End-of-Course Reflections

Prompts generated at last meeting:

Dawn Anderson--Mathematics Education

At this moment in time, I view Critical Pedagogy (CP) as the following:

*CP is a form of activism that empowers the student to use mathematics to critique their position in a socio/historical/cultural place.

*CP is a site for resistance, agency, and activism whereby both the teacher and learner have power within the classroom.

*CP is a perspective that challenges the dominant discourses in education.

*CP and feminist pedagogy are intrinicately connected. In fact, I view feminist pedagogy as a form of critical pedagogy.

I am left to ponder many questions raised from this seminar. One in particular haunts me more than others: How can I "trouble" my teaching practices? This question seems be the core of CP and feminist pedagogy. As a feminist pedagogue, I want to trouble the way that mathematics is taught. I wish to challenge the dominant discourses that surround how we teach mathematics in this country paying particular attention to how our multiple positionalities shape who we are as mathematics teachers. These are just a few of my thoughts.

Beth Crook--Middle School Education

Kursat Erbas--Mathematics Education

Here are some of my end-of-course thoughts and feelings on Critical Pedagogy. First of all, I do not know any of you but most interesting part of the course was the diversity in such a small group of people. Well actually it is not surprising. I do not remember if we were able to put the discussions into a "clear" frame. This phenomena, I think, is the most convincing answer to the issue that most of the people in the class did not have a definition of a CP. After all, I found that it is really difficult to define and put CP in a particular frame. With all the ambiguous questions in my mind let me try to explain what CP means to me and how it should be reflected in inner-personal level and in teaching mathematics.

If I need to summarize what CP is with only two words, these would definitely be domination and balance. Except a few, people know and accept that this world is not a fair ground of play. You can reply the why question here according to your belief systems. Actually, that (i.e., "belief systems") should be the answer. We all are different from many aspects from fingerprint to footprint (I guess). Within complex and diverse identities, we try to be dominant. Now, please do not tell me that you do not. If you think and review your life little bit you will see that whether consciously or not you feel that you are special by some aspects. If you still say "no", let me ask you some simple questions. Are you proud to be an American? Are you proud to be a man/women? Are you proud to be a democrat? Are you proud to be É? And after each, Why? So you believe that something is more important than something else. Even democracy is a domination. Domination of democrats over republics or vice-versa. So, every of us lives and breaths the joy of being dominant race, gender, nation, or etc. Let me remind, after all, as a human being we are the dominant ones. So, there is imbalance toward domination among characteristics. And usually, imbalance means oppression and marginalization of other end. Now there are two basic questions at that point. One is if it is possible to chance the balance for the sake of marginalized. Indeed, yes. And it is happening naturally. Power relations are open to change and not stable. Evidence! Check out a history book from main library. But, this is not the answer to our problem. In fact, it is the same problem in reverse order. The second question is if it is possible to achieve a balance among identity categories. I personally do not believe if we can achieve this in global level. The furthest we can go might be at personal level. Even in this, it will be very limited considering all the possible conflicts in inner and inter personal levels. Two important aspect of balance are awareness and respect. I believe, the ultimate goal of CP is (or should be) to raise awareness to what is going on around us, understand it and respect to the different one. I do not think that the goal is to reverse the balance in power of the previously oppressed. This idea is nothing but an encouragement of chaos and wars between identities and those who think in this way are not different than the ones whom they criticize. So, the issue is not (and should not be) my turn or your turn. Because, everybodyÕs turn will eventually come in this play.

What can we do in classroom as mathematics educators? I will not go into details and everyday spoken wishes of being fair, not favoring one student onto another, and etc. Although I am not sure at that position about how mathematics may directly lead to personal freedom and enlightenment for a more livable and peaceful world but it may at least raise awareness and consciousness toward the problems. Today, everything is statistical and based on data analysis. Mathematics is the powerful language behind those. I believe, real data, numbers, facts and figures should be core of mathematics. Use the data how many child is starving to death in somewhere in the world while we try to be on our healthy diets. Try to use the data how much of the world resources belongs or in control of the first world countries while we as people of those countries discuss the problems there. Facts are everywhere if you are willing to see and use it. I believe every educator who is sincere about CP issues will find ways to integrate important issues to their classrooms. In sum, integration of facts and mathematics will eventually raise awareness about issues concerned in CP. Of course, numbers without explanations and discussions will not mean too much. So, discussion of those issues in the classroom will make a difference.

