I have to confess that I feel somewhat all over the place in my thoughts to this week’s readings, so when reading these scattered ideas, please keep that in mind. Thank you.
I had mixed feelings when I read Lubienski’s chapter because it was difficult not to think of my own upbringing, when in primary school I believe my mother and I could have be classed as lower SES. Yet I saw my mother work incredibly hard to move up the ranks in her organization and I certainly did not feel shy about voicing my opinion in class as suggested by Lubienski’s three examples, Sue, Rose and Dawn. I give a lot of credit to my mum in ensuring that I have confidenc in my abilities and wonder if perhaps Lubienski might be underplaying a little bit the value of parental influence as we discussed last class? However, I do agree with Lubienski and her remarks regarding that outside factors play a big role in student participation (e.g. Sue being called a ‘dumb blonde’ when she asked a questions). I recall my lack of hearing coupled with my lisp made me the butt of jokes in primary and middle school and therefore there are times I would have been quiet, but I do not believe that my lower SES really played a role there (my quietness).
Again, with no disrespect to the author, but the idea that lower SES students want to ‘just know the rule’ I feel certainly does pertain just to them. Having worked in relatively higher SES schools over the last ten years, the question ‘why didn’t you just give us the rule?’ after investigating/working through ideas is one that comes up quite frequently. Perhaps these types of questions reflect more on teaching practices, what the students have been exposed to with respect to learning mathematics much more than their SES status?
Gutiérrez brings up really interesting points, but I wonder if there needs to be a fundamental shift in how people view the teaching of mathematics to try to ensure equity is seen in the math classroom. I certainly agree that there should be no preconceive notion with respect to race, culture, gender, etc. when students enter the classroom. In fact, when there are discussions at the beginning the of the school year regarding student behaviour, I try to close my ears unless the talk turns to learning disabilities and how I can help them because I don’t want to presume to know a student before they enter the classroom. Students change a lot in one summer and they may react differently in your classroom from a previous one.
Also with respect to understanding the development of mathematics, I don’t disagree with Gutiérrez, but there might be challenges on two fronts: first, time to complete the set curriculum and second, teachers’ knowledge of historical facts. In regards to the last point, I believe a lot of teachers may not have taken courses that taught the evolution of mathematics themselves, so this would require teachers taking the time to learn in order to teach. I do no have a problem with that except that it brings me back to the first point, time.
I will confess that I never thought of my math classroom as a place where discussions of social justice can occur – it would not be an instinctive thought. I do agree and certainly endeavour to ensure that equitable practices do happen in the classroom, but I believe both Gutiérrez and Lubienski would require that I take it much further.
Thanks for starting us off, LM!
ReplyDeleteYour post raises a couple of interesting points that I think we should keep in mind when thinking about these two chapters.
First off, with the Lubienski article, we've got to be really careful about interpretation. This is a case study of one classroom and so the author definitely is not trying to say that all working class kids and middle class kids are like those in the article. Second point about this is that she's not saying there is something inherent about working class kids and middle class kids that makes them different - she would probably locate the differences (as you pointed out, LM) in kids' out of school lives but also in kids' in school experiences. Two different kids might hear the teacher say the exact same thing, but interpret completely differently because thhey have a different frame of reference for interpretation.
And, with respect to the Gutierrez article, I agree that many of these recommendations couldn't be implemented by an individual teacher in their classroom. Instead, Gutierrez is asking us to think broadly about what math ed is about, what it should be about, and what it would take to make that happen.
Hi Indigo,
ReplyDeleteI have to admit, and I cannot say why, but Lubienski's chapter struck a chord or two with me. I do understand that she is looking at a specific school and she certainly brings to light some ideas that we need to be aware of in our own classrooms.
Overall, these articles have brought to light how teaching mathematics should certainly not be contained to teaching concepts. For example, to date, I have to confess I have read and thought about gender equity in the math classroom as this is considered a 'hot' topic, but these chapters certainly take the idea of equity much further and I look forward to the discussions on Wednesday.
Lubienski’s chapter helped me clarify my thinking about culture (especially social class) and mathematics education. Several points stick out in my mind:
ReplyDelete“Conceptions of culture have evolved to include [….]multiple group membership, the permeability of boundaries separating groups and the interactive construction of languages and practices (p13).” I have been struggling with how to define culture and examine its impacts in the classroom. This fluid definition fits my experience as a student and a teacher where students seem to change the groups they identify with from day to day and course to course. I think it helps avoid stereotypes as there are multiple influences on an individual- as LM mentions of her mother’s goal setting and influence within a lower SES culture.
