Identity in the Boaler, Nasir, Cobb/Hodge papers

Identity is a hot topic in current math ed research, as some of our authors this week have pointed out. Every author defines the term slightly differently, and usually, quite differently from the way it is used in everyday conversations. So in this post, I've gathered together some of the different definitions and discussions of identity, so we can make sense of them together.

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)

 What thoughts and questions do you have about identity? How are these definitions similar or different? Do they help you understand learning in a new way?

"but much work remains".

There were many parts of the chapter that I found fascinating and immediately reflected on my past teaching practice.  One particular quote captured her big idea in the chapter for me:

Researchers and educators should not assume that learning mathematics through problem solving and discussion is equally 'natural' for all students.  Instead, we need to uncover the cultural assumptions of these particular discourses.  Only then can we identify and seek to address the difficulties that some underserved children could face in reform oriented classrooms. (page 21)

 As a classroom teacher, I focused on problem solving and classroom communication.  I used strategies such as gallery walk, math congress, and bansho to get students to consolidate open-ended problems.  I facilitated discussions.  As a math coach, I encourage teachers to do the same thing.  Not because I did it, but because our board and ministry suggests it.  However, my immediate reaction to reading this quote was not positive.  It suggested to me that all that great work I thought I was doing was actually very superficial.  I never consciously thought about why certain students didn't participate in whole class discussions.  I did notice that some of my students did get caught up in contexts of problems but I never asked myself why.   I had high expectations for all but, as Lubienski suggests, it was not 'sufficient to produce equitable instructional practices".

In looking ahead, I have much to learn about what 'equitable instructional practices' are and how to implement them.  So I hope that new research on identifying the difficulties that some underserved children could face in reform oriented classrooms comes with specifics on how to address these difficulties.  After all, classroom teachers (like myself) are trying to make sense of this new knowledge of and commitment to equity.  

"Strides have been made towards achieving equity, but much work remains".

"Mathematics will gain from having these people participate"

There were many aspects of the Gutierrez's chapter with which I identified and I found myself nodding my head in agreement quite often.

I have seen that equity is becoming a popular topic for companies and schools to tap into, but my concern is that this can often be a label that they wear on their website in name only. There would be much greater equity already if it were as easy as having a diversity committee or a logo. I know that at my school, we have faced some challenges bringing new equity and diversity initiatives forward because there is a concern that parents may be upset.

My favourite part of the reading was the quote by Gutierrez that said “the assumption is that certain people will gain from having mathematics in their lives, as opposed to the idea that the field of mathematics will gain from having these people participate” (37). I love when a quote turns my understanding on its head! I had never thought of learning math in this way and I think it’s such an empowering notion. It says that we expect students to have power and influence in the mathematics community.

I got the sense that Gutierrez was looking for students to achieve their personal best regardless of the other outside factors and I think this is a great way to approach the problem. As an educator, I need to look at power issues and question structures, but I also need to teach my students to do the same. Today I talked to a student in one of my classes and suggested that she take on an equity issue for the open-ended project that I do in that class and she was excited to find a good topic. I’m hoping to use her interest in this area to help her see the relevance of math in her life and what she can do with it.

Although I often struggle with the lack of diversity at my school (SES, race, cultural), there is still a lot that I can be doing to have my students examine the way things are and ask questions. Some of them see the economic and political capital that they have, but most of them are in their own bubble about the way other people live.

How can we ensure equity in the math class?

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.

Balkanization and streaming

Hello everyone,

Am I a balkanized teacher? I am not sure, but maybe I too, am somehow a balkanized teacher (shame on me). Let's see, unlike most of you I have not taught any subject but chemistry. I introduce myself as a chemistry teacher in professional socializations, but I consider myself a teacher in general. I overload my students, my courses, and myself with variety of teacher-centered (old fashion) and student-centered (progressive) tasks and techniques. My students’ learning and likes have priority over the subject; however, the subject is also very important to me. I admit that I am a perfectionist though trying to be a realistic perfectionist, therefore I work hard to do the best I can for my students, and I make them work hard too. I really believe in group work and think students would learn from each other in some ways, however there are barriers. I appreciate any chance to pass the control of class to students, but first, I inform them that is a part of the teaching-learning process. I consider myself a little progressive but more humanistic. nonetheless, as Dewey (1938) argued that no matter traditional or progressive educational philosophy, I utilize whatever works better for my students, and mostly a combination of many styles...