I have lots of things I want to write or discuss. But I think I already covered enough space on the page. So maybe next time we meet, I can bring some of those to live discussion.

Amy Hackenberg--Mathematics Education

At this point (May 2001), I think a critical pedagogical teacher must listen to/learn to know students very closely, in order to understand them as individuals and in order to bring out their ideas and experiences in the context of the classroom. However, I also think that a critical pedagogical teacher must continually grow her knowledge about aggregates (groups) in society, including characteristics of those groups--she needs to be aware of stereotypes and the breaking of those stereotypes. That is, I think that in the classroom teachers must engage in a constant interplay between understanding groups that students may identify with and students themselves as individuals. This first characteristic is a huge job by itself.

I also think that a critical pedagogical teacher must develop her sociological imagination, meaning that she must learn to connect individual difficulties (her own, those of her students, those of her colleagues) with larger social trends and (for lack of a better word at the moment) structures. Maybe this idea is analogous to (or at worse repeats?) the idea in the first paragraph, in that I think teachers must be able to think both psychologically (i.e., focusing on an individual) and sociologically (i.e., focusing on a group within a larger society). In her community (a larger arena than the classroom), a critical pedagogical teacher must then act from her sociological imagination, which may include acting in ways that are not popular, that go against the grain. This second characteristic is another huge job.

Finally (for now)--and maybe this will sound a little simplistic--I think a critical pedagogical teacher must commit completely to the classroom and to her kids. In Zen practice, it is said that you must practice zazen as if your hair were on fire. One way to interpret this phrase is that there is nothing getting in the way of you and your practice--there is a direct line, no excuses, no hiding, no withholding, etc. Usually internal "obstacles" like beliefs and habitual thinking are what most seriously get in the way. A critical pedagogical teacher needs to have nothing internal stand in the way of her goals for kids, the actions she engages in to work toward those goals, and on-going reflection on those actions--reflection that promotes deep and sometimes difficult changes in later beliefs and goals and actions. I suppose I am really calling for ever-evolving clarity of purpose and action, which requires deep thinking, pondering, discussing, inner searchingÉand I suppose that many might argue that this quality is important for any teacher, not just a critical pedagogical one. Maybe if all teachers were to engage in this kind of process, all would be critical pedagogical? Ha. No. But maybe all would be critical in some way that would be an improvement over what happens now.

Bob Ives--Special Education

Here are a couple of questions I've been playing with that we didn't discuss in class.

1) If the goal of critical pedagogy is to effect change towards less oppression of marginalized groups or individuals and towards greater social justice, shouldn't we question our definitions of oppressionâ and social justice? It seems to me that we are operating under implicit definitions that arguably derive from the very same white, male, Western European, capitalist, heterosexual, ... hegemonic box that we are trying to think outside of. In other words, perhaps we use oppression and social justice to address concerns we have about voice, equal access to means of production, ... because those are things WE value from our own traditional views. If we act on our perceptions of oppression and social justice, might we be guilty of the same error as the boy scout who walks the little old lady across the street only to discover that she didn't want to go that way. Our intentions are admirable, but do those in the margins (that we defined) necessarily want what we want for them?

