ncetm :cpd · pdf file•weekly meeting to discuss what the students will find ... (the...

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