Streaming or destreaming/tracking or untracking / segregating or desegregating… Maybe streaming works in adult education system. Nonetheless, I think streaming hurts young students, and I hate them become disappointed. I am wondering instead of those doings and undoings, Why not to try something else like Waldorf education system?

Gap Gazing in mathematics education

Hello everyone,
I am late a bit, but I would like to share a few thought with you.
Unfortunately in the most parts of the world, governments believe that Education system is money consumer and are very mean not spending much money on education system. I agree with Rochelle Gutierrez that some form of gap gazing is harmful. Nevertheless, appreciate every research on the field of education because the least benefit of it is awareness.

I do agree with Sarah Theule Lubienski that analyzing of math (subject) achievement should be focused not only on one factor, but also in conjunction with factors like gender, race, and for example, family income. According Blau (1999) and Alison Aughinbaugh & Maury Gittleman (2003) test score maybe sensitive to not only the family’s own income, but also other factors related to the family’s socioeconomic status such as neighborhood characteristics, peer characteristics, and characteristics of the schools children attend. Furthermore, when framing mathematics achievement, researchers usually refer to individuals; individual achievement and individual failure. As Gutierrez (2008)* argues that it is not only individuals as students or teachers, but “complex learning environments”(p.361) too. For instance, reviewing thirty two studies of mandatory desegregation policies, Robert Crain & Rita Mahard (1978) reported that twenty four of them found positive effects of desegregation on black students’ achievement gains. Moreover, Grissmer, Flanagan, and Williamson (1998) stated the convergence of black and white test scores occurred with massive school desegregation from 1970 to 1990.
* I am not sure if 2008 is correct.

Math for social justice video

David Stocker, Toronto teacher and author of Maththatmatters, just sent me a link to a video that he made with his child. The video makes a mathematical argument about the Transit City project that Rob Ford is so opposed to. I thought some of you might be interested.



As a side note, feel free to embed photos, videos, and links to other sites in your posts if there are resources and such that you'd like to share.

To stream or not to stream

These readings made me critically reflect on my own practice. I have often thought that I don’t think streaming is necessary, but nor have I spoken out against it.

I started teaching Secondary school in Ontario, destreaming had just happened for grade 9 and all the teachers in my school were in an uproar "how can we teach all these different levels". I wondered what all the fuss was about as elementary teachers did it all the time and I had attended an unstreamed secondary school and did very well (turns out that it existed in BC but my school was too small to actually have any streamed courses- instead students chose academic subjects or tech ones)

In that first year of streaming year, teachers made no effort to integrate the levels- some students were taught from one textbook, and the weaker students a different textbook. There was no attempt to improve the instruction so it was meaningful to more students. With no support for changing teacher practices, the change was not successful and shortly there after became applied and academic.

If we are to destream we need to support teachers in examining and changing their pedagogy. I am looking forward to the studies in Mar 9 that will have some ideas how to teach inclusively and well.

Even in streamed classes, some teachers really don’t meet the needs of their math students. I currently have 5 students in my Workplace 11 math because the failed the grade 11 college last year when it was taught by a teacher how strongly believed in traditional mathematical rigour and didn’t take into account for different students’ learning needs. One student after two weeks of being bored silly in workplace math retried the college level math –this year taught by a former elementary teacher who teaches in many different ways- and she is getting a mark in the high seventies.

Having said that, like MP, I have taught many students in workplace & locally developed math classes that were math anxious and very glad to be out of the stressful regular math streams, happy to feel competent and accepted in my classes. Would we still have these math anxious students if we made every preceding math class more meaningful and accessible for students?

Often streaming is more about work habits than ability and I think students in the workplace streams would benefit from having students around with work habits. When my workplace math class went from 13 students to 20- the work habits of all the students decreased. I think the students just realised they could get away with doing less in the bigger class.

