1. Ghiran Byrne Linda Dimos Silvia Kalevitch
Unpacking coaching conversations in Numeracy in primary and secondary school settings
Ghiran Byrne
Linda Dimos
Silvia Kalevitch
NMR

2. Structure Silvia Kalevitch - Whole school approach Ghiran Byrne
- Conversations to build a maths culture in
the classroom
3. Linda Dimos
- Conversations at the individual level

3. Unpacking coaching conversations in Numeracy in Secondary School settings Silvia Kalevitch

4. First impressions…
2o school settings: structure not as clear (huge schools)
Issues getting started as a coach, managed these & started getting accepted/credibility
Teachers picked for coaching not necessarily most suited (class room management issues, not ready…)
Observed everyone doing own thing – no consistency, course not there, kids doing different things in different classes & given different assessment…
No base line  How can we teach to improve student outcome??? ??? Impact of Coach???
Asked to get course outline from somewhere else…

5. Course used at a secondary school in 2008… Course Plan Mathematics
‘………..’ College
Year 8
2008
Course Plan
Each semester consists of
30 classes of core mathematics skills work
18 classes doing task centre activities
18 classes working mathematically activities
14 homework sheet tasks
Topic, Dimension and Chapter
Course used
at a secondary
school in
2008…
Semester 1
Semester 2
Positive and Negative Numbers (NU) Chap 2
Percentage
(NU ) Chap 11
Algebra Expressions
(ST) Chap 3
Indices
(NU) Chap 14 (First two laws)
Perimeter and Area
(MECD) Chap 4
Linear Equations
(ST) Chap 7
Fractions, Decimals, Ratios
(NU) Chap 6
Surface Area, Volume
(MECD) Chap 9
Shapes
(SP) Chap 8
Probability, Simulation
(MECD) Chap 12
Cartesian Plane
(SP/ST) Chap 10
Textbook – Essential Mathematics VELS Edition Year 8 (Cambridge)

6. Year 10 2008 – Semester 1 Timeline
Week
Date
Topic
Course Work 1
01/02/2008
Number. Rational & Irrational Numbers [Ex 1A – 1D]
Chapter 1 2
08/02/2008 3
15/02/2008
Structure: Algebra & Equations
Chapter 2 4
22/02/2008 5
29/02/2008 6
07/03/2008 7
14/03/2008
Space: Linear Graphs
Chapter 3 8
21/03/2008
11/04/2008
18/04/2008

7. Context
There were some agreed course aims, however there is considerable variation in how individual teachers interpret, implement & deliver the curriculum
Many inexperienced teachers in need of assistance & some willing to develop
Similar situation in both schools

8. Aim
To develop a documented course outlines, assessment tasks, capacity matrix and assessment rubrics and agreed teaching practice for consistent application from Year 7 – 10 Mathematics in both schools

9. Action: Ongoing discussion between Coach, Principals & RNL
RNL & Coach put forward proposal to schools
RNL approached leadership from schools for agreement that there was an issue

10. Administration (1)
With the agreement of the two principals and support from RNL, a team of four teachers from each school was selected whose task was to meet and develop course outlines (2 hr meetings per fortnight)
~ 5 meetings in Term
Teachers released for meetings
The selected staff were given time or payment for additional duties if the work to be done was additional to their current role (negotiated with their principals)
Each staff involved was responsible & expected to write/document specific sections of the course outlines as agreed in the working group meetings
hr meetings – to discuss and evaluate the work that is being done between meetings.

11. Administration … (2) Meetings facilitated by T & L Coach and RNL
Teams from both schools plus their Principals attended the meetings
Learning area /faculty convenors in both schools had the additional responsibility of coordinating staff members involved from their schools, liaising with Coach & communicating the process to the remainder of the faculty
2. Meetings alternated each time between the two schools. Lunch provided by hosting school each time. Principals usually turned up to meetings at their own schools except for the first meeting, where all were present

12. Framework (1)
Work done by core group of teachers from each school that met fortnightly to develop the course
Initially developed outlines for Semester (currently used and evaluated in the process) with Semester 2 to be developed early in 2009 for delivery in Semester
Used an agreed documentation format …
Incorporated good practice that already exists at both schools
Based on VELS, incorporating HRLTP (John Munro)
One of the schools is also big on Robert Marzano. I keep trying to tie it in so as to make them feel that it fits in – it does have allot in common with Munro

