Dichotomies Are the Reason Daddy Drinks
Then I feel guilty for wasting paper, struggle through the entire piece (PDF), and, usually, find some ideas that seem to be worth further exploration:
There appears to be an inclination within the education community to dichotomise and an associated tendency to (i) ignore the connectedness of the dichotomous categories, and (ii) on occasion, to privilege one category while denigrating the other . . . .
This paper addresses five of these dichotomies: Teaching and Learning; Abstract and Contextualized mathematical activity; Teacher-Centred and Student-Centred classrooms; the teacher's contemporary dilemma: to Tell or Not to Tell; and the related issue for students: to Listen or to Speak. (376)
[The Teaching and Learning dichotomy] is a particularly insidious consequence of the constraints that language (and the English language, in particular) imposes on our theorizing . . . . this is particularly evident in the various translations of Vygotsky, in which the Russian word 'obuchenie' has been represented as either teaching or learning in different translations (Clarke, 2001). The integration of teaching and learning as components of a jointly enacted single activity also occurs in several other languages, including Chinese, Japanese and Dutch. (378)
Differences in the use of abstract and contextualised tasks seem strongly connected to a perceived need in Western classrooms to present mathematics as relevant to students. (379)
In the Swedish classroom, the students demanded that the teacher justify the relevance of what was being taught . . . . Despite the teacher's efforts, students were outspoken in their lack of belief in the relevance of the mathematics they were studying. . . .
By contrast, in the classroom in Shanghai, mathematics tasks tended to be very abstract in character and the teacher made no effort to demonstrate or argue for the real world applicability of the mathematics being studied. . . . However, in the post-lesson interviews, the Chinese students consistently expressed strong beliefs in the utility of mathematics in general and in relation to the specific mathematics they were studying [ed: There is a bit of apples-and-oranges at work here, so be warned. "Demanding" relevance of what you're studying and "believing" that what you're studying has relevance are two completely different things.]. . . . . Svan has christened this the "Expanded Relevance Paradox" (Svan & Clarke, in preparation) and means, by this term, to refer to the paradoxical character of application-oriented mathematics teaching associated with subjective irrelevance and pure mathematics-oriented mathematics teaching associated with subjective relevance . . . . Mathematical tasks are a constituent element of the social activity in which students engage. Attempts to increase the 'relevance' of these tasks through a figurative contextualisation may be counter-productive if these efforts are perceived by students to be artificial and are interpreted as reifying the very distinctions they seek to dissolve. (380)
One common interpretation of the constructivist manifesto (i.e., that "knowledge is the result of a learner's activity rather than of the passive reception of information or instruction," von Glasersfeld, 1991, p. xiv) has been that it became no longer legitimate for teachers to "tell" students anything. This position is not a logical consequence of adherence to constructivist learning theory, which suggests that students inevitably construct their own mathematics, whatever the classroom situation (Cobb, 1995). However, Telling or Not-Telling have been constructed oppositionally with such success that publications on contemporary pedagogy, . . . while usefully discussing many pedagogical strategies, see no need to address any strategies that might be construed as analogous to "telling" and even articles that purport to address the issue (such as Chazan and Ball, 1999) offer teachers little insight into how (and, as importantly, when) their mathematical knowledge might be articulated explicitly to the benefit of their students.
Labels: education, mathematics, research