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.

Exit Slip - Nov 7th

 When I began to research my inquiry project I expected that, given the presence of competition in our secondary schools, the literature would generally favor the use of competition. It took very little time to realize that much of the literature did NOT advocate for the use of competition; the common critique was ‘Why would we deliberately set up a system in which the failure of the majority is required for the success of a minority?’. In the context of learning, this makes no sense. So, although I had intended to explore competition and its consequences before researching solutions and/or alternatives, I felt it would be more meaningful if I explored non-competitive alternatives. As such, I came to class today with the idea of exploring the benefits collaboration and cooperation.

During our in-class discussion, there were many interesting tangents after I presented my idea. This made me realize that although I was viewing collaboration as a solution to be explored, it is still a massive topic which needed to be narrowed. Leaving our conversation, I settled on exploring how we can incorporate collaboration and cooperation in mathematic classrooms.

Of particular interest during our discussion was Susan’s story. She describes how she was able to leverage technology to efficiently solve a problem individually that was otherwise being solved inefficiently as a group. From this, we saw technology enabling an individual to do something that would have otherwise REQUIRED collaboration. Interestingly, although Susan’s solution reduced the work of many people, she described a small amount of resentment from those she helped. She speculates that this is because she removed these people’s opportunity to cooperate, unselfishly, in a meaningful way.

There are two extremely interesting lessons which I took from this story. The first is the story’s allusion to the value of collaboration for the sake of collaboration. Secondly, it directly demonstrates that, although technology often allows us to work more efficiently, it often reduces the need for collaboration. If there really is intrinsic value to collaboration, this is something we must take very seriously, particularly given that the advantages of AI will only serve to exaggerate this phenomenon.

In the context of my inquiry project, I now pose a new question: Can we encourage collaboration by restricting availability to technology? If yes, how?