7 The Social Construction of Youth and Mathematics: The Case of a Fifth-Grade Classroom
Kara J. Jackson
âThe Dumb Denominatorâ
It is mid-February, and Ms. Ridley (T/R),1 a fifth-grade math teacher at Johnson Middle School, introduces addition and subtraction of fractions with like denominators (e.g., ) for the first time. She tells the students, âRaise your hand and tell me what dumb people might do. Tell me some stuff people do at Johnson thatâs dumb.â The students make comments such as ânot studying for a test,â âmaking stupid noises,â âtalking in the cafeteria from table to table,â âstarting a food fight,â and âchewing gum.â Ms. Ridley then asks, âWhat do smart people do?â The students suggest the following: âthinking before you speak,â âraising hands for every question,â âpaying attention in class,â and ânot making the same mistakes again.â With her studentsâ rapt attention, Ms. Ridley says quietly:
T/R: I have another little secret to tell you âŠ. The denominator in our fraction is dumb. Since itâs dumb, it never studies for the test. It comes time for the testâ
T/R: Think about a dumb decision. If you didnât study for the test.
M/St 1:2 Leave your answers blank.
T/R: No, think about what happens on test day. âŠ
M/St 2: I just write down any answer, almost.
F/St 1: Cheat.
T/R: Yes! If the denominatorâs dumb, what do you think itâs going to do? Itâs going to copy! The denominators copy because theyâre dumb, the numerators are smart, what are they going to do?
F/St 2: Add.
(FN, 2/14/06)3
Ms. Ridley returns to the example on the board. She tells the students to add the numerators (1 + 1 = 2) and that the denominator âcopiesâ and remains a 3. Ms. Ridley exclaims, âYes, letâs try another one!â
However, before moving to another example, Ms. Ridley places a transparency on the overhead that contains âRules for Adding and Subtracting Fractionsâ (see Figure 7.1).
Rules for Adding and Subtracting Fractions
Fact #1: When we add and subtract fractions, the denominators must be the same.
Fact #2: The denominators copy.
Fact #3: The numerators follow the rules.
Figure 7.1 Notes on adding and subtracting fractions (FN, 2/14/06).
After the children have copied the three facts into their notebooks, Ms. Ridley announces, âIf you want, you can put Johnson students in place of numerators. Almost like numerators are good Johnson students, they follow the rules. Denominators are like bad Johnson students, they break the rules.â The students remain quiet, as usual. The class moves on to another example.
Social Construction of Youth and Mathematics
In this excerpt from a fifth-grade math classroom, both mathematics and youth are constructed in particular ways. The addition of fractional parts of numbers is constructed as a procedural task to be carried out with little understanding of the meaning of numerators, denominators, or the addition of parts of wholes, not to mention the multiple meanings that numerals represented as fractions may have (e.g., Thompson & Saldanha, 2003). Simultaneously, Johnson Middle School students are constructed as âgoodâ and âbad.â The talk in this segment both reifies what it means to be âgoodâ and âbadâ Johnson students and potentially identifies particular students as âgoodâ or âbad,â depending on their typical behaviors.
In this short segment of classroom instruction, we are forced to grapple with the reality that mathematics instruction is not a socially or culturally neutral process. Rather, as others have argued, mathematics instruction, like any type of instruction, is laden with social and cultural norms, expectations, and practices (Baker, Street, & Tomlin, 2003). However, in part because the discipline of mathematics is often constructed as an âobjective scienceâ (Dossey, 1992), the social and cultural assumptions and implications of instructional practices in mathematics classrooms have been less explored in comparison to humanities classrooms (for examples of such research in humanities classrooms, see Heath, 1983; Wortham, 2006).
In this chapter, I show how mathematics instruction involves the social construction of mathematics and of youth. As alluded to in the Dumb Denominator excerpt above, how children are constructed informs how mathematics is constructed and vice versa. Furthermore, I argue that the way that both children and mathematics were constructed in this school drew on discourses about poor children of color that circulate beyond the classroom. As a case in point, I illustrate how one instructional practice was consequential to how two students, Nikki and Timothy, and mathematics were simultaneously constructed in Ms. Ridleyâs class.
