I wrote an overview earlier about the structure for this conference, and then a Part 1 about conceptualizing the various aspects of "mathematical tasks"
The topic of the plenary panel was The Calculus of Social Change - Mathematics at the Cutting Edge. Mamokgethi Setati Phakeng (South Africa) was the convenor, and four individuals sat on the panel: David Wagner (Canada), Paola Valero (Denmark), Margaret Walshaw (New Zealand), and Anjum Halai (Pakistan and Tanzania). Each panel member presented their thoughts. This is followed by a response from another panel member, followed by an audience response. At the same time, Mamokgethi somewhat facilitated a twitter discussion through #pme2014panel.
There was quite a bit that was presented, as well as quite a bit that was discussed. I will make some attempt to write about this, but note that any mistake is my own.
~~~
Recently #Ferguson has sparked some more well-deserved discussion on the topic of race. If you aren't aware of what has recently occurred in #Ferguson, it's probably a good idea to swim around Google for a while. But also watch this:
It is depressing, disappointing, and horrifying to think that we require an incident like this in order to engage in these types of discussions. It's even more disappointing to listen and read people who believes that this isn't the issue. Or that we shouldn't be talking about race anymore. Race and racism has not been, and will never be, a relic of the past to be forgotten. It still exists, even here in Canada. It may even take different forms, or even go unnoticed, but it still exists.
But let's pretend it no longer exists. Not one individual in the world is racist. We still have not gotten rid of it. It has unfortunately embedded itself into our history, and therefore into each and every one of us.
So unless we can develop a time machine and change history, as Aamer Rahman suggests...
... It is impossible to wipe the slate clean.
Of course, the issue in #Ferguson isn't just race. There are a lot of issues at play. However, for the purposes of this post, I am going to focus on racial tension and more specifically in the context of education. It's a huge issue that has affected everyone - whether they know it or not.
First, let me begin by describing what came out of the plenary panel, as well as some useful quotes to think about.
In preparation for the panel discussions, the 4 panelists were asked to respond to a fictional retired mathematics education researcher who propose to build a new school in rural South Africa, built on demographic principles. Specifically, the following questions:
The need for social change is something that all mathematics education researchers would agree to and support. However, the fight for social change, regardless of the form the battle takes, is deeply imbued with emotion: Often we want to hear about the life changed, the child educated, the mathematics transformed and the poverty eradicated. We also want to be sure that we contribute to a cause that seeks to better the world, or that volunteering to serve a cause, giving one’s time, money, sweat and tears will achieve a positive impact, however small.This plenary panel was organised in a way that cuts through the emotions and the mere talk and gets to answer a simple question: How can we create a school mathematics education context that is built on democratic principles? As researchers we critique easily, but this panel discussion is an attempt to go beyond critique and theorising to think deeply and engage with the challenges of effecting social change on the ground. -Mamokgethi Setati Phakeng
1. How can I ensure that this school is built on democratic principles?
- Given the context in which the school will be located, how can we deal with issues of learner selection? Whom do we select, how and why?
- What should be included in the mathematics curriculum to ensure that they do not only have access to higher education in science, engineering and technology but that they are also socially aware?
2. What should the projected identity of the school be and how should it be constructed?
- How can we engage with issues about what the learners are becoming as a result of being in the school?
- How can the school deal with the challenge of constructing an identity that is not elitist in a context where success in mathematics is regarded as elitist?
Mamokgethi recognizes that "there are no quick fixes when it comes to mathematics of social change," and stated:
- the socio-political roles of mathematics are neither fixed nor determined
- mathematics education can mean disempowerment or empowerment
- because mathematics education does not contain any strong "spine," it can collapse into dictatorial forms and support the most problematic features of any social development (Mehrtens, 1993)
- In the same way, mathematics education can also contribute to the creation of a critical citizenship and support democratic ideals.
Wagner was the first panelist to present, and I noted the following from his presentation.
"We need to develop curriculum that equips learners to participate in discourses, as well as engage in critical reflection on the discourses (even math discourses)"
"We mathematics educators could do better at accepting diversity: e.g. linguistic diversity, continental prejudices."
