Final Reflections

 So much to say. To start, I note a few ideas and views I now hold strongly which were (at least partly) birthed in this course.

The Garden as a teacher

Thank you Susan for insisting that we learn from an energy / spirt / place that is as wise as this garden. The time we spent here taught me perception, delicacy, and so much more. I plan to continue learning from the land and I hope that I am able to offer my students the same opportunity.

Cities as producers, not (only) consumers

Recently, this idea has been presented to me in many ways. In this course the various weavings we created, as well as the food we enjoyed from the garden were radiant reminders of the gifts hiding right under our nose.  

Alternate ways of knowing

Recalling our conversation relating to Western Binaries, I was again struck by this phrase we hear so often, ‘alternate ways of knowing’. Earlier in the semester, I believed that alternate ways of knowing constituted as understanding the world with different binaries. However, other classes and books now lead me elsewhere. I believe that these binaries exist (and may be even necessary) for our world and psyche – however, it is working towards some sort of paradoxical, sublime ‘third’ option - a synthesis of binaries - which will ultimately constitute as new (old?) ways of knowing.

I’m also extremely grateful this course offered me the opportunity to explore topics of my own interest as a teacher, namely collaboration. I adamantly do not want to be a tyrant in my classroom – I want students to learn from each other and to see me as a facilitator. In this role, I am able to create a safe space for students to explore autonomously. As I move forward in my teaching journey, I hope to find many ways to enable students without insisting on a particular direction (or destination). Currently, I hope to explore potential connections between the culture and norms of drum circles to inform new teaching strategies that serve to cultivate a community of learners.  

I recently visited my sit spot again. The garden has transformed in the recent months – far fewer colors and leaves; a decay which reveals the underlying structure of the place. In my sit spot, I admired the three tree, the hyperbolic gates, and many plants which seem to not notice the cold. As much as death pervades this place, life seeps through the cracks.

I was again moved by the chute I placed; the orange ribbon in sharp contrast to the duller pallet of winter. As I approached the ribbon I saw that strong winds had caused it to fray, tangling some loose threads around a nearby plant. Initially I felt guilty – had I placed the ribbon in an irresponsible way? However, after further inspection, I realized that very little damage had been done. It was in a way beautiful – the ribbon integrating, weaving, winding its way with the land. Neither the plant or ribbon seemed to be in distress, so I took no action other than to reflect. The child of this chute feels like an elder to me – although it is embarrassing to need such a glaring reminder of on whose land I teach, I am grateful for this aid.

Finally, as with most memorable experiences, it is the people who burn brightly in my memory. The math cohort is undoubtably the most passionate group of learners I’ve ever been a part of. The friends I’ve made in this course (and others) are of the highest quality.

It is difficult to hold this much gratitude! Thank you, all that has shaped and been shaped these past months.

Presentation Reflection & Future Speculation

Today’s presentation was fine, though I’m a little sad I wasn’t able to incorporate my activity. This seems to be a common theme of mine – too much information, not enough interaction. Very ironic given the content I presented today… This is something I need to work on in an academic context. Thankfully, I feel I’ve been able to able to be relatively succinct when teaching in high schools.

I found this presentation was chiefly an exercise for my benefit. Although I designed my slide-show to be a resource for others, the creation of this resource was a critical step in helping me understand what has led to my current understanding of collaboration. This understanding will continue to evolve as I continue my research, however I’m particularly interested to see how my views shift as I implement ‘Building Thinking Classrooms’ during my long practicum. The opportunities to facilitate collaboration are abundant and I anticipate many unforeseeable problems. I am so grateful that my school advisor has given me freedom to explore this pedagogy.  

I’d like to touch on my intentions for further research. Recent reflections have led me to believe that my interests would align most strongly with an exploration of the role collaboration plays in community building. There are many ways to target this question – How is collaboration related to community building? Can we characterize different communities by their style of collaboration? What type of community do I hope cultivate in a math classroom? How can teachers use collaboration to cultivate a community of inquiry?

Lastly, a paper I recently wrote for EPSE 308 explored some parallels I’ve noticed between my utopic vision for collaborative classrooms and the community culture of 3^rd beach drum-circles. I am curious to see if this particular line of thought will yield any fruit. I’ve been able to leverage curiosity and intuition thus far in my teaching journey – given that drum circles have been a source of immense creativity and intuition for me, I’m optimistic that many strategies which enable success in drum-circles will have meaningful counter-parts in the context of collaborative learning. Excited for future reading!