In the last 5 years of trying to make my mathematics classrooms more meaningful to the participants, I have been worried about how changes towards a discussion-rich, problem based curriculum would affect students that were very successful in a traditional mathematics classroom, a concern echoed by Lubienski , “any change in classroom culture could privilege those possessing ‘cultural capital’ in new anticipated ways” (p 12). What about students who have difficulties expressing ideas and following multifaceted conversations? Would these conversation turn off students who liked rules and patterning? I loved my traditional math class and where I love conversations about math now, I am not certain that I would have at age 15. Yet I can see how a discourse-rich classroom would benefit others. I once had a very math anxious English teacher talk aloud while solving fraction problems; she remarked several times through the interview that she would have liked math class a lot better if she could have discussed the solutions. I personally recognise many of her descriptions of low SES students in my childhood family and friends and in the students I teach: I definitely felt pressure not to answer or ask too many questions and always sat in the back of class. I would also like to suggest another trait that seems to be associated with students from lower SES: the expectation that all work should be done in the classroom (Chazan, 2000)
Chazan, D. (2000) Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College
I suspect I have typed too much when the blogsite made me cut my post in two- I will attempt to be shorter next week, but this article was so clarifying and my ideas are already written so please excuse:
ReplyDeleteI have struggled with this awareness of different comfort areas in learning math and I have tried balancing old with new but I haven’t been satisfied with the approach. Lubienski’s summary, “Lower SES students have the most to gain from mathematics classroom students that explicitly include problem-solving and mathematical communication as part of the curriculum” clarified my thinking. Today my understanding is that I can and should work toward rich discourse and problem –solving in my mathematics classrooms, but I need to be aware of the different competencies and comfort levels students bring into the classroom, and be prepared to teach/ build those skills.
But then how to build those skills? I have taught students in lower streams how to write tests: when these students were told to guess after eliminating any choices that were obviously wrong, they thought that was cheating, that they should be sure of an answer before they put it down. These students didn’t realise how good test takers made informed guesses.
Just today I had another conversation with young men in my 4U data management class ( a grade 12 course for university bound students). They openly admit that they don’t see the need to practice the work if they followed it in class. I tell them of my son’s experiences in university math with that strategy, and some of them think maybe if they are paying for the education they will feel differently, but aren’t convinced. Is raising awareness the best we can do until the students themselves see a need for a skill?
Generalising and abstracting is another area I I have noticed that a lot of my students from lower SES –but not all- have difficulties with (as did Lubienski) . When discussing investment options workplace math and having students generate the growth of an investment using an online interest calculator, I tried to have my students determine the big ideas that affect the return. It was very difficult to pullout the abstract from these students, I had to write out sentences with blanks to fill in. Many students initially had no idea what the questions were asking.
I think that generalising and abstracting would improve with practice. As evidence, consider the Flynn effect. Flynn noticed that the raw scores on the raven progressive matrices test- a supposedly culture-free, non verbal IQ test that measures in part the ability to generalise and abstract– have increased steadily since the 1920s, while the verbal language test has shown little change. One accepted explanation is the change in culture and schooling- that abstraction is a culturally learned skill which is more valued in today than 90 years ago.
Flynn, James R. (2009). What Is Intelligence: Beyond the Flynn Effect (expanded paperback ed.). Cambridge: Cambridge University Press
I too had problems with Lubienski's conclusions about lower-SES students. While reading that part of her chapter, I felt that she oversimplified many of her observations and ignored other contributing factors, specifically cognitive ability or prior achievement level. In the end of this section, she does conclude that 'although some differences were likely attributable to students' prior mathematics achievement, this was not a complete explanation" (page 18). I would have liked more clarification on this statement. It would have given me a richer context to consider some of her statements as to why lower-SES students struggled to make connections, see the big ideas in open ended problems or lacked confidence in participating in whole class discussions.
ReplyDeleteWhat was interesting to me was her lack of discussion around how teachers' beliefs and knowledge affects the implementation of reformed-based mathematics. In particular, the teacher's comfort in facilitating a group discussion and response to students' errors and misconceptions. Based on various readings by Deborah Ball, I think a teacher's lack of knowledge of mathematics has an affect on whether or not students are able to 'see or figure out' the big ideas in problems and classroom discussions. I have a vague memory of reading a study that found that the teacher's interaction with students from the moment they start solving a problem to the end of the problem solving process was the determining factor in high student achievement.
