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This discussion forum is being moderated as an expression of servant leadership in teaching & learning. As a collaborative tool for brainstorming enriching experiences for students, teacher learning groups, and district learning teams, we can inspire and build experiences to help empower each of us to personal leadership in learning. Thank you, in advance, for your contributions and leadership to realizing outcomes for improving student achievement, equity and well-being.

FROM THE ARCHIVES

the Equity through pedagogy series: thinking classrooms - Revisited

2/19/2019

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Welcome back to Flipping the Focus.
1-Introduction
Part 1 of the "Equity Through Pedagogy" series took readers through an examination of pedagogical practice through the lens of the Thinking Classroom--in secondary Mathematics and English.

According to Dr. Peter Liljedahl (2017), Thinking Classrooms are defined as spaces “...not [only] conducive to thinking but [that] also [occasion] thinking...a space inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion”.

It's important to note that these classrooms go well beyond engagement in vertical spaces--that is, well beyond the Stage 1 elements described in the Part 1 post and summarized by the graphic (see right).

As you reflect upon the elements from Stages 2 to 4, note that these elements serve the conversations we can have with students and one another about refining teaching and learning.

​Altogether, the last nine elements relate to the 'glue' that connects all aspects of our pedagogical practice: 
Formative Assessment. 
The 14 Elements of a Thinking Classroom
The 14 Elements of a Thinking Classroom

"...these classrooms go well beyond engagement in
​vertical spaces..."

As we collaboratively and continuously explore instructional practices that support students and promote respectful and caring learning communities, these elements can guide us in our efforts to better knowing both our learners and the learning.

Let's consider knowing our students and their learning through the context of the interview that follows.
2-The Search for Flow through Thinking Classrooms
Have you ever found yourself in a state where you were so engaged with a task that nothing else mattered? Think back to that time: Were you neither overwhelmed nor just coasting along? If you felt that you were in that space of 'neither', then you were in flow. Flow results from the dynamic relationship between challenge and skill development (Liljedahl, 2016). As teachers, we have a significant role to play in helping students find flow and what to do, alongside their peers, in this space.

In Part 1 of this series, I mentioned that there are a number of educators, in Eastern Ontario, journeying into building Thinking Classrooms. One of these educators is Jaime DePippo (St. Mother Teresa HS, Ottawa, ON). Jaime has been very gracious in speaking with me about her practice, and I am privileged and thankful to Jaime for the opportunity to feature her experiences, here, on Flipping the Focus.

Below, you'll see a continuation of our previous conversation, beginning with Question #4 (previously published). The remainder of the post focuses on Meaningful Notes, ​Spiralling, and Getting Started with a Thinking Classroom.

"Communicating where a student is and where they are going, alongside assessment AS learning, moves student learning forward."

3-A Conversation with Jaime DePippo
Question 4: You explained earlier that students are building and showing autonomy through their "meaningful notes". What does this look like in practice? What are you and your students doing?

Answer:
I use a gradual release model with my students in Applied English and Mathematics.

-A template, that provides some constraints--largely, the space provided for creating notes (i.e., not taking notes)--is shared with students towards the end of a period of learning.

-Students are encouraged to take notes when they need to.

-On a day-to-day basis, exit tickets are used to provide students with feedback.

-Using exit tickets allows me to provide suggestions for next steps. Students can map the next steps into the ‘what’ that they could be writing down in their notes.

-Students are not bound to making meaningful notes only at specific times in their learning.

-I accomplish this by spiralling the curriculum. Through interleaving the content, students have multiple opportunities to revisit and bring greater depth and meaning to their notes.

[The conversation continues, below, with a closer examination of meaningful notes.]

Question 5: In Stage 2 of Dr. Liljedahl’s elements is "Meaningful Notes". "Level to the Bottom" is in Stage 3.

-How fluid/fl
exible might we be in moving between these Stages? For example, should educators seek to fully level with student thinking, then build meaningful notes?
-Simultaneously level and build notes?

Altogether, how might a teacher best coach their students towards building autonomy?


Answer: 
​
At the beginning of a semester, I provide students with a template for creating their own meaningful notes. Essentially, the templates have only the key headings for the concepts students are learning.

[As a side-note, having the templates is important for educators who are teaching through spiralling their curriculum. For the math courses I teach, there are typically 4 spirals (or cycles). The first two cycles tend to be the longest, and by the time we reach cycle 4, there is less new material--i.e., the complexity of the tasks and the interconnectedness of concepts increases towards and throughout the final cycle.

As far as student learning is concerned, students feel more successful when spiralling: there isn’t a need or a feeling that you have to attain mastery right away. One of the primary goals of spiralling is to continuously go deeper with critical thinking and problem solving.]

