Connect with Maths ~Maths leadership series- Session 3- the right knowledge
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Transcript of Connect with Maths ~Maths leadership series- Session 3- the right knowledge
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
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
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
LE
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
E a
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