Restructuring Learning Spaces with Interactive Technology and Transformative Pedagogy

Roland Lucas

CUNY Graduate Center

Answers to IRB Questions

Part III. Protocol Description

III-1. State the purpose of the research.

Include major hypotheses and research design. If the study is part of a larger study, briefly describe that larger study and indicate whether it has received IRB approval from another institution.

The purpose of this research is to extend the existing body of knowledge on effective utilization of interactive technologies and math programs in public high school mathematics classes. It will also serve as a basis for ongoing development of teaching practices that improve student competencies and success in mathematics. The major hypothesis for this research is that high school mathematic students in urban public schools, who are provided interactive technology resources during the normal course work, will experience enhanced learning of mathematics, as well as increases in positive dispositions indicative of their identity development as competent doers of math. Some interactive technologies include: Moodle, Google documents and websites, Power Point, Excel, Maple 15. Another major hypothesis of this study is that through focusing on solving and sharing solution to problems that relate to the life world of students, that students will experience an increase in the levels of solidarity with participants of the course. This will have a positive impact of the learning experiences and performance measures for students in mathematics. Students will also develop an increased value of using their developing competencies with interactive technologies with the mathematics, to analyze issues relevant to their communities that can be modeled with the math they learn. They will see the mathematics then as more relevant to them, and become more engaged with the subject.

The research design is an ethnographic / phenomenological study of evolving attitudes and practices of students as they are engaged with math problem solving using interactive technologies. Students will not be asked to produce any data solely for the purposes of the research. All activities that students do, and all data that will inform the research, will emerge from best teaching practices that are supported by the chief school administrator and that are in agreement with national core state standards. All the methods and strategies employed in this study are ones that I have used over the past six years in my role as a highly qualified math teacher in Newark public schools. Similar IRB approvals have been granted to researchers associated with the CUNY graduate center’s science, math and learning sciences specialty of the Urban Education Department.

III-2. Summary of the research plan:

The research plan is that … Using non-technical language, provide a summary of the research plan in 500 words or less.

During the normal course of my teaching high school mathematics in a Newark public high school, students will relate the skills being taught to real-life scenarios that they identify as existing in their communities. Students will be asked to demonstrate mastery of content skills taught, through their problem solving in the context of these scenarios. Students are also given the option to select problems that don’t relate to their communities, but rather have to do with their career interests.  Students will make use of interactive technology resources throughout the problem solving process. The products of this work (i.e. student developed models with determined solution sets) will be captured in electronic form where possible.  This can be done through computer applications such as in word documents, Power Point presentations, worksheets generated using Excel, calculator, Maple 15, or Geometer’s Sketch Pad, for example. These products will be shared and discussed with stakeholders, such as in teachers, other students and parents. Printouts would be posted on school bulletin boards, along with other exemplary work done by them. The products of student work may be stored in the school’s Moodle repository (content management system), or in shared folders in Google Documents, or in student’s Google Website accounts that are managed by school administrators. The Google Websites can only be viewed by accounts that are associated with the school district. Discourse analysis will be performed on the products produced and will be part of the study. Student identifier information contained in files will not be included in the student.

Students will be asked survey questions about their experience doing this work, as well as questions regarding their attitudes and goals with respect to mathematics.  Answers will be created in school’s Moodle and stored there. The school’s Moodle is a secured site, accessible only to users who are granted access by school personnel. Student responses are not part of their grades for the course. The responses will be submitted anonymously so that students will not feel pressured to respond one way or another.  Students can opt out from answering any of the survey questions. Their responses are the heart of the study. Student responses will be analyzed using discourse analysis procedures, to ascertain if students are developing positive attitudes and competencies as doers of mathematics for their own benefit and for the benefit of their communities.

As the principle investigator, I will take field notes during the research period. I will interpret student dialogue and activity as another data source. The names of these students will not be used in my research.  The students will be assigned pseudo names in my field notes and research documents.  My field notes will be taken when classes are not in session, so that this activity will not impact the normal course of my teaching. The findings of my dialogue analysis performed against all forms of data will be shared with any stakeholder who expresses interest in knowing the results.  There may be whole class discussions on the findings of this research, as a means checking if members feel the results represent their work adequately. My finding will be included in my dissertation.

III-3. Detailed non-technical research plan:

Describe the proposed research plan. Include sufficient detail for the IRB members to clearly understand the procedures involved, the recruitment and consenting of participants, the risks and benefits involved, etc. Describe the data collection procedure below.

Students, who I’ve taught high school mathematics over the past 2 years at my current public high school of employment, have already done the kind of work that I’ve described for this study. I would have my current and future students do this kind of work even if this study were not to take place. There is no risk to students as a result of engaging in the activities that I will examine for this study. If students prefer not to do projects that relate to community, they have the option to do projects on their career interests instead. The below is a description of a project that I’ve already done multiple times with my students, and that would be typical of the kind of student work that will be studied in this research.

“4th Marking Period Project – Using a quadratic function to Model a real-life scenario”

Project requirements:

1) Find a word problem in chapter 4 of the course text that can be modeled and solved using a quadratic function.

2) Solve the problem completely as is.

3) Modify the problem to relate to your community or career interests in some significant way.

4) No two people can work on the same problem, so reserve your problem.

5) You may create your community or career related problem from scratch if you want.

6) Describe your original problem in the Moodle Forum discussion topic Titled, “4th Marking Period Project”.

7) Explain in Moodle discussion topic you created how you modified an existing problem to relate to your community or career interests.

8) Reply to 3 other project descriptions in the Moodle Forum with your feedback on how problem relates to community.

9) Explain the meaning of the vertex and the function intercepts of your problem.

10) Incorporate Excel (i.e. formulas and graphs), Maple, and/or any other appropriate technology to solve and present your problem.

11) Place all the electronic files of your work in a folder on Google Documents that you have shared with me (teacher).

12) You may share your work with any one you decide.

The following are some questions I’ve asked students to respond to within the course Moodle forum at various stages of their math course:

• What is a problem solver?
• Identify a problem / issue in your community that can be modeled by a math function.
• What is the usefulness of doing projects related to community?
• What do you think you want to major at in college? What is your career choice?  How can proficiency in math help in those areas?
• Describe your experience with co-teaching.
• Describe how you think others are experiencing co-teaching.
• Get opinion of community members on the issue you selected to do a math project on.
• Describe your current attitude towards math.
• Describe a past experience with math that helps explain your current attitude towards math.
• Describe how your attitudes towards math may have changed over the course of this school year to this point.

Students will create the descriptions of and solutions to their problem on the school Moodle, in Maple 15 or in Google Documents. All products produced can be shared with teachers and students in the school, once students submit them.

Typically I will ask students to dialogue with each other and other stakeholders about the problem scenario that they are investigating and any solutions that they have discovered. Students will be invited to modify solutions to their problems based on feedback given by others. I will ask students to record or transcribe this dialogue in the school’s Moodle. This dialogue will be used as input data for my study. Students also will be invited to discuss their opinions of this approach to problem solving that references issues encountered in their life world. These voluntary conferences will be held in groups led by fellow students. Representatives of these groups will be invited to share ideas and conclusions discussed, with the whole class. This form of dialogue will typically occur during class time for about 20 minutes.

If a student does not wish to participate in a class conference, then they are allowed to do other class work during that time. The results of this dialogue will be used as a basis by all participants in the course for improving the practice of integrating technology in the classroom. The results may also be used as primary data in my research field notes and integrated into my dissertation. I will perform discourse analysis over this data and draw conclusions about the levels of meaning making, authorial knowledge construction, and solidarity of students in their problem solving endeavors.

III-4. If you are using vulnerable population(s), specify the methods to be used to protect the rights and welfare of any vulnerable subjects. Address issues regarding recruitment, coercion, informed consent and assent.

Students will be asked to answer questions about their math experiences, and submit their responses anonymously on the course Moodle. The course Moodle will be accessible only to those who have a course key provided by me. Moodle allows for anonymous submission of survey responses. I will only use anonymous surveys. Responses to every question will be optional, and will not be factored into student grades. Students will be asked survey questions over throughout the duration of the study. Since NO student identifier that associates student responses with the student will be captured or otherwise used in this study, there is no risk of students feeling pressured to answer one way or another to survey questions. There is no risk of exposure of student’s answers since responses will be submitted anonymously, unless the student decides to share them in normal class discussions with others. Student responses will be analyzed using discourse analysis methods. All students will be made aware that I am studying the impact of doing this kind of work that relates math content to student lived experiences.  When peer-conferencing and sharing of findings with the whole class occurs, students will be given the choice to opt out, and do other work. No student is required to participate during that 20-minute period of dialogue about practices of integrating technology in the course.

Where I perform discourse analysis and report findings using student-produced data such as electronic files, or using field notes that I create after classes, I will not use student identifier information (i.e. file names that may have student names embedded in them). Where necessary I will use pseudo names in place of actual names. Based on my discourse analysis I will draw conclusions as to whether or not students express a marked development of their competencies and identities as doers of mathematics.  I will also draw conclusions about the development of their identities as doers of mathematics on the behalf of their communities. Students will be made aware of my findings after the formal course is completed. Their interpretations of my findings will be welcomed and incorporated into my dissertation.

Students will be given a parental permission form for their parents to sign to use student responses and produced work in the research, even though personal student identifier information will ever be used in this research. My research will involve no deceptive practices of any type, and I will make full disclosure, to all study participants and their parents/guardians, of my dissertation goals and interests.

Roland Lucas

CUNY Graduate Center

Dissertation Proposal

Abstract

My ethnographic research explores ideas around the construction of culturally empowering math learning spaces that mitigate constraining structures in public education, erected in large part by the historically constituted motive force of racism. I am interested in how interactive technologies can be deployed to facilitate the construction of these learning spaces, and accomplish the transformation of constraining structures. This practice entails using interactive technologies in culturally sensitive ways, contextualizing math content and the use of technology tools, with the life worlds and collective goals of students; rather than teaching math and technology tools in abstraction from these. This approach can create a multiplier effect of knowledge and social capital in local public schools and accelerate student achievement. This praxis would be a catalyst for a greater transformation that would cascade through to global levels of school systems and even to fields beyond the porous boundaries of schools. So ultimately I’m interested in promoting equity in local public schools that can have a larger ripple effect and promote equity in our global village.

The Urgency of the Matter

Just as technological innovation increases exponentially, so too does its impact on society increase exponentially. There is a growing divide between the technological advances / demands in society and the ability of students in public schools, particularly African American students, to match those advances / demands. There is a real danger that African Americans and other minority groups will become a permanent underclass that are unable to compete with respect to other groups, if the technical knowledge gaps continue to widen. It is vital for African Americans to demand and devise educational programs that utilize advanced technologies to accelerate their technical knowledge, forming a basis for attainment of their educational and societal goals.

One means of accelerating the closure of the said achievement gap in public education is through interactive technologies backed by a culturally sensitive pedagogy. My project is to model such a learning environment that can be generally replicated in public schools where African Americans predominate. If we can learn how to significantly improve education for African American students in public schools, we would have learned how to improve education for all students in public schools. The sooner we can close the said achievement gap, the closer we will be to producing a truly pluralistic society where all are more capable of meeting the demands of a modern world.

Theoretical Frameworks

One theoretical underpinning useful for conceptualizing the possibilities of significantly transforming urban education is Bakhtin’s ideas on dialogical discourse and “ideological becoming”. I use this lens to envision processes collaborative discourses and knowledge construction that can take place in culturally empowering learning spaces, through use of even using the most modern collaborative technologies. I also borrow heavily from Bourdieu, Collins, Tobin, and Turner for their theories and concepts of cultural structures and social transformation. Any project addressing the transformation of educational praxis must be grounded in a socio-cultural theory of action that accounts for the structures of the school environment as being embedded in larger cultural structures, the motives of the groups involved, and dynamics of social change.

Relations between Culture, Education and Social Transformation

In assessing public school policy and praxis, one must first place the school in the context of the wider socio-cultural field that it is situated in. Learning activity in any school setting are mediated by the macro and meso structures that schools are situated in. Schools are primary sites for the reproduction of the larger cultural values and motives, which often have much to do with reinforcing a stratified system of power relations. It almost goes without saying that these macro and meso structures will deeply shape the educational practices, experiences, and outcomes that occur.

Bourdieu (2000) intimates in his works that schools are sites where the reproduction of the structure of power relationships between classes occurs. This happens through the mechanisms of distribution of cultural capital. Implicating education systems as such, Bourdieu says, “this means that our object becomes the production of the habitus, that system of dispositions which acts as a mediation between structures and practice; more specifically, it becomes necessary to study the laws that determine the tendency of structures to reproduce themselves by producing agents endowed with the system of predispositions which is capable of engendering practices adapted to the structures and thereby contributing to the reproduction of the structures.”

One idea embedded within this statement is that actions by actors are tied up with an engagement of structures (“engendering practices”), which can lead to a reproduction of existing structures. This suggests to me that there must also be other side to the coin, that agents can engage structures with their most egregious elements, but rather transform them according to their own goals. It is this prospect that I consider in a project to use technology resources to support a higher ordered educational praxis for African American youth in public schools.

It is commonplace for those who benefit within a society where the distribution of resources is stratified along racial and class categories, to deny the reality that racism and classism still deeply impinge on the learning outcomes and potential of minority students in public education. This denial serves the purpose of maintaining these limiting structures and shielding their macro and meso level transformation. Bell Hooks, in her book “Teaching to Transgress”, references the need to transform educational institutions into sites of liberation …

“If we examine the traditional role of the university in the pursuit of truth and the sharing of knowledge and information, (Resources), it is painfully clear that biases that uphold and maintain white supremacy, imperialism, sexism and racism have distorted education so that it is no longer about the practice of freedom. …The call for a recognition of cultural diversity, a rethinking of ways of knowing, a deconstruction of old epistemologies, and the concomitant demand that there be a transformation in our classrooms, in how we teach and what we teach, has been a necessary revolution – one that seeks to restore life to a corrupt and dying academy. Hooks, B. (1994).

Racism is not the only force to be reckoned with. Classism, excessive capitalism expressed through globalization and manifesting structurally in local schools, is also a force in need of transformation. Ken Tobin in his paper, “Global Reproduction and Transformation of Science Education”, also makes the link of macro level structures impinging on the local school structures and limiting the educational outcomes / potential of minority students.