2) While we have often referred to the white, male, Western European, capitalist, heterosexual, . . . hegemonic view as an authority that we are questioning, certainly in the context of some groups, such as our class, the views of views of marginalized groups or individuals take on some added credabilitly and authority. Bakhtin suggests that our own ideological identities are often shaped by conflict between the authoritative word and the different word that is internally persuasive. "... an individual's becoming, an ideological process, is characterized precisely by a sharp gap between these two categories: in one, the authoritative word (religious, political, moral; the word of a father, of adults and of teachers, etc.) that does not know internal persuasiveness, in the other internally persuasive word that is denied all privilege, backed up by no authority at all, and is frequently not even acknowledged in society (not by public opinion, not by scholarly norms, nor by criticism), not even in the legal code." This leads me to two questions: first, how do our own ideologies predispose us to hear some words as internally persuasive and some not?, and what do those preferences say about each of us as individuals?

Brian Lawler--Mathematics Education

My end of semester ramblings...

I think this seminar has moved my thoughts and focus along into a realm that once again has me questioning whether much can be done in the public school setting, as it exists now. I have ideas how the singular ("academic") view of what mathematics and mathematical thinking are serves two significant roles in our schools beyond what we as teachers, parents, students, etc. are fully aware. (1) I think this view of mathematics serves to systematically shut out thinkers/learners who possess points of reference and experiences not common to the dominant (mathematics) culture. This shutting out leads to shutting down of self-creativity, self-expression, and self-confidence. As children are intentionally* taught that mathematics is something that is not theirs and not for them, while at the same time we (including the NCTM's current "Math is Power" ad campaign) bombard them with messages of "you must do well in math to do well in life" and "smart people do well in math", we erode further the value of learning and self-knowing that school should be, and move further and further into running soft-prisons as centers for re-education. I don't reserve the dire consequences of this diatribe only to those students who are seemingly failures at this re-education, but also those who possess the illusion of success. (2) In addition to the negative consequences for both the successful and unsuccessful learners of academic mathematics, I believe the hegemonic approach to math education serves only to self-replicate. It is highly unlikely new mathematical thought can emerge when our institution operates in such a manner. Just as an organism requires diversity and intermingling of a gene pool to create the random genetic freakish traits that serve to propagate a species, mathematics must rely on those who think differently in order to flourish.

I am ready to fully reject notions of expert and authority, for any perceived gradation of more full knowing is illusory. I feel the only equitable stance, although problematic, must be that all ways of knowing are equally valid and potentially true. Certainly, each way of knowing is equally true to each knower, provided we operate with the assumption all learners are rational beings and that what they know is viable within their realm of perceptions and experiences. I think it may be more interesting to focus on the acts of living and being human, of pursuing personal intellectual challenges and interests, and of contributing to the better living of others.

Charles Darwin said in The Voyage of the Beagle, "If the misery of our poor be caused not by the laws of nature, but by our institutions, great is our sin." I think as those of us who have the capacity to fundamentally change or abolish our system of public education continue to live our lives with this sin, we cannot be morally content nor satisfied with our own humanity. (So all of you who've read this and know me, I guess I'm still of the mind that bombs (figuratively) must be placed in the corners of each and every public school structure and a community-driven, grassroots effort must emerge to rebuild the system. I am open to ideas of change from within and appreciate seeing significant differences happening in small pockets.)

So, have I written in particular about critical pedagogy yet? I believe so. To me, a critical pedagogy is a classroom teaching practice in which the lead educator shapes visions of what could be explored and understood, generates a passion and excitement for this exploration, and supports each learner's research and learning with reflective, critical, and generative feedback. Beyond study of a discipline itself (and it's relationships with other disciplines and aspects of life), the critical pedagogue encourages further exploration and understanding of the role of the discipline in the society and the society in the discipline. And finally (for as far as I've thought), it is the goal of the critical pedagogue to coach a learner through making decisions whether to understand (know) the dominant culture's way of knowing, to choose to only create a personal way of knowing, or to know both.

So maybe my initial question, "Can this be done in school as it exists now?" is not a matter of building structure, time structure, textbook, or teacher preparation, but really a function of what society expects from it's schools. I believe people want independent, creative, confident thinkers for all our children. But at the same time, society fears (in both overt and in unknowing ways) the possibilities this reality may hold. I suspect as (or sadly, if) this societal re-creation of the purpose of schools were to come about, many "structural" changes would occur as well. Likely, one of the first will be a transcendence of the current efficiency model for public schooling that has been tuned and retuned for the past 150 years.

