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

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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

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Unpacking coaching conversations in Numeracy in Secondary School settings Silvia Kalevitch

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First impressions… 2 o 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…

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Mathematics……….. College Year 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 Semester 1Semester 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…

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Year – Semester 1 Timeline WeekDateTopicCourse Work 1 01/02/2008Number. Rational & Irrational Numbers [Ex 1A – 1D] Chapter /02/2008Number. Rational & Irrational Numbers [Ex 1A – 1D] Chapter /02/2008Structure: Algebra & EquationsChapter /02/2008Structure: Algebra & EquationsChapter /02/2008Structure: Algebra & EquationsChapter /03/2008Structure: Algebra & EquationsChapter /03/2008Space: Linear GraphsChapter /03/2008Space: Linear GraphsChapter /04/2008Space: Linear GraphsChapter /04/2008Space: Linear GraphsChapter 3

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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

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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

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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

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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

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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

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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)

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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

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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.

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Plan & Document Curriculum Introductory session Purpose Purpose: Setting the scene. Where are we at? Look at schools data (On Demand, SNMY, VELS teacher judgement & NAPLAN) Beliefs & Understandings Beliefs & Understandings (role of this group): What do we know about our clientele (DATT – consider all factors, blockers…) structured discussion toolsBone 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)

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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).

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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

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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

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Year 7 Course Outline Dimension: Number Level 5 StandardsYear 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 o Tens of thousands, and decimals to hundredths (3.0) o Size and order of small numbers (to thousandths) and large numbers (to millions) (4.0) -Rounding numbers o Nearest ten, hundred or thousand (3.0) -Adding and subtracting whole numbers o Addition and subtraction involving numbers up to 999 (3.0) -Multiplying and dividing whole numbers o Automatic recall of multiplication facts up to 10 x 10 (3.0) o Multiplication and division of single digits (3.0) o Inverse relationship between multiplication and division (3.75) o Multiplication by increasing and decreasing by a factor of two (3.75) o 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 o Square numbers using a power of 2 (3.25) o Simple powers of whole numbers (4.0) o Square numbers up to and including 100 (4.25) o Use of index notation to represent repeated multiplication (4.25) o Calculation of squares and cubes of rational numbers (4.75) o Mental computation of square roots of rational numbers associated with perfect squares (4.75) o Technology to confirm the results of operations with square and square roots (4.75) -Multiples and factors o Multiples of 2, 3, 4, 5, 10 and 100 (3.0) o Multiples and powers of 10 (3.0) o Creation of sets of multiples of numbers and their representation in index form (3.75) o Sets of number multiples to find lowest common multiple (4.0) o Factors in terms of the area and dimensions of rectangular arrays (4.0) o Factor sets and highest common factor (4.0) -Primes, composites and factor trees o Identify prime and composite numbers (4.0) o Factor trees for the expression of numbers in terms of powers of prime factors (4.5)

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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

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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)

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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)

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Developing a Maths Culture Building Relationships Ghiran Byrne

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Developing a Maths Culture Weekly Outline PurposeLesson sequenceResources 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 Postcards Paper Pencils Day 3 To discover students attitude and feeling towards maths Attitude to maths Consensogram -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 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. To discover students attitude and feeling towards maths Can students identify the role of maths in everyday life 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 4To 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

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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

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What does maths look, feel and sound like?

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Teachers 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

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Day 2: Where is the maths?

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-seeing task as how many of something, how much something costs -interesting the use of words, instead of being specific, they are very general Teachers Observations and Comments

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Day 3: Attitude to Maths

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-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 Teachers Observations and Comments

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Day 4: Analogies

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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 Teachers Comments and Observations

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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.

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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

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

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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

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Skills/Motivation Matrix High Skills Low Skills Low Motivation High Motivation InspireDelegate DirectGuide 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

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Conversations… InspireDelegate 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

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COACHEE B Relatively low motivation Sound teaching and learning skills Willing to try new things with support Conversations… GuideDelegate Conversations revolved around… 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

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COACHEE C Low motivation Lacked confidence in teaching skills Overwhelmed Conversations… DirectDelegate Conversations revolved around… 1.Identifying and setting clear goals with clear timelines 2.Having conversations about what might need to happen next 3.Risk taking 4.Reflection

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Skills/Motivation Matrix 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

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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

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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

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

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

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Coaching conversations at the individual staff level

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