An issue for me with streaming is that students from low SES backgrounds and immigrants don’t have the tools to argue against streaming or even the awareness that they should until it is too late to do anything. I was very moved by the stories in the Sefa Dei et al. paper of how students were streamed and how stereotyping was seen to play a role. I know that my sister-in-law, whose father moved her from advanced to business courses because they were more suitable for a woman still feels the resentment 40 years later.

With all the reforms going on in math education in Ontario, I think we should revisit streaming and how can we teach math without it.

Is streaming best for teachers or students?

I meant for this to be a comment on another post, but I can’t seem to manage that at this point, so I’m hoping this ends up somewhere that makes sense.

I know that I’m coming late to the topic, but I would like to through in that I don’t agree with streaming based on ability. I have experienced the challenge of having students in my class at a wide range of abilities and realize that it would easier for the teacher to have a homogeneous group of students. I don’t think that it’s better for the students.

Part of the problem is the assumption that students perform better when they are with students at the same level. I think that students who are struggling can be helped and inspired by those who are stronger. Those who are performing well can also be challenged to explain their understanding to those who are having trouble. Another problem is the assumption that students can be grouped into those who do well at math and those who don’t. Some students are great at geometry and can’t do algebra. Math is a complex discipline. But the most important idea is that students are always changing in their abilities and we can’t assume that a poor mark one year means that the student won’t be capable of doing university math when the time comes.

It terrifies me that we ask students to make a decision about their university careers

If a student chooses the academic stream because they don’t want to close doors for university, they may end up struggling through the material because the teacher is expecting a different level of mathematical thinking. I think this often contributes to students’ fear of math. If there was no streaming, it would be the teacher’s challenge to make sure that students were challenged at appropriate levels and support was available those who might otherwise be regarded as a lost cause because they’re “in the wrong level”.

What I do agree with is choices in courses based on interest. For example, at the Grade 12 level, students can do Advanced Functions, Calculus and Vectors or Data Management. These represent different types of math and so it makes sense to allow students this option. Which one they take narrows their choices for university, but it narrows it into whatever field they are interested in, not whether they can get into university at all.

Does ability/achievement grouping help students learn math better?

From reading this week's posts, I believe that many of you support the idea of streaming, if not the practice. That is, many people think that grouping students into others who are at a similar achievement level can help them learn.
I'm not convinced, having read some research about how streaming can turn into a self-fulfilling prophecy. For those who do believe in streaming, can you tell me how you learned that this was better? What experiences, readings, philosophies, evidence, helped you decide this?

ITS STEREOTYPING NOT STREAMING

The concept of streaming or tracking is not exclusive to north america, This concept is practiced through out the world with variations ranging from minor to major and under different names. I was not familiar with the term "streaming". I googled it and found out that i myself, as a student, had experienced streaming albeit a more democratic version of it. To explain, back home, we have streaming at grade 9 and 11. The power to make the final decision rests with the students and the parents.

However, I observed that in North America, the term has a negative connotation attached to it. You can trace the real reason back to the origins of streaming. It started coming into use at times when schools in North America were enrolling a growing number of immigrants, so streaming was adopted to sort those children viewed as having limited capacity as compared to native children. The intention must have been noble. However, not surprisingly, it quickly took the appearance of internal segregation.

I would like to refer to a statement by a Caribbean woman Jane in one of our readings this week. she has stated that streaming in West Indies is a way to simplify the way how pedagogy is imparted, its not fighting racism. My experience with streaming was also similar to hers in my home country . I think It is stereotyping in the garb of streaming and not streaming per se that is the root cause of student failures. It does not make any sense that how placement of students into programs that they can possibly handle contribute to increasing drop out rates when it is designed to do the exact opposite. For many students, the stigmatization felt in low stream education overwhelms any educational value he/she receives.

I am a proponent of streaming and truly believe in its benefits and in my opinion teaching in the classrooms where kids are streamed according to their ability and interest would be much easier.. However, the only tweaking i would recommend based on my past experience is that (1) kids and parents should be allowed to make an informed decision and (2) there should be an option to easily switch later to correct any mistakes that might have been committed earlier or to accommodate a change of heart on part of the student, something that happens quite often and quite naturally as the kids mature and become more aware of what interests them.

