Reflecting upon this experience of leading a formative task, I learned much about my students and myself. Firstly, I found that I, perhaps unconsciously, have lowered my expectations of my students’ ability to work on and make meaning of problems independently. The math block in my classroom is often teacher-directed, with little room for my students to use or develop their mathematical thinking (Hiebert et al., 1997, p. 8). However, through this experience of leading a formative task, I learned that my students were capable of and eager to work independently on math problems. During independent practice, I watched as my students discussed the problem, chatter and noise becoming ever present in the room. Yet, although I planned for such an environment, as I listened to this chatter and noise, I also became aware of my uncomfortability with giving up control and allowing my students to messily and collaboratively work. Likewise, I realized I still have deep-seated biases about mathematics from my more traditional education. As discussed earlier, I still privilege the answer over the strategies or processes used to reach the answer. Because of my hyper-focus on the answer, I felt overwhelmed with giving my students agency to use their sense-making as they continually made mistakes. I believed I was not a productive or good teacher because I allowed my students to make these mistakes and struggle (Boaler, 2015, p. 8). I wanted to alleviate these feelings by directly instructing my students and again becoming the authority of correctness. While I should not allow my students to continue with misconceptions without redirection, my attempt at reasserting myself undermined their chances to have first-hand experience with the concepts and actively understand mathematics more deeply through critical exploration and experimentation.
In this vein, turning from what I learned about my students’ mathematical thinking and myself as a teacher, I now want to think about my lingering questions and the next steps I can take to improve my facilitation of formative tasks. The major question that lingers is, having expanded my knowledge about mathematics from this course, how can I use this knowledge to process my own biases and actively and consistently enact these strategies in my classroom? Are there any concrete steps that can help me along this process? Further, paralleling this reflection of my biases toward mathematics, I also want to bulwark and solidify this work by making agentive and active changes in my practices in the classroom. I wish to actively work to create a classroom environment where my students and their productive struggle drive math lessons. For the next semester, beginning with small steps toward creating this environment, I want to work more on utilizing and normalizing “talk moves” in my class to lead to greater class discussion. Specifically, starting with one talk move and moving toward implementing them all, I want to work more on having my students discuss each other’s ideas by asking whether they agree or disagree with a peer’s comment (Chapin et al., 2003, p. 14). First, I will need to establish clear norms and expectations to ensure that these discussions are respectful and productive. Then, I can use such a strategy to move toward my students driving their understanding of the problem and clarifying any misconceptions they may have. From this initial step, I can work incrementally and slowly toward incorporating all the talk moves to truly enact the goal of creating a more accessible and equitable mathematical environment where all my students ways of expression and knowledge are validated.
