Educational Significance

Scholars of mathematics education, drawing from sociocultural theory, have begun to investigate not only what students are learning, but who students are learning to become in their mathematics classrooms, which can vary based on the pedagogy of the classroom (Boaler & Greeno, 2000).  This study investigates how students with learning disabilities understand themselves as math learners in the context of their mathematics classroom, understanding disability in schools as highly contextual (Gabel, 2002).  Conceptions of competence in mathematics, including how learning disabilities is understood and enacted by both teachers and students, affect the kinds of mathematical practices that students experiences and the trajectories available.  This study documents how the mathematical practices in one urban, inclusion classroom position learners, including tracing the effects of classroom interventions such as ability grouping.

Theoretical Frameworks

Instead of relying on a static, singular notion of identity, this study investigates a process in which people participate in, and across, specific social worlds.  In the “figured world” of a math classroom (Holland et al., 1998), participants create and recreate a particular set of cultural practices in mathematics (Nasir & Hand, 2006). Cultural practices always involve working with, and to some degree internalizing, cultural tools such as language and symbolic representations (Vygotsky, 1978). Within that figured world, participants position others and themselves, including through cultural practices such as labeling, or assigning learners to particular roles (Holland et al., 1998). Students take in both the language and the roles of these cultural practices (Bakhtin, 1981; Holland et al., 1998).

Research Design

Setting and participants

Located in a large city, the school predominantly enrolls Latinos (92%) with a poverty rate of 85%.  The class was a seventh grade inclusion class, with 24 total students, 12 labeled learning disabled. The teacher, Ms. Acosta, was a Latina in her ninth year of teaching.

Methods and analysis

Using participant observation methods, I documented the cultural practices of this classroom in weekly visits, including how students are positioned as able or disabled in mathematics, with ten observations video-recorded.  Ten focus students were interviewed in video-recorded semi-structured interviews.  Using field notes and transcripts of class and interviews, I analyzed the “figured world” of the math classroom, how focal students were positioned in the classroom, and how they understood themselves as learners of mathematics.  

Findings

The hybridity of pedagogy in the classroom

Early in the fall, Ms. Acosta asked me if I had noticed the “two different halves” of her math class, what she termed “critical-thinkingish” and “state-examish.”  During “critical thinkingish” work, Ms. Acosta would engage students in discussion of mathematical problems, employing practices such as questioning and revoicing (O’Connor & Michaels, 1993).  Student solved tasks in small groups, justifying and questioning during discussion.  During the fall, Ms. Acosta generally began each topic with these kind of mathematical practices, and then she would gradually introduce “state-examish” procedures, mirroring the presentation of the questions on the upcoming state test.  During “state-examish” activity, mathematical practices included solving many examples of a single kind of problem on worksheets and memorizing procedures.  In January, the class switched to preparation for the state test exclusively, eliminating “critical thinkish” mathematical practices. 

Ability grouping in the classroom

Also in January, Ms. Acosta instituted three leveled groups so that a special education teacher, Ms. Howe, could work directly with students with disabilities. While the teachers never explicitly discussed these groupings, students developed two main theories:1) students were placed into the groups based on their “independence,” or work habits, and 2) the students were placed in groups based on their abilities in mathematics, where Ms. Howe’s group was seen as the “unsmart” group.  Students used these discourses of independence and ability to understand their peers and each other as math learners. 

Different pedagogies construct different competencies

            During “critical thinkingish” practices, competence was constructed through participation in whole-class discussion, particularly asking questions, and challenging others.  During “state-examish” practices, competence was constructed through the speed at which a student recalled and executed procedures. This shift caused some students to appear more disabled, and others less so.  Artemis, a student with a label of learning disability, was initially a concern for Ms. Acosta, who believed that Artemis had difficulty with conceptual thinking.  By the spring, Artemis was no longer a concern, as she was able to memorize and execute procedures called for on the test. 

Mack, another student with a label of learning disability, had the opposite trajectory. In the beginning of his 7^th grade year, Ms. Acosta characterized Mack as a top “conceptual” student.  Mack describes himself as the “talking kind” of math learner, one who enjoys “problems that give you problems” rather than “worksheets,” which do not challenge him.  He identifies as a student who asks questions and isn’t afraid to be wrong.  However, in January, based on his special education status, Mack was placed in Ms. Howe’s group.  Ms. Howe repeatedly called Mack “a behavior problem,” and in that group he was loudly off-task each time I observed him.  During a joint interview, Ms. Howe maintained that Mack “needs” a small group setting to learn mathematics because of his behavioral issues.  Ms. Acosta disagreed, stating that Mack needed to be in a math class that focused on problem-solving, not exam preparation.  Is Mack disabled?  Or is the exam-focused curriculum disabling him?

Mack presents a case in which ability and disability are contested.  When his class is engaged in “critical thinkingish” activity, Mack is deeply engaged.  When activity is state-examish”, Mack is frequently disengaged, and is classified by both 7^th grade teachers at the end of the year as “challenging” and “a behavior problem.”  In interviews at the beginning of the year, Mack rejects the use of the word “smart” to describe students in mathematics, but by the end of the spring, he describes his own group as the “unsmart” group.  If given the opportunity to present this work, I would fully present the portrait both of this classroom, and of students like Mack, documenting how ability and disability were constructed in this mathematics classroom.