3rd (1 2 3 4)
4th (1 2 3 4 5)
Number of Moves
Patterns
What does it mean to be a
mathematics champion?
Watch a short clip of maths at Weeke Primary School
http://www.teachers.tv/videos/ks1-ks2-maths-makingmaths-real
http://www.schoolsworld.tv/
• Comment of the philosophy and ethos of this school
• Compare it honestly to your own school
what do you consider to be the most challenging
aspect for you / your school?
Fractions … misconceptions
LM 1 Fractions
Discuss errors such as the one below
What fraction of the shape is not shaded?
Answer given: 1/3 … why? where next?
Fractions
Models and Images
Part of a whole which is divided into
equal parts
Comparison between a subset and the
whole set
A point on the number line
Comparing two sets of objects
Jo has yellow counters
and Claire has pink
counters. Claire has ¾
the amount of counters
that Jo has.
Comparing the size of two
measurements
Final thought:
• Are a range of models and images used
for the teaching and learning of
fractions in your school?
• Any limitations in each model?
6 key aspects of fractions
1/2
1/2
Fractions
of shapes
Fractions of a number
• 1/3 of 15
Fractional numbers on a number line….
Fractions as divisions (powerful…)
• Links to decimals and percentages..
• ¾ is the same as 3 ÷ 4 (3 pizzas shared between 4
friends)..Each person will have one quarter of each pizza
– three quarters in total per person…
LM2 Division
• Difference between sharing and grouping
1) I share 29 pencils between 6 people.
How many pencils does each person get?
2) 29 people are going on a journey. Each car holds
6 people. How many cars are needed?
3) Work out 29 ÷ 6 correct to three decimal places.
4) You collect 29 CD tokens. You can get a CD for
every 6 tokens. How many CDs can you get?
Sliding Box
÷
=
R
Tests of divisibility
29
59
79
65
33
76
31
4
16
27
21
36
90
37
61
73
44
56
27
33
44
0
3
98
95
Back to menu
Divisible by 7?
• To find out if a number is divisible by seven, take the last
digit, double it, and subtract it from the rest of the
number.
• If you don't know the new number's divisibility, you can
apply the rule again
Example:
• If you had 203, you would double the last digit to get six,
and subtract that from 20 to get 14.
• If you get an answer divisible by 7 (including zero), then
the original number is divisible by seven.
Task
•
•
•
•
Using only odd digits make a 3 digit
number that is:
Divisible by 7 but not by 11
Divisible by 11 but not by 7
Divisible by 11 and 7
Not divisible by either 11 or 7
Always, sometimes, Never true
• If a number is divisible by ‘x’ it will be divisible by
the factors of ‘x’
• The sum of three consecutive numbers is
divisible by 3
Does it then follow that:
• The sum of four consecutive numbers is divisible
by 4
• The sum of five consecutive numbers is divisible
by 5?
Multiplication
‘ Restricting our representations of multiplication
and division to just repeated addition and
subtraction hinders our ability to recognise and
explain some of the properties of these
operations’
Barmby, P. Bilsborough, L. Harries,T. and
Higgins,S.(2009) Primary Mathematics;
Teaching for Understanding. Maidenhead: OUP
Line of argument
• The 4 Properties of
multiplication
• Models which help to structure
learning of these properties
Properties of multiplication
Discuss the meaning of each of these:
•
•
•
•
Repeated Addition
Inverse of Division
Commutative
Distributive
Understanding properties empowers!
 Commutative:
8x3=3x8
 Distributive:
25 x 7 = (20 x7) + (5x7)
(based on place value)
3 x 8 = (2 + 1) x 8
= ( 2 x 8) + ( 1 x 8)
(based on number bonds)
Models
The Set Model
2 X 12 = 24
The Number Line Model
2 X 12 = 24
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
The Arrays Model
2 X 12 = 24
Properties
Models
Set
Repeated addition
Inverse of division
Commutative
Distributive
Number line
Array
Properties
Models
Set
Number line
Repeated addition
(part)
Inverse of division
(part)
Commutative
Distributive
Array
Properties
Models
Set
Number line
Repeated addition
(part)
Inverse of division
(part)
Commutative
Distributive
(part)
(part)
Array
Properties
Models
Set
Repeated addition
Inverse of division
Commutative
Distributive
Number line
Array
Arrays - links to grid method and area
3 X 13 =
X
3
10
3
Grid Method and Fraction Arrays (connections)
5
1/2
Reflection
‘ Restricting our representations of multiplication
and division to just repeated addition and
subtraction hinders our ability to recognise and
explain some of the properties of these
operations’
Barmby, P. Bilsborough, L. Harries,T. and
Higgins,S.(2009) Primary Mathematics;
Teaching for Understanding. Maidenhead: OUP