[Back to the beginning of the semester...]

As we work towards consolidating student thinking in relation to a learning goal/goals, I’ll do some checks for understanding, which can be a small number of individual questions or related task so that students can see how they’re doing. I also use exit cards frequently to gain a better understanding of what students have been taking away from their time thinking alongside their peers. It’s through the exit cards, that I can create another opportunity to provide feedback to students. 

Above all of this, it’s important to remember that consolidation doesn’t always occur at the end of the task--student readiness is important: the exit card is key in my formative assessment and mentally-preparing students for self-assessment. 

With this feedback, students can go back to their notes (template) and write down those things that are important--i.e., meaningful--to them. For example, some of my early feedback would include notes to (and conversations with) students to write down the things that are not as familiar to them, as well as what their next step(s) would be.

By the time we get to Cycle 2, I find that students require less prompting to making their own, meaningful notes: student autonomy is always growing, cycle-by-cycle.

Earlier, I mentioned that conversations are a vehicle for providing students feedback. These principles are still in effect when we’re working on some test items. For example, if there are aspects of a student’s work that are not shining through on a test, I’ll ask them to show me their notes. It’s through their meaningful notes that a conversation about learning opens up (or re-opens). It’s during these moments that you can really tell if a student knows what they’re doing and what our next steps will be. In fact, there has been many times where a student’s assessment of learning has been enriched through conversation.
Question 6: There are many ways that educators can create safe and productively challenging learning environments with their students—some that do not include a Thinking Classroom.

If asked by a teacher why they should consider trying a Thinking Classroom, what advice might you provide to them? On getting started?


Answer:
Students are capable, critical thinkers and problems solvers.  If we deprive our students of these opportunities, they will not grow.  Students need to be actively engaged in their learning.

In any subject, nowadays, the goal of the student experience is not to remember everything. The goal is to create critical thinkers and people with strong collaboration skills, as well as their other global competencies. These are the skills and competencies that students will need moving forward. As educators, we have a great opportunity to show students that anything is possible when they develop and use these kinds of skills. And because we’re our own worst critics, sometimes students need us to point out their strengths: it’s through their strengths that they can develop/use these skills and grow as learners.

All of this said, teachers and administrators should start by attending a workshop or spending time in the practice of other teachers who are practising a Thinking Classroom model for teaching and learning. Asking questions of teachers and students who have immersed themselves in a Thinking Classroom everyday is important.  Hear their feedback about what has changed: engagement, curiosity, achievement, perseverance, etc.

Beyond this, I would say start small; take your time; and seek support from and collaboration with another person. There’s a lot to be said about planning and teaching together. To get a sense of the dynamic that’s possible between students and students and teachers--all of this in relation to the task that’s assigned--there’s a lot to be gained by spending time in and with these types of classrooms. Based on that experience, I would then encourage teachers to try the model by incorporating the Stage 1 elements--good tasks, visibly random groups and vertical non-permanent surfaces/whiteboards. For good tasks, there are plenty of resources available. 3-Act Math Tasks are a great base for teaching through problem solving--examples including Kyle Pearce & Jon Orr and Dan Meyer.

Realistically, it’s tough work to practise a Thinking Classroom model on a consistent basis, but it’s very gratifying and rewarding for both teachers and their students to see and hear themselves growing in autonomy and experiencing success. It has been and continues to be for me.

And I’m still learning! So if you’re starting out, don’t feel like you have to include all the elements of the Thinking Classroom right away. Dr. Liljedahl suggests you start with the top gear (visual included, above), and master that before you move on to the next. It happens in stages: not all right away. Start with something that you find manageable and continuously reflect and challenge you and your students to go deeper. Do some of your planning, teaching and reflecting with someone you trust. For feedback, also have them help you with how you’re going to challenge yourself in going for next steps.
4-Final Remarks
Successful Classroom StrategiesAchieving Excellence in Applied Courses (AEAC, 2017/18)
As this post draws to a close, I am certain of the following: my experience in teaching and learning has been enriched due to the collaboration that was experienced in seeing this post through from start to finish. 

As you reflect upon the final question, below, I would like to encourage you to think about inviting others to share in your experience--e.g., co-planning, co-teaching, debriefing and reflecting towards next steps with Thinking Classrooms and spiralling your curriculum.

Evidence reported from a large number of districts' administrators, across Ontario, is showing that successful classroom strategies for improving student performance in Applied-level Mathematics courses includes co-planning and co-teaching, as well as spiralling and classrooms that include the use of vertical spaces (AEAC, 2017/18; see graphic, right).