However, I do understand that Lubienski does have a bigger picture in mind for mathematics education that goes beyond individual classrooms.
Interesting comments, here, and a lot to think about. The Lubienski chapter always gets people thinking and talking - as does the Gutierrez piece, but in a different way.
ReplyDeletePerhaps next week when I will have some time to lead a discussion, we'll talk some more about issues of culture, ability, achievement, and so on. I have a feeling that we all have our own assumptions of what these things mean and how they are important. For example, I rarely use the word 'ability' because I don't believe there is evidence that people have decontextualized abilities that are not affected by the environments in which they find themselves. Just as I believe that people's personality traits (e.g., shyness) are not inherent but are also context bound. So, to get specific, 'lacking confidence' is not something that belongs to a person - instead, 'lacking confidence' is something that happens within a group of people in a particular setting. And it always has as much to do with the setting as with the people in it.
There were several parts of this article that resonated with me. I have very little experience teaching lower SES students, but when Lubienski mentioned that some "lower-SES students took the contexts more seriously than the test authors intended" on some realistic test questions, I immediately thought of arguments that I have found myself in with some men about sexism. As a woman, I have a hard time looking at sex or gender-based discrimination from a purely theoretical perspective, because it affects my life in a very real way. Similarly, I can see how a student who has had the experience of not having enough food might have a hard time reading a question about sharing pizza as a purely theoretical question without thinking about the possibilities of people getting firsts and seconds.
ReplyDeleteAt the same time, I do think that learning how to figure out what math question a word problem is asking is valuable. However, this needs to be done in a way that respects students' experiences and doesn't turn real problems they might have into trivial theoretical exercises. I'm not sure how this could be done; maybe by looking at questions the students have about anything and finding the math in those questions. Or, maybe we can keep use whatever other variables they bring to the context and include them in the math problem. This might make the math question more complicated, but I think that, if handled well, that could actually enhance learning.
With regards to Lubienski's article, I think that if you were to ask an experienced teacher who has worked with students from different socio-economic backgrounds his or her feelings on Lubienski's study, they would be able to predict some of the themes (pg 18) that Lubienski discusses. Lubienski mentions there are noticeable differences in the characteristics of students from 'lower SES' students (in the classroom) and ‘higher SES’ students. As I believe Indigo pointed out, the author does not suggest there are inherent differences between the different groups of students, just that they experience the institute of education in a different way. Unfortunately, I also feel that the educational structure, I've worked in, does not meet the needs of the 'lower SES' student very well. What no one has been able to answer, to the best of my knowledge, is how can this be done better? There are so many factors – attendance, previous success/learning, attitude towards school etc. – and it is hard to pinpoint which of these contributes to the problem. I think that many teachers begin working with ‘lower SES’ students with the best of intentions but are soon faced with the reality of making the situation work. New initiatives and techniques are tried, but the results are often the same and the teacher reverts back to teaching things that have been somewhat successful in the past. For example, Lubienski points to the fact that in her situation many of the ‘lower SES’ students just want to know how to complete the question. For a teacher working with ‘lower SES’ students this might involve teaching the ‘steps’ as opposed to teaching an understanding of the process. I think that coming up with new teaching practices never really gets to the real issues that underlie the problems that exist between the ‘lower SES’ student and the school system. I don’t claim to know what the problem is, but I do believe that with all the new strategies, that I have seen, that are attempted they are not improving student learning for the lower SES student. I think more research on confidence is one area that should be further studied in addressing equity issues concerning the ‘lower SES’ student within the class. I also think that further brain research, specifically in relation to teaching techniques as they relate to motivation, and memory are necessary to actually address the problem.
ReplyDeleteI really enjoyed reading lubienski's take on research dedicated to mathematics education with equity in mind. I can totally agree with her emphasis on intersectionality and trying to see the inter-relationship of race, class, gender and culture. I do however like Gutierrez's take on how it is so difficult to conduct such a research that analyzes and takes into account such variety of complex issues.
ReplyDeletePrior to reading Lubienski's case study i was of the opinion that students coming from higher SES would lack the drive to speak up while the disadvantaged students would more into discussions that would require their opinion considering the notion that their voice might have been suppressed. It was interesting to see otherwise. This made me realize the importance of the point Lubienski was trying to make about how it would be difficult to have research that would enable us to come up with generalized solutions to problems of equity and reform education but it can be used to realize or make us aware of “hidden issues” so that it can be brought to surface and discussed for possible solutions.