I wanted to get started with my blog, so I have gather some beginning thoughts here:
With respect to Boaler, I was not too surprised by the information that she provided in this chapter. I have often been told that we need to be aware of learning styles of boys and girls, and to ensure that we address them appropriately such that they both will achieve success in the math classroom. I will say that I was happy (and surprised) to see that there was little difference in achievement success between the two sexes, and felt that perhaps this kind of data needs to go out to news agency such as 20/20 or the New York Times so that they can stop perpetuating the doom and gloom regarding girls and mathematics. As Boaler stated eloquently an behalf of equity researchers that they“bear an enormous responsibility for considering the ways in which they are interpreting and framing their data, as well as the “mythologies” of inadequacy they may be constructed” (pp.35); perhaps these news agencies should also think more thoughtfully before presenting the findings that they do. I would hate for anyone to believe that they cannot learn mathematics because the ‘researchers’ have proven ‘it’ to be true.
What Nasir presented in the chapter, I would hope is what teachers strive for in the classroom. The information provided regarding identity, goals and learning seem so logical, that I could not imagine that it doesn’t happen, and yet reflecting on what I have seen and participated in myself, I can see how and where I would need to improve for the future in my classroom. There seems to be so much external pressures that I wonder how effective we can be to ensure that everyone child in math has the opportunity to set goals and develop the identity that allows them to achieve those goals, in a seamless and intertwining way that was shown in the basketball analogy. Nasir states, “the key question then becomes how to structure this successive set of activities in a way that maximizes learning and cognitive developmental outcomes” (pp. 144). This is truly a challenging question to answer. We understand that mathematics will become more meaningful for students if they can see or discover themselves the concepts, and if they can relate it to their own lives/experiences. Yet we often hear of our battle against time; time to complete the curriculum. I believe there would have to be a fundamental shift in thought process and expectations by students, parents, teachers and universities, that would allow for more opportunities as suggested by both Boaler and Nasir that open-ended problems, with or without defined solutions, be presented for students to discover their own route to solutions and rules. Perhaps my first step would be to take the first step, in a small way, that allows students to fully realise (conceptualise) the intertwining nature as Nasir presented of goals, identity and learning.
Although I did appreciate the idea of setting goals and can certainly understand the importance of doing so. I did think the following when reading about goal setting in Nasir’s chapter: When students set goals, how much of it is due to personal gains, e.g. want to improve a particular grade because they feel they can do so, versus future gains, e.g. setting a goal to get a particular grade for future success? Is the latter goal influenced mostly (or perhaps strictly) by social context (peer or family pressure to be successful in the future)?
You make a good point about goals, LM. I was also wondering how many students at the high school level truly know what they want to do with their lives when so many people I know in their thirties are taking steps to change careers. As the new semester started today at my school, I asked m students taking grade 11 functions (university-bound stream) course to write down for me what their goals for this semester and after high school are. As I received the typical answers about wishes for obtaining a high average and attending university for programs in accounting and biology, I wondered how many will end up where they thought and if they will be able, when/if they need to, to re-orient their goals as necessary. I wonder if there is more pressure on girls in some instances to keep their original goals (e.g. due to societal pressures to finish education quickly so that marriage and raising children are still a possibility) so that girls may tend to aim lower...or am I being completely old-fashioned here?
ReplyDeleteResponsibility for Interpreting Data
ReplyDeleteI love the quote that you highlighted:
Deficit Language versus Co-production of Environments
Researchers “bear an enormous responsibility for considering the ways in which they are interpreting and framing their data, as well as the “mythologies” of inadequacy they may be constructed” (pp.35)
I have heard a lot in the two years about avoiding deficit language and Boaler's article clarified my thinking about why we want to do this. It isn’t just being considerate of the people involved, but an acknowledgement of how any deficits are co-produced in the environment. I had read about Amber Hill and Phoenix Park mathematics programs before, but never had I thought about how these programs shaped mathematical identities of the students and reduced gender differences.
Yet why should this surprise me- I have known for 25 years how these culture interacts with individual backgrounds to affect language production and notice how I drop my ‘g’s in some environments and not others and how immersion classes fossilize their language, often creating a dialect and grammar that differs from the target language. I just hadn’t applied this idea of cultural influences to gender and race.