13. Framework … This group is also developing process and strategies:
To ensure all maths staff in the two schools adhere to the course outline, assessment tasks and agreed teaching practices developed
Develop a plan to grow ownership and ongoing evaluation and development of mathematics continuum
Develop a plan to induct new staff & professionally develop new & existing staff

14. Role of this group: Leadership discussion at first meeting
What it will mean to be part of this group??
Leadership discussion at first meeting
Invest the Team with a moral purpose &
a sense of leadership,
challenge & ownership of the problem.

15. Plan & Document Curriculum → Introductory session
Purpose:
Setting the scene. Where are we at? Look at schools data
(On Demand, SNMY, VELS teacher judgement & NAPLAN)
Beliefs & Understandings (role of this group):
What do we know about our clientele (DATT – consider all factors, blockers…)
Bone diagram & Pedagogy teaching tool (structured discussion tools) Setting goals for teachers to improve outcomes
What does good Maths teaching & learning look like?
A shared understanding of the problem and the task
Fractions & Decimals DVD (snippets)
DATT – Direct attention thinking tools (10) by Edward DeBono
Pedagogy: Structured discussion tool for teachers
1. Participants asked to think of teaching situation where they think they have been particularly effective & why?
2. Participants asked to jot down their beliefs about teaching & learning that may be generated by this reflection.
3. As whole group, share the beliefs generated by individuals.
4. Each belief written on separate sheet of paper.
5. Group similar beliefs together onto large sheet and displayed around room
6. Six dots allocated to each person.
7. Each person attaches dots to the 6 beliefs that they consider most important.
8. As whole group participants identify the 6 beliefs considered most important.
9. Provided PoPLT P-12 & asked to compare the list generated by group & those reflected in the Principles .
10. Discuss whether the Principles as stated are a useful basis for reflection on the learning & teaching that takes place at the school.
11. Participants discuss as whole group:
What would classrooms that reflect the Principles (&/or their own beliefs if these are different) look like?
NB> the PoLT P-12 Background Paper provides a rationale for the PoLT & could be used as a basis for further discussion.

16. Homework… their designated dimension VELS 3 – 6 and
At end of session each session teachers were allocated tasks to be completed in two weeks
Teachers worked in pairs - became experts in one dimension (Number, Space, MCD & Structure) each plus Working Mathematically
To summarise the Learning focus within
their designated dimension VELS 3 – 6 and
Working Mathematically within their
dimension (using Venn diagrams).

17. Number – Level 4/5/6 Whole numbers (+ and -) Real numbers
Size and ordering of whole numbers
Fractions and equivalent forms of
Decimals, +,-,x,ing decimals and fraction
Multiples (LCM)
Factors (LCF)
factor sets/trees
rectangular arrays
Square, composite and prime numbers
Simple powers of whole numbers
Ratio and percent of common fractions
Division and remainders as fractions
Estimations
Integers, decimals and common fractions on a number line
Money
Fraction equivalents
Ratio
Factors and primes
Squares
Arithmetic computation involving rational numbers
Powers of numbers
Natural numbers as products of powers of primes
Fraction equivalents:
for a fraction in simplest form
as decimals, ratios and percentages
Decimal equivalents for the unit fractions
Calculate and estimate squares and square roots, and cubes and cube roots of natural and rational numbers
Evaluate natural numbers and simple fractions given in base-exponent form
Express natural numbers in binary form, and add and multiply numbers in binary form.
Compare quantities using ratio
Estimation and rounding
Approximations to π in related measurement calculations
Using technology for arithmetic computations
Real numbers
rational numbers in fractional and decimal (terminating and infinite recurring) forms
irrational numbers have an infinite non-terminating decimal form
decimal rational approximations for square roots of primes, rational numbers that are not perfect squares, the golden ratio φ, and simple fractions of π
Euclidean division algorithm to find highest common factor of two natural numbers
Arithmetic computations involving natural numbers, integers and finite decimals.
Computations involving very large or very small numbers in scientific notation
Arithmetic computations with fractions, irrational numbers (eg square roots) and multiples and fractions of π
Computations to a required accuracy in terms of decimal places and/or significant figures
Rational numbers in fractional and decimal form
Arithmetic operations with rational numbers
Estimation and rounding for decimals
Some calculations with powers
Some approximations with π