"We need to be open to diverse approaches, and recognize value in traditions."
Wagner also struggled with whether he should participate as an advisor to this fictional situation since he is "a creature of privilege: white, relatively wealthy, well-educated, male, and a citizen of a relatively safe and prosperous country."
Some thoughts:
This is a notion that a lot of us well-intentioned teachers struggle -- and should struggle -- with.
With the backdrop of the history of oppression, as well as many other pressures (cultural, economic...etc), the idea that "these teachers are nothing like us and are not interested in knowing about us" is difficult and devastating.
Jason (@jybuell) co-authored this post with Grace (@graceachen) in the summer last year, and have continued to engage in a lot of discussion surrounding race. This post provided some really good thinking about supporting teachers of colour. There was also a global math department session on Big Marker called "Supporting Students of Colour" in March earlier this year. The recording is worth checking out.
The next speaker was Anjum Halai. She states that "setting up a school is not enough. It has to be with conditions for the school to realize." The community in disadvantaged and poverty contexts poses several challenges: uneven access to secondary education; variable digital and numerical literacy; remoteness from opportunity, media, internet; multilingual and multi-cultural intake.
Halai references Fraser's framework (2007) of social justice: Redistribution, recognition, and participation. Where redistribution refers to the access to mathematical knowledge, skills and ideas important for success in mathematics. Recognition represents ackonwledging and respecting the diverse backgrounds and needs of individuals and groups such as gender, ethnic or linguistic minorities. Lastly, participation is the concept of challenging the hierarchical power structures and norms in the classroom to create opportunity for all learners to be active learners.
These are all concepts which are built upon the idea that the learners identity is not a passive recipient of knowledge dispensed by the teacher, and that they identify themselves as becoming mathematically proficient.
Halai carries on to describe her recommendations and implications for this fictional school.
1. Selection of learners
In the context of limited access to secondary schooling, Halai points out that the issue of learner selection are complex. It needs to aim to re-distribute access and provide a multi-faceted admission policies that includes many different criteria. After entry, she recommends that there exist "bridging classes" in the afternoon to support learners that require upgrading of numeracy and digital skills.
2. Relevance of mathematics content and process
"Curriculum content in this school would need to go beyond the usual emphasis in Euro-western mathematics to recognize the mathematics rooted in the historical, cultural background of the learners." Halai also encourage the following recommendations with respect to the pedagogic process: inclusive in terms of high expectations from all learners irrespective of their socio-economic background, culture, or gender, and creation of space for learners to co-construct mathematics knowledge. She also give an example of "intership placement" as a possibility for learners to work on real mathematics problems in work-place situations in the community.
3. Teacher recruitment and professional development
Ideally the teachers would come from the community. Halai recognizes that qualified teachers are most likely not going to come from the communities. Therefore she recommended that "Adequate measures for recruitments and retention would include liaison with key education stakeholder, and a system of rewards and incentives on the basis of a nuanced understanding of education quality that goes beyond the traditional focus on achievement in examination." This is combined with regular professional development.
4. School community links
Halai emphasizes that the school CANNOT be separate from the rest of the community. She recommends a strategically formed board of advisors with members from the local community and the professional community. She also recommends that the secondary school in the midst of a highly disadvantaged community "could strongly support the youth by skilling them to participate in the society and leverage their education to come out of poverty."
Some thoughts:
While Wagner provided some good background thinking, Halai was the one that really "went at it" in terms of recommendations. These things that she mention are not easy, but definitely necessary. With respect to pedagogy, I definitely agree that social change and empowerment is possible through redistribution, recognition, and participation. This not only corresponds with our current frame of mind (group work, cooperation, student-centered), it also provides an additional reason for doing it in the first place. The power dynamic in the classroom can only be exacerbated by an "I talk, you listen; I do, you follow" paradigm.
Listening and watching students share ideas while we construct knowledge together -- is a powerful notion that math educators in North America are still struggling with, even after decades of further understanding the concept of learning. Strategies like the ones that many different educators in the #MTBoS definitely work closer towards this goal of social justice. In these strategies, many of us agree that students need to be the ones doing the learning -- that students need to be the ones that get their hands dirty in order to construct knowledge for themselves.
