In settings in which students are s

In settings in which students are seen as second language learners, rather than as multilingual, the same kinds of tension are present. Khisty (1995), for exam- ple, compared three second-grade and two fifth-grade mathematics classes contain- ing some Spanish-speaking bilingual students. The class teachers were all English- Spanish bilingual to some degree, although Spanish was not used much for mathe- matical discussion. In one classroom considered to be an effective learning environ- ment, mathematics was negotiated through discussion, challenge and debate. This environment frequently required students to explain their ideas and to draw on pre- vious experience to make sense of new situations. For Khisty, the culture of this classroom led to students making mathematical meaning for themselves through in- teracting with both the teacher and other students. Teachers in the study that seemedto be more effective paid more attention to the language of mathematics as well as to the mathematics itself. Through this attention, as in the models described above, students’ informal expressions of their thinking are shaped into more formal math- ematical expression. The same kinds of forces are at work, then, in various settings, with students’ social languages seen as a starting point for developing a more recog- nisably standardised use of mathematical language. Again, I do not see this tension as easily resolvable; the purpose of a fairly standard mathematical register is to fa- cilitate communication of mathematical ideas. Equally, however, there is a danger that this same mathematical register marginalises students at the peripheries.