El Rol e Impacto de los Depredadores

The dialogue around interim research texts can lead the inquirer back for more intensive work with the participants if more field texts are needed to be able to compose research texts that researcher and participants see as authentic and compelling (Clandinin, 2013, p. 47).

How we interpret and are interpreted by others will shape the stories we tell about them. Over the course of the semester, as we developed relationships with the students and discussed those experiences with one another in the research group, we started to label students with characteristics. Early on, we identified that Micah is often skeptic, and so stories featuring him being skeptical got told and written about more often in our weekly field texts. We created, in our discussions and in our texts, a skeptical character whom we called Micah.

As we got to know individual students better and better, we became curious to know more about how they perceive the course and their own behaviour. What do they think the

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aims are? What do they remember from class as important moments? What do they believe it means to think mathematically?

The research group discussed these questions during one of our meetings and decided that we needed to have students contribute to our growing volume of field text. There were two times where we had students engage in composing field texts: once as a reflection assignment within the course (all students were expected to participate), and a second time through an interview (only some students were selected to participate). The reflection assignment was given in the 8th _{week of the course, and the interviews were conducted}

during the last week of the course.

(1) Reflection Assignment

With the goal of getting a better sense of how students experience their own mathematics and mathematical behaviour, we gave the following five questions as one of their weekly assignments:

1. What is mathematics (in your opinion)? What is a mathematician?

2. What are your strengths and weaknesses when it comes to mathematics? Which aspects of doing math do you enjoy/dislike?

3. Think of the other students in your group/class. Which ones do you think are strong (or weak) in doing math and why?

4. What is the purpose of this course? What do you feel you are supposed to be learning? What are you actually learning?

5. What parts of this course (class discussions, forum, assignments, and quizzes) do you find the most helpful/interesting/challenging/boring? Why?

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Only a few students did not complete the assignment, but it was very interesting to read the responses of those students who took the time to answer thoughtfully. In the final drafting of my research texts, I did not make much use of the responses we gathered. Mostly this exercise served to help us understand the students’ perspectives a bit better and to identify which students were more able to reflect on their own mathematical behaviour and might be willing to engage in further conversations about it. When it came time to select students for the interviews, we considered, among other factors, those whose answers to the reflection assignment had been most interesting to us.

(2) Student Interviews

As the semester drew to a close, I was envisioning the final research product of this thesis as a set of short stories (vignettes) organized around the different mathematical behaviours in the model. My goal was to be able to illustrate the different behaviours through these brief accounts of students in the class. I had a vision of creating a set of fictional characters based on some of the students in the class, with each character representing and acting out one of the behaviours in the model. However, I felt I needed more details about the individual students in order to be able to create rich characters.

Working with Nadia and Genevieve, we chose 10 students from the class to interview. We chose students who we felt had shown evidence of the different behaviours over the course of the semester. Each student had displayed some combination of the different behaviours in the model, and together the ten chosen for interviewing covered all the aspects I planned to write about in my final research texts. Because we felt it would make for more interesting

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and revealing interviews, our choice was also based on which students I felt I had developed the best rapport with over the course of the semester.

I prepared for the interviews by re-reading all of the narratives that Nadia, Genevieve and I had written over the course of the semester. For each student I was planning to interview, I would re-read every storied account that we had written about them, as well as their responses to the reflection assignment (see above). After getting a good sense of what a student’s experience/trajectory through the course had been, I composed a short character sketch. I tried to create a short synopsis of their time in the class based on what I had come to know about them through both their work and my experiences working on and discussing mathematical problems with them.

These documents were interim research texts; drawing meaning and detail from the field texts we had written, I wrote storied accounts of particular students, told entirely from my perceptions. Because the field texts and these interim texts I had written arose “from the relational experience that is co-constructed between researcher and participants, they must return to that experience for validation” (Clandinin & Murphy, 2009, pg. 600). Thus, the goal of the interview was to have conversations with the students about their experiences in the classroom and to share with them parts of the character sketches I had written. Together we would re-tell these stories and co-compose new field texts.

Interviews were conducted in an unused office in the mathematics department, were audio recorded, and each lasted between 1 and 1.5 hours. Although I had a set of questions prepared for each interview, I allowed the conversation to be flexible, and tried to let students tell their own stories in their own words as much as possible. In some cases,

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students were particularly engaged in discussing previous math courses, or their family history, and so we would talk about that. In one case a student wanted to discuss a proof he had written for a problem we had been working on together in class.

For the most part, the things students told me about themselves resonated with the perception I had of them, with the notable exception of Micah. We discussed what they enjoyed or disliked about learning math in general and about the way they were learning in MAST 217 in particular. In all cases, I gained a better understanding of who each student was as a person, their character traits, and how their previous experiences may have shaped their experiences in our course.

In the week after completing all 10 interviews, I listened to the recordings and made a set of notes (field texts) about the experience. For each student I interviewed, I wrote a brief account of my own experience/impressions of the interview, and then made note of all the information/details I had learned about each person. Wherever possible, I tried to connect what they had said to some aspects of the mathematical behaviour model I had constructed (chapter 4). I grouped the different discussion points together according to categories of the model, and included my own reflections and commentary about the discussion.

These reflections were more interim research texts, and although at the time I was still not certain how they would be incorporated into the final research texts, it was helpful to be able to create a richer picture of these individual students, of their past present and possible future selves. Experiences are the stories people live, and in a narrative inquiry, the researcher seeks to understand and give meaning to experiences by taking into account all of the different stories a person is living. The interviews and the reflections I wrote about

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them were essential to understanding more about each individual student, and were the last interim research texts I wrote before moving towards final research texts.