Might you consider incorporating a Thinking Classroom into your pedagogical practice?
In closing, I can't help but to think of the conversations that can be inspired when we take collective action to improving student learning. As this blog is a means for readers to network and gradually change the context for how they teach and learn, we all benefit by drawing nearer to the perspectives shared here and shared beyond with our professional learning networks.
​
I am more than happy to collaborate with you and make our learning visible, here, in this blog and across Flipping the Focus' social media platforms, as well as your own. I
f at any time, you have questions or comments, please feel free to reach out to me at Flipping the Focus. 

Sincerely,

Chris Stewart, OCT
Education Leader at Flipping the Focus
CONTACT
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5-References
AEAC Project Team, Ontario Ministry of Education, Student Achievement Division. (2019). Achieving Excellence in Applied Courses: Dialogue with Principals, School Teams and Board Leads (Rep.).

Liljedahl, P. (2017, October 17). Building a Thinking Classroom in Math. Retrieved fromhttps://www.edutopia.org/article/building-thinking-classroom-math

Liljedahl, P. (2016). Flow: A Framework for Discussing Teaching. Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 203-210). Retrieved from http://www.peterliljedahl.com/wp-content/uploads/PME-2016-Flow-and-Teaching-1.pdf


Thinking Classrooms: An Interview with Jaime DePippo [Online Interview]. (2019, January 23).

Thinking Classrooms: An Interview with Jaime DePippo - Part 2 [Online Interview]. (2019, February 18).
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creating conditions for occasioning thinking & Supporting student well-being in mathematics classrooms

3/2/2018

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Welcome back to Flipping the Focus.

In the last post, a detailed look was taken at one means through which school improvement teams could enact their 'How.' For your consideration, a developing series of tools & resources (i.e., for additional learning) have been posted here.

Recently, as set in the context of supporting student and professional learning, a colleague and I were considering strategies to getting to the 'What' of school improvement in a Grade 9 Mathematics class. For contextual purposes, this time of year in Ontario marks the beginning of semester 2 courses, leading up to Spring Break: the perfect time to looking upon students' past learning experiences and contemplating how to increase student engagement moving forward.

As per their school's goal in Mathematics, the importance of students improving their confidence in self-assessment (i.e., in relation to success criteria) had been identified. With this in mind, we set our minds to contemplating the collaborative inquiry we might engage in to helping students come to the knowledge that 'they can?' 

"Yes, I Can!"
A recent publication, "Yes, I Can!," published by the Ontario Ministry of Education (pdf, below) portrays the multi-faceted nature of approaching such problems of practice (i.e., identifying the components necessary to building student well-being through mathematics).

On page 6, one of the key learnings of a five-year inquiry in the Province of Ontario is that
"[s]tudent self-assessment is linked to student well-being." 
​

We know that students require mathematical experiences where they are engaging in uncovering and authoring criteria necessary for understanding and solving problems. And by interacting with descriptive feedback, relating and acting out upon feedback in relation to criteria for success, students become more adept at self-assessment--i.e., knowing what 'good' looks like and when it is achieved.

​It follows that the more experience a student has in developing confidence in their self-assessments, the more capable they become in setting goals for their learning and monitoring achievement of these goals.
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Ontario's Vision for the Mathematics Learner
Picture
The Pedagogical System for the Teaching & Learning of Mathematics
pedagogical_system_for_reflective_practice.pdf
File Size: 449 kb
File Type: pdf
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Returning to the previous statement concerning the correlation between student self-assessment and well-being, "...students [come] to see themselves as successful mathematics students, particularly when they [have] problems that they [are] allowed to approach in many different ways" (Yes, I can!, p7).

Monograph: Yes, I can! Paying Attention to Well-Being in the Mathematics Classroom
yes-i-can.pdf
File Size: 2377 kb
File Type: pdf
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Connections to Well-Being

Returning to the professional discussions with my colleague (i.e., How might we help students come to the knowledge that 'they can?'), it became clear, in part, that we need to use
 problems where students are allowed to approach solutions in many different ways.

Other considerations for creating a space more conducive for students to build their self-confidence are described below.
Picture
Making the Mathematics Well-Being Connection (Yes, I Can!, 2018)

Thinking Classrooms
Recently, a framework for enacting pedagogical practices that can engage both teachers and their students in occasioning worthwhile tasks, developing responsive classroom environments, culturing classroom discourse, and use of tools and representations for thinking is that of "Thinking Classrooms" (see Dr. Peter Liljedahl's summary on Edutopia and 2017 OAME Leadership Conference keynote for background).

This framework presents an interesting opportunity to engage the four, pedagogical practices above, as well as enacting the recommendations made by researchers (i.e., those identified (above) for building student well-being, thus bringing the vision of the mathematics learner to light--for both student and teacher.