*I say it is intentional because: even though we, as math educators, understand and know the existence of this phenomenon, we continue to perpetrate the act.

So be it that these thoughts are jumbled and almost incoherent. That actually may be my most important end-of-semester reflection of them all.

Denise Mewborn--Mathematics Education

I am left with many questions after a semester of reading about and thinking about critical pedagogy. In order to choose between the questions, IÕll select the one that seems to best lead into the summer: What does critical pedagogy look like in the mathematics classroom (or any classroom, for that matter)? My biggest curiosity at this point is whether there is a distinction between critical pedagogy and "good teaching." I know that it is elusive to try to define good teaching, but I suspect that many of us would agree on an example of it if we saw it. OK, so I'm optimistic. IÕll bet that most of us would agree on some elements of good teaching if we saw it. (Leave David and Brian out of it, and IÕll even bet money on it!)

When I think of good teachers that I know, I think that most of them are using practices that would be consistent with the goals of critical pedagogy. They are empowering students to participate in and take control of their own learning. They respect students as people. They also respect students' ideas and genuinely believe that students (even kindergarteners) have something valuable to contribute to the classroom discussion. They do not use students' race, gender, or socio-economic status as an excuse for anything, and they do not allow their students to do so. In one sense, their classrooms are "colorblind" in that they have high standards for everyone. But, in another sense, these teachers are very perceptive about what each student needs, and they strive to meet each childÕs unique needs (socially, academically). They are equitable teachers because they do not treat everyone equally.

The thing I am unsure about is the role of social activism (for lack of a better term) that is implied in critical pedagogy. Most of the good teachers that I know do not overtly or explicitly encourage their students in the direction of social activism. I'm not even sure that most of these teachers would say that this is a goal of their teaching (even implicitly). I wonder if this is related to the age of the children? (All of the examples of which I am thinking are elementary teachers.)

OrÉand here's the big questionÉis it a part of critical pedagogy that teachers should let students make their own choices about what to do? Is it actually against the idea of critical pedagogy for a teacher to tell students what they ought to do (socially)? If critical pedagogy is about egalitarianism (at least in some sense), then what right does the teacher have to be telling students what they ought to do with their lives or with their knowledge? Who am I to say that a child should go to college or should study more math or should want to make a lot of money? Is it my job as a teacher to motivate my students to learn, to help them learn well, and to help them appreciate the value of knowledge? Period? Or does critical pedagogy require me to make my students aware of their plight (at least as I see it) and how education can help them change the course of their lives? This all gets into value judgments. Who says that my students and I value the same things, or even that we should? At what point am I infringing on my students' rights to be free and independent thinkers by deliberately trying to rouse them to some type of social activism? This question, while thorny, is much easier for me to deal with when I'm talking about a mathematics classroom. Somehow things look very different when I think about a mathematics education classroom full of future teachers.

When I think about my preservice teacher education classes, I do think I have some kind of an obligation or right to challenge the way my students think about social issues in education. I cannot in good conscience let students leave my classroom without attempting to make them aware of their views about who can and cannot learn mathematics and the potential impact of these views on their instruction and on students' learning. But where do I draw the line? At what point am I simply imparting my values, beliefs, and ideas to my students? What right do I have to expect them to adopt these as their own? And how would I ever assess their views on such things? Do I have a right to do so? But can I let a racist teacher walk out of my classroom and not say a word?

Aaaaaaarrrrrrgggggggghhhhhhhhhh!

