Zevenbergen, R. (2000). Cracking the Code of Mathematics: School success as a function of linguistic, social and cultural background. In J. Boaler (Ed). Multiple Perspectives on Mathematics Teaching and Learning. (pp. 201-223) New York: JAI/Ablex.
In a 1–year, ethnographic study of three schools (an independent elite school serving a middle- to upper-class clientele, a government school serving a predominantly middle-class clientele, and a government school serving a predominantly working-class clientele), two classrooms were observed and mathematics lessons video recorded throughout the year. Interviews were conducted with students and participating teachers. (p.213)
3 Communicative Strategies in Math Classrooms
- The first is the type of questions commonly found in texts and tests. These represent the register of mathematics that I argue is very structured and that students must come to learn in order to be able to participate in a productive and effective manner.
- Classroom talk, which has its own internal rules that are not made explicit to students but form the basis for communication in the classroom.
- The third and final example is that of what comes to constitute legitimate knowledge in the classroom, and this is bound to the contexts used to embed mathematical tasks (p.201)
Bourdieu argues that:
Linguistic competence is not a simple technical ability, but a statutory ability. . . . what goes in verbal communication, even the content of the message itself, remains unintelligible as long as one does not take into account the totality of the structure of the power positions that is present, yet invisible, in the exchange. (Bourdieu & Wacquant, 1992, p. 146) (p.204)
- McGregor (1991, p. 7) has noted that the prepositions used in mathematics are a cause for difficulty in understanding tasks. She notes the use of prepositions in the following manner: The temperature fell to 10 degrees . . . by 10 degrees . . . from 10 degrees; and the effect of omitting the preposi- tion: the temperature fell 10 degrees. (p.206)
- [Halliday] sums up the notion of lexical density as being “the number of lexical items as a ratio of the number of clauses” (1988, p. 67). Halliday suggests that lexical density contributes to the complexity of written problems in mathematics and may be a further barrier to learning. (p.207)
- Mathematical tasks are often characterized by their conciseness and preciseness, where there are few redundant words and where all words have highly specific meaning. As noted previously, that specificity of meaning may not be the same as in the nonmathematics contexts. To translate a mathematical task into a more accessible form would require, in most cases, a more convoluted and lengthy description. As a consequence, the lexical density results in a high level of complexity in the translation of the problem. (p.207)
- Bernstein (1990) has developed the notion of “relay” to describe the elusive ways in which cultural norms and knowledge are transmitted. Successful interaction patterns are rarely taught explicitly to our students; they must come to learn them covertly. In the following sections, I draw on the work of ethnomethodology that seeks to identify the micro interactions of classrooms that become a component of the culture of classrooms (p.212).
- Triadic interactions serve the purpose of controlling student behavior while also prescribing the content of lessons. (p.213)
- The effect is that the teacher is able to control the flow of the lesson such that responses that are not wanted are either ignored or rejected whereas comments that are sought can be expanded or praised so that the students become aware of what is the “correct” response. Through this process, teachers are able to control behavior and content. However, Lemke is quick to point out that the level of questioning is often low and is aimed at keeping the lesson moving at a brisk pace to keep students motivated while introducing and covering the content that is the focus of the lesson. (p.214)
- However, during the “work” phase of the lesson, the patterns of power are somewhat more equal and students can express their lack of understanding. The role of teachers’ questions are critical in controlling the interactions with classrooms. (p.213)