18. Further sessions…
Course outlines were mapped out from each dimension for Years 7 – 10 (Slide 19)
As a group - discussed and put together as sequence and content
Time frames were allocated for the units
Teachers then collected suitable resources to add to their course outlines within their dimensions (this was the longest and most difficult part)
Progress was monitored and discussed at each meeting

19. Year 7 Course Outline Dimension: Number Level 5 Standards Year 7
Semester 1
Arithmetic computations (mental and/or written methods) involving rational numbers
Place value to determine the size and order of whole numbers
Whole Numbers
Place value
Tens of thousands, and decimals to hundredths (3.0)
Size and order of small numbers (to thousandths) and large numbers (to millions) (4.0)
Rounding numbers
Nearest ten, hundred or thousand (3.0)
Adding and subtracting whole numbers
Addition and subtraction involving numbers up to 999 (3.0)
Multiplying and dividing whole numbers
Automatic recall of multiplication facts up to 10 x 10 (3.0)
Multiplication and division of single digits (3.0)
Inverse relationship between multiplication and division (3.75)
Multiplication by increasing and decreasing by a factor of two (3.75)
Division of integers by two-digit divisors (5.0)
Factor sets for natural numbers and express these as powers of primes
Simple powers of 2, 3 and 5
Calculate and estimate squares and square roots, and cube and cube roots of natural and rational numbers.
Natural numbers and simple fractions in base-exponent form.
Number Patterns
Powers
Square numbers using a power of 2 (3.25)
Simple powers of whole numbers (4.0)
Square numbers up to and including 100 (4.25)
Use of index notation to represent repeated multiplication (4.25)
Calculation of squares and cubes of rational numbers (4.75)
Mental computation of square roots of rational numbers associated with perfect squares (4.75)
Technology to confirm the results of operations with square and square roots (4.75)
Multiples and factors
Multiples of 2, 3, 4, 5, 10 and 100 (3.0)
Multiples and powers of 10 (3.0)
Creation of sets of multiples of numbers and their representation in index form (3.75)
Sets of number multiples to find lowest common multiple (4.0)
Factors in terms of the area and dimensions of rectangular arrays (4.0)
Factor sets and highest common factor (4.0)
Primes, composites and factor trees
Identify prime and composite numbers (4.0)
Factor trees for the expression of numbers in terms of powers of prime factors (4.5)

21. Achievement Milestones (end of 2008)
By end of 2008, Semester 1 Year 7 – 10 Curriculum documented and ready to launch for 2009
Developed ownership and shared approach among group (no longer working in isolation)
Effective team (Maths) leaders – assigned a year level each to manage within their own school
Agreed high expectations for staff (teams) and students
PROFESSIONAL LEARNING TEAMS
One of the most significant things a Numeracy coordinator can do is develop an effective professional learning team
Characteristics of Effective Professional Learning Teams
(Johnson & Scull, 1998)
1. Learning teams require a reason to learn and a purpose to engage in collaborative professional development practices. Projects provide reason and purpose, and allow an integrated approach to the implementation of curriculum improvement.
2. Learning team projects are best focused on collective responsibility for producing more effective learning for all students.
3. Learning teams benefit from a combination of outside-provided and work-embedded support.
4. Effective learning teams practise many forms of collaboration and systematic reflection on practice.
5. A sense of ‘personal productive challenge’ and a balance between pressure and support characterises the work of effective professional learning teams.
6. Learning teams require knowledgeable, skilled and supportive formal leadership.
7. Successful learning teams address the tensions inherent in the formal leaders’ role and in the personal and professional relationships within the learning team.
8. In effective learning teams all members consider themselves to be change agents and leaders.
9. When challenged by a change proposal, effective learning teams practice ‘mutual adaptation’ and stay in control while implementing change for the purpose of improvement
10. Learning Teams implement change in ways and at rates different from one another.
SCHOOL LEADERSHIP TEAM
promoting a culture that values mathematics learning and protects the learning environment from unnecessary interruptions
facilitating a review of early mathematics teaching and learning practices
creating leadership positions in the early years
reviewing school organisational structures and timetables to support the establishment of a one-hour block of time for mathematics teaching and learning

