1. Numeracy Link Teacher Day 1 Seminar 2012
Session 1
Drumcondra Education Centre
David Mc Mahon
Introduction, housekeeping. Please ensure the following are available at each table for participants:
- post it notes
Miniature tab notes
Markers
Today’s seminar will focus on the SSE guidelines and materials as launched by the DES recently.
School self-evaluation is a process through which schools can bring about improvement and development.
Note to Presenter: Change name of EC and date accordingly on opening slide

2. Overview of Seminar Rationale SSE and Literacy and Numeracy Strategy
Session 1
9.20 – 10:50
Rationale
SSE and Literacy and Numeracy Strategy
Instructional Framework for Mathematics
10.50 – 11.10
Coffee
Session 2
11.10 – 12.45
Fractions: Learning Trajectory
Fractions Manual: Practical Tasks
12.45 – 1.30
Lunch
Session 3
1.30 – 3.00
Successful Whole School Implementation
‘Between Session Tasks’
(Outline detail of each session and start/finish times for the day – please amend the start and finish times in accordance with your own seminar details.)
Today is about upskilling you in the area of fractions so that you can, in turn, support teachers in your own school. This will require you to lead numeracy in your school in conjunction with your principal. The ultimate aim is that you will be enabled to bring about change in classroom practice. With that in mind, today’s seminar will focus mainly on 2 aspects:
Your role as link teacher
The teaching and learning of fractions from 1st to 6th classes

3. Session 1 Objectives
To outline a rationale and set the context for the link teacher model
To provide participants with a brief overview of SSE and aspects of the Literacy and Numeracy strategy
To familiarise participants with an instructional framework for mathematics 
This session will focus on the following objectives:
To outline a rationale and set the context for the link teacher model
To provide participants with a brief overview of SSE and aspects of the Literacy and Numeracy strategy
To familiarise participants with an instructional framework for mathematics

4. Why the link teacher model?`
Distributed
leadership
“The most successful schools actively seek out leadership talent beyond the formal leadership structures” (Harris and Townsend, 2008)
Why the link teacher model?`
Teacher as Leader
Catalysts for Positive Change
Teachers as central to decision making
Primary concern is to improve student learning (Gronn, 2003)
School leadership second only to classroom instruction as an influence
Click 1 – Distributed Leadership
The notion of distributed leadership has gained prominence in recent years with a recognition of a need to introduce more democratic leadership structures in schools, harness the ability of every teacher to lead according to areas of strength /interest and relieve the ever growing burden of principal ship demands.
A considerable body of research and studies strongly indicating improved learning outcomes that emerge from a perspective that recognises multiple leaders and which acknowledges the work of all individuals who contribute to leading practice whether they hold formal or informal positions in the school.
Leadership can no longer lie solely with those in formal leadership positions.
Schools of the 21st century will have to harness all the available leadership capacity and capability and maximise all form of human intellectual capital (Harris,2008).
Within the private and public sectors there is an increasing focus on leadership at all levels in order to strive with modern day demands
Teacher leaders recognise that with the ever-increasing demands on today’s schools, administrators cannot perform the entire scope of leadership tasks alone, thus amplifying the need for teacher leaders to oversee some of the curricular and instructional tasks within the school.
Click 2 – Teacher as Leader
Flexible models of leadership are needed which “…require new ways of working, a greater degree of team interaction and problem solving…an expansion of leadership responsibilities” (Gronn, 2003). The idea of teachers as leaders embraces the core principles of distributed leadership because it is based on lateral, networked and fluid ways of working.
The literature on teacher leadership challenges the notion that distributive leadership is mere delegation. It is not imposed upon them – they opt to take on lead roles in a certain area and instigate opportunities for change. They operate with a high degree of professional choice and autonomy and responsibility. There is growing evidence that dev teachers as leaders positively influences organisational dev and in schools has a greater influence on student outcomes than traditional forms of hierarchical leadership. (From American study of 180 schools over 6 yrs)...they found that school leadership was second only to classroom instruction as an influence on student learning and that in successful schools many different people exercised leadership roles
Institute for Educational Leadership study states that it is imperative for teachers to be part of policy shaping, decision making and collaborative leadership in schools where they work. A collective commitment has been proven to have significant impact to improvements in learning outcomes. The focus is primarily on the interactions of these teachers and the development of a communities of learners within the school. Teacher leaders can have an impact on students, colleagues, and themselves with the ultimate end goal being improved student achievement

5. Timeline of CPD model Nov./Dec. 2012: Link Teacher Day 1
Dec – Spring 2013: Back in school + follow on support
March 2013: Link Teacher Day 2
Follow on support
(school/clusters/workshops)

6. Targets in the L & N Strategy
Increase the percentage of primary children performing at Level 3 and Level 4 (the highest levels) in the National Assessment of Mathematics and English Reading by at least 5 percentage points at both second class and sixth class by 2020
Reduce the percentage of children performing at or below Level 1 (minimum) in the National Assessment of Mathematics and English Reading by at least 5 percentage points at both second class and sixth class by *Summary available on ERC Website
There are both qualitative and quantitative targets in the strategy. The quantitative targets outlined here focus on testing.