Valero was the next to present. She begins with a slide titled "Theory is action," acknowledging that "it would be arrogant to say 'based on my research, you should...'"
"What then can I offer?" she continues "Theory, analysis, not more than that" and it is the most powerful tool we have.
She then defines theorizing as "the practice of imagining what is not yet possible," and states that "without thinking seriously, there is no change."
Valero then provides some definitions and backgrounds of mathematics education, as it relates to power and poverty. Notably:
"Mathematics education is no other than political, and effects power through its organization of the population, the schools, the classrooms and the teachers and pupils as well..."
"Such organization though, does not happen in a vacuum but is part of historically constituted forms of thinking about the Self and the Other."
"Education is an institution that classifies, selects, and grants credit to some and, at the same time, has to inscribe failure in others as the very same pre-condition for its functioning. The failure of many in mathematics is the precondition for the success of the very few. It is the failure of the many what grants value to the few who succeed." *side note: True, and what a devastating model that we have built as human beings.
Valero indicates that in the effort of "decentering the curriculum, no matter what we do in education, there are always power effects: the rethinking of mathematics education is not an easy task if a strong political concern is taken into consideration." She comments that her analysis is "not as optimistic as [the intentions of the proposal]... [but states that] Not being optimistic does not mean that such an initiative should not be realized."
She concludes with the following two insights:
- The mathematics education affects power through the fabrication of children's self, that is, their subjectivity; and performs simultaneously inclusion and exclusion
- School mathematics curriculum could be articulated around the construction of children's subjectivity. This displaces mathematics as the core of the curriculum, to open for subjectivity to become the articulating axis around which mathematical forms of reasoning and acting could be organised.
Thoughts:
These were important considerations that, in my mind, further support the need of providing student-centered opportunities within the classroom. The concept of displacing mathematics as not being at the center is also more closely tied to one of my broader dreams for education: one where students are working on projects that they are interested in, and "subjects" like mathematics are learned as part of their problem-solving process. Several smaller schools have been doing this. So instead of forcing ourselves to apply mathematics to either the real or abstract world, we should be (as France Caron said during CMEF 2014) thinking of it as involving mathematics.
Margaret Walshaw was our last panelist that spoke, and she further explored the relation to the political, psychoanalytic, and cultural dimensions. She framed these in terms of questions.
First, the political question:
"How might we address the point that there is no emancipatory space ‘outside’ normalising discourses."
What does this mean? Let me include some other quotes that would shed some light on this...
"At what price does one become a mathematics student in this school?"
Under the context that not all learners would be selected for this school, deciding who enters the school has huge implications not only for those who are part of the school, but also those that are not.
And lastly, Walshaw poses the cultural question:
"What might be included in the mathematics curriculum?"
She continues:
A large number of teachers on #MTBoS has focused on engagement. Approaches such as #3act is one of the ways we tackle this. Often than not, I prefer pictures and videos that I or students have taken. Similar to what Walshaw thinks about with localized issues.
~~~
The above recap was hopefully a good place to start in terms of surfacing some large issues in the context of the simulated school. Some of these issues are ones that we as educators are unable to tackle. They are more immediately controlled by policy makers and administrators. Instead, I will focus on what us teachers can do.
I think I will pose a few questions, as well as "type out loud" for a bit.
The questions I pose are less global, and more about what we, as teachers and educators, do.
Race. How do we think about this in the mathematics classroom? How do we talk about this in the mathematics classroom? Do we even talk about it at all? What about stereotypes that the students have already "bought into"? What are our ways of mitigating that?
Jay Smooth, someone whose opinions I value, eloquently spoke on "how to tell someone they sound racist" about 6 years ago:
I thought, and still think, that this is an excellent video for addressing racist comments. Here is an adapted article from Jane Bolgatz on how to talk about race and racism in the classroom. But I have come to realize that those aren't the difficult conversations. The difficult conversations are the ones that never happen in the first place -- and offer no obvious opportunities for us to engage in.