Eduarda Moura--Mathematics Education

Charles Roberts--Mathematics

David Stinson--Mathematics Education

Rethinking Mathematics Education from a Critical Pedagogy Perspective - fancy title for a seminar, but what does "it" mean. I wish that as one of the initiators and a participant of the seminar for fifteen weeks, I would KNOW (or at least have some better understanding) what "it" meant. However, I have discovered through the course readings and class discourse that I am left only with additional puzzling questions and uncomfortable emotions. One of those puzzling questions is: How does Critical Pedagogy "look" inside a classroom or school? Although I do not know the answer to this question, I do believe the key to successful critical pedagogical classrooms or schools begins with a classroom teacher who is a critical pedagogue.

Now the question becomes: Who is a critical pedagogue? I believe the answer to this question is a teacher that believes in the Freirian definition of dialogue; the following lengthy quote is from Freire's (1970/2000) book, Pedagogy of the Oppressed:

The bold face words in the above selection are my emphasis. When I first read this passage from Freire during the seminar, I understood why critical pedagogy is important to me. In a few words Freire was able to articulate how I felt and what I attempted to accomplish when I was a classroom teacher. I believe the concepts of reflection, action, transform, love, humility, faith, trust, hope; and critical thinking are the foundational characteristics of a critical pedagogue. If the classroom teacher is not in possession of a belief structure that includes these concepts any attempts of implementing a critical pedagogical ideology in schools will ultimately fail.

Freire, P. (1970/2000). Pedagogy of the oppressed. New York: Continuum.

I have many pressing questions that (have) arisen from the seminarâ and still feel as if I am wandering around in a critical pedagogy fog. While I have too many questions to address here, I want to examine a few with you. In order to do this, I want to first give my own personal perspective as a human and as a teacher.

While engaged in this seminar, I usually try to read the articles on a personal level. This is a new technique for me as I try usually to look at issues objectively, in context. However, in order to view issues of critical pedagogy in context, I felt it was necessary to reflect on my own perspectives subjectively ö to dissect what I personally bring to the table of mathematics education.

As you have probably discerned, I grew up in a poor environment ö poor in the sense that we had very little money. There were ten in my family, including my grandmother who lived with us most of my childhood. My father was in the Navy so we moved a lot . I have told you about his background. He was one of eight children and his father died when he was nine. From that point forward he was sent to different family members to live. At one point (I think he was 12), his sister kicked him out of her house because he suffered a compound fracture of the leg and could no longer work. He was sent to a boys home for two years to recuperate. Later, while he lived with his two spinster aunts, he graduated from high school and enlisted into the Navy. I do not know why he had such strong convictions to make the "rightâ" choices in order to become educated and elevate himself to middle class. My mothers family came from share croppers and during the depression and prohibition, my grandfather made bathtub gin to sell illegally to the speakeasies in order to feed his family. My grandmother hired out as a servant in order to complete her high school education when her family moved on to the next farm. My mother's background, while harsh, was family oriented and perhaps that is where her values were learned which were later passed on to me.

I tell you this little bit of personal family history in order for you to understand my perspective that hard times and hard choices do not mean no choices. I do agree that some choices are available just because a person is white, just as some choices are available just because a person has a certain name, has a certain religion, is heterosexual, etc. These choices are unfair to those against whom they discriminate. It is important and necessary to recognize them and rectify the situation. Sometimes, we need to recognize within ourselves that we do have some choices, and through those choices, we create other choices.

