The African american affinity group and math identity construction

The African american affinity group and math identity construction

By Roland Lucas

CUNY Graduate Center

Doctorate of philosophy

Urban Education Department

Science Math and Technology

April 18, 2010


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 an “affinity group” that has a different set of challenges, hence, a different set of immediate goals than other student groups. Gee describes a “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.”[1] I will use the definition of semiotic domain, as Gee does, to refer to the various disciplines taught in schools, though my focus is on the situation of African American students in the math, science and technology 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 and science, 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 College in Massachusetts, always sitting together. The college 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 acquisition of skills and knowledge necessary to be productive and self-sufficient not only for one’s self, but for the advancement of one’s group in the society, and the advancement of society as a whole.

It is worth investigating how the African American student located in economically depressed urban areas, sees it’s self 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 construct the African American student self perception here. Rather 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.

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”. [2] 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 realities 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.”[3] 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. I will give an example of how I use technology in my advanced math classes to do just that.

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.  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.”[4] 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 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 understanding 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 multimodoal 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.” [5] 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.

Modeling and Feedback in Collaborative Learning Spaces

The NRC report “How We 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 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 We 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.”[6] 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 affords promising opportunities to students in urban schools tomorrow facing a daunting digital divide today.

Collaboratories: Collaborative Virtual Learning Spaces for Building Knowledge Capital.

One other concept discussed in the “How We 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 We 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.

Student As Teachers, As Doers of Mathematics, As Mathematicians

The following describes a project that I am currently implementing in my algebra 2 classes, and that addresses the development of the projective identities of my students as practitioners of mathematics. Technology is used throughout to facilitate the project. I will call it “Students As Teachers”. The project was for students to pair up in teams of two and select sections of the textbook that we had purposely skipped over during our preparations for the state standardized test. The students were required to learn the concepts independently and then seek my help with areas they did not understand. They were to create, “big ideas” statements, identify essential questions to explore, develop lesson plans, assessments, class work, and real life word problems that were changed to relate to their community. They were instructed to incorporate technology into the instruction. All these components were to be stored in electronic format on the class Moodle, a course content management system. This preparation took about two weeks. After that time student teams would teach the lesson. I served as a coach on the side. Student teams had two days to deliver the lesson. My initial findings are that students are highly engaged in the doing of mathematics. The have ample opportunity to work on their self esteem, identity as mathematics practitioners, and that they welcome opportunities to use technology, not only to develop their lessons and understanding of the content, but to help others to verify “by hand” solutions with technology solutions. It is my expectation that in the long run, these students will develop a healthy level of self-efficacy and identity construction as math practitioners, resulting in their higher achievement.

Many acknowledge the problem of low student achievement by African American students and are attempting dynamic ways to address it, including using technology to enhance learning. However, many are ignoring the problems and continue with the same old practices creating skill sets that cannot keep pace with the current demands of a technologically advanced globalized economy. African American students vitally need the establishment of collaborative learning spaces where they can construct and share knowledge about the local and global problems they face in common. This is the kind of work that I have left the corporate field to be a part of.



John D. Bransford, Ann L. Brown, and Rodney R. Cocking, Editors. How People Learn. Commission on Behavioral and Social Sciences and Education, Chapter 9. Washington, D.C.: NATIONAL ACADEMY PRESS, 2007.

[1] (Gee 2007, 19)

[2] (Gee 2007, 59)

[3] (Gee 2007, 55)

[4] (Gee 2007,222)

[5] (Gee 2007, 40)

[6] (How We Learn, 2007 205)


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