Nikki Martin and Timothy Smith were both African American youth from the same low-income neighborhood, attended the same schools, and were in the same fifth-grade math classroom. On the one hand, Nikki and Timothy were restricted mathematically in similar ways because of institutional discourses about poor, urban children of color as related to discourses about mathematics that circulated in Johnson Middle School. On the other hand, social construction is an interactive, dynamic process (Holstein & Gubrium, 2008), and Nikki and Timothy illustrate that individuals negotiate discourses about youth and mathematics in unique ways. As a result, their social and academic trajectories varied.
Mathematical Socialization and Social Identification
There is a rich tradition of attention to processes of socialization and social identification in studies of learning to speak, read, and write (e.g., Heath, 1983; Street, 1993). For example, it is well established that children engage in two concurrent, related processes when learning to speak: âsocialization through the use of language and socialization to use languageâ (Schieffelin & Ochs, 1986, p. 163, italics in original). Children not only learn to speak the language around them (socialization to use language); they also learn about the role that language plays in socially and culturally organized ways of acting, and they use language as an entrĂ©e into mastering those ways of acting (socialization through the use of language). Furthermore, language socialization is an âinteractive process,â and âthe child or novice ⊠is not a passive recipient of sociocultural knowledge but rather an active contributor to the meaning and outcome of interactions with other members of a social groupâ (Schieffelin & Ochs, 1986, p. 165).
Sociocultural theorists argue that learning is as much about individuals experiencing a change in their understanding of some content as it is about changing who one is with respect to the community to which that content is central (Lave & Wenger, 1991; Packer & Goicoecha, 2000). Over the past 15 years, there has been an increasing number of scholars who have drawn on sociocultural theories of learning to understand studentsâ learning of mathematics (e.g., Boaler, 1997, 2000; Cobb, Stephan, McClain, & Gravemeijer, 2001; deAbreu, 1999; Greeno & Middle School Mathematics Through Applications Project Group, 1998; Kieran, Forman, & Sfard, 2001; Martin, 2000; Nasir, 2002). Recent work has shown that, as with literacy, mathematics is embedded in social and cultural practices that are inextricable from power relations (Baker, Street, & Tomlin, 2003; Street, Baker, & Tomlin, 2005). Such situated accounts of learning mathematics have illustrated how mathematical practices are related to the development of âmathematical identitiesâ (Boaler, 1999; Martin, 2000, 2006b; Nasir, 2002). In turn, mathematical identities afford and constrain different opportunities for learning and participation in wider contexts (Anderson & Gold, 2006; Martin, 2000, 2006a, 2006b).
Horn (2007) explicitly investigates the relationship among the construction of mathematics, students, and teaching practices. In a study of two high school mathematics departments in the midst of a detracking reform, Horn found that teachersâ constructions of students hinged upon their construction of mathematics. Teachers who tended to construct mathematics knowledge as a âsequentialâ series of topics to be mastered tended to construct students in terms of their motivation, which in turn limited the pedagogical actions the teachers might take if students did not achieve at expected levels (p. 43). Alternatively, teachers who tended to construct mathematics as a body of connected ideas had more latitude in how they identified their students, and therefore, if students were not achieving at expected levels, they had more latitude in the pedagogical actions they might take.
Hornâs work, as well as the body of situated accounts of learning mathematics mentioned above, has illuminated the need to attend to the social processes of learning mathematics. However, this body of work has been less attuned to how such social processes within local settings, like classrooms, are connected to discourses that circulate outside of local settings. An exception is the work of Martin (2000). Martin developed a model of âmathematics socializationâ based on research of high- and under-achieving African American mathematics students in a low-performing middle school. Martin found that he could not explain (under)achievement in school mathematics among African American youth without attending to broader socio-historical and community forces. This led him to explore discourses about racially based differential access to mathematics that circulated among the communities and homes in which these students lived. Through interviews with students, parents, and community members, Martin found that individualsâ experiences with mathematics were intricately connected to their cultural and social identification as African American. Significantly, Martinâs work captured the relationship between culturally and socially organized discourses about mathematics, race, and individual achievement.