“The Neoliberal demand expressed through Globalization and reaching down to the public school system, tends to define education for mostly African American and Latino students in such narrow terms that are not in my view compatible with their overarching goals of becoming independently successful by their own definitions.” (Tobin, K. 2009)

Tobin asks, “How should access and appropriation of resources be included in a theory of freedom in science (any) education?” Tobin (2010) I extend this same question here by asking, how can technology resources be accessed and appropriated in culturally empowering ways to help these groups reach their overarching goals of becoming independently successful by their own definitions? I propose that collaborative spaces using interactive technologies can enhance learning for minority students, if constructed in culturally empowering ways that take up the challenge of developing positive student identities as agents for personal and collective uplift.

Bakhtin’s Dialogical Discourse and Identity Development

Agency involves an actor using available tools, structures or resources to carry out actions to obtain a goal. My unit of analysis is not the agency of African American students as individuals or even as a group onto themselves. Too often this kind of focus produces deficit theories, finding the problem of under achievement by African American students in their own bodies, minds and ethnic culture. It is not the African American student in isolation, even connected to advanced tutorial software applications that I consider. I consider activities of groups of students in collaboration through interactive technologies for the purpose of increasing their agency to offset much of the limiting structures of racism and classism as manifested in their local schools and communities. I consider how through their collective activities they can proactively solve problems that are relevant to their group and to their communities. I consider how having access to timely, relevant, and up-to-date knowledge capital and processes afforded by interactive technologies, can serve as vital resources to accomplish this.

Furthermore, collaborations in online learning spaces involving a community of students tend to make the construction of knowledge less centered on the adult teacher, and less an exercise of reproducing established knowledge and power structures. That is, knowledge production in interactive environments would be less authoritative, monological and passive as Bakhtin (1986, 2004) describes it. They would rather be more in keeping with Bakhtin’s concept of inner persuasive discourse where participants actively scrutinize, challenge, change, reject and argue over, existing knowledge to suit their needs and evolving understandings. Multiple “utterances” or dialogues are then considered, synthesized or otherwise reshaped as needed. New products that students appropriate and generate can be acted upon to support their agency and identity formation. Existing knowledge and relational structures will be reproduced only if they support the motives of the collective. If not, these structures will be targeted for transformation, thus providing for agency and liberating education.

Students will no longer fall into serving the intentions of dominant groups, nor channel the words, ideologies, goals, and problems of dominant groups. Students become critical thinkers, not just in their ability to analyze data and problems, but to do so in relation to their uplift and that of their communities. Without this critical facility, they would simply implicate themselves in sustaining the reproduction of their own subordination in society through a mis-educational system. They would “recite by heart” other people’s voices or structural rules. They would, in the Bakhtin sense, parrot authoritative discourses, rather than retell their stories in their own words. Learning to privilege one’s own critical voice is what Bakhtin (1981), refers to as “ideologically becoming”. This is education proper and is sorely lacking in public schools where African American students predominate. A culturally empowering learning space would encourage this kind of critical thinking and development of “voice” or ideological self through the process of sharing with and building upon ideas of others having liberating motives in a collaborative space.

Educational Transformation, From Meso to Maco Structures

Turner (2007) expresses a concept of social change through emotionally charged act emanating from the micro level of the human encounter, and cascading through meso and macro structures … “emotional arousal at the level of iterated encounters spreads through networks of meso structures, changing key corporate and categoric units or perhaps creating new meso-level structures, that change macro level structures. … For most encounters however, the culture of meso-structures is reinforced and reproduced which in turn, sustains culture at the macro level of social organization.”

I believe that the enactment of transformative education through the construction of culturally empowering learning spaces locally, can have a cascading and enduring transformative impact on how education is practiced on macro and even global levels, in public education. Turner’s cultural theory helps to conceptualize how such a transformation of educational practice can be initiated from local levels to meso and macro levels. It is my hope that such a model project of creating culturally empowering learning spaces, and the accumulated knowledge capital that it produces, will touch off cascading series of meaningful events that will durably transform educational practices.

Cultural Historical Activity Theory

The CHAT theory, also has promise in conceptualizing transformative, agentic educational practice that can further the educational goals of the African American collective. The unit of analysis of this theory reaches beyond the individual personal activity and subjective reality, in isolation from the context of the wider fields of social interaction. According to this cultural theory, individual activity, including learning in the classroom, is in symbiotic or dialectic relation with the wider community within which individual activity is embedded. “CHAT leads to changes in the location of representing what is educationally relevant: Its inherently dialectical unit of analysis allows for an embodied mind, itself an aspect of the material world, stretching across social and material environments” (Roth & Lee, 2007). Hence, individual learning goals, must be considered in context of the wider goals of the community within which the individual is situated. This is precisely the thrust of my approach on urban educational practices. I see collaborative technologies as tools that enhance the agentic activity of individual | collective African American student achievement. They can facilitate knowledge construction in iterative and accumulating developments, not unlike the multiplier effect of money in a closed economic system, thereby magnifying the capital wealth (knowledge capital) of the entire community.

Culturally Sensitive Pedagogy

“I want you to know that we as a people will get to the promise land.” (Martin Luther King Jr.)

This statement is an affirmation that African Americans see themselves as a unique cultural collective, having distinct historical experiences, ways of knowing, ways of being, values, problem sets, and goals that are not in total the same as other collectives. This unique cultural background must be considered if we are to reach and teach African American students, especially in schools where they predominate, such as urban schools. Ladson-Billings expresses this by saying:

“Without greater exposure to the students’ culture teachers lack the tools with which to make sense of much that transpires in the classroom” (Ladson-Billings, 1995).

Considering their unique cultural reality, it follows that that not only the methods of teaching African American students must be appropriate for this group, but also that the goals, short term and long term, of teaching African American students must be viewed as a guide to their education. Further emphasizing this point, Gay is quoted as saying, “Teaching is a contextual and situational process. As such, it is most effective when ecological factors, such as prior experiences, community settings, cultural backgrounds, and ethnic identities of teachers and students are included in its implementation” (Gay, 2000).

The above is a basis for my belief that pedagogy and curricula must be designed to address the needs of schools where African American students predominate. It must be designed in culturally sensitive ways that will address the unique learning styles and goals of African American students. With this imperative in mind it then becomes vital that teachers are trained to deliver this culturally sensitive curricula and instruction. This requires that teachers are given training and a directive to do so, without which it is by no means a likelihood to occur, since most teachers of African American students come from a different cultural background to them, and have not be accustomed to the culture of African American students. Even when the cultural backgrounds are similar, it is not a given that teachers will deliver the curricula and instruction in culturally sensitive ways, because many African Americans teach how they were taught, from a Eurocentric perspective.

As it is now education of predominately African American students takes on a much different directive, and accomplishes not their goals, but largely the reproduction of existing unequal power relations. This reality is made manifest through various means. Martin helps us conceptualize some of the ways that this occurs when he address head on the question, “Who should teach mathematics to African American children? He states, “I claim that the manner in which this question is addressed in mainstream research and policy contexts is largely a function of (a) the simplistic ways in which the aims and goals of mathematics education for African American children are framed (i.e., closing the so-called racial achievement gap, increasing course enrollments, preparing students for the workforce) and (b) the problematic ways in which African American children are socially constructed as learners with particular kinds of deficiencies in relation to students who are identified as white and Asian” (Martin, 2007).

Martin makes the argument in answering the question of who should teach mathematics to African American students, and I agree, are people who have sensitivity to the learning styles and goals of African American students.

“For me, teacher dispositions, racial competence, and commitment to anti-oppressive and anti-racist teaching are just as important as knowledge of subject matter; a teacher who is truly highly qualified must demonstrate competence in all of these” (Martin, 2007).

In some cases this cultural sensitivity will be a natural outgrowth of teachers having the same cultural background. Yet I do not believe that having the same culture guarantees that the teacher knows how to teach in culturally sensitive ways. In most cases teachers do not have this cultural sensitivity, and require training to learn how to teach African American students by leveraging their existing cultural capital. In my view, it is not enough for teachers to learn how to speak the code language of African American students and act like “they are down” with the kids, though this can be a great aid. It’s not enough to have teachers with strong content knowledge and pedagogical skills, though this too is essential. Teachers must be aware of the socio-economic realities, pressures, ideologies, and structures that limit the life opportunities of African American students. They must be willing to conspire against these structures along with the student and develop counter structures that promote student agency. Teachers must be willing to organize the curricula and instruction to help African American students engage these structures in agentic ways to help them reach their self defined goals. By that I mean uncovering the aspirations of African American students, given the obstructions they face, to fulfill those aspirations. This approach should be reflected in lessons taught on a regular basis. It should form the praxis of teaching for liberation and preparation for the demands of a 21^st century global economy. There must be recognition that this kind of teaching, as with any, is deeply implicated in identity formation of students as competent managers of knowledge capital and other resources to meet the collective goals of their communities. Any teacher who is willing and tooled to do this kind of teaching is qualified to teach African American students.

Discourse on Difference

The conceptual context and theoretical perspective(s) of El-Haj in her book, “elusive justice”, relates strongly to my research interests and I think is an exemplary of culturally sensitive training material I think teacher education programs should require. The following captures in her own words, her understanding of difference:

“Focusing on differences that make a difference in education as if they were located in the particular bodies/groups, rather than in the relationships of difference created by the arrangement of institutions – relationships that are political in the most fundamental sense that they produce distributions of power – is dangerous. It tends to lead us to wonder about either the “deficits” or the particular needs of some groups of people and not see the power afforded, the by reigning practices of schools and society, to people who are not marked different. … Difference is best understood as a marker of political relationships set up through everyday institutional practices” (El-Haj, T.R.A, 2006).

Key concepts and theoretical perspectives taken up in this book are:

§  Examination of the relationship between discourse, practice and power is a key for enacting social action and change. Discourse about difference can structure possibilities for action.

§  Substantive inclusion in school – the capacity to participate fully, and to contribute to meaningfully to all its activities – should be the aim of educational justice.

o   This is realized when educators respect the moral equivalence of all people.

o   A relational view of difference: “Focusing on the ways that individuals and group differences become a “problem” only in relationship to existing routines, norms, and values opens up the possibility for creating classrooms and schools that are just” (El-Haj, T.R.A, 2006). At the heart of this (her) view of educational justice rests a relational understanding of difference, one that we must adopt if we have any hope of making all the difference in education.

o   Recognition – or having one’s group affiliation fully acknowledged and included and equally valued is an essential component of a fair and just education. Recognition acts as a corrective to the exclusion wrought by refusing to see differences – differences that entail values, norms, knowledge, and experiences. This has ramifications for standardized testing (El-Haj, T.R.A, 2006).

I see the applicability of all the concepts listed above as relevant to my research interests. Examination of the relationship between discourse, practice and power is a key for enacting social action and change. Discourse about difference can structure possibilities for action. A relational view of difference will relate the problem sets of African Americans to the historical context of oppression (racism). It will reveal how those historical patterns continues to limit current educational possibilities of African Americans, as played out in maco social-eco-political structures that public schools are situated in. A relational view will see that just as African Americans have been targeted as a collective for oppression (slavery, Jim Crow, institutionalized racism) in ways that have limited their educational opportunities, so too must they be targeted as a collective to remedy the damage caused by these limiting structures, with new liberating structures. My conception of networked learning spaces targeting African Americans is such a remedy. Though this is a project targeted to African Americans, its processes can be generalized to other groups. Though this project is targeted to directly aid African Americans, its benefits will be felt wide and deeply throughout the country, as equality for one, is equality for all.

Recognition of African American students through a project such as the one I propose, will act as a corrective to the exclusion wrought by refusing to see difference in the values, norms, problem sets, aspirations, knowledge, and experiences as valid and deserving of equal consideration that treatment. African Americans have a different problem set to those of other groups, due largely to the effects of racism, past and present. Those problems should be recognized and dealt with aggressively. I see the questions raised by El-Haj to be the same questions I have. I have only taken these questions a step further by acknowledging the powerful impact harnessing advanced technologies in service of enhancing education, can have in advancing the collective learning goals of African Americans. My premise is that such a project cannot hope to be effective, unless it has the backing of sound pedagogical practices. These questions by El-Haj brings to the forefront the need to examine what that pedagogy needs to look like, and what it’s aims ought to be, prior to operationalizing it into practice.

I am embracing a frame of analysis and the development of praxis that will serve to empower African American students to obtain their individual goals, and collective motives. This is not to say that there is just one goal that can be identified; nor is it to say that I, or any one person can speak for the entire African American collective. I think most people can use their natural powers of perception to recognize what is empowering and what is not. Recognizing the benefits of a culturally sensitive pedagogy and curricula is not hard to do. What is hard is mobilizing the will to bring it into practice and praxis, in the face of strong opposing ideological winds of oppressive power structures that serve an opposing motive. Along with these oppressive power structures and motive forces, are frames of analysis and constraining pedagogical practices that tend to reproduce power differentials in education, reaching down into the level of the classroom. These structures have to be exposed, circumvented, or otherwise countered with structures, resources, and praxis that provides agency for African Americans to achieve their self defined goals. I don’t think there is any one approach, method, or program that will provide this agency. However I think training with exemplar methods, practices, tools and techniques is essential for teachers of every background.

Attributes of Empowering Pedagogy That Leverages Cultural Capital

There are some essentials that must span any serious praxis of culturally sensitive teaching. Chief among these is incorporating collaborative instruction that is relevant to the student and to the community from which the student comes. Students must be taught proven and in novel ways to apply what they learn in school to solving the real problems of development faced by their communities. They must be taught how to work collectively to achieve collective motives of their communities. This is a skill just like solving an algebraic problem is a skill. The mathematics must be taught in the context of their life worlds. We cannot assume that this skill will be developed in our youth unless it is consciously taught.

Below is a summative listing of essential attributes of a culturally empowering classroom. By culturally empowering, I mean the development of “voice”, the ideological self, and the facility to use resources to accomplish individual and group goals. If these are lacking in some critical degree in the classroom environment where African American students predominate, then old epistemologies and relations of dominance will persist.

1)    Teachers are not only highly qualified in a given content area, but know how to use technology to enhance the curriculum.

2)    Ideally there are consortiums of collaboration with other people who are involved with the same learning topics, or who are otherwise stakeholders in the learning process. The classroom is not “walled in”, but is extended in its reach from local through global contexts of education. The collaborative technologies facilitate this synchronous and asynchronous cross-pollination.