Hopefully this new awareness of co-production will help me as I teach students coming from lower SES backgrounds. Even though I respect the students in my workplace math class, Indigo caught my negative language discussing them in my first essay. I have had some of the most frustrating classes of my 12 year teaching career this last semester as I tried to incorporate some tasks that asked for critical thinking and generalising into this class where a lesson works really well one day and then the follow-up the next day is a wash.
I agree with MP (Jan 26) that this population is not served well, but wonder if MP is correct when MP asks, “What no one has been able to answer, to the best of my knowledge, is how can this be done better?” I think some better ideas are out there: Boaler’s article suggests that there are materials that improved the learning of all students. I don’t think these resources are easily available to most teachers, and even if they are available, would a teacher trained traditionally be able to use them in the way that made the materials successful. In the original article about Amber Hill and Phoenix Park, Boaler describes teacher collaboration in creating the problem-solving curriculum. I think it would be had to do and keep up the effort alone.
I know I sometimes spent hours getting a good lesson ready, one that allowed students with different background knowledge to participate fully and engage their interests. Sometimes the lessons went great and really seemed to help the students understand. Other times I insulted the knowledge of some of the students in the class. Sometimes I think the lesson was okay but was derailed by social issues occurring outside the class. Sometimes I was just so tired by managing the social dynamics that the students got the workbook pages that bored and frustrated them.
Having a ready source of thoughtful materials would help me from being overwhelmed by the day –to day realities, time to consider the larger issues of power and identity in the class and how I might affect the dynamics that are sometimes disruptive.
Boaler J (1998) Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education.
Hey DT - Just to clarify, I think there are practices out there that are more effective in lower SES classes, but I also think that these are often just superficial solutions. The students as a socio-economic group end up in the same place as their parents. Anytime we change practice, and there are places and systems out there that do have alternative pedagogical methods, the results are the same. Based on what I've seen and read (and I do believe that there is plenty out there that I haven't read and this might change my mind about the matter) there are practices that have been changed but this has not been effective. Take for example the Applied stream in the Ontario school system where the structure has been changed but the results have not. I think it is important to note that many changes are implemented, but they aren’t really that different from what has been done before. I think that with regards to the statement I made (which was probably hastily written for blog’s sake) “What no one has been able to answer, to the best of my knowledge, is how can this be done better?” part of what I’m trying to get at is that maybe we’re not asking the right questions yet and we really don’t understand the problem. As a result, a great deal of practice is just recycled past practice and it doesn’t really change anything because we don’t really have a clear understanding on why the system is not equitable for some groups of students.
ReplyDeleteWith all of the articles that we looked at this week there was a common theme that we really don’t have a good understanding of why certain groups of students are having difficulties in the system. Even more troubling, the articles suggest that we have made inappropriate conclusions based on prior research. Boaler’s article (chpt 2) looks at how conclusions based on prior research about gender are not valid, because some important variables (specifically the learning environment) were not considered. Cobb and Hodge’s article (chpt 11) states that we need to look at the identities of students in the classroom to maybe better understand what is and isn’t working in the educational system. I have a feeling that trying to create a more equitable school environment involves understanding how students identify with the class/educational society. I don’t think that we have a good grasp on this yet.
I didn't read Boaler's article as advocating the idea of 'learning styles.' The concept of learning styles seems based on the idea that there is something enduring about how a person learns or prefers to learn across a variety of contexts. This is something that belongs to the individual and not to the context. But, Boaler continued to argue that gender is a response to a context, so all gendered patterns would have to be ascribed to both context and the people in it.
ReplyDeleteI think the language of the Boaler chapter does sometimes lead to thinking that there is something inherent about girls appreciating 'connected knowing' that does not vary across context. I wonder if she meant to say that... I think that the conclusion that girls all want connected knowing goes directly against the position that gender is a response. Unless (and I didn't see this articulated in the chapter, but might have missed it) Boaler is arguing that there is something common across those many contexts that calls out this response in many girls.
I think the question about where goals come from is an important and interesting one. I certainly make the argument that goals develop as individuals interact in the social contexts with others, and that they are positioned as being on track toward particular goals (e.g. being college-bound) by other people. Clearly, socially assumed goals and trajectories play a role here, but there is also individual agency to resist, conform to, or reject the goals others position you as having.
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