7. Targets in the L & N Strategy
Create greater awareness of, and more positive attitudes towards, Mathematics among the public
Promote better attitudes to Mathematics among children and young people
*Outlined in ERC Summary Report / Literacy & Numeracy Strategy
However, there also qualitative targets regarding mathematics in the strategy – these ones are applicable to primary schools. The targets that focus on attitudinal change and level of engagement are as valid as those that focus on exam results and standardised testing.
While these may seem like ‘soft’ targets they are not to be underestimated. These targets lie at the heart of what the strategy is trying to achieve.

8. Under the strategy all schools must engage in :
Robust Self Evaluation
Prepare a 3 year School Improvement Plan
Set Specific Targets
The strategy outlines a number of requirements for schools. Your principal will recently have attended inservice training on the use of the school self-evaluation guidelines. The next few slides are a broad overview of that SSE process and what is required by schools.
The PDST is funded by the Department of Education and Skills
under the National Development Plan,
© PDST, 2010 8

9. SSE: Broad Requirements
Schools are asked to:
Build on existing school development planning processes by engaging in school self-evaluation of teaching and learning from 2012/13
Evaluate the quality of teaching and learning in literacy, numeracy and at least one other curriculum area in the four years from 2012/13 to 2015/16
Write a short SSE report for the area examined
Devise a School Improvement Plan for aspects of practice identified for improvement
Experience has told us that it takes a number of years to build good self-evaluation processes in schools. Change will take time to become fully established and that teachers, principals and others involved will need to be supported. Over the next 4 years, schools are expected to evaluate literacy, numeracy and one other aspect of teaching and learning. You and your staff choose your focus after taking stock of what you already know about how your school is doing in these areas.
BACKGROUND KNOWLEDGE FOR PRESENTERS
As per circular - SCHOOL SELF-EVALUATION IN DEIS SCHOOLS
Schools within the DEIS programme have been required to develop and implement school improvement plans (called DEIS action plans) as part of the requirements for DEIS funding since 2006/07. The work required of schools in forming and implementing DEIS action plans is very similar to that required in the school self-evaluation process. With effect from the date of this circular, DEIS schools may meet the planning and reporting requirements for DEIS funding through completing the school self-evaluation process.
* See Circular 0039/2012

10. The Teaching and Learning Quality Framework
Teaching & Learning Framework
SSE Guidelines p.24 / p.25
Learner outcomes
Learning experiences
Teachers’ practices
Theme
Attainment of curriculum objectives
Learning environment
Pupils’ engagement in learning
Learning to learn
Preparation for teaching
Teaching approaches
Management of pupils
Assessment
The SSE guidelines provide schools with a teaching and learning framework which ensures that schools engage in SSE in a focussed and cohesive way. It prevents the process from becoming ad hoc or random.
The school in considering all 3 themes, will scan now the subthemes in order to broadly identify what is going well/not so well in the teaching and learning of Literacy/Numeracy. They will as a result choose subthemes or aspects of subthemes which will provide the lens for the evaluation of Literacy/Numeracy/Other area
For example they may choose to structure the evaluation of literacy/numeracy as follows:
Outcome ( Attainment of curriculum objectives)
Teacher Practice (Teaching approaches, Assessment)
Pupil Experience (Student engagement in learning. Learning to Learn)
NB:
Not all subthemes need to be evaluated.
Not all criteria within a subtheme need to be evaluated
It is best for schools to choose a small number to begin with.
This process is Not mandatory but does highlight the value of the framework
Using the quality framework with themes, sub-themes and related criteria allows a school to initially review t and L in its broadest sense
The selection of specific subthemes for evaluation and undertaking an in-depth enquiry into teaching and learning with regard to these only keeps it manageable
The rewards are reaped when commencing the 6 step process - step 1 will now have a definite focus and the questions that we pose in step 1 will be based on the aspects of the subtheme that we want to evaluate.
Sub-themes 10