3)     The teacher is aware of structures at play that will tend to limit the educational outcomes of students, such as racism, local manifestations of globalized neo-liberalism.

4)    Focus is given to curriculum design that mediates the tension between the push for standardized testing, and the deep need for African American students to develop skills that address problems specific to their local community developmental needs.

5)    Technology tools, particularly those that foster online collaboration, will not only be deployed to elevate the efficiency and effectiveness of problem solving, but will be directed to solving problems that are relevant to the life world of African American students.

6)     Not only are technology resources made available for appropriation by students, but also the ideologies that support the positive identity formation of students as agents capable of achieving goals relevant their community.

7)    There is recognition that identity development is central to the education process. Identity formation of the individual student is tied inextricably to supporting the motives of the wider community.

8)    Stakeholders will recognize the existence of authoritative ideologies that have been established by the limiting motives of racism, classism and globalization. These ideologies will be present, consciously and unconsciously, in the bodies of administrators, teachers, peers, and adopted by students themselves. In these culturally empowering learning spaces there will be countering liberating ideologies that come from students, teachers, and other stakeholders. These ideologies will compete for predominance in the minds of teachers and students at any given moment. The environment will have available the physical, virtual, and mental resources to the student, to fashion empowering solutions to individual and collective problems.

Incubating in such culturally empowering environments, developing the mastery over the resources available to them, becoming grounded in liberation ideologies that can disarm constraining ideologies, students will establish positive identities as agents for individual and collective uplift. Students will gain the facility to examine problems in relation to wider structures that tend to reinforce the problem of their subordination and domination in society at large. With the development of the “ideological self”, a positive affective identity formation, students will gain the agency necessary to counter and transform limiting ideologies and structures (internal and external). As students are afforded opportunities to appropriate the resources in a culturally empowering learning environment, they will simultaneously develop identity constructs that will persist even in the face of more deeply constraining structures established on the meso and macro levels. There is even a chance that this enhanced critical awareness will position them to participate in efforts to transform these structures.

Collaboration and a Multiplier Effect of Knowledge Capital

As I’ve already intimated, another essential aspect that must span any serious effort towards liberation education on the behalf of African American students is that teachers must be trained to effectively leverage technology to help students reach their goals. In particular, collaborative technologies foster the acceleration of the interactive transforming exchanges needed to accomplish the progressive development of African American communities. Collaborative or interactive technologies foster the acceleration of the interactive transforming exchanges needed to accomplish the progressive development of African American communities. Collaborative technologies can facilitate a multiplier effect of knowledge capital that can reverse the knowledge and achievement gaps faced by African American students. An increase in the number of persons (nodes) distributing information (capital) in a closed networked system will increase the frequency that each person will receive a form of capital, in the Bourdieusian sense. Each exchange of capital is the equivalent of an injection of new capital in the system, thus representing a multiplier effect. That is, the net gain in capital of each person in the system is increased many more times than if a person was acting alone or with a very few other persons (nodes). The goal then in urban schools is to utilize tools, processes, and approaches that will increase the frequency that students in a networked system (extended classroom) can share information with stakeholders. In this paradigm students appropriate interactive technology tools that facilitate sharing of timely information. The more knowledge capital that is circulated the better the overall quality and effect of produced products that have embedded in them the knowledge. What promotes effective meaningful discourse around problem scenarios engaged by students, also promotes an increase in meaning potentials for effectively solving those problems. Through the improvement of the means of transacting forms of capital in the Bourdieusian sense, comes a multiplier effect of net capital accumulation, including knowledge capital.

Modeling and Feedback in Collaborative Learning Spaces

The NRC report “How People Learn” also offers critical insights into how the use of technology, backed by sound pedagogical principles, can enhance the learning of African American students and help close the knowledge and achievement gaps they face. One method it discusses is using technology as a modeling tool. Modeling problems visually through technology, in my experience has tremendous advantages for students with math weaknesses. There is a strong trend in modern societies of visually modeling or simulating a problem set using advanced technologies such as CAD (Computer Aided Design). It is popular in current gaming design and many fields, such as medicine, meteorology, architecture, film, and aviation to name just a few. There is no reason why this approach should not be taken full advantage of to aid students in tackling complexities in math and science in the classroom, particularly for those who struggle in these fields.

Another advantage that using technology to aid learning has is that it gives students and teachers more opportunities for feedback. Think of the power that we may currently take for granted of writing a paper electronically and submitting a draft for review to peers and a teacher who are sometimes a half a world away. The reviewer can offer critique by marking up the document electronically next to the original text, without changing the original. The student author can then accept or reject some or all of the changes. The student can explore what the results would be (see how it reads) if the changes were accepted. This also applies to the math and science models. Students can construct a model of a problem along with a possible solution set and submit it for review. A teacher can in the same sense as a text document, markup the model or otherwise point out to the student areas where the model may be enhanced for a better solution. Students can then explore the suggested solution path. This aspect of scaffolding is critical for students who are weaker in a given semiotic domain and who are struggling to navigate it. It also enables students to become more reflective and aware of successful strategies in navigating the semiotic domain. As stated in “How People Learn”, “technology creates opportunities to incorporate into curricula a meta-cognitive approach to instruction by using an inquiry cycle that helps students see where they are in the inquiry process” (How People Learn, 2007). The end result is that students learn the processes of becoming adept at a particular semiotic domain. They develop self-efficacy as authors / designers who not only adequately function in the semiotic domain, but also advance the semiotic domain to wider frontiers though unique authoring / designing contributions. The sound pedagogical use of technology by teachers affords promising opportunities to mediate academic weaknesses in math and science that African American students tend to have in typical urban schools.

These aspects of scaffolding are critical for students who are weaker in a given learning domain and who are struggling to navigate it. It also enables students to become more reflective and aware of successful strategies in navigating the given field of study. Technology thusly creates opportunities to incorporate into curricula a meta-cognitive approach to instruction by using an inquiry cycle that helps students see where they are in the inquiry process. The end result is that students learn the processes of becoming adept at a particular learning domain. They develop identities as authors / designers who not only adequately function in the semiotic domain, but also advance the learning domain to wider frontiers through unique authoring / designing contributions. Students engage in guided, reflective inquiry through extended projects, and with the use of sophisticated concepts and skills embedded in models, generate ever more complex products. Students become actively engaged partners in meaning making by considering and building on multiple perspectives. I believe if you couple the above benefits of collaborative technologies with initiatives of culturally sensitive pedagogy, students will be empowered in rich ways to address the developmental needs of their communities.

On-line learning networks – “Collaboratories”

One other concept discussed in the “How People Learn” report that I will extend to address the learning needs of African American students is that current technologies can provide opportunities for these students to collaborate with peers, teachers, experts, and anyone associated with a particular semiotic domain of interest, via virtual learning spaces or what the NRC report refers to as “collaboratories”. In my experience, African American students already have adeptness in using collaborative technologies, such and cell-phones and Facebook on the web. The problem is that this collaboration tends to focus not on academic and collective socio-eco-political problems, but rather on non-academic, social circle concerns. Educators should leverage the familiarity of African American students with the later usage of technology and apply it to the more frequent usage for the former type to address the knowledge and achievement gaps they face.

The knowledge and achievement gaps in math and science faced by African American students have deep historical and macro causes. The digital and knowledge divide are macro national problems requiring macro national solutions. The beauty of the Internet and collaborative technologies with respect to these problems is that it is designed to solve problems that are distributed over dispersed geographical domains as easily as problems that are locally situated. Furthermore, the technology can be used to roll-up or incorporate solutions of local problems, into models that treat the same problem from a macro or global perspective. The “How People Learn” report used the example of students collecting and analyzing local data related to global warming and then through collaborative technologies, uploading their local findings to a centralized global model of the phenomena for shared use. In the same way, African American students can roll-up their solutions to local problems into models that treat the same problem from a macro or global perspective, through the vehicle of collaborative learning spaces.

Students can be engaged in online learning communities for creating, sharing and mastering knowledge: exchanging real-time data, deliberating alternative interpretations of that information, using collaboration tools to discuss the meaning of findings, and collectively evolving new conceptual frameworks. Knowledge and meaning is obtained through the synthesis of multiple dialogues and points of view, where each “utterance” in the Bakhtin sense, is predicated on those that came before. In an interactive virtual learning space, these utterances can be contributions to a threaded discussion on a discussion board. To accomplish this I have for example, used the Moodle collaborative software as a collaborative tool in my high school math classes. The outcomes of this collaboration benefit not just the individual student, but can become a repository of relevant knowledge capital by and for the community at large. It becomes a collective competency directed at meaning making that is meaningful to both the individual and the community the individual comes from. It will remain a collective competence so long as the discourses and knowledge produce remains directly relevant or synchronous to the common problems faced by the collective. Once this golden rule is violated, then the environment has been compromised. An accumulation of compromises past a critical point will render the collaborative environment ineffectual in the uplift of both the individual and collective. This possibility has to be vigilantly mitigated by both the participants and designers of the learning space.

Research Questions and Authenticity Checks

I generally judge the merit and benefit of this study based on how well I can myself synthesize answers to the essential questions posed in this study. Just as important the data, analyses and insights produced through the study must position participants and stakeholders to answer these questions for themselves. My overarching rational for these questions is that student achievement must be assessed in relation to their developing identity, critical sense, knowledge construction towards self-relevant problems, and developing agency to achieve individual and community goals. A synthesis of ideas from the various cultural theories mentioned will hopefully afford a deep understanding of the processes of meaning making, and growing agency of participants to appropriate resources (including interactive technologies) that will advance their individual and group goals. The below is a restatement of the essential questions that I hope to answer through this study, along with their corresponding authenticity and validity checks.

1)    How, if at all, do these students’ discourses and authored products express the development of their ideological self, privileging their own “voices”; meaning their own ideas of what learning activities will benefit themselves and their community. This question is meant to ascertain if students feel free to counter ideologies and structures that impinge on their agency in education. Data that will answer these questions are: synchronous and asynchronous dialogue, student journals, blogs, individual and group interviews, authored products, as in essays and Power Point presentations. The first authenticity check for this study is that students will experience an expansion of their own “voice” to express what knowledges and activities are beneficial for themselves. They will be less likely to accept and follow uncritically, ideas and practices that do not serve their own defined criterion for what benefits their self-defined goals. If most students on the other hand consistently express the sentiment that they feel imposed upon by using say Moodle (a course content management system), or by being encouraged to focus on community problems, saying that these encumber their ability to effectively perform the tasks necessary address the learning objectives of the course, then this would indicate a need to reevaluate the effectiveness of the project.

2)    How, if at all, do these students’ discourses and authored products express development of their affective identities as competent actors in their semiotic domain? This question builds on the first and tracks the students’ agency to proactively appropriate resources as needed to accomplish their individual goals. Data that will answer these questions are: authored products as in concept models, discourses, topic selections, all produced over time and demonstrating the application of concepts learned towards problems relevant to the participants and their communities. The second authenticity check then for this study is, students will increasingly identify their constructed knowledges and activities as having benefit to not only themselves, but also to their communities. Local stakeholders in the school and community will likewise identify the collective praxis of participants as establishing an educational paradigm that actually supports educational objectives aligned to the enduring best interests of students. If on the other hand most students and other stakeholders, over the span of the course, consistently express that they don’t see their body of work as having relevancy to their community, but rather express that this work actually reduces the relevancy of what they produce to the needs of their community, then that is an indication that the benefit of this project must be reevaluated.

3)    How, if at all, do these students’ discourses and authored products express that they identify their problem solving activities and goals as advancing the motives of their group and larger community? This question examines if students associate their individual agency with the goals of their wider group, family, and community. Data that will answer these questions are authored products that result from their activity in projects; extended school activities such as community service co-op courses, mentorship programs, all manner or social activism. A third authenticity check then for this study is that students constructed knowledges and activities actually serve to transform existing educational practice on not only local levels, such as classroom and school, but also on, meso levels such as district and region. The established praxis captured by this study would further serve as a model for transformative education on macro levels, as in urban education for minorities across districts, states and throughout the entire country. If this transformation does not occur after implementation across departments in a given school after at least three years, despite being fully resourced materially and with teachers with supportive ideological perspectives, then the project must be reevaluated as to its benefit to students.

Ethnography In My High School Math Classes

During the course of the second half of the current school year I’ve engaged students in projects that I hope will develop their identification of themselves as doers of mathematics not just for their own benefit, but to the greater good of the community from which they come. This is in keeping with the unit of analysis that I mentioned. It is not the student’s activities in isolation, even if it involves advanced technologies. Rather, I consider activities of groups of students in collaboration through interactive technologies for the purpose of increasing their collective agency for the uplift of them selves and of their communities. This goal was reflected in the project requirements in one way or another, as I attempted to develop this collective identify of my high school math students. For example, listed below were the requirements of the first project.

“1) Analyze and model a problem that relates to your community. The problem should directly impact your community in some important way. The key word here is “relevant” to your community’s uplift.

2) Work in teams of two.

3) The problem can be modeled using a mathematical function (linear, exponential, quadratic etc.

4) There is data that can be collected or otherwise retrieved that reflects the development of the scenario you are modeling.

5) You are able to dialogue about the problem with members of your family, community and your teachers.

6) You must be able to record in writing the perspectives of these people on your problem. At least 3 different people from your community, one being a family member, others can be your teammate or a teacher from another discipline (not math).

7) You must ask the same three people to give their perspectives prior to you developing your math model and after you developed your math model

8) Suggested questions to ask your participants:

a. How do you see this problem affecting your community?

b. What kind of math information and/or modeling would help you to understand the problem and its possible solution better?

c. How do you think my proposed model can help your understand the problem and solution better?

9) All dialogue must be captured in a Moodle forum. If you record a conversation, you must transcribe it in written form into the Moodle forum.

10) Your math model should reflect the input of your participants in a significant way. “

The requirements for other projects had a similar emphasis on solving a problem that was relevant to students’ community, and on using interactive technologies to provide a multiplier effect of knowledge capital. This last point means that students accrue knowledge by sharing learned artifacts with each other, building on previous works, accessing online resources and obtaining my input, all done in multiple iterations until the time for them to engage stakeholders with their products. The following are some details of activities I engage my class with:

1)    Access resources on the Moodle that were placed there either by other teachers, other students or myself. Students can modify copy and then modify contents.