School Streaming

This article really did make me rethink the way our schools are streamed. I do agree with notion that students learn better when they are with others who are at the same level, but who determines what that is? If parents and students are not well informed, they rely on the teacher to make that decision. But how well does the teacher really know the student?

I entered high school the year the new curriculum was introduced in Ontario. The terms academic, applied, open, college, university and workplace as types of course were new to us, our parents, and our teachers. We were told at the time that ‘academic’ was more theoretical and ‘applied’ was more hands on, but that both courses learned the same material and is was possible to switch from one to the other. Since none of the courses had actually been taught before, I think those notions were based on government descriptions not real teacher experience. Still, most of the kids I went to elementary school chose the academic stream (this choice might also be related to the fact that I went to a French immersion school) and it was only in grade 11 and 12 that my friends who were interested in arts considered the college stream for the math and science they had to take. I don’t remember there being very many applied sections in my school.

Having gone back and looked at the courses again as a teacher, I now see that the curriculum between streams is not the same at all. I have only worked in high school as a student teacher, but what I saw was a large gap between grade 9 applied math and grade 10 academic math. Perhaps we are helping students who struggle by allowing them to take a grade 9 course that moves at a slower pace, but they would have to work twice as hard and twice as fast to learn what they missed if they ever wanted to switch to the academic stream. In my opinion, grade 9 is far too young an age to have students choose their career paths, but it seems though that is what we are making them do by choosing between academic and applied.

At the college where I work, we make students take a math placement test before they start our program. Our programs are all heavily chemistry and biology based, so they need a firm basis in math. This test does not affect whether or not they get admission to the program, but it tells us which courses they need to take. When I first started teaching two years ago, students would take the test and those who placed high would enter math173, those who placed low would take math148. These two courses were meant to have the same curriculum but the lower lever course met for 1 extra hour per week in order to give students more time to learn. The two courses had different tests and different exams, but at the end students were suppose to have the same level of mathematical proficiency. Of course, this did not happen. The lower level course moved at a slower pace, and though they still covered the same topic as the higher course, they were not able to do so in as much depth or ask questions that were at the same level of difficulty. The expectations were much lower. Students came out of that course not having learned the more complicated material within each topic, but still receiving an equivalent credit for their work. In some ways, doing poorly on the placement test was advantageous, because you were put in an easier course. Of course you were at a disadvantage when you needed that math in an upper year course. Streaming did not work in this case.

The courses are much different now. When students do well on the placement test, they take math173. When students do poorly on the placement test they take math148 and then math173. This system works well because it gives students who need it the opportunity to learns the basics, but also recognizes students who do well on the test. The students who score low on the placement test do end up taking an extra course, but it is to their advantage since it brings them up to the level where they need to be to be successful in the next course. It allows everyone, regardless of their math proficiency coming into the college, to reach the high expectations we have for them in math. I don’t know if this type of system can transferred to the secondary system, but it works very well for us.

Thoughts about Streaming & Balkanisation

I have to admit these three articles had me thinking about a lot of different things that would make this blog go on forever, so I decided just to take a couple of points.

1) Streaming – I wonder if discussion of streaming rises with as much fervour as it does in mathematics. It certainly seems to rear ‘its’ head in every school I have worked in, and generally the math teachers were always in favour of streaming. Now I have to admit I have worked mostly in schools where the streaming was academic and enriched, general was not offered; therefore the students who were in academic were not at risk of limiting their future choices as seen in the chapter by Dei et al. Do I agree with streaming, I have to confess there are days when I will say yes, and then other days when I will say no. It is a subject that I have never been able to be definitely on one side or the other.

Many years ago I was asked to research the viability of deciding to stream from grade 7 on. I did the research, I went to a few schools where streaming was instigated to ask why and teachers’ thoughts about it, and I have to say that again I could find arguments for and against – it was a somewhat frustrating journey. This is not a topic with a clearly defined right or wrong answer. Again, I do speak from a unique perspective of academic vs. enriched, so my concerns for streaming may not be necessarily the same as seen in the report or chapters. Except for perhaps the concern that enriched courses may be seen as status symbols – ‘ins’ versus the ‘not-ins’ as described by these authors. This always tends to be a frustrating topic for me.