22. What next… 2009
Team leaders in their school have responsibility (Year 7 – 10). Their task (made explicit):
Lead regular team meetings (effective teams – common planning time)
Ensure curriculum adhered to and developed
Support teachers in their level team – improve Maths dialogue, moderate work
Assist with introduction of formalised process of classroom observation, modeling and coaching
Develop courses for Semester 2 (to be completed by mid Term 2)
Use regular assessment for learning. Over time gather and analyse own data, becoming better informed
Give teachers a moral purpose - Case manage kids who are shared with whole team (develop bank of strategies to teach them)

23. Milestones needed for change in practice and behaviour:
Open up their practice in a supportive environment, build consistency in content and methodology, capacity and ownership of curriculum
Establish formalised coaching and modelling of good practice between members of the year level teams.
‘Learning Walks’ – the model for classroom observations to be implemented in Term 2
Our approach to teacher capacity building will be built around teachers sharing professional dialogue (effective teams) and using data (to inform their understanding of students and of their practice as teachers)

25. Developing a Maths Culture
Building Relationships
Ghiran Byrne

26. Developing a Maths Culture Weekly Outline
Purpose
Lesson sequence
Resources
Day 1
To discover students’ perceptions of mathematics
To identify similarities and differences between student and parent
To discover what prior knowledge students are bringing to school
What does maths look, feel and sound like
In small groups use Structured brainstorm- 4-5mins on each question
What is maths?
Where do we use it?
What makes someone good at maths?
What can help you with maths?
Share and list responses
Homework task
Students ask the above questions to parents
Collate and compare homework task results
What similarities and differences did you find between student and parent responses?
Display in room
A3 paper
Textas
Day 2
Can students identify maths as more than just numbers
Can students identify the role of maths in everyday life
Where is the maths?
Distribute postcards
Ask students where is the maths in the postcard?
What do you now know about maths?
Can we add any further information to our “what is maths” brainstorm?
Postcards
A3 white cover paper
Day 3
To discover students’ attitude and feeling towards maths
This picture makes me think….
Use postcard to express feelings/thoughts/attitudes about maths
Paper
Pencils
Attitude to maths
Consensogram
Students place post-it note on scale
Hate it, find it difficult, do not enjoy it and do not see its purpose, do not think I am any good at it
5- I like it, I find it challenging but I see its purpose. I think I am alright at it
10- Love it! I am good at it, I enjoy solving puzzles and problems, I get excited about it
-Signs
-Scale
-Post-it notes
-A3 paper
-Coloured pencils
Day 3 cont.
Analogies
Model- How can maths be like a car?
Provide examples
Maths is like a telephone
Maths is like a rollercoaster
Students independently draw and write(brainstorm)( how maths is like something
Share
Display responses
-A3 Paper
Day 4
To find out what are students perceptions of what makes someone good at maths
Maths stereotypes
What is a stereotype?
Discuss
True/false statements
Categorise/Debate
Stereotype cards
paper

27. Purpose
To provide teachers with tools that can be used to discover students’ beliefs, attitudes and perceptions/misconceptions
Providing teachers with opportunity to observe what students have to say and think about maths
To provide an opportunity where coach and teacher can share in professional discussions
To enable teachers to use this information for future planning purposes

28. What does maths look, feel and sound like?

29. Teacher’s Observations and Comments
- “Students see maths as number”
“So many students think being good at times tables makes someone good at maths”
“They are not making the connection between terms eg fractions decimals percentages”
“many of the students hold the same beliefs about maths as their parents e.g.: maths is times tables, maths is hard or maths is about thinking, problem solving, taking risks”
“No mentions as maths being about patterns or estimation”

30. Day 2: Where is the maths?

31. Day 2: Where is the maths?
¾ level

32. Day 2: Where is the maths?

33. Teacher’s Observations and Comments
“seeing task as how many of something, how much something costs”
“interesting the use of words, instead of being specific, they are very general”