Resources include:

1. PowerPoint slides on math lessons
2. Videos on particular skills
3. Assessments
4. Journal entries in forums
5. Stored files

2)    Shared folders in Gmail where students can share electronic files with each other and I.

3)    Web sites for students in Google to establish virtual math identity and share files with public (rest of school).

4)    Smart board to facilitate whole class sharing of products

5)    Google survey, Word Press, Geometer’s sketchpad, Maple 15. Maple 15 allows students to create narratives or problem scenarios and seamlessly embed math into them. They can then share this with others by exporting it as an html file.

6)    Co-teaching and cogens are mechanisms for students to share their perspectives on math.

With my overarching project in mind, I was always on the lookout for student expressions that would evidence their developing agency to solve problems of their communities. I have not yet asked students to answer survey questions to elicit this evidence. Instead I have asked open-ended questions regarding their experience of doing projects like this and on their understanding of what a problem solver is.

Below are some feedback questions I’ve asked of students thus far:

§  What is a problem solver?

§  Identify a problem / issues in your community that can be modeled with a math function.

§  What is the usefulness of doing projects related to community?

§  What do you think you want to major at in college? What is your career choice? How can proficiency in math help in those areas?

§  Describe your experience with co-teaching.

§  Describe how you think others are experiencing co-teaching.

§  Parents – Please describe your expectations of your child and of me in our math class.

§  Get opinion of community members on the issue you selected to do a math project on.

§  Describe your current attitude towards math.

§  Describe a past experience with math that helps explain your current attitude towards math.

§  Describe your community? Who makes up your community?

Discourse Analysis

Before the school year ends I think it will be valuable to ask more focused questions that may help gage their identification with being a problem solver on the behalf of their community. Below are places where I’ve considered looking for this evidence:

1)    The selection of the problem students chose to address

2)    Some of the insider language that indicates identification with the problem. For example, terms such as “my problem” or “my community” may indicate this identification.

3)    The answers to my posed question “what is a problem solver” may be revealing. One student answered as follows to the question of what was his experience with doing this project:

“I think this project was good in helping us recognize some of the problems existing in our community but it wasn’t really enforceful, I don’t think it had a very powerful effect on me. I felt that this project was just a brush up on my presentation skills, but yea it was an ok experience”

This indicates to me that the goal of helping him to become aware of the problems was achieved. He was looking for a more “powerful effect”. Though at first glance this may seem to be a negative evaluation, it could also indicate that he is ready to go beyond the awareness phase to a phase where he is actually making a difference with his research. He use the term “enforceful” which could be read as “full of force” to make a difference in the problem area. Another student wrote the following in response to the question of what is a problem solver:

“A problem solver is someone or something that solves problems by making it easier or coming up with more than one solution. In math, a problem solver can be a calculator or a formula that helps solve an equation. In life a problem solver is someone who helps others with their issues, for example, a therapist or a complete stranger can be a problem solver.

I took particular note of her saying “In life a problem solver is someone who helps others with their issues”. This is an indication that the student understands that problem solving has importance in relations to others, which for me indicates a development of collective identity formation.

4)    The effort students make to surround the Power Point slides with meaningful pictures and self-placed captions is a good source of evidence. Looking at the pictures the student selected to surround the information in the slides one can surmise that this student has formed a definite ideological opinion on the community problem and endorses active involvement by sympathetic listeners to help with this problem. For example, the selection of the below pictures in a Power Point on the community problem of abortion evidences the formation of a definite ideological opinion. Generally I think these power points evidence the development of ideological identities in students as agents for their communities.

5)    The spontaneous dialogue students engaged in while presenting is another important signifier of identification with community. There was not much of this dialogue in the first two projects. I think the reason for this is students went into the project thinking that they would just give a presentation. In some cases however, students spontaneously engaged each other is dialogue about the problem. I made a conscious effort not to interject my own ideas and comments while students were presenting so that I would minimize my influence over students ideas. Towards the end of the presentations I decided to participate more my asking students questions and encouraging them to ask each other questions. I think entrained or focused dialogue among students is evidence of identification with being problem solvers on the behalf of their communities. Recognizing this, I decided for the next project to allow students to be teachers of problems they selected, not merely presenters. I will then see if there is more of this interested dialogue that evidences identification with problem solving on behalf of their communities.

6)    During presentations, students seemed very interested to express the opinions of their “community members” on the problem they presented. At this point I can only speculate why this may be so. I will venture to say that it may be because students feel it adds an authentic voice about the problem, which infuses a greater relevancy of the problem to the student.

7)    When I asked students, subsequent to their previous projects, to modify an exiting problem in some significant way, I had in mind to see if their modifications reflect in any way an attempt to address problems they saw in their communities. If this were the case, then this would also be evidence of a growing identification with community problems.

8)    The eagerness of a few students to showcase their work by doctoring up a bulletin board outside of the classroom for the whole school to see is an important indication of student identification. See attached photo of bulletin board done by two students.

9)    Another source for the evidence I seek can be the portfolios that students were asked to complete for the 3^rd marking period. With the portfolio I asked students to focus not on collecting their body of work, but rather to comment on the work that they did and their level of acquired understandings. I think that this product can be revealing as to how students value the project work that we did in comparison to the other types of math work, and if they found it more relevant to their developing competencies as problem solvers on the behalf of their communities. Here is an excerpt from the portfolio introduction done by a pre-calculus student:

“However, after the HSPA we moved onto better things like matrices. Not only did we learn how to plug matrices into a calculator, we learned how to create our own problems in Excel. We also learned about synthetic and long division with polynomials. It was very fun. Now we are working on a group project dealing with any community problem of our choice. We have to model the problem with ‘dummy data’ and then get real data that shows the function of our problem.”

One can surmise from this statement that this student gives a positive valuation (“we moved onto better things“) of the group project dealing with a community problem.

Coding for positive evaluations of student discourse as they work towards collective and individual goals would need to take place over all the types of products that were collected while students engaged with math content using technology tools, such as the ones I mentioned. The following is a tool for doing discourse analysis on student dialogue and authored products that I adopted and adapted from Lisbeth Amhag and Anders Jakobsson, who used it in their analysis of student dialog while taking an online course. This tool is in keeping with Bakhtin’s ideas of ideological becoming.

The below table summarizes what has been said of my research questions and data.

Research Questions and Data

I’m in my 7^th year of teaching mathematics and using interactive technologies to enhance student learning as I’ve described. I have seen indications of my students developing an ideological stance and identity as a problem solver on behalf of student communities. Using the above dialogical tool will be helpful going forward to determine the level of student “Ideological Becoming”, in the Bakhtinian sense. Another means to ascertain that students in urban classrooms are developing positive identity as doers of math on behalf of their communities, is to gage the level of synchrony and entrainment amongst students and teachers in the classroom in the sense given by Randall Collins in his book, Interaction Ritual Chains (2004):

“As persons the person become more tightly focused on their common activity, more aware of what each other is doing, and feeling, and more aware of each other’s awareness, they experience their shared emotion intensely, as it comes to dominate their awareness”.

This solidarity on a sustained and continuous level, towards a common goal of community uplift is what I hope to engender in my students.

 Micro data analysis

Ken Tobin has done extensive work in this area of microanalysis of videotape, looking for evidence of synchrony and prosody in the classroom, and has demonstrated its usefulness.

“We show that specific prosodic features in face-to-face encounters—alignment and misalignment—are associated with the production of solidarity and conflict, which in turn are associated with successful and unsuccessful lessons. They are also associated with different degrees of solidarity and emotional energy that participants in science classrooms experienced.” Roth & Tobin (2010)

Micro level data, as in video taping of students as they are engaged in the type of collaborative project work that involves community, can be coded for prosody, entrainment or sustained focus, and synchrony. This data can be compared to the same type of micro level data of students engaged in typical teacher centered lessons. Though I have not carried out this micro level analysis and comparison with my students, I have notice higher levels of student engagement, entrainment, and synchrony when students were allowed to author their own math products and were free to present them in the role of class teacher. I would not want to overstate what this micro level analysis can reveal in terms of identity formation. I think that looking at micro level data in isolation from wider cultural structures that students are embedded in, can lead to misinterpretation of events. For instance simple smiles my students in and of themselves can be interpreted as positive emotional engagement, but can actually be an expressions of subversion or carnival (in the Bakhtinian sense) to a teacher’s practice. However this is true for all of the forms of evidence that I have listed thus far. It is only when one form of evidence is held together with all of the other student produced cultural artifacts that we can gain higher confidence levels that this collaborative, student centered approach cultivates in students a positive identity formations as doers of math on the behalf of their communities. Having stated this caution, it is my experience that the levels of solidarity are markedly higher when students are given freedom to work on problems that are relevant to their life worlds, and are allowed to present them without undue teacher interventions to their classmates and other stakeholders. This may also translate into higher levels of student achievement in math and science, as well as entry into these professions.

Where does this lead? I think this can lead to a feedback loop of cultural capital forming a habitus, or educational praxis that support not just individual positive affective identity formation, but positive collective group identity formation that can be the basis for transforming dominant structures that have to this day thwarted the educational aspirations of African American students. I refer again to Turner for aid conceptualizing prospects for transformative agentic action, as the outcome of positive affective identity formation of participants in my project: “the flow of positive sanctions in an encounter tends to circulate among the participants to the encounter, with individuals mutually sanctioning each other in ways that build up local solidarities, although at times this flow of mutual positive sanctioning can work its way up to meso-structures and macrostructures” Turner (2007). This reminds me again of the multiplier effect of circulating money in a closed system repeatedly before allowing it to leave the system, as a means of accruing wealth exponentially. This then provides a cultural capital accumulation that may reach a critical mass, allowing for transformation structures in the educational arena. The wider goal of this project is no less than such a transformation of meso-structures and macrostructures that tend to constrain the educational and life possibilities of African American students.

Contradictions an Opportunity for Further Revelations

One contradiction that often presents itself is that students often times bite the proverbial hand that tries to feed them. For example, after coaxing my students to the first “community problem”, in my math class, when presented with an opportunity to do another, many simply chose to work on more simplistic problems that don’t seem to relate to the serious issues of their community. Some topics chosen were, quadratic functions as they relate to catapults, tossing balls, kite tails, and kicking a soccer ball. I was initially disappointed with these selections, thinking that my efforts to scaffold them into these important roles and identities as problems solvers for their community, has not born much fruit. However, upon deeper reflection, I must allow for room for young students to get comfortable with their identities through play. Is it not the case that most mature identities start off from baby steps in play and less risky identities? There has to be room for development. It would be unrealistic to expect students to be prepared to go out and become activists as a consequence of doing three projects. Indeed it would be unrealistic to think that many students will be activists at all. The ways students will express their developing identities as doers of math for community uplift will be diverse and stratified across multiple fields of activity. No doubt many students have been conditioned to dislike math. Many are just eager to satisfy their high school math requirements and never take math again unless to meet minimum requirements for college or a job. These are all negative dispositions that must be contended with. For such a student the challenge is to help them rediscover math in the context of empowering them to analyze and contribute to solutions of real-life problems in their communities.

Implications of Passivity and the Third Space

In striving to transform educational environments predominated by African American and Latino students, I have largely focused on the structure | agency and production | reproduction relationships. I’ve embraced being conscious of macro and meso level structures of society that tend to constrain the educational attainment and life chances of these groups. This focus on having awareness of oppressive structures and awareness of the agentic ways we can act to transform these structures, producing new structures that are less constraining, has perhaps led me to neglect other equally pertinent dialectical aspects of the habitus of said learning environments. As I am concerned with production of new structures through agentic actions, I must also give careful consideration to the creation of culture, or structures that occur not through agentic means, but through passive means. By passive I do not mean conscious acquiescence to domination. I mean the state of being receptive to enculturation or to inscriptions of others who are scaffolding the agent’s eventual agentic acts. This also has to do with the subtle and not always visible process of identity formation. Identify formation does not always occur in the active doing by agents, but also in their passive, observing, imagining, being with, and unconscious following the other. There are also the unconscious schema that students and teachers have adopted over time that are brought learning environment, and that impacts what gets enacted. Sometimes we refer to this as second nature. It is be business of educators to move conscious liberating practices to the realm of second nature for our students. For example we hope that through practice and drill on solving problems of a certain type, that students will commit this skill to second nature or conditioning so that when presented with this problem type in some new context, that students will have the natural disposition to solve this problem without resort to relearning as if from scratch. I have assumed in my teaching practice that if we reflected and focused on the agency side of producing culture where students are enacting practices in the math classroom and beyond where they are reaching their individual and community goals, that the latent, unconscious, passive side of the agency | passivity dialectical coin will take care of itself; that it wont interfere with agency. I do believe that humans have all kinds of conditionings, many of which tend to reproduce relationships of their own domination. These conditionings that make students and teachers complicit this reproduction must be considered along with agency.

There is also a middle ground between agency and passivity to consider, a third space. I believe that despite our best efforts of being conscious of structures that constrain our goals and life chances, which we are in constant negotiation with these structures, and sometimes acquiesce to them in the moment so as to get on with our larger project of transformation on a broader landscape that transcends the immediate event or circumstance. It’s like giving up an immediate battle, but not the larger war. In recognizing the obvious forms of racism that permeate public schools where African students predominate, I do not necessarily advocate boycotting these schools, or myself refusing to teach in them, insisting or their transformation before proclaiming them fit to teach our students. I advocate transforming them from the inside out, sometimes with great obvious affect, and sometimes with latent, yet potent affect. Sometimes the transformation occurs deeply on the subtle levels, the in-between or third space of the agency | dialectic. Such transformation cannot occur without engagement and negotiation with existing structures.

How should we deal with student identity development as competent doers of mathematics in support of their goals and that of their communities, when they are not acting in overt ways and even conscious way to do so? Enculturation is not always conscious. Habits of mind are formed through daily practice in a variety of settings and circumstances. The apprentice is not always and everywhere aware that she is learning from the master, even during some innocuous moment. Availing students to the resources and opportunities to effect positive change without always directing outcomes has its place. This is one of the beauties of student teaching. Students do not necessarily realize that when they are teaching others, they are mastering the concepts for themselves. Students also don’t necessarily realize that as they are promoting their individual interests, they are increasing their potential to elevate their community. Here I think it is important to monitor and guide students to applying acquired competencies to the uplift of their communities, without directly requiring them to do so. How do we teach students to embrace selfless service to their communities without compulsion? I think one answer is by showing through example. Students, who see teachers giving selflessly to the school community and loving it, may become passively inscribed and habituated to want to do the same for their communities.