Collaboration Slide Deck

Some good resources which specifically target the question: 

What is the role of a teacher in a collaborative classroom?

https://docs.google.com/presentation/d/1tt4AEcPq2W34VpOXSiPHxxcNkFSVhZso/edit?usp=sharing&ouid=113246720186703432874&rtpof=true&sd=true

Inquiry Update

 Over the course of the semester, I struggled to find an explicit question for my inquiry. Initially, I was inspired to explore the effects of competition in the classroom; the effect it has on students, as well as how it is implicitly incorporated in modern pedagogy. In my initial literature, I found excessive evidence pointing to the negative qualities of competition on learning; this is not to say it does not have a place, however it was clear that I would not need to dig deep to demonstrate negative qualities.

Hoping to explore anti-competitive classroom cultures, I opted to focus my attention on collaboration. There was a tremendous amount of literature from the 80s and 90s suggesting the benefits of collaboration, however much of it was theoretical and did not offer practical suggestions. The main exception to this was a beautiful book titled ‘Collaboration in Mathematics Classrooms’ (1990), which compiled essays from various teachers explaining how they organize their class to emphasis collaborative activities. This book offers many useful strategies, however there is minimal consideration of the teacher’s role beyond facilitator / organizer of the class. Reading this book, I realized what I was searching for: research explaining how teachers might encourage a collaborative culture in their classroom.

My next deep dive into the literature was successful: I found two papers which extensively detail the ways teachers build a collaborative classroom culture. The first paper is an extensive study of a senior teacher leading an ‘average’ class of Math 8s using a whole-class, inquiry-based pedagogy. The paper details many explicit strategies used by the teacher to facilitate this classroom, as well as how the teacher ‘taught’ the class to adopt more collaborative attitudes. The second paper is a general review of how collaborative learning is implemented in the classroom; it specifically considers how to improve the quality of student interactions. The development of ‘Common Ground’ is a notable theme common to both papers.

These lengthy papers were dense with strategy – there are a few other papers I hope to review before presentations, however I feel summarizing & connecting the two I’ve mentioned will be immensely valuable for anyone hoping to facilitate a collaborative classroom. I also plan preface this conversation with my earlier research by discussing questions such as: ‘What is collaboration?’, ‘What are the benefits?’ and ‘When does it work?’.

Annotated Bibliography

1.       Schleifer, M., Daniel, M. F., Pallascio, R., & Lafortune, L. (1999). Concepts of cooperation in the classroom. Philosophical Inquiry in Education, 12(2), 45-56.

This paper provides some useful language for how we might think about collaboration as a form of cooperation. Considers what is required for collaboration to have a positive impact in learning.

2.       Davidson, N. (1990). Cooperative learning in mathematics: A handbook for teachers.

This book provides a survey of various collaboration techniques being used at the time (1990). Includes explicit strategies and offers solutions to common problems

3.       Samuel J. Milner, Carolina Azul Deque, Susan Gerofsky. (2019) Dancing Euclidean Proofs: Experiments and Observations in Embodied Mathematics Learning and Choreography. Bridges 2019 Conference Proceedings

 

This piece shows an example of a highly collaborative math activity which serves to deepen the participant's understanding of math in a land-based pedagogy

 

4.       Staples, M. (2007). Supporting Whole-class Collaborative Inquiry in a Secondary Mathematics Classroom. Cognition and Instruction, 25(2–3), 161–217.

This is a detailed study of an experienced teacher leading a (mathematically) ‘weaker’ class through whole-class collaborative inquiry. The author identified 3 critical roles that the teacher plays and identified many explicit strategies used to achieve these ends. The author also discusses the classes development as a collaborative whole over the course of the semester.

5.       Manfre, J. (2021, April 13). Using student-led collaborative learning to empower math students. Edutopia. https://www.edutopia.org/article/using-student-led-collaborative-learning-empower-math-students/

This article highlights how the use of a scribe for small group problem solving gets students talking to each other and engaged in the problem solving.

6.       Kuhn, D. (2015). Thinking Together and Alone. Educational Researcher, 44(1), 46–53.

This paper considers what factors influence whether or not collaboration is likely to be fruitful (from the POV of cognitive competence). Suggests the value of argumentative discourse. Collaboration as a skill to be developed in and of itself

7.       Phelps, E., & Damon, W. (1989). Problem solving with equals: Peer collaboration as a context for learning mathematics and spatial concepts. Journal of Educational Psychology, 81(4), 639.

Study demonstrating the benefits of peer collaboration in 4^th graders. In particular, this article aims to determine if students of equal ability can make mathematical progress with minimal adult assistance.