11. Key steps in the SSE process
Gather the evidence
Analyse the evidence
Make judgements about strengths and areas for development
Write school self-evaluation report
Devise a 3-year school improvement plan
Implement and monitor improvement plan
Once a school has decided upon the subthemes for evaluation, they are ready to embark on the 6 step process of SSE which provides direction for schools
The 6 step process is iterative in that it facilitates repeated cycles of analysis or a return to a previous stage of the cycle as required. Schools and teachers will already be familiar with many of these steps from their experience of school development planning (SDP).
Gather the Evidence – Schools already gather data for a variety of purposes and much of this will prove beneficial in the SSE process. Teachers’ views and their records of assessment are useful examples of evidence. The views of pupils and parents should also be gathered.
Analyse the evidence - Schools need to analyse the information they have gathered and to check the quality of their practice against a set of standards taking due cognisance of school context.
Make Judgements- Schools will want to draw conclusions based on their analysed evidence. They will determine, affirm and celebrate the strengths they identify in the aspects of practice being evaluated. They will also acknowledge the areas prioritised for improvement.
Write school improvement report - This step ensures that schools maintain a record of their self-evaluation and particularly their findings. Each year schools will complete a short school self-evaluation report. The report will outline the focus of the self-evaluation, along with the strengths and areas for improvement identified
Devise 3 year SIP - Having identified the aspects of practice prioritised for improvement or development, the school should devise a school improvement plan. The school improvement plan should outline the targets for the improvement of learning outcomes for pupils over a three-year period, along with the actions to achieve these targets
Implement and Monitor - The final step, implementing and monitoring the improvement plan is vital if the SSE process is to bring about improvement. Having outlined the actions to be taken over a three-year period, all teachers should ensure that the agreed actions become part of the normal teaching and learning process.
The implementation of the actions for improvement will be monitored, progress will be reported on a regular basis and changes to the targets will be made if necessary.
The first three steps outline the review element of the SDP process. These important steps ensure that conclusions about strengths and areas for improvement are based on evidence from a range of relevant sources. The next steps ensure that schools retain a record of the evaluation and describe the actions for improvement. The final step, implement and monitor, takes place over a three-year period.

12. Key Messages for Day 1 The key messages for today’s seminar include:
The link teacher for numeracy is a facilitator of change for improvement
A variety of learning experiences enhances the understanding of mathematical concepts/skills and allows for differing abilities and learning styles
Mathematical thinking is developed by eliciting, supporting and extending children’s mathematical ideas
The key messages for today’s seminar include:
The link teacher for numeracy is a facilitator of change for improvement.
A variety of learning experiences enhances the understanding of mathematical concepts/skills and allows for differing abilities and learning styles.
Mathematical thinking is developed by eliciting, supporting and extending children’s mathematical ideas.

13. Challenges
What are the challenges to teaching mathematics in Irish primary schools?
What are the obstacles to developing reasoning and conceptual / higher order mathematical skills in our students learning?
Now I want you to consider the following 2 questions in groups of 4/5.
What are the challenges to teaching mathematics in primary schools?
What are the obstacles in developing reasoning and conceptual understanding?
(Allow 5 minutes for teachers to discuss this in groups. Take whole-group feedback.)

14. Sources NAMER Inspectorate DES / NCCA
Low focus on reasoning and problem solving
Whole-Class Teaching v Differentiation
Over-reliance on textbooks
Under-use of concrete materials
Teacher as sole validator of mathematical ideas
Insufficient pair and group work
High focus on procedure and drill
Sources
NAMER
Inspectorate
DES / NCCA
These challenges or difficulties have been identified in research in Irish primary classrooms within the last decade. This includes national research, for example, the ERC research findings (NAMA, NAMER, etc.); inspectorate reports; and international reports, for example, TIMSS.
How do these findings compare with the items that you came up with in your group discussions?

15. Fractions See Fraction Manual p.12 & p.13
Ok so we have spoken generally about mathematics up to this point. From here on, we will focus more specifically on the teaching and learning of fractions. We will now do an ice breaker activity to get you warmed up and thinking about fractions. How many possible fractions can you see in this visual representation?
(Ice breaker
Take feedback with explanations. Model the language from the instructional framework when taking the feedback (see appendix B) e.g.
Are there other possibilities?
Explain how you did it.
So you think that …
Can you explain what Mary said in your own words?
Did anyone else see other possibilities?
Distribute the fractions manual (one between 2 participants). Take participants into page 12 of the manual to highlight this misconception about fractions.
TAKEN FROM PAGE 12:
Social conventions can restrict the possible fractions within a situation, for example, pupils may assume that a visual diagram always represents the number 1.
Askew (2000); Anghileri (2007).
Thus, a pupil may identify this fraction diagram (correctly) as representing 3/5 or 2/5 or both; However, they are less likely to see other possible representations, for example, 1 2/3 or 2 ½, 1 ½ or 2/3 These latter representations are made possible when it is understood that the whole unit can represent numbers other than the number 1.
See Fraction Manual p.12 & p.13

