Boaler - although Boaler did not define or really use the term identity much, I thought it was helpful to include comments on gender here. Instead of seeing gender as a property of an individual, as is usual, Boaler draws on contemporary queer theory to argue that gender is a response to a situation. We could say the same thing about identities in general. For example, in the Cobb/Hodge article, their definition of 'personal identity' seemed to be a response to a particular classroom context.
Nasir - draws on Wenger's work on identity in communities of practice. Some quotes:
- constructed by individuals as they actively participate in cultural activities” (p. 134)
- “a fluid construct, one that both shapes and is shaped by the social context” (p. 135)
- Nasir also says that identity does not fully belong to an individual, nor does it fully belong to the context. You can't think about identity apart from a cultural practice.
- Identity is developed through the processes of engagement, imagination, alignment (this is taken directly from Wenger's work)
Cobb/Hodge - draw on Gee's work to discuss Discourses and identities
- Normative identity: “as a doer of mathematics established in a particular classroom indicates the identity that students would have to develop in order to affiliate with mathematical activity as it is realized in that classroom” (p. 166)
- To analyse this, look at what are the routine obligations that are expected of students. Might see this more in the breaches.
- Core identity: drawing on the work of Gee. “students’ more enduring sense of who they are and who they want to become” (p. 167)
- Emphasizes student active role in constructing identity – through their own personal trajectory
- Personal identity: “who students are becoming in particular mathematics classrooms” (p. 168)
- How they have reconciled their core identities with the normative identities (e.g., how they feel about the obligations of the math class)
Thank you for getting us started, Indigo.
ReplyDeleteI don't know about everyone else but the readings have challenged my thinking this week. Your reference to 'queer theory' is completely new to me!
Boaler's definition of gender got me thinking all week because I am one of 'those people who believe that males and females have equal intellectual potential, and vary in the extent to which they conform to stereotypes and generally regard gender as a characteristic of the different sexes". I have never thought of gender as 'a response to a particular set of conditions".
Students have different responses, at different times. So, what types of conditions do we want to create in our classrooms? What is the learning environment that we want to create?
Thinking about gender, culture, and identity as co-construction has made learning (and teaching) mathematics complicated to me.
I wonder if all three readings are making a strong case for why we must teach 'reform mathematics' since the focus of such teaching is on mathematical discourse and reciprocal learning environments. Or is this an oversimplification of the issues?
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ReplyDeleteReflecting more thoughtfully about the word identity I often wonder as a woman if we can ever escape the preconceive notion of what women are 'better at'. It saddens me to think that in the 21st century, girls are still hearing that boys are good at math and girls at English. How can this thought/belief still permeate in today's society? I definitely cannot provide a good answer. I have worked in many math departments that had females outnumbering the men, and still girls would say to me that 'math is more for the boys', yet ironically science was an area for them! How do we change this around?
ReplyDeleteNasir's idea of identity seemed very logical to me with respect to the idea of cultural context. Mathematics would be more meaningful if it was presented in a context that had meaning for the student. In this case, stats was better understood and utilised because these boys want to improve their playing. They identified themselves as 'ballers', so the math they are recording was math that will help to solidify this identity, but more importantly provided them with the tools and evidence on how to improve upon this identity (and set goals). I guess the biggest challenge for me to ensure that this kind of cultural context occurs would be the actual math concepts that have to be taught. I have always loved teaching stats and probability because it was an area that more easily translated to 'real-life' situations that students understood with respect to their own lives - other topics, not as much. I believe that the next step in mathematical discourse now that we have begun to understand better the theory, is to find practical ways to help our students discover their identity, help them to set goals and provide a learning environment that ensures that both these areas grow as they do.
Looking at the readings from an "identity" perspective makes sense for me. I, sort of, get that "identity does not fully belong to an individual, nor does it fully belong to the context" and how "You can't think about identity apart from a cultural practice", but I am having a hard time getting past the idea of basketball as a cultural practice. Who's culture? and why specifically african american (black) kids as the example for basketball? maybe its an american thing, maybe its because its 3 a.m., but I am having a hard time getting past this stereotype. Could the example of basketball not be used as a culture in itself for all kids who engage in that 'culture' of basketball? When I look in my school yard and neighbouring ones I associate the ball playing with a culture of poverty.
ReplyDeleteOK, "identity is developed through the processes of engagement, imagination, alignment", but the identity that is developed with basketball (from what I see) is almost forced upon the students through a stereo type. The opportunities to engage in other sports or activities is not readily there and available to the students. Maybe I am going off on my own tangent here, but I could not get past this idea of using basketball to understand the way "African American" kids think about math. Students (in general) who play basketball, I would think, would use statistics in the same way or have the same connection to using it for measures that involved proportional relationships, averages percentages etc. and that relevance or relationship with the math in a "real life" context is what is important. I agree that it is important for us to attend to "how the schooling environment supports children's developing identities as students, through the nature of their engagement, but in doing so we need to be careful of the stereo typed identities we may place on them.