8.       Liljedahl, P. (2021). Building thinking classrooms in mathematics, grade K-12: 14 teaching practices for enhancing learning. Sage Publications Inc.

A particularly influential text which emphasises the value and effectiveness of collaborative board work as the primary way of exposing students to a new topic. Strategies are supported with extensive empirical evidence.

9.       Kaendler, C., Wiedmann, M., Rummel, N., & Spada, H. (2015). Teacher Competencies for the Implementation of Collaborative Learning in the Classroom: a Framework and Research Review. Educational Psychology Review, 27, 505-536. 

Identifies the importance of teacher as a facilitator in collaborative classrooms. Identifies 5 critical roles / skills for teachers facilitating a collaborative classroom: Planning, monitoring, supporting, consolidating, and reflecting.

Exit Slip - Nov 14th

 Generally, I haven’t been exposed to many academics that focus their efforts in highly creative spaces. As such, it was fascinating to hear Kathryn speak about how they have continued to innovate in creative spaces throughout their life. I was particularly interested I how Kathryn spoke about energy and being a ‘conduit’. Often, I hear creative people speak about ‘giving or sharing their energy’ – this was not the language Kathryn used. Rather, they spoke of drawing inspiration from objects, stories, and archetypes. For Kathryn, I understood their creative process as a channeling of energy, rather than a giving or sharing of energy. This is an important distinction! It speaks to the unpredictability that characterizes Kathryn’s work. It also gives me comfort, as a creative person, that I need not feel responsible for ‘deciding’ what to create. Rather, the creative process is one in which you allow your body and skills to act in accordance with something else (a story, an archetype, a letter, etc.).

 I was deeply impressed by the ingenuity my peers demonstrated in tying Kathryn’s highly suggestive objects to math, however there are two I want to highlight. The first was how Teij (and others - I forgot who was also in this group) suggested using story to teach equations of lines. I realized that when we are teaching students about relationships, lines and equations are simply tools to abstract and distil much more potent ideas. By associating subjective qualities (such as happiness and fantasy) with each axis, we can more intuitively what we try to represent with lines. For example, I feel stories have the potential to clearly show students the meaning of vertical or horizontal lines – namely, it is the change in 1 quality while keeping another constant.

The second idea I want to highlight was presented by Madison. She suggests that as an exit slip, we use colored popsicle sticks to quickly and intuitively assess the student’s engagement and overall satisfaction. There are many ways to execute this, but generally I am drawn to this idea of leveraging the relative ambiguity of color to get a sense of the student experience. A few prospective prompts may be: “How was your experience today?”, “Are you excited to continue learning about this topic?”, and “Do you feel you ‘got’ what was being taught?”. I’m sure there will be many unpredictable nuances to consider if / when I try this in a classroom, but regardless I am excited to apply color in my approach to exit slips.

Entrance Slip - Nov 14th

 Could have sworn I posted this Wednesday night.... Better late than never. 

I chose to read Kathryn Rickett’s piece: “Bitter Toughness Meets Fierce Love: Narratives Unwrapped from Teen Mothers’ High School Experiences”.  

I was struck by Kathryn’s description of unexpectedly becoming the subject of (re)search in this project. As teachers, modern pedagogies place teachers as both the source and transmitter of knowledge – there are few teachers who meaningfully see their students as sources for knowledge, or that they (the teacher) will have opportunities to learn during class. In this piece, Kathryn quickly realizes that not only is this possible, but it is necessary for her to connect with the mothers participating in her project. Additionally, the unique needs and confidence of the participating mothers meant that the way forward would not follow any sort of prescribed schedule. By acknowledging the role that these mothers place in their own learning, the burden of ‘teacher’ was shared by all in flexible, intuitive ways. This defies traditional (colonial) ways of knowing and interacting with experience/knowledge. With an understanding that all research is subjective, we embrace and embody our work so as to shed ourselves of expectations.

It also strikes me how desirable the culture Kathryn helped cultivate sounds for any student, not just those who are steeped in the responsibility of caring for another person. When teachers/facilitators wonder: “What are [my students] stories?”, a dialogue can begin that is devoid of expectation. If teachers really mean this question, we won’t be asking it with the intention of leveraging the student’s story to suite our own vision of their learning. Rather, it offers us a way to ‘meet the student where they are’. It is the first step towards understanding and meeting a student’s unique needs.

I’m very interested to hear how Kathryn describes the role of teachers in classrooms with cultures such as this.