16. Classroom Culture Most important Least important See Manual p.9
Creating and maintaining the correct classroom culture is a prerequisite for developing and enhancing mathematical thinking. We will now engage in an activity which explores classroom culture in more detail.
(Classroom Culture activity.
Hand out flashcards and complete the following activity. Complete a diamond 9 (ranking activity) for the classroom culture pre-requisites (which can be found on page 9 – see text below. There are 10 pre-requisites in the manual regarding the teacher’s role; however distribute the 9 flashcards outlined below to each group).
Creating and maintaining the correct classroom culture is a pre-requisite for developing and enhancing mathematical thinking. This requires the teacher to: :
cultivate a ‘have ago’ attitude where all contributions are valued;
emphasise the importance of the process and experimenting with various methods;
facilitate collaborative learning through whole-class, pair and group work;
praise effort;
encourage pupils to share their ideas and solutions with others;
recognise that he/she is not the sole validator of knowledge in the mathematics lesson;
ask probing questions (see Appendix B for a list of sample questions and sample teacher language);
expect pupils to grapple with deep mathematical content;
value understanding over ‘quick-fix’ answers;
Least important
See Manual p.9
See Manual p.89

17. Revoicing Technique
Forman & Larreamandy-Jones, 1998, p. 106
‘…the reporting, repeating, expanding or reformulating a student's contribution…'
Another important aspect of classroom culture is revoicing. Here we can see definition of what it is. Revoicing is a powerful tool for clarifying and extending mathematical thinking. I hope to model the use of the revoicing technique throughout the day.
(After the activity is completed, bring participants into the manual to locate the classroom culture pre-requisites on page 9)
BACKGROUND INFO FOR PRESENTER:
The full definition on revoicing is below:
Revoicing is ‘the reporting, repeating, expanding or reformulating a student's contribution so as to articulate presupposed information, emphasise particular aspects of the explanation, disambiguate terminology, align students with positions in an argument or attribute motivational states to students' (Forman & Larreamandy-Jones, 1998, p. 106).

18. Read and discuss your section Summarise and record the main points
Instructional Framework: Strategies for Supporting and Developing Mathematical Thinking
Read and discuss your section
Summarise and record the main points
Report back to your home group
I now want you to briefly scan the instructional framework on page 8. (give 1-2 minutes for participants to scan page 7)
We will now do an activity which explores this instructional framework in more detail. You will be familiar with this type of collaborative activity – it is sometimes called Home-Expert Groups and is sometimes called a Jigsaw Activity.
(Divide participants into groups of 3 (home group). Then one participant from each group goes to one corner of the room - one corner for eliciting, one for supporting and one for extending. Tell teachers to bring a piece of paper and a pen in order to take notes so that they can report back to their home group.
They become experts and return to their home groups to share what they have learned.)
Advise participants, when they return to their home group to give the feedback in the order of 1. Eliciting, 2. Supporting and 3. Extending.
Activity based on Manual p.8
Eliciting
Supporting
Extending

19. Instructional Framework p.8 Background Knowledge p.11
Book Walk Activity
Resources p.4
Differentiation p.5
Instructional Framework p.8
Background Knowledge p.11
Fractions Trajectory p.19
Fractions Level A p.29
Fractions Level B p.39
Fractions Level C p.51
Fractions Level D p.63
Fractions Level E p.81
Appendix B p.88 / p.89
Appendix D p.94
Appendix E p.98
The teacher’s manual for fractions is an attempt to provide teachers with some tools to overcome ALL of the challenges difficulties regarding mathematics teaching and learning which we have already discussed.
(Now that the participants have the manual in front of them take them on a BOOK WALK:)
Pg. 8 (instructional framework)
pg. 10 (background knowledge)
pg. 19 (fractions trajectory)
pg. 28 (teaching and learning experiences)
pg. 87 (appendices)

20. Teacher Reflection Exercise
Current Teaching
Same
Instructional Framework
Different
It is now time to reflect on your own classroom practice. This is an individual, private activity where you can compare and contrast your current mathematics teaching with that advocated in the instructional framework. This activity also allows you to reflect on potential challenges that this type of teaching might present.
(Give out Teacher Reflection handout for each teacher to complete.)
*See Reflection Framework

21. Session 1: Recap before break
To outline a rationale and set the context for the link teacher model
To provide participants with a brief overview of SSE and aspects of the Literacy and Numeracy strategy
To familiarise participants with an instructional framework for mathematics 
Just before coffee, we will recap on our objectives for session 1. Our objectives were to ….
Hopefully, we have achieved these objectives.

22. Numeracy Link Teacher Day 1 Seminar 2012
Session 2

23. Key Messages for Day 1
The link teacher for numeracy is a facilitator of change for improvement
A variety of learning experiences enhances the understanding of mathematical concepts/skills and allows for differing abilities and learning styles
Mathematical thinking is developed by eliciting, supporting and extending children’s mathematical ideas
Welcome back after coffee. Just to re-iterate that the key messages for today’s seminar include:
The link teacher for numeracy is a facilitator of change for improvement.
A variety of learning experiences enhances the understanding of mathematical concepts/skills and allows for differing abilities and learning styles.
Mathematical thinking is developed by eliciting, supporting and extending children’s mathematical ideas.

