ncetm :cpd · pdf file•weekly meeting to discuss what the students will find ... (the...
TRANSCRIPT
NCETM :CPD
Shanghai Maths…PISA….
Hmmmm
Prais, S.J. (2003) “Cautions on OECD’s Recent Educational Survey (PISA),” Oxford Review of Education, 29(2): pp 139-163.
“these reservations...are sufficiently weighty for it to be unlikely that anything of value for
educational policy in the UK can be learnt from the PISA survey”.
looking “at other, non-English contexts ...is of course a slightly risky enterprise,
intellectually and practically... Indeed, factors that are associated with success in a Pacific Rim
culture which celebrates a very different view of the nature of humankind, and a very different
view of the proper relationship between an individual and the collectivity, may need careful
evaluation before they are in schools of a different culture”.
Reynolds, D. And Farrell S. (1996) Worlds Apart? A Review of
International Surveys of Educational Achievement involving England. London: Office for Standards in Education.
He tells us that China has the best education system because it can produce the highest test scores. But, he says, it has the worst education system in the world because those test scores are purchased by sacrificing creativity, divergent thinking, originality, and individualism. The imposition of standardized tests by central authorities, he argues, is a victory for authoritarianism. His book is a timely warning that we should not seek to emulate Shanghai
After one lesson After a sequence of lessonsAfter watching the teachers
teach our students
a. Starting with an example from real lifeb. The REASONc. Lots of Q and A (25 mins Q&A vs 10 mins book work)d. Hard questions – even on topics that appear simplee. Mixing up skills (factors-fractions – simplifying)e. There are always students completing questions on the board so they are available for discussion afterwards
Lesson structure
1. One lesson, one point.2. Careful sequencing of topics3. Addressing misconceptions head on 4. Giving students the vocabulary/tools of maths5. Attention to detail eg k≠ 0,
Overall:
Planning structure
• Team of teachers teaching just one grade• Range of experience (we always try to have 20yrs plus in
each grade)• Weekly meeting to discuss what the students will find
difficult• Teacher research groups – focus on test results, key
questions• Feedback is not about the choice of activities. It’s about
what the students could do – the point of the lesson.
How many times have you seen students stuck on:
7x = 5?
How many times have I squished together equivalence and
simplifying then wondered why they still can’t do it…
How many times have I wondered why students can’t make the
denominator the same when adding fractions?
10
6
5
2
5
4
Lesson 1:
The point of the lesson is that 𝑝
𝑞= 𝑝 ÷ 𝑞
Lesson 2:The point of the lesson is to find equivalent fractions
Lesson 3:The point of the lesson is to simplify fractions (the last topic was HCF and LCM)
Lesson 4:The point of the lesson is to compare two or three fractions
Lesson 5:The point of the lesson is to add and subtract fractions
Lesson 6:Mixed numbers to top heavy fractions
Lesson 7:Multiplying fractions
Lesson 8:𝑝
𝑞×𝑞
𝑝= 1
Lesson 9:Dividing fractions
Lesson 1:
The point of the lesson is that 𝑝
𝑞= 𝑝 ÷ 𝑞
Video 1
Feedback:
Teacher presents their thoughts
You didn’t spend long enough on q6. They didn’t understand what the whole is.
Same lesson that afternoon:
Lots of them got q6 wrong…
The teacher spent a long time talking about it and going through it.
15kg of apples are shared between 4 people.Not enough emphasis on the two meanings.This is the point of today’s class
Other comments from the feedback meeting:
The definition is the most important thing here. If we can’t understand it, we can do nothing.
We ask questions to force errors so we can address them
Our final target is that the students help the students not the teachers help the students
UK teacher: How do you ensure that all of the students have understood?
Shanghai teachers (all!) … GUFFAWS!!!
No way we can make sure all students understand 100%..it’s too difficult for us
Each student makes gradual progress. We should admit that students are different. We want each student to have basic knowledge. But there is a balance between teacher and
student needs.
REPEAT:If the numerator and the denominator are multiplied by the same number, the original fraction and the resulting fraction are equal.
nb
na
kb
ka
b
a
)0,0,0( nkb
Favourite question of the lesson:
a and b are integers
2b
a Is equivalent to
18
7
Find a and b.
12
30
This is linked in with HCF… our last topic
12 ÷ 2
30 ÷ 2=
6
15
12 ÷ 3
30 ÷ 3=
4
10
12 ÷ 6
30 ÷ 6=2
5
12
18=2 × 2 × 3
2 × 3 × 3
12,18 = 2 × 3 = 6 12
18=12 ÷ 6
18 ÷ 6=2
3
Favourite question of the lesson:
a and b are integers
Is equivalent to a fraction. The numerator and the denominator of this fraction add to 156.Find the fraction!8
5
Video 1
I didn’t see the rest but the book is interesting….
x
x
After one lesson After a sequence of lessonsAfter watching the teachers
teach our students
Any thoughts??
Student thoughts
I think I did well because the put it in a way that was easy to
understand.
I joined in because she describes so well that I thought I should?
Amazing, boring…
Miss Wong made sure that we weren’t stuck. She would ask
if we understood every step of the
way.
I think I did well…but
then we all did well.
My favourite part was Miss Wing making sure we
understood before moving on
Omitting numbers
Candy cards!
Teacher thoughts……
The variety of routines
Differentiation – is everything we have
done good for them? Are we making gaps
bigger?
Not having support and extension?
Do you agree with her?
Am I instructing a concept? Or
investigating a phenomenon?
It’s ok to be
teacher led.
Random thoughts from Shanghai
Students don’t use a + b=b + a
• This makes their arithmetic a bit clunkier e.g. 97 + 15 + 3• But this means they find simplification concepts new..e.g. 7x + 8 + 3x = 7x + 3x +8• But also means they struggle with negative numbers e.g. -2 + 2• Which means they find solving equations more difficult! Eg -2x + 2x
= 0
Students don’t understand/use a – (b + c) = a – b – c
• I’m thinking of finding missing angle in triangle problems 180 – (30+40) or 180-30-40 or 30+40=70 THEN 180 – 70.
• Again this means that they are struggling more with negative numbers e.g. 12 – 7x – 3x = 12 – (7x+3x) = 12 –10x
Students can’t do negative numbers
• This is causing problems all over the place and not just in negative number questions. (eg sub x=-2 into an equation).
• They don’t understand that -9+9=0 and -2x+2x = 0 and this means they don’t really understand what they’re doing with equations.
• And this is before we get near –(-7)+(-7) etc
Students struggle with inverse operations
• Do they know that division is the inverse of multiplication?
• Do they know that if 5 = 3+2 then 5-3 =2? • Do they know that if 3x4=12 then 12÷3=4 etc
How much do students understand that (a+b)xc = ab + bc?
• This is underpinning all sorts of things e.g. brackets, grid multiplication etc
Why can’t we?
• Teach more than one class in one year group instead of two classes across two different year groups?
• Just have maths lessons in the morning?• Set homework when we need to so that it can be
properly planned into a series of lessons?• Observe each other doing exactly the same lesson?
Top Ten Most Sensible Things:
10)Magnets
9) The reason
8) Hard questions
7) Mixing up skills
6) Addressing misconceptions head on
5) Students up at the board every lesson
4) Giving students the vocabulary and tools for maths
3) Sequencing
2) One lesson – one point
1) Teacher Research Groups