Now, I would like to share with you some of my experiences as a high school teacher in order for you to understand my perspective of teaching. My collective students came from such diversified backgrounds, as most of your students probably did as well. My experiences with them are just as diverse. I have had students that fall asleep in class because they had to work to support their families or because they partied all night. I have counseled students who were pregnant or were abused. One of my students cried in my arms because her husband was dying from AIDS and she had found out that she and her three children had HIV. Another student sobbed fearfully in my arms after witnessing a stabbing. I rescued one student from a gun fight and counseled him at my dinner table while his gun was locked up by my husband in a cabinet. I've called social workers for evidence of harsh punishment in the form of cigarette burns and I've secretly handed off homework assignments to a student with unexcused absences who could not attend class because a gang war threatened his grandmother's life and he had to stay with her for protection. I've had students with ADD, ADHD, with various learning disabilities, and with behavior disorders. I've taught limited sight children and also deaf children. At times when the interpreter did not show, I have interpreted in sign language while I taught math. I have bought countless number of lunches and ferried students back and forth to games and practices and home. I even took one student home to change her clothes that were too revealing. At the bequest of my students, I have traveled on the team bus to attend away games, traveled up to six hours to attend tournaments, attended uncountable home games and practices, dance recitals, funerals, police interviews, court appearances, baby showers, and poetry readings. I have helped to sponsor musician trips to Europe, basketball and football and band championship state tournament trips, and have sent money and letters of encouragement to freshmen in college. I have tutored over the phone via local and collect calls and have written letters of recommendation. Some of my students are professional and collegiate athletes. One of my students has published a book of poems and one is wanted for first degree murder.

Are you tired of reading yet? I am sure you have similar experiences which brings me to my first two points (or questions as it were). First, since you can probably relate to these experiences, then you are involved with and knowâ something about your students. So, why do we have to be lumped with the uninvolved, uncaring, unknowing teachers of our readings? Please do not say that they are not talking to me. "Teachers" is not the same as "teachers except Nancy and her colleagues". The readings generalize and I thought the point of critical pedagogy was to not generalize. Second, while I have managed to involve myself with my students, my main focus was and still is teaching math. Math is the empowerment that will enable my students to have more choices or math is the art from which they may find beauty. But, they must choose to learn the math no matter the circumstances just as I have chosen to focus on the math no matter the circumstances. Now I read that the Math is suspect. So, what is the Math that I need to teach? It seems that none of the articles address such, only what we should not teach and I find myself in disagreement in much of those rare glimpses of concrete approach. While I agree that I need to knowâ my students for effective teaching and optimum learning, which is quite impossible I might add, my main goal should be to teach math. For if I do not, then I have dropped the ball and left it for someone else to carry.

The direct purpose of each math class that I teach is to teach math, not to become a social forum. I agree that social context is the responsibility of the entire school and should be addressed daily. But, in my math classes, social awareness is an underlying part of the atmosphere in the respect I demand for myself and each of my students. It is not usually addressed directly, although it may be if the occasion arises. I try to incorporate into my lessons the new things I have learned as I become more socially aware. There is not enough time in the school year to teach my part of the big picture (math) and address the social ills of the system directly on a daily basis.

Am I taking all of this too personally? You bet I am. I have come to this seminar with the excitement of learning new information concerning new ways to be further socially aware in order to better reach my students equitably. From my standpoint, I have learned little of how to do this. I have learned that others are concerned about the social awareness of the system and it's failure to incorporate these concerns. I have some idea of what critical pedagogy is, although if you put a gun to my head I could not define it in words. I have come to realize that the overthrow of the capitalistic society is advocated and that socialism is the preferred economic (political) system du jour. I have learned that other perspectives including the "post" and feminist perspectives are entertained, but that some are frowned upon ö including mine which is not in favor of jumping from the frying pan into the fire. I do not yet have a sense of what I can do in my classroom in a practical way to further promote social awareness while teaching mathematics. Perhaps later, when I have a better understanding of what is needed in my own classroom, I will be better equipped to spread the good news. As of now, all I am hearing is bad news.

We are preaching to the choir here, and I need a new song. I don't want to lead the choir in the form of radical social reform. I don't want to sing solo where my experiences are all that I portray in my classroom. I want to harmonize so that my ideas and experiences along with the shared ideas and experiences of others will blend together to help us to continue (or begin) laying a solid foundation of social justice in our (math) classrooms.

It was my intention today to address issues of critical pedagogy in the form of a critique of the last article as representative of our concerns. However, my fog is quite thick and I fear that I do not have much of anything intelligent to say. I have only questions about and issues with what is being addressed, although some of my feelings concerning the article are positive. Since you have read this letter, would you want me to still try to post it?