1. Awareness of Facilitation of Mathematics Inquiry
Welcome. I am ___________ and we will spend our time together today building an Awareness of Facilitation of Mathematics Inquiry.

2. Learning Focus
Build awareness of and confidence in skills needed to facilitate professional learning
Understand the role of an interactive presenter, coach and facilitator of mathematics inquiry
Emphasis:
Notice and name the actions involved in the role of a facilitator of mathematics inquiry
Develop strategies to continue improving in the role of facilitator of mathematics inquiry
<<Note to Presenter: text enclosed by << >> are notes for the presenter and not part of the script>>
Our learning focus for today is to:
<<read the bullets>>

3. Agenda
Item
Identifying the Roles of Interactive Presenter, Coach and Facilitator of Mathematics Inquiry
Facilitation vs. Presentation
Math Talk – Representing Fractions
Introducing Visible and Invisible Facilitator Actions
Applying Understanding of Visible and Invisible Facilitator Actions
Visible and Invisible Actions across Roles
Paradoxes, Challenges and Supports
Our work today is through the lens of facilitating mathematics. Effective facilitation of mathematics learning requires an understanding of mathematics as well as facilitation.
During this session we’ll begin with differentiating the roles of a presenter, a coach and a facilitator. Through observation of a video, we will analyse the facilitator’s actions to inform our reflection on and sharing of our own experiences.
We will wrap up with identifying essential attributes of successful facilitators and take an inventory of our own strengths and opportunities for growth to move forward in our role as facilitator.
<<allow time for participants to read slide>>

4. Creating the Climate
Engage in the tasks and the discussions - enrich everyone’s experience
Embrace the learning
Actively seek connections between the research and your experiences
By better understanding facilitation actions we better understand our strengths and refine our skills.
We create a positive climate by... <<read the slide>>

5. Identifying the Roles of Interactive Presenter, Coach and Facilitator of Mathematics Inquiry
Each participant will select and read a quote.
The other group members determine who would say the quote:
interactive presenter
coach
facilitator of mathematics inquiry
To explore the roles of interactive presenter, coach and facilitator of mathematics inquiry, we have a number of quotes written on slips of paper <<BLM 1>>. Each participant will select and read a quote and the table mates will determine who would say it, either an interactive presenter, coach or facilitator of mathematics inquiry. Examining these quotes will give you an idea of the different ways each role is performed.

6. A Mathematics Interactive Presenter…
…delivers professional learning that starts with a need that has been identified externally (e.g., school, board, provincial). The session(s) include opportunities for participants to collaboratively engage in mathematics learning tasks. In this role, the presenter provides pre- determined content to build participants’ mathematics knowledge.
In each of these roles, the overall goal is to deepen participants’ mathematics knowledge for learning, teaching, and leading. We will now look at definitions of each role.
<<have the participants read the slide>>
In this role, the presenter provides pre-determined content to build participants’ mathematics knowledge and strategies for effective instruction in mathematics.
In this session, when we use the word presenter or presentation we will be meaning it relative to an interactive presenter or presentation.

7. A Mathematics Coach…
…works with individual teachers over a period of time. The work starts with understanding the strengths and beliefs of the teacher and the needs of their students. The coach leverages the teacher’s strengths while creating dissonance to support instructional change. In this role the mathematics coach co-plans, co-teaches and consolidates with the teacher.
<<have participants read the slide>>
The Mathematics Coach pre-plans with the teacher. The coach and teacher then co-teach a lesson, including the debriefing and consolidation with the students. The coach would then work with the teacher to consolidate their own mathematics and instructional learning. This is typically one-on-one work that fits with the needs and teacher at a particular time.

8. Facilitator vs. Facilitator of Mathematics Inquiry
A Facilitator
Remains neutral
Guides the process
Keeps people on task
Enforces group norms
A Facilitator of Mathematics Inquiry
Guides but also manages and engages in the process
Is not neutral
Some people may have an understanding of “facilitator” as a neutral actor guiding a process. A facilitator of mathematics inquiry participates in the process to guide it, highlighting learning opportunities and offering insight. This facilitation is not neutral.