Martin contends that (under)achievement in mathematics, particularly for African Americans, but likely for other groups of students as well, is best understood as a dynamic interplay between processes of socialization and identity formation. According to Martin (2006b),
Mathematics socialization refers to the experiences that individuals and groups have within a variety of contexts such as school, family, peer groups, and the workplace that legitimize or inhibit meaningful participation in mathematics. Mathematics identity refers to the dispositions and deeply held beliefs that individuals develop about their ability to participate and perform effectively in mathematical contexts and to use mathematics to change the conditions of their lives. A mathematics identity encompasses a personâs self-understandings and how they are seen by others in the context of doing mathematics. (p. 150)
Martinâs work raises an important issueânamely, there are various contexts in which socialization and social identification happen. For the purposes of my analyses, I investigate processes of socialization and social identification that happen in and across institutional and local contexts. In particular, I focus on the prevalence and deployment of particular discourses. I draw from the work of Jim Gee (1990/1996), in which he defines discourses as âways of behaving, interacting, valuing, thinking, believing, speaking, and often reading and writing that are accepted as instantiations of particular roles (or âtypes of peopleâ) by specific groups of people. ⊠They are âways of being in the worldââ (p. viii, italics in original). Discourses, for example regarding who is âgoodâ at mathematics, regiment thought and action in that they shape (but do not determine) how individuals get recognized as particular sorts of people at any given moment given their actions (e.g., speech, behavior, dress).
In my work, then, when I discuss processes of social identification and socialization that operate at institutional contexts, I focus on discourses that circulate throughout institutions, like schools. By local contexts, I mean the discourses that circulate in particular classrooms, like Ms. Ridleyâs fifth-grade math classroom at Johnson Middle School. Institutional and local contexts are by no means isomorphic. Rather, discourses that circulate at broad, institutional contexts are inflected in particular ways in local contexts, like classrooms (Wortham, 2006). There was a distinctly local character regarding mathematics and youth evident in Ms. Ridleyâs classroom, as reflected in the Dumb Denominator excerpt above. However, I argue below that more widely circulating institutional discourses about poor children of color, particularly African American children, and their ability to do mathematics, shaped the local approach to mathematics. In other words, the peculiar way in which Ms. Ridley introduced the addition of rational numbers was not merely a product of idiosyncratic pedagogy.
Research Context
The data presented are from a 14-month study of how two African American 10-year-olds (Nikki Martin and Timothy Smith) and their families learned mathematics within and across home, school, and occasionally neighborhood contexts. The overarching goal of the study was to understand how individuals learn mathematics across distinct contexts and over time. I used ethnographic methods (e.g., participant observation, interviews, document collection) to document how the participants experienced, and made sense of, their participation in, across, and exclusion from, a variety of mathematical practices. There were four major sources of data for this study: fieldnotes based on more than 300 hours of participant observation in multiple sites; 35 hours of interview data; document collection at all of the sites; and 36 hours of video-taped recordings of 18 parent math classes held in the neighborhood that at least one of the focal childrenâs parents attended. Although I began data collection when Nikki Martin and Timothy Smith were in fourth grade at their local elementary school, for the purposes of this chapter, I am only drawing on the data of the childrenâs participation in the fifth-grade math classroom at Johnson Middle School, including fieldnote, document, and interview data. (For more detail on the research design of the study, see Jackson, 2007.)
My analyses for the larger study focused on how individuals interacted with other individuals and resources in particular events, as embedded in social practices. I traced contingent events to understand how strings of events amounted to longer time-scale (Lemke, 2000) processes of mathematical so...