24. Session 2 Objectives
To provide participants with a clear understanding of the Learning Trajectory for Fractions
To promote a child-centred approach to the teaching and learning of fractions
To highlight the use of a variety of approaches to cater for individual differences, abilities and learning styles
This session will focus on the following objectives:
To provide participants with a clear understanding of the Learning Trajectory for Fractions.
To promote a child-centred approach to the teaching and learning of fractions
To highlight the use of a variety of approaches to cater for individual differences, abilities and learning styles

25. Concrete Pictorial Abstract
Fractions Trajectory
Developmental
Based on PSC
Concrete Pictorial Abstract
Set
Area
Linear
5 levels
We will now do a book walk of the fractions trajectory in the manual. (as participants are looking through the trajectory draw their attention to the following). As you can see there are 5 levels to the trajectory. These conceptual understandings are based on the objectives for fractions in the primary school mathematics curriculum and so are developmental. You will see that within each level of the trajectory, the concepts are developed in 2 directions – horizontally and vertically.
The horizontal progression is from Concrete to Pictorial to Abstract. This is a recommended approach for the teaching of all mathematical concepts. It is widely accepted that children move from the concrete to the pictorial to the abstract. Children need opportunities for exploration at all three stages; however, there should be fluidity regarding the progression through these stages. It is not rigid and will be dictated by the child (this effectively is differentiation in action).
The vertical progression includes the Linear, Area and Set Models. This is a recommended approach specifically for the teaching of fractions. Too often, the area model (e.g. pizza) is over-used. Children need hands-on experiences with all 3 models and they need opportunities to make connections between all 3 models as often as possible. These models will be explored further throughout the activities today.
Give teachers opportunity to scan the trajectory for 2-3 minutes.
See Manual p.20
See Fractions Trajectory A

26. Level B.1 and B.6
Compare, order, count and identify fractions and equivalent fractions
Denominators 2, 4, 8, 10
Denominators 3, 5, 6, 9, 12
GET TEACHERS TO FLICK THROUGH TEACHING & LEARNING EXPERIENCES IN LEVEL A FIRST
Time restraints do not allow us to explore the manual in detail so I have chosen some tasks from a number of different levels of the trajectory in order to give you a broad flavour of the teaching and learning experiences which are outlined. I hope these tasks will illuminate the type of approach which is advocated in the manual. Furthermore, I hope that by engaging with these tasks, the possibilities for the use of the manual in your classrooms will become evident.
The first tasks which I have chosen to highlight come from Level B.1 and Level B.6: Compare, order, count and identify fractions and equivalent fractions…
*Prior Level 1 Brownie Activity p.29 / p.30

27. Counting (Appendix D on p .94)
Sound of a Number p.95
Feely Bag p.95
Rope Activity p.97
Stand & Sit Game p .95
Counting Stick p.94
Target Boards p.96
Firstly, I want to demonstrate a number of counting activities. (do the counting activities on the slide)
Now, if you turn to page 94 of the manual you will see these counting activities and many more are outlined in Appendix D (give participants 2/3 minutes to scan these pages)

28. Compare, order and identify fractions and equivalent fractions
Linear
Paper Strips p.39
String and Paper Clips p.40
Cuisenaire Rods p.40
Area
Geoboards p. 41
Dotted Paper p.42
Rectangular Pieces p.42
Pie Pieces p.42
Set
Vehicles p.43
(Bring participants through these tasks modelling the instructional framework through the teacher voice (page 38 – 43). See teacher’s manual for teacher voice i.e. the necessary script)
(After the end of each activity, bring participants into the manual to locate each of this activities)
See Manual p.87
*Learning Log

29. Benchmarking & Estimation
Benchmarks are helpful for pupils to develop their number sense in relation to fractions.
Estimation is central to applying benchmarks. Pupils need lots of opportunities to compare fractions to benchmarks.
The most important reference points or benchmarks for fractions are 0, ½ or 1.
Benchmarks and estimation … (as per slide)
We will now do an activity which might be useful for you to do with children in order to develop estimation skills and to apply benchmarks.
(Distribute fraction pairs task worksheet. Afterwards, direct participants to this activity on page 44 of the manual)
See Manual p.45
Fractions Pairs Activity

30. Consolidation Activities
Fish for Fractions Game p.90
Fraction Dice Game p.34
We will now try out 2 consolidation activities.
Firstly, we will play the Fish for Fractions game. There are only 3 players in this game so I will get 3 volunteers to play this game as a fishbowl activity. 3 of you can play and the rest of us will watch in a circle. You will notice that the linear, area and set models are included in this game. This really enhances consolidation.
(complete fish for fractions)
Now I want 2 different volunteers to play the Fraction dice game. (use fishbowl activity as above)
(bring participants into the manual to locate these activities – page 90 and page 33)

31. Level B.2 - Level B.5 Activities Level C - Teaching & Learning
Book Walk Activity p.47 – p. 54
Level B.2 - Level B.5 Activities
Level C - Teaching & Learning
Unifix Cubes p.52
Benchmarks Number line p.52
Fraction Pieces p.53
Fraction Wall p.54
We have engaged in some of the tasks from level B.1. I now want to do a BOOK WALK of the teaching and learning experiences from Level B.2 to Level C.2 (pages 46 to 53).