9. A Facilitator of Mathematics Inquiry…
orchestrates professional learning that starts with an authentic need to learn more about both student learning and participants’ learning. The facilitator guides the group to a common goal. Throughout an agreed upon process they ensure meaningful questions surface before solutions are sought or actions taken. In this role the facilitator exists as leader and co-learner.
<<participants read the slide>>
A facilitator of mathematics inquiry partakes in the process as leader and co-learner and can share aha moments. This facilitator both focuses and re-focuses the group. For example, if the group is looking at student work samples and they are focusing on what students don’t know, the facilitator could refocus the group so that it begins to identify what students do know. (Math content knowledge helps identify what students do know even in an incorrect solution.)
In this session, when we use the word facilitator or facilitation we will be meaning it relative to a facilitator of mathematics inquiry.

10. Identifying the Roles of Interactive Presenter, Coach and Facilitator of Mathematics Inquiry - Revisit
Based on the definitions re-read the quotes.
Adjust your decision as to whether it would be said by:
an interactive presenter
a coach
a facilitator of mathematics inquiry
<<provide a copy of the slides with the definitions on them to each table>>
Given the definitions, re-read the quotes and take a minute to adjust any of your previous decisions on who you think would have said it.

11. Facilitation vs. Presentation
The purpose of the professional learning session determines the structure and the skill set used to deliver it.
Both facilitation and presentation
involve participants developing knowledge and skills
can lead people to new knowledge and new ways of thinking
require clear communication and clear goals/intentions
There are similarities between Facilitation of Mathematics Inquiry and Active Presentation in terms of the skills used.
<<discuss with a group that coaching and facilitation both incorporate skills of facilitation>>
For the purpose of today’s session, we are going to focus specifically on facilitation and presentation. By analysing the differences between the roles, the aim is to deepen understanding your role as facilitator.

12. Distinguishing the Role
Reflect on the differences in actions of facilitators and presenters
Identify each action as pertaining to facilitator or presenter
On each of the slips of paper we are giving out now <<BLM 2>>, there is a written description of an action. To reflect on what exactly facilitators and presenters do in their role, we ask you to sort the actions that correspond to each role - either facilitator or presenter.

13. Distinctions Facilitator Presenter
Fosters discussion and two-way sharing
Lectures using interactive style
Speaks regularly but solicits ideas from group
Speaker does majority of talking
Guides process of knowledge creation
Delivers information
Shares question finding and goal setting
Imparts knowledge to motivate, inspire change
Encourages participants to take on various roles
Considers the group an audience
Supports positive group dynamics
Values pace, visuals and capturing attention as well as content knowledge
<<this is a wrap-up of the sorting activity BLM 2>>
This slide shows how we have divided up the duties. This is not an exhaustive list – you may have encountered more in the work that you do.

14. Essential Attributes of a Facilitator of Mathematics Inquiry
Mathematics knowledge for teaching
Knowledge of mathematics across the grades
Understanding of how mathematics is acquired
Sensitivity to the complex and often intimidating journey of math learning
Ability to identify and reveal windows of opportunity to deepen mathematics understanding
A skilled facilitator of mathematics inquiry requires attributes that incorporate content and pedagogical knowledge, and the ability to apply diverse and complex visible and invisible actions.