Radiating Waves of Social Transformation

What becomes essential in the deployment of interactive technologies is not the technology itself, but the meaning making, liberating ideologies, and problem solving that are all directly relevant to the participants acting for their own benefit and that of the wider collective from which they come. New forms of computer models coupled with increasing ease and power of modifying and sharing these models without regard for distance or time, makes possible a broader, more powerful repertoire of pedagogical strategies that can be pressed into service to accomplish common goals of the collective.

Culturally empowering learning spaces that utilize advanced interactive technologies, coupled with liberating ideologies embedded in the curriculum, have the potential of producing educational experiences for African American students in public schools that are transformative of existing constraining structures in public schools, affording agency for both individuals and collectives. These spaces are not isolated enclaves that locate the problems facing African American students in the bodies of the students or in their ethnic practices. Rather, there is a recognition that agency of students is interlinked with how students and stakeholders access and manage available resources to construct meaning and knowledge that can be applied to their collective problems and motives. These learning spaces can serve as models for a public education generally, for not only minority students, but for all students. So these learning spaces in particular localities can have a transformative effect on meso and macro level structures of education and society as a whole.

References

Bakhtin, M. M. (1981). The dialogic imagination: Four essays by M. M. Bakhtin (C. Emerson, & M. Holquist, Trans.). Austin, Texas: University of Texas Press.

Bakhtin, M. M. (1986). Speech genres and other late essays (V. W. McGee, Trans. Vol. 9). Austin, Texas: University of Texas Press.

Bourdieu, P. (2000). Cultural reproduction and social reproduction. In R. Arum & R. Beattie (Eds.), The structure of schooling: Readings in the sociology of education (pp. 56-68). Mountain View, CA: Mayfield Publishing Company.

Collins, R. (2004). Interaction ritual chains. Princeton, NJ: Princeton University Press.

El-Haj, T. R. A. (2006). Elusive justice. Wrestling with difference and educational equity in everyday practice. New York and London: Routledge.

Gay, G. (2000). Culturally responsive teaching: Theory, practice, & research. (p. 21) New York: Teachers College Press.

Gee, J. (2007). What video games have to teach us about learning? New York, NY: Palgrave Macmillan.

Hooks, B. (1994). Teaching to transgress. Education as the practice of freedom (p29). New York and London: Routledge.

Bransford, J.D., Brown, A.L. & Cocking, R.R., Editors. How People Learn. Commission on Behavioral and Social Sciences and Education, Chapter 9. Washington, D.C.: National Academy Press, 2007.

Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465-491.

Lisbeth Amhag , Anders Jakobsson (2008). Collaborative learning as a collective competence when students use the potential of meaning in asynchronous dialogues. Computers & Education 52, 656–667.

Martin, D. B. (2007). Beyond missionaries or cannibals: Who should teach mathematics to African American children?. High School Journal, 91(1), 6-28.

Roth, W-M., & Tobin, K. (Eds.) (2007). Science, learning, and identity: Sociocultural and cultural-historical perspectives. Rotterdam, NL: Sense Publishing.

Scheff, T., Microsociology: Discourse, Emotion, and Social Structure. The University of Chicago Press, Ltd London.

Turner, K. (2007). Human emotions: A sociological theory. (p. 73). New York, NY: Routeledge.

Wolff-Michael Roth and Yew-Jin Lee. Review of Educational Research, Vol. 77, No. 2 pp. 186-232

Tobin, K. (2010). Global reproduction and transformation of science education. Cult Stud of Sci Educ DOI 10.1007/s11422-010-9293

Tobin, K. (Ed.). (2007). Teaching and Learning Science: A Handbook. (Paperback version)–New York: Rowman & Littlefield.

Wolff-Michael Roth and Yew-Jin Lee (Jun., 2007). “Vygotsky’s Neglected Legacy”: Cultural-Historical Activity Theory. Review of Educational Research, Vol. 77, No. 2 pp. 186-232

Leveraging Interactive Technologies to Accelerate Math Learning in Urban Schools

By Roland Lucas

CUNY Graduate Center

Urban Education Department

Mathematics and Technology

Abstract

Worldwide technological capacity is growing exponentially, and in doing so it increases human memory sense perception, data search, retrieval and processing powers. Our collective human power of analysis and synthesis supersedes that of any previous era due to technological advances. Transnational businesses with local reach are ever employing these leading edge technology tools, and are increasingly requiring that their workforce, even the low skilled worker, have competencies for using them. Students can hardly keep up with this exponential growth of data processing speed and knowledge production. Certainly our public schools in urban areas fall far short overall in preparing our youth to meet these demands, due in large part to outdated teaching methods and insufficient resources. If there are advances, in teaching methods and resources, these advances tend to have a linear growth rate, whereas what is needed is an exponential or radical growth rate to match the exponential demands of a modern workforce. One means of helping students to adapt is to fight fire with fire; use technology to help them keep up with technological advances. Students attending our urban public schools have already immersed themselves into technology to varying degrees in their activities outside of formal school settings. Leveraging this social and knowledge capital in more formal educational public school settings is one means of enhancing their academic learning experiences and narrowing the achievement gaps they face.

What can youth teach us about learning through their practices on friendship-driven on-line network spaces?

In 2006 the MacArthur Foundation sponsored a study to help determine how digital media are changing the way young people learn, play, socialize, and participate in civic life. In this study, researchers identified three broad patterns of behavior practiced by youth while using on-line public networks. These behavior patterns are categorized in the study as “hanging-out”, “messing around”, and “geeking out”. They convey varying levels and intensities of cultural capital production and exchange. The findings have much to teach us about how to leverage student tendencies and competencies, habitus, in these fields of activity to enhance learning in more formal educational settings.

“Hanging-out”

Youth these days hang out with each other not only face-to-face but on social networks. We all know that the social bonding of hanging out outside of the school setting can cross over the school boundary and significantly affect the cultural climate, hence learning, in schools. The hanging out that youth do on social networks is similar in many ways to how its done face-to-face; however; there are many new affordances to on-line hanging out that adult educators would be wise to recognize. Referring to on-line hanging out, the white paper from the study posits that, “while hanging out with their friends, youth develop and discuss their taste in music, their knowledge of television and movies, and their expertise in gaming. They also engage in a variety of new media practices, such as looking around online or playing games, when they are together with friends” (Living and Learning with New Media, 2008). Later in this paper I will discuss some of what educators can learn from students play with on-line games, using the theoretical lens of James Gee.

“Messing Around”

The “Living and Learning with New Media” white paper gave the following distinctions of the messing around on-line activity by youth: “Unlike hanging out, in which the desire is to maintain social connections to friends, messing around represents the beginning of a more intense, media-centric form of engagement. When messing around, young people begin to take an interest in and focus on the workings and con­tent of the technology and media themselves, tinkering, exploring, and extending their under­standing. Some activities that we identify as messing around include looking around, searching for information online, and experimentation and play with gaming and digital media production” (Living and Learning with New Media, 2008).

The below I list some salient aspects of student on-line messing around from a social cultural perspective, that I think are important to leverage in public school teaching practices. I will give more descriptions of my social cultural frames of reference following this discussion of student on-line activity.

1)    The messing around by youth in virtual spaces is a form of social production, or enactment, where learning and identity formation is continuously happening to varying degrees. Participants exchange information, ideas, and give each other mutual support. They sanction each other when activity does not agree with the common interests that fundamentally bind the group. They positively reinforce each other when actions do support the group, thus strengthening group bonds. Participants of these spaces are inscribed by the ideologies, consciously and unconsciously of others in the shared space.

2)    Distance between participants is not necessarily an issue. Participants can still connect in on-line spaces despite even never having met in person, and influence each other’s learning and identity formation.

3)    Youth members are the main directors and authors of the cultural production that occurs. The activity is primarily self-directed, with adults on the periphery. Even though adults may have designed and continuously maintain elements of the shared space, the youth are in control how resources are used within the given constraints, making new cultural artifacts and new cultural inscriptions of each other.

4)    Time is not as great a factor either. Participants are able to access each other practically at anytime of day, synchronously or asynchronously. Dialogue is constrained only by their access to a networked electronic device.

“Geeking out”

Youth on-line geeking-out has all of the aspects of hanging out and messing around, but with higher intensity levels of activity that also entail more specialized knowledge and associated competencies. The white paper says of student on-line geeking out that …

When young people geek out, they are delving into areas of interest that exceed common knowledge; this generally involves seeking expert knowledge networks outside of given friendship-driven networks. Rather than simply messing around with local friends, geeking out involves developing an identity and pride as an expert and seeking fellow experts in far-flung networks. Geeking-out is usually supported by interest-based groups, either local or online, or some hybrid of the two where fellow geeks will both produce and exchange knowledge on their subjects of interest. Rather than purely “consuming” knowledge produced by authorita­tive sources, geeking-out engagement involves “I am the Greater God of video edit­ing”  (Living and Learning with New Media, 2008).

The following are some salient aspects of youth on-line geeking out that I think are important to leverage in teaching practice.

1)    Youth will usually demonstrate highly skilled competencies in producing the artifacts that signify the learning and enculturation that has taken place.

2)    The cultural enactment and learning that takes place can push boundaries of existing knowledge because the processes of knowledge creation are not completely bounded by traditional rules, conventions, values and sanctions of what constitutes knowledge and valid forms of expression. These spaces then create forms of knowledge and competencies that are divergent from mainstream or dominant forms of knowledge. This is a basis for innovation. Confirming this point in it’s reference to on-line collaborative gamming spaces the white paper posits, “In all of these cases, players are engaging in a complex social organization that operates under different sets of hierarchies and politics than those that occupy them in the offline world” (Living and Learning with New Media, 2008).

3)    Youth take pride in their self-authored products and unique competencies. They take pride in the recognition received by members of their group for producing specialized knowledge and artifacts.

4)    The positive reinforcement received is a motivator for continued and deeper incursions into the specialized field of knowledge and cultural production.

5)    These competencies can often transfer into other fields that have resemblances to the spaces where they were initially developed in. Youth evidence higher ordered learning by being able to transfer and apply their specialized knowledge and competencies to novel situations. Adults may be involved with the learning and production that occur, but they are not leading or directing it. Adult educators may find themselves in the reversed role of being a student of the youth who is leading the way.

Through on-line hanging out and geeking out, youth demonstrate highly engaged modes of cultural enactment and learning that inextricably involve their identity development as well as competency development. They demonstrate adaptability to using on-line networks for production and exchange of knowledge and media artifacts.

As a math teacher who uses technology in the curriculum, I consistently observe students demonstrating a readiness to transfer their developing on-line competencies into the classroom. Students continuously search for ways to express their evolving identities through their competencies in school and out. The fields of their private social life have porous boundaries that are always in interchange with their school life. Students bring their acquired self-directed competencies, experiences, and tendencies to the school table, whether this fact is recognized and leveraged by school educators or not. Teachers should ask, what can the on-line self directed activities of students teach us about how to teach youth today? Teachers and other stakeholders can leverage the cultural and knowledge capital produced and created through student on-line activities to enhance and accelerate student learning. Teachers can evolve effective strategies of teaching that plug into this on-line habitus of students, and leverage it to reach more formal educational goals. This means mobilizing the same or similar resources out of school online network spaces that can produce the same or similar products in school.

Interests and Positive Sanctions

1)     Student on-line activity out of school is primarily self-directed towards self-interested goals. In my experience with public high school student in math courses, they often don’t recognize how the study of math aligns with their self-interested goals. Teachers need to recognize the value of continuously negotiating with students how the skills taught can align with student interests, developing ideologies and cultural identities. Teachers must allow students freedom to explore, experiment, and exercise a degree of autonomy without penalizing them for straying from predefined requirements or convention. Meaning making must be recognized as a joint and negotiated venture between students and teachers. Not a one-way dictate from teachers. Furthermore, the products they produce should be validated so long as they relate in a significant way to the learning objectives at hand. Even when student authored products don’t seem to do so, they may express a serendipitous insight by the student that should also be validated. “Among fellow creators and community members, the context is one of peer-based reciprocity, where participants can gain status and reputation but do not hold evaluative au­thority over one another” (Living and Learning with New Media, 2008).

Students are motivated not just to get a grade by teachers, but also to gain acceptance and positive reinforcement by their peers and teachers, which can occur face to face or through an online activity.

Solidarity

Another important lesson to learn from student self-directed on-line activity is the importance of solidarity to youth inhabiting these spaces. Fostering collective social bonds should be recognized as essential in the context of formal student classes as well. Students in self-directed context are willing to show each other the ropes of the specialized field of activity. Teachers should foster this solidarity among students; this understanding that everything that happens in the course affects everyone, and that their collective goals can be reached more effectively if everyone supports each other. The learning experience then transcends the individual and extends out through a ripple effect to all members of the group, and even to the wider community. Students learn in effect citizenry through their specialized contributions.

As a teacher of mathematics who is keen on integrating technology into the curriculum, I see high value in leveraging self-directed student social / cultural capital and competencies in the classroom to enhance their meaning making potentials and success with math. I think students are prepared to meet us more than half way in doing so.

Theoretical Frameworks

I use Bakhtin’s theory on dialogical discourse and “ideological becoming” to envision processes of positive collective identity development, through collaborative discourses and knowledge construction that can take place in culturally empowering learning spaces. I also borrow heavily from Bourdieu, Tobin, and Turner, for their theories and analyses on multi level social \ cultural structures, and how these theories can support a vision of social transformation. Any project addressing the transformation of educational praxis must be grounded in a socio-cultural theory of action that accounts for the structures of the school environment as being embedded in larger cultural structures, the motives of the groups involved, and dynamics of social change.

Bakhtin’s Dialogical Discourse and Identity Development

Agency involves an actor using available tools, structures or resources to carry out actions to obtain a goal. My unit of analysis is not the agency of African American students as individuals or even as a group onto themselves. Too often this kind of focus produces deficit theories, finding the problem of under achievement by African American students in their own bodies, minds and ethnic culture. It is not the African American student in isolation, even while connected to advanced tutorial software applications that I consider. I consider activities of groups of students in collaboration through interactive technologies for the purpose of increasing their agency to offset much of the limiting structures of racism and classism as manifested in their local communities. I consider how through their collective activities they can proactively solve problems that are relevant to their group and to their communities. I consider how having access to timely, relevant, and up-to-date knowledge capital and conduits afforded by interactive technologies can serve as vital resources to accomplish this.