Cobb and Hodges mentioned one view of culture as a way of life passed on from one generation to the next and the other view, which to me better applies to Canadian students, of culture as shifting social networks. People identify themselves or are identified by others during social interactions. This second view I can relate to personally and with what I observe in my classroom with my students as well. If I look at this through my mathematics class I can see how the students have changed their identity with relation to the class dynamics. Although this is at the Elementary level, I think it is still relevant because this change is easier to see. For me I believe it is recognized in the change in the students self confidence/esteem. The change in their "normative" identity slowly impacts their "core/personal" identity and is more readily visible because the growth in this early age moves in leaps. I believe the personal identity at this earlier age is intertwined with their core identity. The identity moves at a faster rate or is a larger change (than in secondary) and is sometimes even stated out loud as they themselves discover this change in themselves. As I increase mathematical discourse and the students work more in groups they recognize themselves as having more to contribute and the gap between who they believed to be "the smartest" and where others and themselves are not to be as wide as they first perceived. This I have recognized through the level of their participation, the confidence level at which they talk or justify their answers for many students. So, although it may not be as visible at the secondary level I believe the growth/change is still happening. Also mentioned by Cobb and Hodge is a having a concern for who the students are becoming when we focus on the students' mathematical reasoning and this will enable issues of equity in the mathematics classroom. Not an easy task, but I think it is a doable goal to work towards.
This blog will be focussing on the Cobb and Hodge chapter and I do start with a few random thoughts.
ReplyDeleteGreat sentence: “Discourse about who it is important to be and who it is possible to become is continually changing and may be in conflict with who people view themselves to be and who they want to become.” (pg. 162)
Clarification: I just wanted to make sure that I understood something. Are the authors saying that there is a ‘disconnect’ between what students learn in math class to what they know/learn/work with in their everyday, out of school lives? If this is the correct interpretation, I can understand how this could be so as the topics we teach, especially in higher-level courses, tend to be more on the theoretical side that it can be quite challenging to bridge the gap. Would Boaler and Nasir’s suggestion of offering more open-ended problems/projects help to bridge this gap?
Looking more closely ad Cobb & Hodge’s ideas of identity. I would say that normative identity is an instinctive one developed by both teachers and students in the classroom. Teachers actively encourage students to be ‘doers of mathematics’ (pg. 166), even the shy ones; ones who do not feel comfortable to openly show they are participating. We try to find other avenues for them to participate in an environment where they feel comfortable, for example small group activities. I feel/believe (hope?) that the norms suggested by Cobb & Hodge are seen in every classroom besides mathematics.
If I have understood correctly, I would say that core identity could be considered the most delicate identity where the power of words and action, by teachers and peers could have a devastating effect on a student’s perception their core identity. What I mean is I have often heard students say that they can’t ‘do the math’ and they were ‘never good at it’, therefore they feel that their future options are narrowed. If students develop this belief of a lack of ability at a young age, then the possibility of ‘who they will become’ could be limited. I agreed with what was presented here with respect to Ogbu’s research about marginalised students’ resistance to instruction because I did face this resistance when I was teaching in New Zealand. My Maori and Polynesian students did not believe that there was much purpose in learning higher mathematics as they felt it was already pre-ordained that they would go on the dole the minute they finished high school. No matter how much encouragement or attempt to engage them, they had shut down. However, I do believe this shutting down is not limited to a cultural resistance. I feel that students from all walks of life will resist learning if they feel or learn that they just cannot do it. Trying to help students change this thought/attitude around is very hard, especially in the older grades – oftentimes, they have given up. This is why I feel that developing the core identity needs to be done so carefully as it appears that it can be so easily cracked.
I will admit that personal identity was not as concrete to me as the others, but if understood correctly, I would say how a student’s personal identity is created is closely tied to his/her core identity. I feel that if a student has a strong sense of self now and for the future than fulfilling the norms would come more easily for him/her. Whereas the opposite would be true for someone whose core identity is, for a lack of better words, weak. Their belief in themselves and their mathematical abilities is not there then for these students the idea of “developing oppositional idenities” (pg. 169) would occur more readily. This would reemphasise my belief mentioned before that helping students to develop strong core identities is so crucial in order for these other identities to flourish.
Overall, I felt that these chapters truly made me sit back and understand better what my role in the classroom should be.
JWallace, you make some really good points. Hopefully Nasir will respond, but in the meantime, I think we should talk about this tonight in class. Let's go back to the chapter and see if we can find where/how Nasir defines cultural practice. Every practice is a cultural practice, and I am pretty sure she was not trying to say that basketball is only an African-American practice. But it was something that the boys she studied were drawn to and participated in, and that is what led to the formation of goals, identity, etc.
ReplyDeleteInteresting reflection JWallace, but I fear that you may have misunderstood what I was intending to convey. When I use the term cultural practice, I use it in the scientific sense, and not in the common usage sense. In other words, by 'cultural practice' I don't mean a practice that people who belong to a certain culture do. Rather, I mean any activity that involved three or more people. I do not locate culture inside of people or groups of people, but rather in interaction between people. As such, I am not implying a one to one correspondence between basketball and African American culture-- that would be reductive and problematic.
ReplyDeleteHaving said that, it is true that I focused on the practice of basketball in this study because it is a practice that is commonly engaged in African American communities. Because I am interested in African American learners, I wanted to understand HOW learning is organized in settings outside of schools, in ways that did not frame the students as having a learning problem, and expected their success with respect to learning. It may be that a superficial reading of this piece would lead one to conclude that it reifies stereotypes of African Americans as being good at basketball and not at school, but what I am trying to point out, on a deeper level, is that the basketball setting made BOTH learning opportunities and opportunities for positive identities possible by the way activities were structured, and that in doing so, provides a potential model for the design of learning settings.
Thanks, Na'ilah - it's helpful to have your clarification. We discussed this a little bit in class, and I pointed out that the article would lose some of its power if you had chosen a less typical activity like, say, chamber music.
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