2) Balkanisation - I can understand where the teachers are coming from in Roxburgh High. I do believe that teachers do gain a comfort level in their teaching and feel that their ‘methods’ are working so why change them. I confess that for the last couple of years I felt that I was falling into a rut myself and decided it was a good time to leave teaching for the year to earn my Master’s. I feel that I can honestly say that the courses I have taking thus far has forced me to reflect on my practices and determine what I may be able to do when I return to teaching. However, having said that I know that once I step back into the school environment I am going to have to fight against a lot of bureaucracy and pressures that comes with an ‘academic’ setting that may slow down my chances of implementing new ideas, especially if positive results are not seen quickly. Perhaps this is a possible concern of teachers at Roxburgh? Why change what is working? Yet from the article, it would seem that the teachers were not aware that what was happening was not in fact working for the students in the general courses.

In the IB programme, students are to take a course from six groups (first language, second language, humanities, science, math and arts), but in actual fact they can opt out of taking a course in Group 6 – the arts. Generally, a lot of students choose to do drop arts and take a second science or humanity course. I never thought to ask my colleagues how they felt about this option for students to drop out of Group 6, but I would have to think that there must be (?) some level of discontentment that this is allowed. I really should find out!

I think I am going to stop here for I believe I could write a lot more.

Thank you.

School structures and math education

So, after reading this week's readings, I'd love to hear from you all about how you think a) department structures, and b) streaming, affect the ways you interact with students, the ways you teach, and the ways you learn or learned as a student.

I went to high school in Ontario when it was streamed into Basic, General, and Advanced. And at the time, I remember noticing that kids from different neighborhoods tended to be streamed differently. I also sort of recognized that there were socioeconomic differences between the neighborhoods. But it all seemed normal and natural to me - probably because I was in the Advanced group so it didn't seem unfair.

As a teacher, department structures definitely affected the way I interacted with students. I only ever knew the other math teachers - but then again, I was only a student teacher so not really part of the school. But I really only had access to math teachers and their opinions about the students and about appropriate teaching methods. Streaming also played a big part because the teachers I was working with had very definite ideas about what was appropriate for the high vs. low streams. Don't get me wrong - I don't think there is anything inherently wrong in teaching differently to different classes of students. What I have a problem with is that a) these assumptions about what is appropriate tend to be made before teachers even know their students - you just know, for example, that it's an 'applied' or an 'academic' class, and therefore b) teachers seem to place a lot of faith in the streaming process and in the idea that students learn better when they are with others 'like them.' I'm not convinced that this is true. Other studies of tracking have shown that students tend to learn more in the higher tracks - what with higher expectations and more rigorous work.

I'm curious about how department structures and streaming affect(ed) your teaching and learning experiences.

First week's reading

Gap-gazing to me is also a new term but considering the fact that i am new in Canada i will be coming across lots of terms in maths and in various fields of education that i think i will not be familiar with, and i am hoping that Ms. Indigo and all experience teachers in my class will help me understand the education system of Ontario . Last year i was watching CNN and i found out that in year 2009 out of every 25 student 19 students are asians who beat americans in maths in SATs and GMATs. I am not sure about all the factors that are creating this achievement gap but after reading this article i can see Rochelle Guiterrez preoccupation with gender, race etc seems to suggest that the full set of factors that actually create the learning gap might not have been fully brought to light or might be wrongly attributed to race, gender etc. A case in point could be the impact of cultural differences across different nations that affects math learning. Chinese parents, for example, have a much stronger desire to see their children succeed in life and subject them to a much more rigorous learning process. Many chinese children attend chinese schools on weekends where they are exposed to a much advanced level of mathematics. This extra practice and exposure to advanced mathematics makes it so much easier for them to excel in the weekday schools. Another example is the lower education levels of latino and black parents and therefore their lack of awareness and inability to help out their children as compared to white parents. Hence further fact finding and a more nuanced analysis would definitely bring factors such as these to the fore and allow a more targeted and effective problem solving.