Furthermore, collaborations in networked learning spaces involving a community of students tend to make the construction of knowledge less centered on the adult teacher as only source of knowledge that gets deposited with students; less an exercise of reproducing established knowledge and power structures. That is, knowledge production in interactive environments would be less authoritative, monological and passive, as Bakhtin (1986, 2004) describes it. Dialogue would rather be more in keeping with Bakhtin’s concept of inner persuasive discourse where participants actively scrutinize, challenge, change, reject and argue over, existing knowledge to suit their needs and evolving understandings. Multiple “utterances” or dialogues are then considered, synthesized or otherwise reshaped as needed (polyphony). New products that students appropriate and generate can be acted upon to support their agency and identity formation. Existing knowledge and relational structures will be reproduced only if they support the motives of the collective. If not, these structures should be targeted for transformation, thus providing for student agency and liberation education.

Students would no longer fall into serving the intentions of dominant groups, nor channel the words, ideologies, goals, and problems of dominant groups. Students become critical thinkers, not just in their ability to analyze data and problems, in direct proportion to how they problem solve for the uplift of their communities. Without this directed critical facility, they would simply implicate themselves in sustaining the reproduction of their own subordination in society through a mis-educational system. They would “recite by heart” other people’s voices or structural rules. They would, in the Bakhtinian sense, parrot authoritative discourses, rather than retell their stories in their own words. Learning to privilege one’s own critical voice is what Bakhtin (1981), refers to as “ideologically becoming”. This is education proper and is sorely lacking in public schools where African American students predominate. A culturally sensitive approach to education that respects difference and builds upon the life experiences of students would encourage this kind of critical thinking and development of “voice” or ideological self. It would furthermore facilitate sharing with and building upon ideas of others who have common liberating motives. It would very much be involved with building solidarity for the purpose of helping students reach their collective and individual educational goals.

Extending James Gee’s Ideas On What Video Games Teaches Us About Learning

It is my understanding as an educator and an African American who has gone through the public education system in New York, that African American students in public education view themselves and are treated externally, as a Diaspora or “affinity group” that has a different set of challenges, consequently, a different set of immediate goals than other student groups. James Gee, in his book “What video games have to teach us about learning”, describes “semiotic domain” as “any set of practices that recruits one or more modalities (e.g., oral written language, images, equations, symbols, sounds, gestures, graphs, artifacts, etc.), to communicate distinctive types of meaning.” (Gee 2007) I will extend the definition of semiotic domain to refer to the various disciplines taught in schools, though my focus is on the situation of African American students in the mathematics semiotic domains. For Gee an “affinity group” is simply any group associated with a particular “semiotic domain”. I will refer to the subset African American students situated in public schools and who generally struggle with math, as an affinity group that I am principally targeting in this discussion.

The legacy of institutionalized racism as manifested in the public education of African Americans specifically, and in society generally, has contributed to the formation of the African American student affinity group that is set apart from normalized groups. As I say this, a memory comes to mind of seeing all Blacks in the cafeteria at the college I attended, Westfield State University in Massachusetts, always sitting together. The university was 95% White and 2% Black. I will note here that every individual and group have unique measures of achievement. I see achievement as the attainment of knowledge and the development of competencies or habitus, necessary to produce structures that will enable an individual to successfully reach goals that uplift not just the individual, but the collectives that the individual identify with (Gee’s identity groups).

It is worth investigating how African American students located in economically depressed urban areas see themselves in the context of the public education system. Though this inquiry is germane to the topic of this paper and touches on Gee’s “identity principle”, I will not venture to present a review of attitudes that shape the African American student self perception here. I do agree with Boykin’s “triple quandary” and Dubois’ “double consciousness” as concepts that illuminate general dispositions of African Americans in the context of the public education system. I will focus on the issue of how this affinity group can utilize current technologies effectively to close the knowledge and achievement gaps they face. Tied to this, is the inquiry into practices that can promote the positive “projective identity” of weaker African American students in their study of math and science, which I will discuss.

Affinity Groups and Math Identity

Gee talks about how members of an affinity group can enter a semiotic domain with performance weakness, therefore needing a “psychosocial moratorium”, which he describes as “a learning space in which the learner can take risks where real-world consequences are lowered” (Gee 2007). Applying this concept to the subset of African American students that are weaker in math and science, teachers of these students must not only be sensitive to the academic weaknesses they bring to these classes, but effectively use methods that can mediate the complexities of problems that often defeat weaker students. This is where the use of technology in the classroom can be a vital asset. But first there needs to be an understanding that education in large part has to do with identity construction and the building up of self esteem or self efficacy. With African American students, who may have developed oppositional attitudes to public education due to their experience of various forms of racism in society, it is vital to address these attitudes in positive ways, starting with acknowledging the prevailing structures of racism experienced by students. The teacher must encourage the development of a constructive and engaged projective identity capable of transcending student conditioned responses to racism, and the structures of racism themselves in the students’ environment. Gee says, “Without such an identity commitment, no deep learning can occur. The student will not invest the time, effort, and committed engagement that active, critical learning requires.” (Gee 2007). Once the student is on the path of developing a healthy projective identity, believing that he/she can learn the subject at hand, it is then vital to reinforce this identity formation by scaffolding methods.

Mathematics Identity Building In My High School Classes

In preparing my algebra 2 classes to take the New Jersey state standardized high school proficiency exam in mathematics, I make heavy use of graphing utilities, like a graphing calculator and Maple 15. Though I teach my students how to handle challenging questions about functions and their graphs analytically or “by hand” I frequently reinforce the concept at hand by using the graphing utility. Sometimes I may even present the concept with the graphing tool first. The reasons are several and critical. My students tend to be more receptive to visual representations of a problem and its solution as opposed to simple text representations. In my view, teachers should embrace multiple approaches to teaching students in need of remediation. Gee refers to this as the “multimodal principle”, where “meaning and knowledge are built up through various modalities (images, texts, symbols, interactions, abstract design, sound etc.), not just words” (Gee 2007). This is not to imply that African American students or any other group can’t master textual representations as well.

Since my students do tend to have weaknesses in analytical problem solving, the graphing utility scaffolds around those weaknesses, thus providing the immediate satisfaction of understanding and solving the problem at hand. We can then spend more time talking about the solution and its potential value or relevance to them, than not. Once they are aware of the solution and its possible value to them, it is then easier for me to “sell” to them the value of knowing how to handle the same problem analytically. They also trust that I will successfully guide them to the solution “by hand” as I did by the graphing tool.

Through scaffolding students are able to, for example, bypass having the adeptness of graphing functions “by hand” and analytically solving for unknowns, by simply entering the function definitions into a graphing utility and displaying the results. The various attributes of the function can be readily known by visual inspection (such as, critical points, local maxima/minima, asymptotes, tail end behavior, domain, range, undefined points, inflection points, roots, intersections with other functions to solve for an unknown etc.) with relative ease, compared to discovering them analytically. Shielding students from undue complexities affords them more time to engage in higher ordered thinking, and the thrill of solving more complex problems, thus boosting their sense of self efficacy. This speaks to Gee’s concept of “psychosocial moratorium”, where success is not dependent on managing all the complexities of a problem all at once.

The above approach exposes students to the sphere of higher ordered thinking as it relates to the math semiotic domain. Student weaknesses can then be addressed from a position of gleaning the big picture, increased engagement, self-confidence, and self-motivation, all translating into progressive achievement. Gee sums up the positive effects of applying good gaming principles to education when he says “they situate meaning in a multimodal space through embodied experiences to solve problems and reflect on the intricacies of the design of imagined worlds and the design of both real and imagined social relationships and identities in the modern world.” (Gee 2007). I take this to mean, as it relates to the unique learning needs of African American students in math and science, that we must empower them to be active doers of math in these creative learning spaces. I will add that for this to be accomplished, weaker students must engage in math that is relevant to the unique challenges they face in both the education realm, and the larger society. These learning spaces must actively prepare them to be critical thinkers and to solve the unique problems they experience. Throughout the process we must be consciously aware that education is certainly deeply involved with identity construction. With the above approach, I have witnessed increased student engagement and willingness to work through math problems.

Let’s CHAT

The CHAT, cultural historical activity theory, also has promise in conceptualizing transformative, agentic educational practice that can further the educational goals of the African American collective. The unit of analysis of this theory reaches beyond the individual personal activity and subjective reality, in isolation from the context of the wider fields of social interaction. According to this cultural theory, individual activity, including learning in the classroom, is in symbiotic or dialectic relation with the wider community within which individual activity is embedded. “CHAT leads to changes in the location of representing what is educationally relevant: Its inherently dialectical unit of analysis allows for an embodied mind, itself an aspect of the material world, stretching across social and material environments” (Roth and Lee, 2007). Hence, individual learning goals, must be considered in context of the wider goals of the community within which the individual is situated. This is precisely the thrust of my approach on urban educational practices. I see collaborative technologies as tools that enhance the agentic activity of individual | collective African American student achievement. They can facilitate knowledge construction in iterative and accumulating developments, not unlike the multiplier effect of money in a closed economic system, thereby magnifying the capital wealth (knowledge capital) of the entire community.

What the Computer Field Taught Me About Education

What I will attempt to do here is reflect on some of the things that I have learned from my past academic and professional experiences that I consciously, and sometimes not consciously, attempt to parlay into transformative educational practices for my students on a daily basis.

Standards

My first employment position coming out of college was as a database administrator / programmer at Chemical Bank on Park Avenue in N.Y. In that first indoctrination I learned that field definitions were centrally defined and standardized. All of the developers depended on these standards to accomplish their individual work. My job was to make sure that this central repository of data definitions was maintained according to given naming conventions and standards for common access. Even the slightest error could affect many programmers and many new or existing applications. Immediately was gone the notion of just doing my own piece of work. My work was inextricably lined with the work of others at every turn. When I teach my students I want them to experience this interdependence with each other in the tasks and projects they do. I want to teach them that their problem solving may be for some immediate individual gain, such as passing a quiz; however in the long term their skill sets should be view by themselves as resources and affordances for their communities.

Groupware

In the late mid to late 90s, with the advent of the Internet, the methods of developing computer applications changed, and I was keenly aware of this sea change. There was a greater push towards collaborative application development, and the collection of computer software tools used to accomplish this was called group ware. The application development platform I jumped on while I worked at J.P Morgan and Marsh & McLennan was called “Lotus Notes” and subsequently Java. It was called RAD, Rapid Application Development. It allowed for users to access company resources and computer processes remotely through the company intra net and through the World Wide Web. I was truly fascinated by this type of technology and I quickly became certified to do this work, which I did for the later 10 years or so of my career. As the technology matured these companies moved to other platforms, which I did not keep up with.

This kind of collaborative work fed beautifully into my vision on how African American communities needed to work collaboratively to solve collective problems. Later as I moved into the educational field I transferred that same vision to how students needed to work to learn how to solve collective problems of their communities. It’s this same vision I pull from today when I assign group projects to my students that use Moodle (Content Management System) and Google Mail, WordPress.com and powerful math modeling tools such as Maple 15. All students in public schools must become adept at using Web 2.0 tools, where they not only access the world’s information via the internet, but learn how to manage that information, author their own contributions to existing knowledge stores, and multiply their collective knowledge of solutions to problems by leveraging collaborative technologies. I advocate strongly that teachers help students to learn how to use resources in a Web 2.0 enabled classroom to solve problems that are relevant to the student and the community from which they come. In schools where African Americans predominates, this means teachers teaching in culturally sensitive ways that will help African American students to learn how to solve the deep problems facing our their communities. This is not a separatist imperative, to foster the continued divergence of Blacks from Whites. It is an attempt to level the playing field so that Blacks can compete and hold their own in an increasing technologically demanding workforce and fast paced society.

Maintainability & Extensibility

One of the main lessons I learned as an application developer is that your applications must be both maintainable, and extensible. Maintainability in this context means that once your application is rolled out it should be easy for someone else to come behind you to locate fix any bugs in the application. The application should be documented and the code modularized well enough to isolate and solve the problem quickly. Furthermore, any application should be extensible such that newer functionality can be added easily without requiring much rewrite of existing code or radically changing existing processes. Not only that, extensibility could also mean expanding the capacity and scope of an existing application. As I mentioned in the financial industry applications should function across regions and time zones. I think these concepts can be applied to teaching African American students by emphasizing that they must learn underlying principles governing a field and be able to apply these principles in novel ways that address the unique problem sets of their communities. They must use the skills learned in math and science and extend them to the problem domain of their communities. Furthermore they should see their contributions as contributing to the collective knowledge capital of their communities so that it will be easier for the youth who are coming up behind them to further maintain and extend their current solutions sometime in the future; rather than have to start from scratch. So solutions to unique problems faced by African American communities and devised by vanguards of these communities should be well-documented maintained, and designed for extensibility. African American student developers should be taught these methods, as I learned them in corporate America.

Obsolescence

One of the painful lessons I learned during my career as an application developer is that due the exponential growth of technology, that the computer toolkit we had acquired became obsolete in increasingly shorter time periods. I had to constantly “retool” to keep up with these changes. At one point for example I was learning the Java platform because I was anticipating that the “Lotus Notes” platform was dying out. This constant need to retooling also accelerated my desire to leave the field, as it was not my intention to keep up with all of these changes. I was becoming critically aware that it was time to use my foundational knowledge to assist in initiatives to help underserved communities value and leverage technology to reach their goals. Failure of these communities and the educational systems in them to help their youth come up to speed with the changes in technology would clearly result in these youth not being able to adjust to demands of a 21st century economy. They would consequently become themselves obsolete, and enter the lower rungs of society, and likely remain there.

I can probably go on with more ways that I can apply what I learned as an application developer in corporate America to the problems faced by African American students in public schools and the stakeholders of their education. I think the point is that exponential advances in technology are changing the way we have to address the ongoing issue of racism and its various manifestations of oppression. We have to recognize that these changes are speeding up the movement towards a condition where African Americans collectively will not develop the necessary survival tools to avoid becoming a permanent underclass in society, or a non-existent factor in total. As one who has become intimately involved in the forces of change due to technology in both the corporate world and the educational world, I could not and would not in due conscience not involve myself in researching how to advance the unique educational needs of African American students who push to the extreme abyss by the technological engine of change.