With current research recommendations, our professional practice, a keen desire to know and support our learners, and a school-level inquiry into the impact of students' self-confidence upon their achievement in mathematics, we had much to go on in setting directions with students to teaching and learning in ways that might better serve both teachers and students.

Picture
Pedagogical practices present in Thinking Classrooms

Getting Started with a Thinking Classroom in MFM 1P: Observations & Reflections
In this section, you'll notice that our observations, reflections, and considerations for developmental next steps have been provided (pdf, below). Further along, a slideshow has been built in (ppt included for download) to provide further context as to how we went about conducting our lessons for the first, two days of our journey into a #thinkingclassroom. 

The lesson elements, observations, reflection and developmental next steps (i.e., for students and ourselves) are also linked to both the four domains of the pedagogical system and where these elements might also occur in a lesson using guided inquiry (stages of Before, During, After) through the 5 Practices for Orchestrating Productive Mathematics Discussions. 

File: Our Observations & Reflections from Days 1 & 2
journeying_into_introducing_vnps___vrg_in_gr_9_applied_math_days_1___2.pdf
File Size: 771 kb
File Type: pdf
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Slideshow: Making Space for You & Your Peers to Think Mathematically
File: Sample PPT Lesson
collaborative_problem_solving_in_mathematics_thinking_classrooms_an_introduction.pptx
File Size: 31340 kb
File Type: pptx
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Some Final Thoughts
In reflection, the experience for both teachers and students over these two days lead to considering what is possible when we work collaboratively to culture #thinkingclassroom environments that engage the four domains of the pedagogical system.

As co-teachers, we did just that: planned and taught together. We experienced an excellent 'back-and-forth:' What was invisible to one of us was made visible by the other. When we made 'moves,' we not only explained them to one another, but we modeled this for students and explained why we were making them. We openly shared our reflections and invited input from students about process and what we might consider doing differently. We were empowered by students to facilitate their learning because we had access to their ongoing and developing thinking...we were (all of us) engaged in assessment for learning.

For students, we (in a short time), engaged them in considering learning through a non-traditional manner (e.g., rich/open problems, collaborative work with #vnps, and making visible & discussing their thinking to uncovering what was important...meaningful). And most significantly, we noted how quickly their knowledge was mobilized, noticed and referenced by others using this type of classroom setting.

As per classroom discourse, this is an area of great interest and development for us.

What value do we see in/place on it?
What value do students assign to it?
Altogether, if we value it, how will we co-construct and enact principles for occasioning it?


In short, teachers and administrators recognize that for many classroom types to thrive (e.g., #thinkingclassroom, #flipclass, #blendedlearning), both teachers and students need to engage in making and discussing their thinking in a visible manner; that is, we need to respectfully occasion and remain within spaces of argumentation where we are productively reasoning and proving one another's conjectures to derive a deepened sense of mathematical understanding and ability to solve problems--supporting both the individual and the group. In these 'spaces,' we have the potential to gain traction in creating and sustaining vibrant, mathematical communities. 

And in relation to this class, our collaboration, and this school's improvement processes--where students see themselves as assessment-capable and confident learners--we are laying the groundwork for supporting students' well-being. Through these types of experiences, students can come to the understanding that 'they can' and that 'we can', too.
​

Some Questions for Your Reflection

-How have you helped/are helping students occasion thinking in mathematics such that they come to know that 'they can'?

-How have you worked/are working with school teams to create/creating an understanding that 'we can'? How are you taking action on this understanding?

-What elements of the #thinkingclassroom (or other classroom) are you and your students working on? What has been the impact upon student learning and your 'moves' as an educator?

-What are you wondering about student-centered approaches to teaching and learning? Student-centered leadership?


In closing, I hope that you have not only found this post informative but supportive towards how you can better address your face-to-face time with students, colleagues, and/or network partners, as you engage in exploring your professional and school improvement practices that can be potential 'game-changers' for student achievement, equity and well-being.

Be sure to check the blog and/or website, periodically, for updates regarding a depository of  several tools & resources to help you in your teaching and/or instructional leadership journeys. 

​

​Professionally Yours,

Chris Stewart, OCT
Learning Partner, Upper Canada District School Board
Founder & Educational Consultant, Flipping the Focus
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    I am passionate about leadership for learning and teaching and learning through inquiry. Through collaborative exploration of high-yield, pedagogical strategies, I have been able to further engage students to deepen their learning and fellow educators in continuously growing their practice--Flipped Learning, Thinking Classrooms, and culturing Student Voice as examples.  I hope that this site serves you well in your educational journey through teaching and learning by moving professional learning into your time ... your space. If you have questions or feedback, please feel free to contact me. Sincerely, Chris Stewart (OCT).

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