I agree with dimensions of studies on equity, however just like Diane i am not sure i clearly understand “power” as a fourth dimension.

Gap-gazing: Abandon Ship?

Like Leslie, “gap-gazing” for me was a completely novel term albeit an interesting one. Gutierrez’ article does well to outline the dangers of maintaining an achievement-gap focus. She describes that gap analyses and statistics, more than often, paints a static picture of inequalities and can also perpetuate narrow definitions of learning and equity (pg. 357). Gutierrez advocates that we move away from gap-focused analyses towards more “accessible” and contextualized research.

As the world of science and technology advance, society in turn has come to value efficiency and productivity. In turn, studies of efficiency and productive have come to depend on scientific methods and statistical research. Case in point – Media and Ad campaigns have used familiar tags such as “scientifically proven” or “scientifically tested” in order to market and sell products (capitalism served on a plate). With this view in mind, it is not surprising that educational institutions have standardized evaluations – afterall, aren’t schools the “factories” that generate the workers of tomorrow? If so, then why not measure their efficiency? Before we condemn the achievement gap analyses, let us stop and think. Many of us are here because we are math educators or at least value math education. Aren’t some of us math experts that pride numeracy and the power of statistical analyses? If we are to abandon research that documents gap analyses like Gutierrez suggests, then aren’t we being hypocritical?

The problem here is that we have learned to take gap analyses literally. Correlation does not mean causality. The way I see it, gap analyses simply displays variance, nothing more. A number itself does not have meaning. By simply placing equality on the notion of how “similar” EQAO results are ultimately does not do justice. At the same time, I do not think it is suffice to simply abandon research on gap analyses. We must not forget some of the positive outcomes of gap analyses (i.e. more funding for schooling, credit recovery programs, and elementary and secondary mathematics initiatives).

Before we abandon ship, let’s work to fix it.

Struggles to understand identity and power

I think Gutteriez talks about what is ultimately important in education- pursuing excellence where as Lubienski speaks about what is pragmatic in terms of making changes.

I found Gutteriez four elements:

-access

-achievement

-identity and

-power

helpful expand my thinking about equity, but I feel my understanding of the latter two still foggy. For years as a teacher I have focussed on access to meaningful mathematics and promoting high achievement. I would even add “Awareness” to this list, helping students see the value of marks and the conventions of schooling and middle class.

As for identity and power- a bit of background may help to put my comments in context. I am from Northern BC- 1 hour from the Alaskan Panhandle. I realise now that we were statistically poor, but so was the rest of the community so we didn’t know it (one we only had 1 TV channel). Almost everyone I knew was self-employed or worked small family companies in logging or ranching. Independence was a very prized commodity, as was community; strategic behaviours to get promoted or noticed was completely absent.

Since I have lived all over Canada and in Europe a couple of times and my understanding of power and identity have been challenged. For years I just wanted to move “home” because I had a community there. It is only in recent years, that I realised that a lot of this was a struggle for identity, the communities I live in now have different norms and I not really sure I know how to fit into them.

I almost didn’t go to university because no one I knew did but a guidance counsellor put a lot of pressure on me and my sister to go because we were strong students. I loved it my sister didn’t like the environment and dropped out after a year. No one in the family questioned her decision- “Do what you want to do” (Just an aside in terms of equity- She has way more work experience than I do, yet I make double her salary). My parents were proud of me for completing a BA and MA, but openly questioned the value of a PhD.

When I first became aware of “power” in a course for my Bed, I was very uncomfortable with openly teaching about it. It seemed to me that the activities I saw would build resentment among the less powerful and I didn’t see the value in that. As a teacher, I did what I thought was best for my students, and this was informed by my experiences in a community that didn’t value schooling. I acted as the schools IT coordinator, and initially I had a lot of influence on decisions being made in the school, but with a change in administration, I become voiceless in the school and resentful of the fact. Starting my MA, was a result of this. I can now see some ways that other teachers behave to have a voice in school decisions in the school, but I as try out new behaviours, I think sometimes I come on too strong and may come of abrasive. I also struggle with who I want to be- brown-nosers were really looked down upon in my world. How to act proactively yet maintain some sense of identity?