Multiplier Effect of Collaborative technologies

Collaborative or interactive technologies foster the acceleration of the interactive transforming exchanges needed to accomplish the progressive development of African American communities. Collaborative technologies can facilitate a multiplier effect of knowledge capital that can reverse the knowledge and achievement gaps faced by African American students. An increase in the number of persons (nodes) distributing information (capital) in a closed networked system will increase the frequency that each person will receive a form of capital, in the Bourdieusian sense. Each exchange of capital is the equivalent of an injection of new capital in the system, thus representing a multiplier effect. That is, the net gain in capital of each person in the system is increased many more times than if a person was acting alone or with a very few other persons (nodes). The goal then in urban schools is to utilize tools, processes, and approaches that will increase the frequency that students in a networked system (extended classroom) can share information with stakeholders. In this paradigm students appropriate interactive technology tools that facilitate sharing of timely information. The more knowledge capital that is circulated the better the overall quality and effect of produced products that have embedded in them the knowledge. What promotes effective meaningful discourse around problem scenarios engaged by students, also promotes an increase in meaning potentials for effectively solving those problems. Through the improvement of the means of transacting forms of capital in the Bourdieusian sense, comes a multiplier effect of net capital accumulation, including knowledge capital.

Specific Affordances of Interactive Technologies

Interactive technologies in education offer powerful tools for addressing field trip and meeting constraints, access to experts in a given discipline with video-based problems, computer simulations, electronic communications systems that connect classrooms with communities of practitioners and experts in science, mathematics, and other fields. This all allows students to collaborate in wider collaborative learning communities. In these spaces, students can use shared collaborative and visual tools and see how their local data fits into a larger model (e.g., local environmental studies of climate issues). Integrating this approach into the curriculum results in positive student attitude towards and engagement with complex problems.

Students can be engaged in online learning communities for creating, sharing, and mastering knowledge: exchanging real-time data, deliberating alternative interpretations of that information, using collaboration tools to discuss the meaning of findings, and collectively evolving new conceptual frameworks. Knowledge and meaning is obtained through the synthesis of multiple dialogues and points of view, where each “utterance” in the Bakhtin sense, is predicated on those that came before. In an interactive virtual learning space, these utterances can be contributions to a threaded discussion on a discussion board. To accomplish this I have for example, used the Moodle collaborative software as a collaborative tool in my high school math classes. The outcomes of this collaboration benefit not just the individual student, but can become a repository of relevant knowledge capital, by and for the community at large. It becomes a collective competency, directed at meaning making that is meaningful to both the individual and the community the individual comes from. It will remain a collective competence so long as the discourses and knowledge produce remains directly relevant or synchronous to the common problems faced by the collective. Once this golden rule is violated, then the environment has been compromised. An accumulation of compromises past a critical point will render the collaborative environment ineffectual in the uplift of both the individual and collective. This possibility has to be vigilantly mitigated by both the participants and designers of the learning space.

Technology can make it easier for teachers to give students feedback about their thinking and for students to revise their work. It creates opportunities to incorporate into curricula a reflexive approach to instruction that helps students see where they are in the inquiry process and to act in ways that oppose harmful influences of socialization and social structure. Processes called reflective assessment can be used, in which students reflect on their own and each other’s inquiries. Opportunities to interact with working scientists, as discussed above, also provide rich experiences for learning from feedback and revision. These processes can make students’ reasoning more visible and encourages reflective thinking. With support from the instructor, these processes engage students in dialogues that integrate information and contributions from various sources to produce knowledge.

Scaffolding And Powerful Modeling Technology Tools

Using powerful Graphical User Interface (GUI) tools and forth generation computer languages (4GL), students can construct a model of a problem along with a possible solution set and submit it for collaborative review. A teacher can in the same sense as a text document, markup the model or otherwise point out to the student areas where the model may be enhanced for a better solution. Students can then explore the suggested solution path. I am currently exploring a power math tool called Maple 15 that does this kind of modeling combined seamlessly with student co-authored rich text.

This aspect of scaffolding is critical for students who are weaker in a given learning domain and who are struggling to navigate it. It also enables students to become more reflective and aware of successful strategies in navigating the given field of study. Technology thusly creates opportunities to incorporate into curricula a meta-cognitive approach to instruction by using an inquiry cycle that helps students see where they are in the inquiry process. The end result is that students learn the processes of becoming adept at a particular learning domain. They develop identities as authors / designers who not only adequately function in the semiotic domain, but also advance the learning domain to wider frontiers through unique authoring / designing contributions. Students engage in guided, reflective inquiry through extended projects, and with the use of sophisticated concepts and skills embedded in models, generate ever more complex products. Students become actively engaged partners in meaning making by considering and building on multiple perspectives. I believe if you couple the above benefits of collaborative technologies with initiatives of culturally sensitive pedagogy, students will be empowered in rich ways to address the developmental needs of their communities.

More On Practices In My High School Math Classes

During the course of the second half of the current school year I’ve engaged students in projects that I hope will develop their identification of themselves as doers of mathematics not just for their own benefit, but to the greater good of the community from which they come. This is in keeping with the unit of analysis that I mentioned already. It is not the student’s activities in isolation, even if it involves advanced technologies. Rather, I consider activities of groups of students in collaboration through interactive technologies for the purpose of increasing their collective agency for the uplift of them selves and of their communities. This goal was reflected in the project requirements in one way or another, as I attempted to develop this collective identify of my high school math students. The following are some activities I engage my class with to do this:

1)    Access resources on the Moodle placed there either by other teachers, other students or myself. Students can modify copy and then modify contents.

Resources include:

1. PowerPoint slides on math lessons
2. Videos on particular skills
3. Assessments
4. Journal entries in forums
5. Stored files

2)    Create shared folders in Gmail where students can share electronic files with each other and I.

3)    Create Web site for students in Google to establish virtual math identity and share files with public (rest of school).

4)    Smart board to facilitate whole class sharing of products

5)    Google survey, Word Press, Geometer’s sketchpad, Maple 15.

6)    Co-teaching and cogens are mechanisms for students to share their perspectives on math.

7)     Maple 15 allows students to create narratives or problem scenarios and seamlessly embed math into them. They can then share this with others by exporting it as an html file.

Micro Discourse Analysis

Coding for positive evaluations of student discourse as they work towards collective and individual goals would need to take place over all the types of products that were collected while students engaged with math content using technology tools, such as the ones I mentioned. The following is a tool for doing discourse analysis on student dialogue and authored products that I adopted and adapted from Lisbeth Amhag and Anders Jakobsson, who used it in their analysis of student dialog while taking an online course. This tool is in keeping with Bakhtin’s ideas of ideological becoming.

I’m in my 6^th year of teaching mathematics and using interactive technologies to enhance student learning as I’ve described. I have seen indications of my students developing an ideological stance and identity as a problem solver on behalf of student communities. Using the above dialogical tool will be helpful going forward to determine the level of student “Ideological Becoming”, in the Bakhtinian sense. Another means to ascertain that students in urban classrooms are developing positive identity as doers of math on behalf of their communities, is to gage the level of synchrony and entrainment amongst students and teachers in the classroom in the sense given by Randall Collins in his book, Interaction Ritual Chains (2004):

“As persons the person become more tightly focused on their common activity, more aware of what each other is doing, and feeling, and more aware of each other’s awareness, they experience their shared emotion intensely, as it comes to dominate their awareness”.

This solidarity on a sustained and continuous level, towards a common goal of community uplift is what I hope to engender in my students.

Ken Tobin has done extensive work in this area of microanalysis of synchrony in the classroom and has demonstrated its usefulness.

 “We show that specific prosodic features in face-to-face encounters—alignment and misalignment—are associated with the production of solidarity and conflict, which in turn are associated with successful and unsuccessful lessons. They are also associated with different degrees of solidarity and emotional energy that participants in science classrooms experienced.” Roth & Tobin (2010)

Micro level data, as in video taping of students as they are engaged in the type of collaborative project work that involves community, can be coded for prosody, entrainment or sustained focus, and synchrony. This data can be compared to the same type of micro level data of students engaged in typical teacher centered lessons. Though I have not carried out this micro level analysis and comparison with my students, I have notice higher levels of student engagement, entrainment, and synchrony when students were allowed to author their own math products and were free to present them in the role of class teacher. I would not want to overstate what this micro level analysis can reveal in terms of identity formation. I think that looking at micro level data in isolation from wider cultural structures that students are embedded in, can lead to misinterpretation of events. For instance simple smiles by students in and of themselves can be interpreted as positive emotional engagement, but can actually be an expressions of subversion or carnival (in the Bakhtinian sense) to a teacher’s practice. However this is true for all of the forms of evidence that I have listed thus far. It is only when one form of evidence is held together with all of the other student produced cultural artifacts that we can gain higher confidence levels that this collaborative, student centered approach cultivates in students a positive identity formations as doers of math on the behalf of their communities. Having stated this caution, it is my experience that the levels of solidarity are markedly higher when students are given freedom to work on problems that are relevant to their communities, and allowed to present them, without undue teacher interventions, to their classmates and other stakeholders. This may also translate into higher levels of student achievement in math and science, as well as entry into these professions.       

Where does this lead? I think this can lead to a feedback loop of cultural capital forming a habitus, or educational praxis that supports not just individual positive affective identity formation, but positive collective group identity formation, that can be the basis for transforming dominant structures that have to this day, thwarted the educational aspirations of African American students. I refer again to Turner for aid in conceptualizing prospects for transformative agentic action, as the outcome of positive affective identity formation of participants in my project: “the flow of positive sanctions in an encounter tends to circulate among the participants to the encounter, with individuals mutually sanctioning each other in ways that build up local solidarities, although at times this flow of mutual positive sanctioning can work its way up to meso-structures and macrostructures” (Turner 2007). This reminds me again of the multiplier effect of circulating money in a closed system repeatedly before allowing it to leave the system, as a means of accruing wealth exponentially. This then provides a cultural capital accumulation that may reach a critical mass, allowing for transformation structures in the educational arena. The goal of this project is no less than such a transformation of mesostructures and macrostructures that tend to constrain the educational and life possibilities of African American students.

Modeling and Feedback in Collaborative Learning Spaces

The NRC report “How People Learn” also offers critical insights into how the use of technology, backed by sound pedagogical principles, can enhance the learning of African American students and help close the knowledge and achievement gaps they face. One method it discusses is using technology as a modeling tool. Modeling problems visually through technology, in my experience has tremendous advantages for students with math weaknesses. There is a strong trend in modern societies of visually modeling or simulating a problem set using advanced technologies such as CAD (Computer Aided Design). It is popular in current gaming design and many fields, such as medicine, meteorology, architecture, film, and aviation to name just a few. There is no reason why this approach should not be taken full advantage of to aid students in tackling complexities in math and science in the classroom, particularly for those who struggle in these fields.

Another advantage that using technology to aid learning has is that it gives students and teachers more opportunities for feedback. Think of the power that we may currently take for granted of writing a paper electronically and submitting a draft for review to peers and a teacher who are sometimes a half a world away. The reviewer can offer critique by marking up the document electronically next to the original text, without changing the original. The student author can then accept or reject some or all of the changes. The student can explore what the results would be (see how it reads) if the changes were accepted. This also applies to the math and science models. Students can construct a model of a problem along with a possible solution set and submit it for review. A teacher can in the same sense as a text document, markup the model or otherwise point out to the student areas where the model may be enhanced for a better solution. Students can then explore the suggested solution path. This aspect of scaffolding is critical for students who are weaker in a given semiotic domain and who are struggling to navigate it. It also enables students to become more reflective and aware of successful strategies in navigating the semiotic domain. As stated in “How People Learn”, “technology creates opportunities to incorporate into curricula a meta-cognitive approach to instruction by using an inquiry cycle that helps students see where they are in the inquiry process” (How People Learn, 2007). The end result is that students learn the processes of becoming adept at a particular semiotic domain. They develop self-efficacy as authors / designers who not only adequately function in the semiotic domain, but also advance the semiotic domain to wider frontiers though unique authoring / designing contributions. The sound pedagogical use of technology by teachers affords promising opportunities to mediate academic weaknesses in math and science that African American students tend to have in typical urban schools.

Collaboratories – Virtual Learning Spaces

One other concept discussed in the “How People Learn” report that I will extend to address the learning needs of African American students is that current technologies can provide opportunities for these students to collaborate with peers, teachers, experts, and anyone associated with a particular semiotic domain of interest, via virtual learning spaces or what the NRC report refers to as “collaboratories”. In my experience, African American students already have adeptness in using collaborative technologies, such as cell-phones and Facebook on the web. The problem is that this collaboration tends to focus not on academic and collective socio-eco-political problems, but rather on non-academic, social circle concerns. Educators should leverage the familiarity of African American students with the later usage of technology and apply it to the more frequent usage for the former type to address the knowledge and achievement gaps they face.

The knowledge and achievement gaps in math and science faced by African American students have deep historical and macro causes. The digital and knowledge divide are macro national problems requiring macro national solutions. The beauty of the Internet and collaborative technologies with respect to these problems is that it is designed to solve problems that are distributed over dispersed geographical domains as easily as problems that are locally situated. Furthermore, the technology can be used to roll-up or incorporate solutions of local problems, into models that treat the same problem from a macro or global perspective. The “How People Learn” report used the example of students collecting and analyzing local data related to global warming and then through collaborative technologies, uploading their local findings to a centralized global model of the phenomena for shared use. In the same way, African American students can roll-up their solutions to local problems into models that treat the same problem from a macro or global perspective, through the vehicle of collaborative learning spaces.

Some Criteria For Implementing an Interactive Learning Environment

The following are details the requirements of an online collaborative learning environment.

• Teacher can create new content to augment any pre-existing content.
• Student authors and mashes up content.
• Organize teacher and student authored content in context of the lesson.
• Allow for shared objects and models.
• Allow for organization of authored Asynchronous content
• Allow for synchronous dialog
• Allow for controlled multi-user access to content
• Handle wide array of multimedia objects
• Ease of use
• Scalability to Web 2.0 tools
• Easy setup and access
• Scalable cost
• Capture student feedback
• Allow for simultaneous or near simultaneous control and manipulation of objects within the context of a lesson.

These areas would be assessed in a given locality on a scale of: none existent, recently implemented, low, medium, and high). It would be important to give a locality periodic feedback on how well it is doing with regards to its implementation of a collaborative learning environment across the curricula. The promise of such feedback and subsequent advice would be a selling point to encourage a school to participate in this project initiative.