15. Math Knowledge for Teaching
This is all the mathematical knowledge important for teaching – the knowledge that teachers need to carry out their work as teachers of mathematics (Ball, Thames & Phelps, p.4)
This research reflects the idea that doing mathematics is not the same as teaching mathematics which is far more complex. For example, when a student gets a wrong answer, what you do with this is more important. Teachers need to recognize what a child does understand in an incorrect solution as well as recognize when a correct solution reflects a lack of understanding.
<<For more information see – Deborah Ball’s video (image is hyperlinked to
Common Content Knowledge is the knowledge that is used in settings beyond the classrooms and includes evaluating the correctness of an answer, being able to provide definitions of concepts, and modeling procedural steps. It is the math that parents know!
PCK is the blend of knowing the content contained within the curriculum (what to teach) and the knowledge of how students learn in general and of their thinking (this is evidenced in anticipating common student misconceptions) and the knowledge of the content and the impact on teaching (such as sequencing, time, which examples to use).
SCK is part of what distinguishes the skills and knowledge of teachers of mathematics from others who utilize mathematics in their professional and/or personal lives. This extends beyond the knowledge we expect students to possess at the respective grade level and includes knowledge of how the mathematical concepts connect (such as the different interpretations of each of the operations – subtraction as ‘take away’ and as ‘comparison’). Teachers must not only be able to do mathematics but they also need to unpack elements of the mathematics to make it apparent to students. They need to be able to explain why in a variety of ways and to use correct and appropriate language to do so. This would include selecting a number line as a representation for students to use when learning about the meaning of fractions.
Finally, Thames and Ball discuss the knowledge at the mathematical horizon. This is the knowledge of the mathematics being taught within the context of what learning has preceded it and what will come in the future. It is a deep understanding of the connections between the conceptual understanding and the procedural algorithms, the connections of operations across number systems, the general mathematical properties which will hold true in other contexts. It allows teachers to build and extend student thinking as a strong foundation for subsequent learning, perhaps without making these connections explicit to the students.
<<image taken from

16. Representing Fractions
Represent two fifths or four tenths in as many ways as possible.
<<Have participants represent the two fractions in as many ways as possible using manipulatives, paper and pencil and or mathies.ca learning tools.>> Now share some of your representations with your table partners. What similarities do you see? Were there some unique representations?

17. Introducing Visible and Invisible Facilitator Actions
Now we want to watch a short video clip of a facilitation scenario.
Background:
In this scenario a group of five classroom teachers discuss the fraction task with the facilitator, researcher and board lead. This is the third meeting of the group.
In the first meeting, the group was introduced to the focus of fractions and discussed common areas of need which they have observed in their students. The educators were given a pre-assessment to administer to their students.
In the second meeting, the results of the assessment were discussed and the fraction task was developed.
On the third meeting day, the group observed students completing the task in a grade 3-4 classroom. The video begins with that teacher sharing her observations.

18. First Viewing of the Inquiry Session
We are going to watch the video <<King George Debrief_without bubble>>several times today. This first viewing is intended to allow you to see the overall flow of the discussion.

19. Visible Actions
Review the visible actions of a facilitator of mathematics inquiry.
Which actions resonate with you?
Which actions do you have questions about?
Let’s look at the list The Visible Actions of a facilitator on BLM 3 Visible Actions.
Take 5 minutes at your table to read the visible actions and discuss the questions on the slide.
Now we will view the video clip again.
As you view the video a second time, identify visible actions of the facilitator. Try to identify supporting evidence like gestures, phrases, body language, etc. For example “the facilitator is navigating here because…”

20. Second Viewing of Inquiry Session
<<After the video, King George Debrief_without bubble, give participants time to consolidate thinking before they share their comments. Lead a group discussion.>>
<<Lead questions>> What action did you identify? What kind of evidence can you provide?
<<See Facilitation_Awareness_Presenter Notes 1.docx for anticipated actions and evidence.>>

21. Invisible Actions
Review the visible actions of a facilitator of mathematics inquiry.
Which actions resonate with you?
Which actions do you have questions about?
Let’s look at the list The Invisible Actions of a facilitator on BLM 4 Invisible Actions.
Take 5 minutes at your table to read the invisible actions and discuss the questions on the slide.
Now we will view the video clip again.
As you view the video a third time, identify invisible actions of the facilitator. Try to identify supporting evidence like gestures, phrases, body language, etc. For example “the facilitator is window finding when she…”

22. Third Viewing of Inquiry Session
<<After the video <<King George Debrief with thought bubble>>, give participants time to consolidate thinking before they share their comments.>>
<<Lead questions>> What action did you identify? What kind of evidence can you provide?
<<See Facilitation_Awareness_Presenter Notes 1.docx for anticipated actions and evidence.>>

23. The math that is important to know...
Comparisons do require precision
Precision is less important when representing
When representing, if there is a strong conceptual frame, then precision becomes less important
As you wrap up the video analysis portion of the learning highlight the important math concepts that were raised within the group.
With this task it is important to note that:
When we compare fractions precision is important
When representing fractions precision is less important
If a student has strong conceptual frame about fractions, when representing precision becomes less important