It is this recent awareness of education politics that makes me appreciate Lubienski’s argument. Test results are important to policy makers. And we need these people to invest in education.

These reflections developed in my forties with a lot of education, and I consider my culture to be fairly close to mainstream (maybe I am wrong about that). How do we help students of other races and cultures feel they can participate effectively in the mainstream and yet maintain their identity? How do we raise these issues in the classroom without alienating students that feel as I once did?

Thoughts on this week's readings

Re: EQAO & Gap-gazing

To begin with I have to admit that I have never heard of the term ‘gap-gazing’, the concept, yes, but not this terminology. Also, I have to say that I have had the opportunities to read and research gap analyses as defined by Lubienski; the idea of looking at results of students on achievement tests and seeing these results used as a comparative tool (e.g. White-Black, White-Latino, etc.). I do agree with Lubienski that these tools can be used effectively in changing my teaching practicing and in fact every year as an IB teacher I receive three pieces of information: individual student result, math grade results compared to world and a report that explicitly gives feedback to what areas (topics) were considered difficult. I use this information to change what/how I teach the following year. I feel that this is invaluable.

However, I understand Gutiérrez’s concern that comparing White-Black, White-Latino, etc. is a very limiting tool and I was surprised to learn that longitudinal studies have not been done (or not enough) to look at how a particular group (Blacks, Latinos, Asian, girls, boys, etc) has gained (or not gained, if this should be the case) understanding of mathematical concepts over the years, that only the above achievement results are truly looked at. This is a concern for how can any teacher help a student or group of students if we do not truly understand what success or failure, what concepts do they understand or not understand, if we only see how one group succeeded against another. I have to admit I work in a fairly homogenous environment, but even in this environment I could provide a more enriched learning environment if I had research information that shows me clearly what works for my group of students. I did find it interesting that Gutiérrez still approved of standardized tests; I would have thought that the high stakes aspect of these tests and the overwhelming role that the results could play in policy making (in the US, school results could mean lost of funding or even school closure, happily EQAO results have not led to this for Ontario thus far), that Gutiérrez would like to see these tests removed. Yet she feels that these tests measure her concept of excellence, but do they really?

With respect to the EQAO article, I found this paper to be too ‘rah-rah’, but understandable as this is a government created organization and they want to show the stakeholders (parents, students) that improvement is being seen in mathematics. However, if one looks closely at the numbers, the EQAO claims are a bit generous. Yet, I do not feel that I can comment too much about the validity of these tests as currently my school does not administer any of these tests other than the Grade 10 Literacy test. I look forward to talking to other teachers about these tests and if they are a) good indicators of improvement b) helpful in the teaching of the math curriculum or c) if the results do help teachers to change practice accordingly.

Thank you.

Leslie

Gap-gazing and the EQAO

It was really interesting to read Gutierrez's critique of 'gap-gazing' right after reading the EQAO report on mathematics achievement in Ontario. Specifically, I found that even though the EQAO is not really presented as an analysis of gaps, and the authors don't explicitly articulate a stance on equity, a lot of the analysis in the report is about the gaps.
On the one hand, I appreciate the way the report focuses on excellence by looking at how many students from various groups achieved levels 3 and 4 (achieved expectations). This is in contrast with just looking at gaps between groups. So, for example, the problem for applied students is that not many of them are achieving proficiency - rather than articulating the problem as being that they don't achieve as well as the academic students (on average). This focus on excellence matches Gutierrez's recommendation for equity research.
However, I think Gutierrez would critique the recommendations that were made for teachers (the last few pages of the selection we read). These definitely treat problems of achievement as 'technical' problems - ones that can be saved by a few changes to pedagogy, a little tweaking, but no real fundamental change. There was no mention of sexism or gender bias in the section on gender, and no mention of racism or xenophobia in the section on English Language Learners. But I believe (as Gutierrez also articulated) that the political and social contexts of schools have a big impact on the learning that is made possible, and I don't believe that small cosmetic changes in teaching (like using Universal Design or differentiated instruction, or mixed-gender group work) will make the kinds of changes that are required.