Ripple Effect of Micro-Level Transformative Education On Macro-Level Structures

What becomes essential in the deployment of interactive technologies is not the technology itself, but the meaning making, liberating ideologies, and problem solving that are all directly relevant to the participants acting to their own benefit and that of the wider collective from which they come. I have been involved with student learning in the math domain; however, what I have said about interactive technologies I think applies generally to the various science domains as well. New forms of computer models coupled with increasing ease and power of modifying and sharing these models without regard for distance or time, makes possible a broader, more powerful repertoire of pedagogical strategies that can be pressed into service to accomplish common goals of the collective.

Culturally empowering learning spaces that utilize advanced interactive technologies, coupled with liberating ideologies embedded in the curriculum, have the potential of producing educational experiences for African American students in public schools that are transformative of existing constraining structures in public schools, affording agency for both individuals and collectives. These spaces are not isolated enclaves that locate the problems facing African American students in the bodies of the students or in their ethnic practices. Rather, there is a recognition that agency of students is interlinked with how students and stakeholders access and manage available resources to construct meaning and knowledge that can be applied to their collective problems and motives. These learning spaces can serve as models for a public education generally, for not only minority students, but for all students. So these learning spaces in particular localities can have a transformative effect on meso and macro level structures of education and society as a whole.

The exponential advances in technology are changing the way we have to address the ongoing issue of racism and its various manifestations of oppression. We have to recognize that these changes are speeding up the movement towards a condition where African Americans collectively will not develop the necessary survival tools to avoid becoming a permanent underclass in society, or a non-existent factor in total. As one who has become intimately involved in the forces of change due to technology in both the corporate world and the educational world, I could not and would not in due conscience not involve myself in researching how to advance the unique educational needs of African American students who push to the extreme abyss by the technological engine of change. If we can close the achievement gap faced by lower achieving groups, we would have learned valuable praxis for closing the achievement gap between America and other countries that have surpassed America in student achievement. Perhaps if educators of good will can bridge the technological learning gaps faced by minorities, we will also be able to bridge economic and social gaps as well thus promoting a greater cosmopolitanism in American society.

References

Bakhtin, M. M. (1981). The dialogic imagination: Four essays by M. M. Bakhtin (C. Emerson, & M. Holquist, Trans.).  Austin, Texas: University of Texas Press.

Bakhtin, M. M. (1986). Speech genres and other late essays (V. W. McGee, Trans. Vol. 9). Austin, Texas: University of Texas Press.

Bourdieu, P. (2000). Cultural reproduction and social reproduction. In R. Arum & R. Beattie (Eds.), The structure of schooling: Readings in the sociology of education (pp. 56-68). Mountain View, CA: Mayfield Publishing Company.

Collins, R. (2004). Interaction ritual chains. Princeton, NJ: Princeton University Press.

Gee, J. (2007). What video games have to teach us about learning. New York, NY: Palgrave Macmillan.

Bransford, J.D., Brown, A.L., & Cocking, R.R., Editors (2007). How People Learn. Commission on Behavioral and Social Sciences and Education, Chapter 9. Washington, D.C.: National Academy Press.

Roth, W-M., & Lee, Y-T. (2007). “Vygotsky’s neglected legacy”: Cultural-historical activity theory. Review of Educational Research, 77(2), 186-232.

Roth, W-M., & Tobin, K. (Eds.) (2007). Science, learning, and identity: Sociocultural and cultural-historical perspectives. Rotterdam, NL: Sense Publishing.

The John D. and Catherine T. MacArthur Foundation Reports on Digital Media and Learning | November 2008. Living and Learning with New Media: Summary of Findings from the Digital Youth Project [White paper].

Turner, K. (2007). Human emotions: A sociological theory. (p. 73). New York, NY: Routeledge.

Integral knowledge, Being and view: Perspectives backing transformation of habitus in public schools

Roland Lucas

CUNY Graduate Center

Mathematics and Technology

November 5^th, 2011

Abstract

Determining “what counts as knowledge” involves the convergence of one’s epistemological and ontological standpoints, which will inevitably shape the quality of one’s inquiry into a subject. In quantum physics there is a concept that the experimenter will always influence the outcome of an experiment by the very act of selecting what to measure. This may be difficult to wrap the mind around, but I think it is true that the strictest of positivist in their very selection of data to analyze, does expresses a convergence of epistemological and ontological standpoints, despite any claims of complete objectivity devoid of influence from personal frames of reference or values. The following discourse explicates my perspectives on the nature of knowledge construction, being, and value, that permeate my approach to transformative education in public school predominated by African Americans and Latinos.

Integral VS Partial Knowledge

Knowledge can be partial or integral. Partial knowledge is where one takes a part and ignores the whole, or sees the whole and ignores its myriad expressions and revelation in the part. Integral knowledge knows the part to be inseparable from the whole. It is able to see or reach the whole through the part. It realizes that the part reveals the whole in a way that defies the logic of a subset not being able to contain the set. Integral knowledge sees the interconnectedness, wholeness or oneness of all things, from the macro levels, through to the micro levels. It embraces this wholeness, this oneness of all things while acknowledging the validity of every expression of the whole. This knowledge is intimately tied or yoked to ones’ conception of self. One can view the self as isolated, disjointed, and in the extreme in opposition with the other. This is related to partial vision or knowledge. If there is a partial self- knowledge, there must then be a partial comprehension of the world. On the other hand, one can know ones’ Self to be joined in oneness, interconnected, with the essence of all things. All things then become a part of one’s self. This vision is intimately tied to integral knowledge. This is the basis of a collective consciousness or Being within groups.

Social Application of The Unified Field Theory

My approach to life in ALL of its modalities is seeing it as an integral whole with extended parts that are always connected to the whole. The Whole is always behind supporting the extension, and the extension is always giving expression, in whatever degree, to the whole; whether the part “realizes” it or not. Einstein spent much of his life seeking a “theory of everything” that would integrate the various laws of the universe into one whole. With this theory one could express the integration of the various laws of the universe into one comprehensible whole as a mathematical equation no longer than an inch. This endeavor has its parallels in the quest to understand human evolution, knowledge systems, and societal organizations, “the whole”, expressed in various time periods, nations, states, communities, and yet these can be depending on context, “the parts” of a larger Whole.

If I were forced to offer an equation that would express the relationship of the whole to the parts in mathematical terms it would be as follows: A:X::X:B or A/X=X/B; where for example, A and B can be any two events or experiences (past or present), and X is the whole that can be the collective experience/memory or Collective Consciousness and Being of humanity on a global, national, ethnic, state, regional, or local neighborhood levels, depending on the context. A and B are all integrated with the whole, and therefore with each other. The part can be the experience of a person, neighborhood, region, state, ethnic group or nation that is always related to, and gives expression to, a more comprehensive whole and at the same time is related to all other parts. From the macro to the micro and vice-versa, this formula extends as an infinite series in all directions.

In my theory of everything as it relates to human evolution and organization, human collective consciousness on any level is not static, and is not bounded by concepts of birth and death, past or present. It is continuous and integrated. The collective human consciousness of today is connected to the collective human consciousness from ages ago; hence the terms collective memory, collective awareness, cultural heritage, national progress, and soul of a nation. As I engage a subject of inquiry from whatever level or vantage point, I am always using this worldview as a basis. Knowledge that cuts of the relationship of one thing to another, that ignores the relevance of one experience to associated ones, or that declares one body essential while related ones irrelevant, is in my view partial. It represents partial awareness, and a restricted consciousness. There are always polarities of the same essence. We slide along the poles with varying degrees of awareness of the essential oneness between poles. We are always swimming in a unified ocean passing through waves of expression, experience, or knowledge.

Transformation | Reproduction | Agency | Structure | Production | Creation – Multilectic Aspects of Social Life in Public Schools

In attempts to have a more holistic view of education practices in public schools, in the spirit of the integral vision I expressed above, and after devoting much focused attention to the transformation, agency, and production aspects of habitus in my math classes, I’ve subsequently made a conscious effort to pay attention to the reproduction, passivity and creation aspects that always complement the former in dialectical relations that together can be said to form ever present “multi-lectic” bases of social life across fields in the life-world of students.

In striving to transform educational environments predominated by African American and Latino students, I have largely focused on the structure | agency dialectic. I’ve embraced being conscious of macro and meso level structures of society that tend to constrain the educational attainment and life chances of these groups. This focus on having awareness of oppressive structures and awareness of the agentic ways we can act to transform these structures, producing new structures that are less constraining, has perhaps led me to neglect other equally pertinent dialectical aspects of the habitus of said learning environments. As I am concerned with production of new structures through agentic actions, I must also give careful consideration to the creation of culture, or structures that occur not through agentic means, but through passive means. By passive I do not mean blind acquiescence to domination. I mean the state of being receptive to enculturation or to inscriptions of others who contribute to scaffolding the agent’s eventual actions. This also has to do with the subtle and not always visible, development of identities. Identify formation does not always occur in the active doing by agents, but also in their passive and sometimes radical, listening. It occurs too in their observations, identifications, being with, imitating, following, and ideological scrutiny of others. I must also consider that students and teachers bring to classrooms, ideologies and schema accreted throughout their respective histories, that impact consciously or unconsciously what gets enacted. Sometimes we refer to this as second nature, or disposition. It is the business of educators to move conscious liberating practices, to the realm of second nature or disposition in our students. The common example in mathematics is that we hope through practice and drill on solving problems of a certain type, that students will commit their new found competencies to second nature or conditioned response, so that when presented with this problem type in some new context, that students will have the natural disposition to solve similar problem types in novel situations, without resort to relearning as if from scratch. The uncommon example is that we hope that through teaching social justice mathematics, that students will employ their acquired competencies in mathematics towards the uplift of their communities in an ongoing basis once they graduate.

I have assumed in my teaching practice that if we reflected and focused on the agency side of producing culture where students are enacting practices in the math classroom and beyond where they are reaching their individual and community goals, that the latent, unconscious, passive side of the dialectical coin will take care of itself. I do recognize that humans have all kinds of conditionings, many of which tend to reproduce relationships that limit their power potentials. I also recognize that despite our best efforts of being conscious of structures that constrain our goals and life chances, we are in constant negotiation with these structures. Sometimes we acquiesce to them in the moment so as to get on with our larger project of transformation on a broader landscape. It’s like giving up on an immediate battle, but not the larger war. Recognizing the obvious forms of racism that permeate public schools where African students predominate, I do not necessarily advocate boycotting these schools, or refusing to teach in them until such time that they are transformed before being proclaimed fit to teach our students. I advocate transforming them from the inside out, sometimes with great obvious affect; and sometimes with latent, yet potent affect. Sometimes the transformation occurs deeply on the subtle levels, the passive side (passive resistance) of the agency | dialectic.

This begs the question, how best to manage the passive side, integrating it into a holistic vision of a multi-lectic space? How should we cultivate it so that it is in agreement with the agentic side? How should we deal with student identity development as competent doers of mathematics in support of their goals and that of their communities, when they are not acting in overt or even conscious ways to do so? Enculturation is not always conscious. Habits of mind unconsciously applied, need the precursors of drill and practice in a variety of settings and circumstances. The apprentice is not always and everywhere aware that she is learning from the master, even during some innocuous moment. Availing students to the resources and opportunities to effect positive change without always directing outcomes has its place. This is one of the beauties of student co-teaching. Students do not necessarily realize that when they are teaching others, they are mastering the concepts for themselves. Students also don’t necessarily realize that as they are elevating themselves, they are also increasing their potential to elevate their community. I say potential to do so because it is not a given one-to-one outcome of teaching content. I think it is important to monitor and guide students to applying acquired competencies to the uplift of their communities, without directly requiring them to do so. How do we teach students to embrace selfless service to their communities without compulsion? This is another aspect of passivity. I think one answer is through example. When students see teachers giving selflessly to the school community and loving it, they tend to want to do the same for the school community. This would then become a lasting characteristic of the student that they bring with them to all other fields of their life-world, particularly their community environments.

There is another dialectic, the conscious | unconscious, that needs to be accounted for when trying to transform the habitus of students such that students are better positioned to appropriate resources to reach their individual and collective goals. What happens when administrators, teachers and students are not aware of structures that will effectively thwart any real attempts to establish agentic practices on behalf of students?

Suppose for a moment that the movement for national standards and high stakes testing as it is applied to a “school in need of improvement” produces teaching methods that focus on route learning, teaching to test, and non-critical thinking. Yet in their zeal, administrators and teachers overwhelmingly think that there can never be too much inculcation of this kind focus in students. Suppose in actuality this focus on high stakes testing eclipses modes of inquiry, critical thinking, and project based learning that is benefits solving real-life problems relevant to the life-world of students; yet only a few teachers and administrators (say a lone math teacher) in the school are aware of this. If this or some other constraining structure is firmly entrenched in unconscious ways, what can the few conscious persons involved do to produce a pervasive consciousness that will begin a healthy transformation of the school environment? How should these few teach, in this climate, not wanting to do a disservice to the holistic education of students, but also not wanting to be categorized under the existing organization as a troublemaker? This is where one needs skill at being inwardly firm to your principles yet outwardly flexible. In such a climate in may not be advisable or fruitful to attempt everywhere and every time a transformation of the structures that structure the environment in overt ways. Subversion, to use a term, would be called for. Educating educators and students alike, means creating practices that will help them reach their goals. Yet in this scenario, it is clear that not everyone may have compatible goals, or compatible ways of achieving them. In this case, we can see that everyone, or every faction, has to decide if the environment they operate in has enough potential to become transformed in significant ways, or is it simply intransient.

Given that transformation and reproduction are always present, the question is more of degrees and timing. Can egregiously constraining structures be transformed into another state that increases the attainment of educational goals of students in a reasonable time frame? Since the technological engine of society pushes the demands towards ever richer competencies of students, transformation of practices that do not allow students to address these demands within a reasonable time, may seem not be a worthwhile endeavor. Perhaps then, it’s best for conscious educators to coalesce their common vision and focus it on levels and subfields where there is a greater potential for radical transformation, given the radical demand. Revolutionaries are smart to choose their fields of battle wisely else the revolution may never catch on and come to fruition. Such fields may not show shoots of visible transformation, but may have rich soil ready for seeding that will eventually sprout throughout in luxuriant growth. This seeding may be done invisibly, reaching the subconscious passively of students, but eventually germinating into agentic actions of students that can transform their habitus and that of their communities.