For example, I am thinking about when a student has a deeply rooted belief that they are not good at math because of their gender or race. Or equally devastating, when a student believes that they (as in their culture or race) should be good at math, but they are not, and therefore they believe that they are stupid. Preconceptions and cultural stereotypes are truly horrifying in this way - especially since we often don't know the extent to which it operates in our own classrooms. Let me spell it out with some hypothetical examples that may or may not sound familiar.
1. A black student is down on herself because she isn't understanding something in mathematics. Other people attribute this to her being black. It was a casual comment, but she hates what others are saying. She hates other people's ways of classifying her as something simply because of the colour of her skin. Math isn't fun but she tries hard anyway. She tries to dispel the idea that she isn't good at this stuff, but every time she runs into difficulty (as we often do when problem solving), their words loom in the background. Slowly she begins to believe it. "Maybe I really am not born to know this stuff."
2. An asian student is distraught because she is suppose to be good at math. People tell her this. Society tell her this. In the hopes of a better future -- her parents tell her this. But she isn't. She has become used to the belief that she isn't. Perhaps it is also due to the stereotypes that she has grown to hate it. All of the efforts that she used to put into mathematics were always explained away as "oh you're just good at this stuff because you're asian." She begins to rebel. She rebels against the stereotype in order to somehow establish her own identity as "not just an asian student." She rebels against societal and parental expectations in order to feel alive.
These are just two examples of many many different circumstances. During conversations with other teachers, I have often heard the belief that students are just born a certain way. Students are pegged as "level 2" students or "A" students.
Maybe it is because it's easier on our conscience, or our own personal capabilities as facilitators of thinking, but we have developed these dichotomies of "smart" and "dumb." We have, in addition to this, developed simplified methods of explaining why they are smart or dumb. All the while ignoring all the different factors that go into "being good at math."
Race isn't the only issue that we deal with though. Other issues -- that we have unfortunately created through our failure to understand and communicate with each other as human beings -- are equally bad. For example, #1 may be replaced with a female student. We have, for some reason, developed social stigmas, racial stereotypes, and form judgement upon first meeting someone based on the colour of their skin, their gender, their sexuality, their age (yes even this one), their wealth, or their religion...etc. I believe these issues can only be dealt with by seriously thinking about it. Thinking about it out loud. Thinking about it with students. Thinking about it with the community. Thinking about it with families. But how do we do this?
As math teachers who are interested in the well-being and development of our students, we know that engagement is important. But to what extent do we seek pictures and videos that not only offer potentials of discussing mathematics, but also allow discussion of larger issues?
I feel like we've recently come to more of a consensus (or at least in my head, we have), that we engage student interest first and foremost with something like the following
*see more examples at this wonderful website.
We help students develop curiosity. We help them develop questions. And then we help them develop a process for reaching answers.
But a huge dilemma hides under our bed. What about those that are maybe not interesting, but are deeply important. Such as issues of race, gender, sexuality...etc.?
A few years ago I attended a few workshops on mathematics that are geared towards social justice. While important to think about, they unfortunately shared a common trait: There was a lot of reading (and somewhat boring.
They also seemed contrived. Instead of lecturing students about distance and triangles, let's lecture about distance and triangles on the platform of the slave trade throughout the 16th to 19th centuries. Maybe it is primarily the delivery that I am concerned about. If the concepts are demonstrated in a boring way, then perhaps we are missing the mark. Perhaps we are lacking the impact that these issues should have.
What do we do then? I have been thinking about this for a while. Recently about the nature of our mathematics tasks and considering the construction of the "real" and "fake" world. Before that, I have even abandoned a task that I've spent some time developing, for something more interesting. One that has implications to bigger societal issues: bullying. Why did I make that call? I think it was because I was noticing that there wasn't the intended conversation that the task was suppose to serve. If it doesn't serve this additional purpose, then it may as well not be there.
How do we develop opportunities for engaging in these types of conversations without them being contrived? How do we make them engaging?