32. Slicing Squares Activity
Level C.3: Construct Algorithms for Equivalent and Simplified Fractions p.58 & p.59
Slicing Squares Activity
REITERATE THAT WE HAVE SKIPPED ON TO A DIFFERENT LEVEL IN THE MANUAL
Assuming that pupils had covered all of the previous activities, they would be ready to progress onto this slicing squares activity. In order to be able to add, subtract, multiply and divide fractions, pupils need to be proficient in identifying equivalent fractions and in simplifying fractions. This activity is one way of developing this conceptual understanding.
(Distribute slicing squares handout and get participants to do activity as on page Use slicing squares HIDE AND REVEAL follow-on activity also.)
(After the activity is completed, bring participants into the manual to locate this activity- page 57 to 59)

33. Session 2: Recap before lunch
To provide participants with a clear understanding of the Learning Trajectory for Fractions
To promote a child-centred approach to the teaching and learning of fractions
To highlight the use of a variety of approaches to cater for individual differences, abilities and learning styles
Just before lunch, we will recap on our objectives for session 1. Our objectives were to ….
Hopefully, we have achieved these objectives. Enjoy lunch!

34. Numeracy Link Teacher Day 1 Seminar 2012
Session 3

35. Key Messages for Day 1
The link teacher for numeracy is a facilitator of change for improvement
A variety of learning experiences enhances the understanding of mathematical concepts/skills and allows for differing abilities and learning styles
Mathematical thinking is developed by eliciting, supporting and extending children’s mathematical ideas
Welcome back after lunch. Just to re-iterate that the key messages for today’s seminar include:
The link teacher for numeracy is a facilitator of change for improvement.
A variety of learning experiences enhances the understanding of mathematical concepts/skills and allows for differing abilities and learning styles.
Mathematical thinking is developed by eliciting, supporting and extending children’s mathematical ideas.

36. Session 3 Objectives
To promote a child-centred approach to the teaching and learning of fractions
To examine appropriate modes of assessment for fractions
To clarify the role of the link teacher
This session will focus on the following objectives:
To promote a child-centred approach to the teaching and learning of fractions
To examine appropriate modes of assessment for fractions
To clarify the role of the link teacher

37. Common Errors
What are the common errors that children make with fractions?
Adding
Subtracting
Multiplying
Dividing
See Manual p.12 & p.13
In pairs, please discuss this question:
What are the common errors that children make with fractions?
Adding
Subtracting
Multiplying
Dividing
Please use the post-it notes to record your answers.
(Record on post-its and display on flipchart)
Bring participants back to pupil misconceptions on p.12 and 13 of the manual.

38. Level D.1 Add and subtract fractions (first with like denominators, then repeat with unlike denominators) +
- –
STRESS THAT THIS IS FURTHER DOWN THE TRAJECTORY
Estimation is the starting point for all addition and subtraction of fractions. If children have a solid grasp of estimation and make use of benchmarks, they are more likely to recognise if their answer is right or wrong. Furthermore, operations involving fractions should be clearer and make more sense to them.
The following activity is one way of developing these skills. I need you to work in pairs:
Estimate whether your answer is closest to 0, ½, 1 or 2.
Record your estimate on an empty number line. Participants draw this number line themselves.
NOTE: This is an example of estimating with unlike denominators. Estimation with like denominators will have occurred prior to this.
Bring participants into the manual to locate this activity- page 63
Estimate using Benchmarks of 0, ½, 1 or 2
See Manual p.63

39. Concrete – PICTORIAL – Abstract
Two brothers ate some pizza. John ate of the pizza and Mark ate How much of the pizza did they eat altogether?
Concrete – PICTORIAL – Abstract
In session 2, we explored a lot of concrete representations of fractions. This example progresses onto the pictorial. It could also been done concretely using fraction pie pieces depending on the child’s needs. Now, I want you to represent this problem pictorially in as many different ways as possible without using the algorithm.
(Think-pair-share after a few minutes - to share and explain their representations. When taking feedback use revoicing technique).
The whole purpose of this activity is to lead children to discover the need for a common denominator. (bring participants to page 65 of manual – see below)
ERROR ANALYSIS
The most common error when adding fractions is to add both numerators and denominators. These errors should be discussed at a whole-class level when they occur. Discuss the following ‘solution’ for adding + in terms of whether the pupil could be correct or not. Also discuss why. (De Walle, 2008)
Remind teachers that: Research suggests that circular area models are the most effective for developing the concepts of addition and subtraction of fractions (Cramer, Wyberg & Leavitt, 2008). see page 64 of manual
See Manual p.64

