Session 3: Right Knowledge

The implications of beliefs and knowledge on resources

Shade in a fraction of a shape which already has been broken into equal parts.

Identify fraction of a group using lines, circles

Naming parts of a fraction

Count on or back in 1s, 10s from multiples of 10,100

Identify value of each digitMake biggest number

Expanding numbersWrites in digits and words

Right or WrongAdd up ticks to make judgement

65% did not recognise or value understanding in

the standards

Throughout 2015 and 2016, 175 teachers illustrated their belief and understanding of the Achievement Standard

A ‘C’ level is beyond just recall of rehearsed procedures

Identifies fraction of shapeIdentifies fraction of collectionName, understand a fraction

Locates on a number lineRepresent as part of whole

Explains the use of fractions in everyday life

Recognise & read numbers from digits up to 10 000Models 4 digit numbers

Adds, takes 1s, 3s, 10s from 4-digit numbers

Create and explain patterns of their own

Right or WrongAdd up ticks to make judgement

Varied responses.Consistency via moderation and annotations. Right ≠ full marks

The ACARA work samples can help teachers understand the requirements for a satisfactory level.

O p e n y o u r m i n d s t o m a t h s

OPEN ENDED TASK

ONE QUESTION

ONE FOCUS

F O R E V E R Y S T U D E N T, E V E R Y D AY

AC

CE

SS

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AN

D E

NJO

YAB

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M I S T A K E S A N D R I S K S A R E W E L C O M E H E R E

LISTE

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VA

LUE

STUDENT RESPONSE

S

NUMBER SENSE

Activities: Number Sense

NUMBER FACTS STORY( drawing or oral )

A chef made 10 cakes and I ate 2 of them. There are 8

cakes left

RELATED FACTS EXTENDED FACTS

If I know 8 + 2 = 10 then I also know:-

80 + 20 = 100100 – 20 = 80

Remember to emphasise unknown PARTS100 – [ ] = 80 [ ] – 8 = 2 8 + [ ] = 10

8 + 2 = 102 + 8 = 10

10 - 8 = 210 – 2 = 8

OPEN ENDED Yr1-6

Whose story is it?

7 = 3 + 3 + 17 = 3 + [ ] + 1

What is the missing number?How can we prove it?

Commutative and Associative Properties

Match the beads with the symbolsModel a story on

the beads as it is read out

A Adds in order 7,5,3,5 and then 6 all on fingers

B Colours in grid squares in their grid book and counts all

C Says 7 and 3 make 10, 5 and 5 make 10 and 6 more is 26

D Says 5+5 = 10 , then 6 + 3 = 9 so 19 and counts on the 7

E Takes 2 from 7 and adds it the 3 to make 4 x 5 = 20 + 6

F Says 7 + 5 = 12 and 6 + 5 = 11. writes them down . Adds 3

26 = 7 + 5 + 3 + 5 + 6

Numeracy requires Number Sense Yr 1 and 2

Students in conceptually orientated classes for mathematics out perform those in a procedurally

orientated class in tests, attitudes and disposition towards maths

Cain 2002 Masden & Lainer 92 Fuson et al 2000

Numeracy requires Number Sense Yr 5 and 6

Activities: Cognitive Activation Tasks

Deepening Knowledge Yr4

• Place your numbers on a number line and be ready to defend your positioning using benchmarks

• With the five digits you rolled, make the third largest number you can and be ready to defend your decision

More examples Yr4

Rob Proffitt-White NCR: August 2016

One question: Routines for reasoning

1. DISCUSS and DEFEND

With your elbow partner decide on an answer and be ready to clearly explain your choice

Can they prove their decision by representing the amounts with 0-99 board, bundling sticks, beads, place value houses etc

2. DESTROY the DISTRACTOR

In pairs can you find a wrong answer and prove it is wrong to the class

A B C D1, 3, 5, 7 8, 10, 12, 14 2, 4, 5, 7 20, 40, 60,80

3. PREDICT and POSE

In groups can you pose a problem or predict what the question might be?

The Curriculum states that problem solving should see students investigate and pose questions. This promotes critical thinking and builds a student’s mathematical literacy. Some teachers have highlighted words students use to show differences.

Jess takes a peg out of this hoop.

Can you see a blue peg in the hoop?

If yes it is possible. You can take one out.

Can you see a yellow peg in the hoop?

If no it is impossible. You can’t take one out.

One question: Reason and Communicate

In pairs choose an answer you think is unreasonable. If our can clearly communicate

your reasoning it will be destroyed

Estimation – you will not need a calculator. NO

One question: Estimation & Calculation

Critical and contextualised thinking

Activities: Student Feedback

Generating Student Responses

One question: Student Responses

Rob Proffitt-White NCR: March 2015

Moderating the responses is essential

O p e n y o u r m i n d s t o m a t h s

OPEN ENDED TASK

ONE QUESTION

ONE FOCUS

F O R E V E R Y S T U D E N T, E V E R Y D AY

AC

CE

SS

IBLE

AN

D E

NJO

YAB

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M I S T A K E S A N D R I S K S A R E W E L C O M E H E R E

LISTE

N, SH

AR

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nd

VA

LUE

STUDENT RESPONSE

S

NUMBER SENSE

Influential Support for Initiative

I was most impressed by the diagnostic assessments that have been developed, in particular the

focus on the proficiencies is exemplary .

I was also impressed with the attention to detail in the moderating process, the

associated diagnosis and the feedback given to students.

2015 2016

It is an outstanding example of “grass roots” collaboration and initiative to improve the experience of learning mathematics. It is a model that can be used by clusters generally.

Sustaining the sense of Urgency

The Region The Schools The Key TeamClear lines of sight

Influential Experts

Long term goals

Long term commitment

Funding Coaches, TRS

Networking

Support & MentorValued

contributionsConfident & Passionate

Visibility. Commitment. Ownership

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

High Schools involved (2014,2015,2016) High School Not involved

Measuring Relative Gain ( 7-9)

0 20 40 60 80 100 1200

5

10

15

20

25

30

35

40

45

Year 3 - 5 Relative Gain ( Top 20%)

Primary Schools involved (2014,2015,2016) Primary Schools Not involved

Measuring Relative Gain (3 - 5)

Targets: Surface or Deep? Student or School?

Our Initiative is about making the ‘Right Choice’ (Guy Claxton)

To get good results, AND produce young people who are

passive, dependent and anxious about failure

To get good results, AND produce young people who are

inquisitive, imaginative and independent

"It takes three to five years for change in practice to clearly show up in a change in learning," he said. "Sometimes it can

take up to seven years to turn a school around.“ Peter Goss: Grattan Institute, August 2016