One way that I saw a lot of potentials in, was to harness news paper articles. We allow students to develop questions without narrowing it to mathematics. We explore the questions and allow time to think about them. Conversations about mathematics then follow. But then what is "too soon?" What hits too close to home? This would largely depend on the relationship that we build with our students: What is comfortable for them to talk about... whether they feel safe enough in the classroom in order to share opinions...etc.
What are your thoughts?
First, the political question:
"How might we address the point that there is no emancipatory space ‘outside’ normalising discourses."
What does this mean? Let me include some other quotes that would shed some light on this...
Students, like their teachers, participate in a social web of power. What this means is that a new proposal for mathematical access and opportunity will govern, regulate, and discipline students as well as teachers. In other words, the identities that students construct of themselves will be made in and through the proposal’s pronouncements, its interests, and its investments in others. Power will do its work through the material, discursive, pedagogic and technological forms, as well as through the proposal’s discourses that relate to categories of gender, ethnicity, and a range of other social determinations. In short, a vision of change that is conceived of as emancipatory will always, at the same time, be regulatory.Second, the psychoanalytic question:
"At what price does one become a mathematics student in this school?"
Under the context that not all learners would be selected for this school, deciding who enters the school has huge implications not only for those who are part of the school, but also those that are not.
And lastly, Walshaw poses the cultural question:
"What might be included in the mathematics curriculum?"
She continues:
A curriculum transported globally overlooks important local knowledge about language, culture, family systems and values, citizenship and community. In other parts of the world, a number of researchers (e.g., Civil, 2002; D’Ambrosio, 1985) have privileged local knowledge and attempted to design their curricula around it. They have engaged with the local culture, its history, its demographics, and identified points of difference within that culture, not at a superficial level, but at the level that generates understanding of the day to day practices, the belief systems, and the power struggles. Engagement with these realities is a crucial starting point. The engagement will likely not only unravel details of life ‘lived at the edges’ but also important modes of operating within the social order. As one instance, you note that transport is expensive. Rather than centralising the teaching and learning opportunities in one site, you may choose to create village campuses—hubs of teaching and learning, not reliant on technology, in a number of localities... A low-definition curriculum might be called for. An analysis of current classroom and everyday life might suggest a need to go against the grain of mainstream theories of teaching and learning. A rigorous assessment will pave the way for informed curriculum policy decisions—decisions that are not simply based on inherited ideas from other cultures in order to play the game of developmental ‘catch-up’. A curriculum developed with careful thought will give expression to the key point that curriculum policy development sits at the nexus of culture, history and placeThoughts:
A large number of teachers on #MTBoS has focused on engagement. Approaches such as #3act is one of the ways we tackle this. Often than not, I prefer pictures and videos that I or students have taken. Similar to what Walshaw thinks about with localized issues.
~~~
The above recap was hopefully a good place to start in terms of surfacing some large issues in the context of the simulated school. Some of these issues are ones that we as educators are unable to tackle. They are more immediately controlled by policy makers and administrators. Instead, I will focus on what us teachers can do.
I think I will pose a few questions, as well as "type out loud" for a bit.
The questions I pose are less global, and more about what we, as teachers and educators, do.
Race. How do we think about this in the mathematics classroom? How do we talk about this in the mathematics classroom? Do we even talk about it at all? What about stereotypes that the students have already "bought into"? What are our ways of mitigating that?
Jay Smooth, someone whose opinions I value, eloquently spoke on "how to tell someone they sound racist" about 6 years ago:
I thought, and still think, that this is an excellent video for addressing racist comments. Here is an adapted article from Jane Bolgatz on how to talk about race and racism in the classroom. But I have come to realize that those aren't the difficult conversations. The difficult conversations are the ones that never happen in the first place -- and offer no obvious opportunities for us to engage in.
For example, I am thinking about when a student has a deeply rooted belief that they are not good at math because of their gender or race. Or equally devastating, when a student believes that they (as in their culture or race) should be good at math, but they are not, and therefore they believe that they are stupid. Preconceptions and cultural stereotypes are truly horrifying in this way - especially since we often don't know the extent to which it operates in our own classrooms. Let me spell it out with some hypothetical examples that may or may not sound familiar.