40. Empty number lines 3 ¼ - 1 ½ See Manual p.69
Pupils who have strong fraction number sense will often be able to add and subtract fractions with like denominators without ever getting a common denominator. The number line is an excellent tool through which fractions can be added or subtracted mentally.
(bring participants into the manual to locate this - page 69)
See Manual p.69

41. Level D.3 Multiply a fraction by a whole number
6 ×
Represent this equation pictorially
*See Manual p.72
(Ask participants to do this individually. Then take feedback on how they did it, modelling the teacher language and questioning as outlined in appendix D)
Now I would like you to read the manual from pages 72 to 75 in order to explore multiplying by a fraction.

42. Assessment (Appendices)
Whole- Class Checklist p. 100
Individual Pupil Checklist p. 106
Teacher Reflection p. 111
(Bring participants to pages 98 to 111 of the appendices where they will find:
A Whole-class checklist (appendix E)
Individual pupil checklist (appendix E)
Teacher reflection (appendix G)
Explain how these might be used.)

43. Where to next? Classroom & School
We will now discuss what steps are needed to ensure that what you have learned today can be implemented successfully at school level.
Where to next?

44. Exploring The Role of the Link Teacher
The role of the link teacher is not prescriptive and the various responsibilities within the role will vary from school to school. However there are a few general areas that comprise effective teacher leadership. WE are presenting a menu of possible duties rather than a rigid list. It is vital to agree upon the finer details of the role with the school principal who has ultimate responsibility for all teaching and learning activity. Remember the link teacher is rooted in the distributive model for leadership – the promotion and development of a subject area is everybody’s responsibility and it is important that you are not solely responsible for all of the above.
The formation of the subject team will ensure that the workload is shared and that a number of people are held accountable. The role is less about the title and more about the interactions that are generated at whole school level
The link teacher is the conduit for the various duties involved and although will arrange for these to take place, will not necessarily carry out them all.
A good analogy is – the teacher leader presses the start button but is not solely responsible for holding it in!

45. Responsibilities of Link Teacher
Maintenance
Dynamic
Promoting positive change
Facilitating staff reflection and the sharing of good classroom practice
Engaging teachers/parents and community
Facilitating a range of continuing professional development opportunities for staff
Keeping school informed of current policy reforms and initiatives
Promoting Numeracy in accordance with the needs of school
Supporting the SSE process
Accessing and organising resources
Remaining up to date with current research
The teacher leader role can be broadly divided into 2 categories :
Maintaining the status quo (keeping the routine tasks things moving and tipping along) and
Dynamic which involves exploring new territory, taking risks, experimenting, challenging current practice and problem solving.
Both are important and will overlap but for real change and improvement it is necessary to move beyond the maintenance phase in order to remain abreast of constant educational change and to promote desired improvement.
Maintenance :
The teacher leader serves as a bridge for information flow between the school staff and the external ed environment. This may involve attending conferences/serving on relevant committees. It may also simply involve keeping abreast of and communicating new policy initiatives (NCCA/DES) by e mail/staff memos or reporting at a staff meeting
Areas in need of particular development should be identified and highlighted as needing intervention. These might emerge from standardised test results , staff reflection or professional conversations. An awareness of how pupils are assessed in the subject is crucial for the link teacher to have the bigger picture with regard to assessment
Although not solely responsible for the SSE process , it is helpful for the link teacher to be central to the process given its role in school improvement.
Keeping the school equipped with appropriate instructional resources / reviewing textbooks for quality / liaising with ICT co-ordinator
Auditing existing resources and ensuring they are aligned with current teaching requirements. Resource responsibilities might include:
maintaining an inventory of all the materials and equipment available in the school for the teaching of your subject.
keeping an overview of the ICT resources available for your subject and helping teachers to use them
organising storage and a system for accessing materials and equipment
maintaining equipment and materials in good order and noting what needs replacing each year
making decisions in collaboration with colleagues about how any money available for resources should be spent
Knowledge of current research will help the teacher leader make all sorts of informed decisions around new ways of operating, effective instructional approaches, assessment, resources and to have real credibility with regard to the subject area.
Dynamic:
The teacher leader is an engineer (maintenance) but must also be an architect of new maps and pathways to the future
The ever changing world we live in demands that the ways we work in schools continues to evolve. The teacher leader can play a visionary role in translating these changes into school culture. It involves first establishing core values and beliefs around literacy/numeracy
It means seeking to move from where we are now to a more improved place . It means asking how we are doing now and how we could do it better. The process of visioning is a good place for the teacher leader to start with the staff
“Where do we see literacy/numeracy in our school 5 years from now? “ What will the teachers be doing?” what will the pupils be doing? In what ways will this be different/better?
The teacher leader role will involve developing plans for change. Planning is vital for successful change and involves an anticipatory approach to potential problems associated with change and their solutions
How are people likely to react? What information do they need initially? How can this be communicated in away to get initial buy in? How will the change impact on the school/classroom activity/the way teachers/pupils work/ parents/ resources and money
Part of the change process may be the adoption of new approaches and methodologies. The link teacher can encourage staff to share practices that are working well and facilitate the cross fertilisation of professional knowledge/expertise/experience
Engaging parents and community and harnessing their potential requires effective communication mechanisms to be in place. Teachers need to be fully aware of parental /community involvement and the implications it has for their schedules/plans of work. The teacher leader may assume the responsibility of communicating all subject related updates/news etc. Other ideal ways of involving the wider community is through school literacy/numeracy events which are designed to promote the subject.
Any plans for staff development must be rooted in the needs of the teachers. More on this later

