unpacking coaching conversations in numeracy in primary and secondary school settings ghiran byrne...

Unpacking coaching conversations in Numeracy in primary and secondary school settings

Ghiran ByrneLinda DimosSilvia Kalevitch

NMR

Structure

1. Silvia Kalevitch

- Whole school approach

2. Ghiran Byrne

- Conversations to build a maths culture in

the classroom

3. Linda Dimos

- Conversations at the individual level

Unpacking coaching conversations in Numeracy in Secondary School settings

Silvia Kalevitch

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…

Mathematics

‘………..’ College

Year 8 2008Course PlanEach 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

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)

Course used

at a

secondary

school in

2008…

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 Number. Rational & Irrational Numbers [Ex 1A – 1D]

Chapter 1

3 15/02/2008 Structure: Algebra & Equations Chapter 2




7 14/03/2008 Space: Linear Graphs Chapter 3




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

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

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

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 4 2008

• 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

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

Framework(1)

• Work done by core group of teachers from each school that met fortnightly to develop the course

• Initially developed outlines for Semester 1 2009 (currently used and evaluated in the process) with Semester 2 to be developed early in 2009 for delivery in Semester 2 2009

• Used an agreed documentation format …

• Incorporated good practice that already exists at both schools

• Based on VELS, incorporating HRLTP (John Munro)

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

Role of this group:

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.

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)

Homework…• 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).

Whole numbers (+ and -)

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

Estimations

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

Arithmetic computation involving rational numbers

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

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

Year 7 Course OutlineDimension: 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

oTens of thousands, and decimals to hundredths (3.0)oSize and order of small numbers (to thousandths) and large numbers (to millions) (4.0)

-Rounding numbersoNearest ten, hundred or thousand (3.0)

-Adding and subtracting whole numbersoAddition and subtraction involving numbers up to 999 (3.0)

-Multiplying and dividing whole numbersoAutomatic recall of multiplication facts up to 10 x 10 (3.0)oMultiplication and division of single digits (3.0)oInverse relationship between multiplication and division (3.75)oMultiplication by increasing and decreasing by a factor of two (3.75)oDivision of integers by two-digit divisors (5.0)

Factor sets for natural numbers and express these as powers of primesSimple 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

oSquare numbers using a power of 2 (3.25)oSimple powers of whole numbers (4.0)oSquare numbers up to and including 100 (4.25)oUse of index notation to represent repeated multiplication (4.25)oCalculation of squares and cubes of rational numbers (4.75)oMental computation of square roots of rational numbers associated with perfect squares (4.75)oTechnology to confirm the results of operations with square and square roots (4.75)

-Multiples and factorsoMultiples of 2, 3, 4, 5, 10 and 100 (3.0)oMultiples and powers of 10 (3.0)oCreation of sets of multiples of numbers and their representation in index form (3.75)oSets of number multiples to find lowest common multiple (4.0)oFactors in terms of the area and dimensions of rectangular arrays (4.0)oFactor sets and highest common factor (4.0)

-Primes, composites and factor treesoIdentify prime and composite numbers (4.0)oFactor trees for the expression of numbers in terms of powers of prime factors (4.5)

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

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)

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)

Developing a Maths Culture

Building Relationships

Ghiran Byrne

Developing a Maths Culture Weekly OutlinePurpose Lesson sequence Resources

Day 1 To discover students’ perceptions of mathematicsTo 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 likeIn 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 responsesHomework task-Students ask the above questions to parents-Collate and compare homework task resultsWhat similarities and differences did you find between student and parent responses?Display in room

A3 paperTextas

Day 2 Can students identify maths as more than just numbersCan 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?

PostcardsA3 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

PostcardsPaperPencils

Day 3 To discover students’ attitude and feeling towards maths

Attitude to mathsConsensogram-Students place post-it note on scale 1.Hate it, find it difficult, do not enjoy it and do not see its purpose, do not think I am any good at it5- I like it, I find it challenging but I see its purpose. I think I am alright at it10- 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. To discover students’ attitude and feeling towards mathsCan students identify the role of maths in everyday life

Analogies Model- How can maths be like a car?Provide examplesMaths is like a telephoneMaths is like a rollercoaster-Students independently draw and write(brainstorm)( how maths is like something-ShareDisplay responses

-A3 Paper

Day 4 To find out what are students perceptions of what makes someone good at maths

Maths stereotypesWhat is a stereotype?-DiscussTrue/false statements -Categorise/Debate

Stereotype cardspaper

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

What does maths look, feel and sound like?

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”

Day 2: Where is the maths?

- “seeing task as how many of something, how much something costs”

- “interesting the use of words, instead of being specific, they are very general”


Day 3: Attitude to Maths

- “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”


Day 4: Analogies

• “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”

Teacher’s Comments and Observations

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”.

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

Coaching conversations at the individual level

Conversations at the whole school level

Conversations at the PLT/classroom level

Coaching conversations at the individual level

Skills/Motivation Matrix

High Skills

Low Skills

Low

Motivation

High

Motivation

Coachee A

Coachee B

Coachee C

• Low motivation• Confident teacher• Strong leadership skills

• Relatively low motivation• Sound teaching and learning skills• Willing to try new things with support

• Low motivation• Lacked confidence in teaching skills• Overwhelmed


High Skills

Low Skills

Low

Motivation

High

Motivation

Inspire Delegate

Direct Guide

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

Conversations…

Inspire Delegate

COACHEE A• Low Motivation• Confident teacher• Strong leadership skills

Conversations revolved around…

1. Building leadership skills through engaging in conversations about improving student outcomes

2. Inspiring innovation and ownership over the initiative – sharing/reflecting

3. Delegate leadership responsibilities to Coachee A – coaching/facilitating

4. Short term actions with immediate success

COACHEE B• Relatively low motivation• Sound teaching and learning skills• Willing to try new things with support

Conversations…

Guide Delegate


1. Building on current teaching skills

2. Trying new things – share and reflect

3. What success the coachee is looking to achieve

4. Risk taking/challenging

COACHEE C• Low motivation• Lacked confidence in teaching skills• Overwhelmed

Conversations…

Direct Delegate


1. Identifying and setting clear goals with clear timelines

2. Having conversations about ‘what might need to happen next’

3. Risk taking

4. Reflection


High Skills

Low Skills

Low

Motivation

High

Motivation

Coachee A

Coachee B

Coachee C

Coachee A

Coachee B

Coachee C

• More focussed on data and student outcomes

• Developing ability to ensure purposeful teaching at a range of levels

• Developing leadership skills

• Planning lessons to cater for student diversity – data use

• Building on repertoire of teaching skills

• Structure and delivery of lessons

• Mathematical content knowledge increased

• Sequential planning

• Lesson delivery

Action ResearchBoreman 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

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

Reflection…

What type of conversations do you envisage you might need to have?

• -Whole school

• -Classroom and team

• -Individual level

Contacts

For further information, please do not hesitate to contact :

• Ghiran Byrne – [email protected]

• Linda Dimos – [email protected]

• Silvia Kalevitch – [email protected]

mailto:[email protected]



unpacking coaching conversations in numeracy in primary and secondary school settings ghiran byrne...

Documents

faculty slide

schools rnl

issue slide

agreed course

schools data

individual level slide

area mecd chap

cambridge course