A Teacher and a Mathematician
MTCs have enormous potential to affect “the identity element” — teachers’ beliefs about themselves and about mathematics.
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A Math Teachers’ Circle immersion workshop is an intensive experience focused on mathematics and creating community. Recommended as the first “big event” for a new Math Teachers’ Circle, an immersion workshop has enormous potential to affect teachers’ beliefs about themselves, their mathematics abilities, and the nature of mathematics—or their mathematics identity. The MTC immersion experience puts teachers in the sometimes uncertain and uncomfortable role of mathematics learner. The experience of working through this discomfort can have a profound effect on teachers’ identities, which underlies their mathematics teaching actions.
Anderson (2007) defines identity as “the way we define ourselves and how others define us” (p. 8). Mathematics identity, then, can be thought of as how people see themselves as mathematically capable (Martin, 2000). It may include elements of productive disposition (National Research Council, 2001), beliefs about mathematics, and self-efficacy or self-concept beliefs. In the case of MTC participation, it is also important to consider the unique role of collaboration and community-building. Normative identity, or the set of desirable practices for members of a group, interacts with personal identity, the way that individuals identify with, comply with, or resist the normative identity (Cobb, Gresalfi, & Hodge, 2009). Each MTC site creates a normative identity, and participants’ personal identities reflect their engagement with or acceptance of those practices.
Why should we, MTC leaders, care about identity? Teachers hold multiple interacting identities. Their mathematics identities are closely tied to their mathematics teaching identities; that is, their mathematics experiences affect how they teach, and vice versa (Hendrickson, 2016). Teachers’ identities are strongly influenced by their past experiences doing and learning mathematics. Math Teachers’ Circle can provide a positive, productive, challenging experience in doing mathematics.
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In summer 2016, I studied teacher identity with the help of MTC leaders and participants across the country. Participants answered surveys, completed written reflections, and participated in interviews, as I attempted to explore and understand shifts in the teachers’ identities after participating in a weeklong immersion for the first time.
Many of the teachers in this study began the week feeling nervous about their abilities compared to others in the MTC. They felt frustrated or uncertain when they first encountered open-ended problems—but by focusing on the problem-solving process rather than on the solution, exploring multiple solution paths, and using their strengths to approach problems, the teachers began to experience success. Improved confidence around mathematical problem solving stimulated perseverance and persistence with future problems. As one respondent put it, “When I was able to actually solve some of the problems, I was like, ‘Oh, hey. This isn’t so bad.’ It helped boost confidence in regards to the ability to be a problem solver.”
Collaboration was essential to the process, not only because it contributed to successful problem solving, but also because the discussions helped the teachers understand that their peers had similar anxieties about problem solving. “By the end of the week, my sense of math security had greatly improved,” said one teacher.
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The following recommendations for MTC leaders, based on my research, can help teachers to develop positive and productive mathematics identity:
“It helped me to see myself as a mathematician.”
Identity is an important outcome of the MTC. To ultimately affect teachers’ classroom practice, it is important to consider the effects of the MTC experience on teachers’ identities. Identity is complex and deeply held, and influences beliefs and actions in the classroom. Math Teachers’ Circle can influence how teachers see themselves as doers and teachers of mathematics. MTC leaders should consider the evolution of identity through such experiences, and carefully work to create a community of practice (Cobb et al., 2009). The goal of such a community is for teachers to see themselves as members of the group and to develop their personal identity in relation to the normative identity of the group.
“As the week progressed, I realized that everyone felt that same way at one time or another.”
The immersion experience is key. A weeklong MTC workshop immerses teachers in problem solving and allows them to experience both success and failure. Teachers who are nervous or anxious during the first few days begin to feel more confident taking problem-solving risks later in the week. Professional development that takes place over a single session or a single day does not allow enough time for teachers to fully engage in the activities and begin to internalize the teaching methods. It takes time to develop the MTC community and establish the normative identity of the group (Cobb et al., 2009).
“It’s easy to fall back into old ways.”
Provide follow-up sessions. The teachers in this study had already begun to experience significant shifts in their mathematics identities by the end of the immersion workshop. They intended to use MTC problems and pedagogies in their classrooms, but anticipated challenges when the normative identity of their schools differed from the normative identity of the MTC. Regular follow-up MTC sessions can give teachers opportunities to continue to rethink their ideas of effective problems and pedagogy, and to ask questions about implementing these ideas in their classes.
“I’m trying to become more student-led. And I need help.”
Consider having pedagogical conversations. Teachers’ mathematics identities and teaching identities are intertwined and it is important for professional development to consider both. When leading an MTC, it is easy to focus on the mathematics content to the detriment of problem-solving pedagogy. To assist teachers in using new pedagogical strategies in their classrooms, sessions should focus explicitly on transferring ideas from the MTC to the classroom. The teachers in this study learned from both content-focused activities and pedagogy-focused activities. However, the teachers who were the most confident and specific about changes they planned to make in their classroom were most likely to have attended MTCs with sessions devoted to making this transition.
“Having to do the math puts you in the role of student.”
Engage teachers as learners. In MTC, many teachers experience mathematics learning differently than they ever have in the past. The mathematics content and the pedagogy engages them as adults and allows them to experience perplexity, frustration, and success. Authentic engagement as a learner is important for teacher identity development (Cohen, 2010). Because their mathematics identities and teaching identities tended to be closely intertwined, the MTC helped them to build connections between mathematics problem solving and mathematics teaching.
“I took comfort in knowing that my peers all felt the same way.”
Teamwork makes the dream work! Collaborative groupings in the MTC are important for successful problem-solving experiences, developing perseverance, and modeling a successful pedagogical technique. Collaboration can also assist in the development of positive mathematics identities. The teachers in this study who worked with their peers began to realize that their fears and anxieties were not unique to them, and that getting stuck is a natural part of the problem-solving process. They also saw different ways of approaching the same problem, gave assistance, received assistance, and began to understand that everyone’s contributions—including their own—were valuable.
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Teachers’ reflections on their MTC experiences indicated the desire to help their students to develop positive mathematics identities through similar experiences. One teacher said, “I hope to give them maybe more challenging problems at a higher level than I maybe would have attempted previously, and I think they can do it with collaboration. I think that they would probably have the same experience I did, be apprehensive at first. If they stick with it and endure, and are successful, I think they can build a lot of confidence that way.”
The development of identity, and mathematics identity in particular, can be a critical outcome for teachers participating in MTCs. An intensive MTC immersion workshop is an opportunity for teachers to develop a productive and positive mathematics identity.
This article originally appeared in the Winter/Spring 2017 MTCircular.
|Katie A. Hendrickson works on state policy and advocacy for Code.org. She earned a doctorate in Mathematics Education in 2016 from Ohio University, where she co-founded the SouthEast Ohio MTC.|