46. Facilitating In-School Models of CPD
Opportunity to report on a course attended
Facilitated sharing of successful classroom practice
Working together to produce and share resources
Lesson Study
Action Learning
Coaching & Mentoring
Update Resources, Approaches & Planning
One of the dimensions of the link teacher role might be facilitating the arrangements of CPD opportunities for staff. This does not mean that you yourself have to provide the CPD but put structures in place to ensure that staff CPD needs in relation to literacy are met
Teachers like all adult learners need a variety of CPD experiences to direct and develop their own learning.
However in general it is those models that go beyond the transmission of ideas or information that are more effective at bringing about a change in practice
Those that involve the teacher as a reflector, as an experimenter, as a researcher
Those that comprise networks of learners and which involve all in the decision making process
Lesson Study- a critically acclaimed form of CPD where having identified an area of concern, a group of teachers collaboratively design a lesson and try it out as critical friends followed by an evaluation and redesign of the lesson
Action learning - basically involves the teacher in identifying a particular problem that he or she wants to investigate and setting up an experimental lesson designed to meet the problem.
Coaching and mentoring – particularly helpful when inducting new teachers but has massive potential for the development of all teachers
Pair mentoring/peer observation - only if there is general acceptance of this-not to be forced on any one. This should always involve a preliminary discussion about what the teacher intends to do and suggestions about what would be useful feedback.
What kind of in school CPD happens in your school? How does it operate? Who arranges it? When does it happen?
Remember CPD can be informal also – reading an article / current research, browsing the internet for ideas, reflecting on a lesson after school
Anything that increases or enhances our professional knowledge constitutes CPD

47. Different strokes for different folks!
Ready to Go 20% Wait and see 60% Put on the brakes
Link teachers themselves need a clear understanding about the change process and the human element is massively important here.
The overall goal in any change effort s to gain enough buy in and consensus so that enough people are supportive and participate- the reality is you may not get everybody on board at first.

48. Between session tasks Discussion with principal
Identify and source resources for fractions
Use the manual as a teaching tool
Present some of the content to staff or groups of teachers
Avail of CPD opportunities
(Discuss the possible actions to be taken by link teachers. After this discussion, get them to complete the planning diary where they identify the tasks which they will complete before day 2.)
*Planning Diary Activity

49. ICT / Future Support Numeracy Link cluster meetings In-school support
Clustering of schools
Fraction workshops for other staff members
Online support
PDST Technology in Education
PDST Maths & ICT Curriculum Links
Scoilnet Fractions
Cluster meetings – it is envisaged that these will take place before Day2. Link teachers will receive an invitation. They will be held locally in an education centre or in a school probably 3.30 – 5.30 (flexible)
In-school support – advisor can support the school in a variety of ways
NCTE - Online ( provide Face to Face courses in local Education Centres for a Whole School or for group of 10 or more teachers (can take place in school also). The courses are Beginner to intermediate levels and are Fully funded for teachers. There is a focus on ICT use across the curriculum and for specific subject areas but all with a Literacy and/or Numeracy focus.
Technologies include digital media, internet, blogging, audio recording & podcasting, interactive whiteboards, presentation software, Scratch programming, visualisers
GIVE OUT ICT HANDOUT

50. Focus for Day 2
Percentages
Decimals
Place Value
The focus for day 2 will be on percentages, decimals and place value. As already mentioned, day 2 seminars will be in March. It is anticipated that you are the teacher who also attends day 2 in order to ensure consistency and continuity.

51. Recap: Session 3
To promote a child-centred approach to the teaching and learning of fractions
To examine appropriate modes of assessment for fractions
To clarify the role of the link teacher