34. Day 3: Attitude to Maths

35. Teacher’s Observations and Comments
“Did they mark themselves high to please me?”
“Girls were fairly positive in their response”
“These boys are good at maths, but they gave themselves a low score”
“It has been interesting when we have revisited, students have changed their rating for different maths topics”
Followed up

36. Day 4: Analogies

37. Day 4: Analogies

38. Day 4: Analogies

39. Teacher’s Comments and Observations
“They were able to think outside the box with this activity and become creative about maths”
with a little bit of prompting they started to give ‘real life’ examples – this highlighted the need to teach using real life activities”

40. Teacher Reflection
“I noted the importance of finding out how the students think and feel about maths and developing a new maths culture in order to dispel or challenge any misconceptions about mathematics that the students may have and to guide future teaching”.

41. As a Coach
The teacher gets to know their students before delving into the content
It has made the thinking visible
Encourages teachers to actively promote mathematics
Valuing and encouraging maths in a range of contexts

42. Coaching conversations at the individual level
Conversations at the whole school level
Conversations at the PLT/classroom level
Coaching conversations at the individual level

43. Skills/Motivation Matrix
High Skills
Low motivation
Confident teacher
Strong leadership skills
Coachee A
Low
High
Relatively low motivation
Sound teaching and learning skills
Willing to try new things with support
Motivation
Motivation
Coachee B
Low motivation
Lacked confidence in teaching skills
Overwhelmed
Coachee C
Low Skills

44. Skills/Motivation Matrix
High Skills
Inspire
Delegate
Low
High
Motivation
Direct
Guide
Motivation
Low Skills
COACHEE A
Low motivation
Confident teacher
Strong leadership
skills
COACHEE B
Relatively low
motivation
Sound teaching
and learning skills
Willing to try new
things with support
COACHEE C
Low motivation
Lacked
confidence
in teaching skills
Overwhelmed

45. Conversations… COACHEE A Low Motivation Confident teacher
Strong leadership skills
Inspire
Delegate
Conversations revolved around…
Building leadership skills through engaging in conversations about improving student outcomes
Inspiring innovation and ownership over the initiative – sharing/reflecting
Delegate leadership responsibilities to Coachee A – coaching/facilitating
Short term actions with immediate success

46. Conversations… COACHEE B Relatively low motivation
Sound teaching and learning skills
Willing to try new things with support
Guide
Delegate
Conversations revolved around…
Building on current teaching skills
Trying new things – share and reflect
What success the coachee is looking to achieve
Risk taking/challenging

47. Conversations… COACHEE C Low motivation
Lacked confidence in teaching skills
Overwhelmed
Direct
Delegate
Conversations revolved around…
Identifying and setting clear goals with clear timelines
Having conversations about ‘what might need to happen next’
Risk taking
Reflection

48. Skills/Motivation Matrix
More focussed on data and student outcomes
Developing ability to ensure purposeful teaching at a range of levels
Developing leadership skills
High Skills
Coachee A
Coachee A
Planning lessons to cater for student diversity – data use
Building on repertoire of teaching skills
Structure and delivery of lessons
Low
High
Motivation
Motivation
Coachee B
Coachee B
Mathematical content knowledge increased
Sequential planning
Lesson delivery
Coachee C
Coachee C
Low Skills

49. Action Research Boreman et al (2005, pp 70-71) found:
“only tenuous links between professional development and
classroom instruction for many teachers. Most teachers seemed
to experience a disconnection between their professional development experiences and their day to day classroom experiences.” (cited in Fullan, M; Hill, P; Crevola, C (2006); Breakthrough, p. 23)
Prompted me to work within an Action Research model to promote ‘collective responsibility’ and gather tangible evidence of improvement

50. Action Research Discussed the action research model
Linked theory to practice
Collected baseline data
Set ‘action’
As action research progresses, can see a more tangible improvement in skill level

51. Reflection…
What type of conversations do you envisage you might need to have?
-Whole school
-Classroom and team
-Individual level

52. Contacts For further information, please do not hesitate to contact :
Ghiran Byrne –
Linda Dimos –
Silvia Kalevitch –

53. Coaching conversations at the individual staff level