1. A black student is down on herself because she isn't understanding something in mathematics. Other people attribute this to her being black. It was a casual comment, but she hates what others are saying. She hates other people's ways of classifying her as something simply because of the colour of her skin. Math isn't fun but she tries hard anyway. She tries to dispel the idea that she isn't good at this stuff, but every time she runs into difficulty (as we often do when problem solving), their words loom in the background. Slowly she begins to believe it. "Maybe I really am not born to know this stuff."
2. An asian student is distraught because she is suppose to be good at math. People tell her this. Society tell her this. In the hopes of a better future -- her parents tell her this. But she isn't. She has become used to the belief that she isn't. Perhaps it is also due to the stereotypes that she has grown to hate it. All of the efforts that she used to put into mathematics were always explained away as "oh you're just good at this stuff because you're asian." She begins to rebel. She rebels against the stereotype in order to somehow establish her own identity as "not just an asian student." She rebels against societal and parental expectations in order to feel alive.
These are just two examples of many many different circumstances. During conversations with other teachers, I have often heard the belief that students are just born a certain way. Students are pegged as "level 2" students or "A" students.
Maybe it is because it's easier on our conscience, or our own personal capabilities as facilitators of thinking, but we have developed these dichotomies of "smart" and "dumb." We have, in addition to this, developed simplified methods of explaining why they are smart or dumb. All the while ignoring all the different factors that go into "being good at math."
Race isn't the only issue that we deal with though. Other issues -- that we have unfortunately created through our failure to understand and communicate with each other as human beings -- are equally bad. For example, #1 may be replaced with a female student. We have, for some reason, developed social stigmas, racial stereotypes, and form judgement upon first meeting someone based on the colour of their skin, their gender, their sexuality, their age (yes even this one), their wealth, or their religion...etc. I believe these issues can only be dealt with by seriously thinking about it. Thinking about it out loud. Thinking about it with students. Thinking about it with the community. Thinking about it with families. But how do we do this?
As math teachers who are interested in the well-being and development of our students, we know that engagement is important. But to what extent do we seek pictures and videos that not only offer potentials of discussing mathematics, but also allow discussion of larger issues?
I feel like we've recently come to more of a consensus (or at least in my head, we have), that we engage student interest first and foremost with something like the following
*see more examples at this wonderful website.
We help students develop curiosity. We help them develop questions. And then we help them develop a process for reaching answers.
But a huge dilemma hides under our bed. What about those that are maybe not interesting, but are deeply important. Such as issues of race, gender, sexuality...etc.?
A few years ago I attended a few workshops on mathematics that are geared towards social justice. While important to think about, they unfortunately shared a common trait: There was a lot of reading (and somewhat boring.
They also seemed contrived. Instead of lecturing students about distance and triangles, let's lecture about distance and triangles on the platform of the slave trade throughout the 16th to 19th centuries. Maybe it is primarily the delivery that I am concerned about. If the concepts are demonstrated in a boring way, then perhaps we are missing the mark. Perhaps we are lacking the impact that these issues should have.
What do we do then? I have been thinking about this for a while. Recently about the nature of our mathematics tasks and considering the construction of the "real" and "fake" world. Before that, I have even abandoned a task that I've spent some time developing, for something more interesting. One that has implications to bigger societal issues: bullying. Why did I make that call? I think it was because I was noticing that there wasn't the intended conversation that the task was suppose to serve. If it doesn't serve this additional purpose, then it may as well not be there.
How do we develop opportunities for engaging in these types of conversations without them being contrived? How do we make them engaging?
One way that I saw a lot of potentials in, was to harness news paper articles. We allow students to develop questions without narrowing it to mathematics. We explore the questions and allow time to think about them. Conversations about mathematics then follow. But then what is "too soon?" What hits too close to home? This would largely depend on the relationship that we build with our students: What is comfortable for them to talk about... whether they feel safe enough in the classroom in order to share opinions...etc.
What are your thoughts?
No comments:
Post a Comment