Download Shanghai Teacher Exchange Programme

Shanghai Teacher
Exchange
Programme
September 2015 -
The story so far…..
• In September 2015 70 maths
teachers from across the country
travelled to Shanghai.
• In November 2015 70 primary and
secondary teachers from Shanghai
travelled to the UK to teach maths to
English students.
Pre-conceptions
• The teachers will be much
better than me
• The students will behave
impeccably
• All the children will be
really clever.
UK
China
Teachers in the UK have a
broader depth of
expertise.
Teach approx. 170
students
Differentiation for abilities
in a class
SEN provision
Highly experienced in the
curriculum structure
Once a fortnight?
Same day marking
Intervention….
Everyone expected to
keep up with the pace.
Same day intervention not
seen.
Teach approx. 50 students
Struggled to plan lessons
for low ability set
None
Organisation in China
Organisation….
• The Curriculum is planned small
objective by small objective. It links
together primary, middle and secondary
curriculums so that there are no gaps.
• The curriculum is stable.
• Teachers are trained using the
curriculum. Everyone teaches the same
method…but other methods are
explored
It’s a team effort…
• Lessons are planned by more than one
teacher
• The lesson belongs to the whole
department
• Lessons are observed by other teachers
and refinements are made to the plan.
• It is always the teaching and the lesson
plan that is being judged and never the
teacher
• TRG’s occur in school and at
district level
• Text books support the lesson.
Every pupil had his own book.
There was no copying from the
board
Topic Progression
On your tables…..
Discuss how you would teach a
sequence of lessons up to and
including adding fractions.
This is how the Chinese would do
it…
1.Prime and composite numbers
2. HCF
3. LCM
4. Exact division
5. Proper, improper and mixed fractions
6. Comparing fractions
7. Equivalent fractions
8. Reduction to simplest form
9. Finding a common denominator
10. Adding and subtracting fractions.
Part I
Prime number
&
Composite number
Challenge 1 :
Both a and b are prime numbers.
If a+b=9，a × b=_________。
What is a factor?
Rigorous definitions

True or false
a)
b)
c)
d)
e)
f)
g)
h)
36 is a factor of 72
34 is a factor of 17
5 is a factor of 20
5 is a factor of 0.5
3 is a factor of 18
38 is a factor of 19
4 is a factor of 0.2
3 is a factor of 17
The concept
and the nonconcept
Conceptual
variation
Listing Factors
 In
pairs Factors of 18
1 & 18
2 & 9
3 & 6

Write down all the factors of 16
Write down all the factors of 13
Concept 1
Prime number: A prime number (or a
prime) has exactly two factors, one and
itself.
Composite number:A composite number
(or a composite) has more than two
factors.
Ex 1:
List the numbers from 1-10 which are:
 (1) Odd numbers: 1, 3, 5, 7, 9
 (2)
Even numbers:2,
4, 6, 8 ,10
 (3)
Prime numbers: 2,
 (4)
Composite numbers:4,
3, 5, 7
6, 8, 9,10
Ex2:Prime or Composite, why?
(1)
27
27  1  27  3  9
Composite
The factors of 27 are 1,3,9,27
29 Prime
29  1  29
The factors of 29 are 1,29
(3) 35 Composite
35  1  35  5  7
The factors of 35 are 1,5,7,35
(2)
37  1  37
37 Prime
The factors of 37 are 1,37
(4)
 By
examining the number of factors of a
number you can determine whether the
number is prime or composite?
1
 Is
1 a prime or a composite number?
11, 21, 31, 41, 51, 61, 71, 81,91
Prime
Composite
Of the positive integers, 1 is
 A)
the smallest odd number
 B) the smallest even number
 C) the smallest prime number
 D) the smallest integer
Plan for misconceptions
Of the positive integers, 4, is
 A)
the smallest odd number
 B) the smallest even number
 C) the smallest prime number
 D) the smallest composite number
What if a factor is also a prime
number?

Find all the prime factors of 48
2
48
2 24
2 12
2 6
3
48= 2x2x2x2x3
5
35
7
35=5x7
2 60
2 30
3 15
5
60=2x2x3x5
Which of the following shows 24
written as a product of prime
factors?
 A)
24=2x3x4
B) 24=2x2x2x3
 C)
24=1x2x2x2x3
D) 24=2x2x6
Shanghai Lesson Structure
• Review/recap of previous lesson
• Introduction of key concept
• Definitions of key concepts with rigorous
mathematical language
• Conceptual variation
• Procedural variation –use of different method
• Student solutions analysed
• Step by step instructions
• A more challenging problem that requires
application of the concept
What number should be added to the
2
denominator of , when 4 is added to
5
the numerator so that the fraction
remains the same value ?
TRG - Angles on
straight lines