24. Connecting to Your Practice
Reflect upon a brief, specific incident in your experience with facilitating inquiry.
Identify the visible and invisible skills you used or could have used.
Share with an elbow partner.
<<Facilitate the discussion using the prompts in the slide.>>

25. Most Frequent Actions of Facilitators
<<If difficult to read on the ppt handout or go to page 3 of the brochure accessed at
This graphic shows findings from the Collaborative Action Research project which generated the Facilitating Mathematics Professional Learning brochure. The graphic displays the significance of the visible and invisible actions in the participants practice.
<<Lead questions>> How does this align with your experience? What surprises you?

26. Applying Understanding of Visible and Invisible Facilitator Actions
With a partner, choose one of the scenarios on your table.
Identify which of the visible and invisible actions could be applicable and provide a rationale.
Share your insights with your table group.
<<Handout BLM 6>>Each scenario is a snapshot from a facilitation session.
<<Share instructions on the slide and circulate to nurture the discussion.>>

27. Now about me… Where are my strengths as a facilitator?
What do I want to learn more about?
Now it’s time to reflect on your practice and take inventory of your strengths.
Ask yourself if there are some actions you haven’t thought about before today.
What is something you want to learn more about?
Where can you see opportunity for growth in some actions?
How has this exploration of visible and invisible actions informed your practice going forward?

28. Actions Across Roles Visible Actions Invisible Actions
This graphic (BLM 7) was generated by a group who, realizing that the actions described are components of presenting, coaching and facilitating, considered the extent to which each action plays a part in the role The size of the dot indicates the extent – small dots indicate a small part while large dots indicate it is a significant part of the role.
When you look at this graphic, is there anything that surprises you? What do you notice about each role?
Are there any conclusions you can make by looking at the graphic?
<<For example, participants may realize that they have skills that will support them in the facilitation of mathematics inquiry but that the skill will play a larger part in that role than in other roles they may be more experienced in, such as coaching.>>

29. History of the Brochure
Arose out of the experiences of a small group facilitating collaborative action research projects in mathematics who began to recognize that facilitation of mathematics inquiry has unique challenges
January 2013 – started the collaborative action research with a small group of facilitators
Products included a report and this brochure
The brochure was created following a collaborative action research project led by Dr. Cathy Bruce of Trent University. The research participants were facilitators of board and provincial professional learning, as well as Ministry of Education staff. Collectively, the group identified research questions and collected data. The brochure contains information that emerged out of a process of coding and analysis of that data.
The BLMs used in this session are slightly modified versions of the brochure material. The BLMs broaden the perspective to include facilitation of mathematics inquiry beyond collaborative action research.

30. Paradoxes of Facilitating Mathematics Inquiry
focus on the big stuff
yet
narrow in on the details
anticipate
be open to surprises
honour individual differences
fuse perspectives and goals
create new knowledge
convey known knowledge
participate as a co-learner
facilitate simultaneously
reveal decision making
not obviate every decision
use cultural capital
suffer self-doubt
empower others
be powerful
be flexible
be goal oriented
be problem oriented
have clear expectations
Facilitation of inquiry presents unique challenges, as identified within the research project. Facilitators need to be aware of and prepare for the paradoxes involved in inquiry sessions.

31. Challenges Being Knowledgeable Lack of Cultural Capital
Anticipating Needs
Loneliness
Mismatch
Complexities
Facilitators are faced with unique challenges as well. These are the ones identified in the research – you may be able to identify others as well.
Look for a separate learning module that will expand on and offer strategies to mitigate these challenges.
<<distribute brochure if you have not already>>
<<Have participants review the descriptors of each challenge on page 3 of the brochure and share in their table groups their experience with and/or overcoming these challenges.>>

32. Strategies to Support Facilitators
The back page of brochure offers strategies to support facilitators going forward.

33. Resources
The brochure is located in Facilitation Supports Facilitation under the Professional Learning Facilitator tab on EduGAINS.ca – Mathematics.