Mathematics Teachers’ Didactic Strategies: Examining the Comparative Potential of Low Inference Generic Descriptors

Abstract

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The Cultural Location of Teachers’ Mathematical Knowledge: Another Hidden Variable in Mathematics Education Research?

“…The consensus seems to be that teachers employ pedagogical strategies which, through repeated enactment, are not only typical of a country's lessons but also beneath their consciousness (Cogan & Schmidt, 1999). This sense of typicality has found confirmation in Andrews' research in which mathematics teachers from four European countries have been observed to behave, at least as far as seven generic learning outcomes and ten generic didactic strategies are concerned, in ways that align them closely with their national colleagues and distinguish them from their overseas colleagues (Andrews, 2007b(Andrews, , 2009a(Andrews, , 2009b. Explanations suggest that cultures "shape the classroom processes and teaching practices within countries, as well as how students, parents and teachers perceive them" (Knipping, 2003, p. 282).…”

“…This provides a basis for evaluating the effectiveness of the tripartite curriculum as a complementary framework to the Shulman-related model discussed above. To facilitate this process, the percentages, drawn from Andrews (2009aAndrews ( , 2009b, of all Flemish and Hungarian episodes coded for each of the generic learning outcomes and didactic strategies are presented in Table 1, alongside the same summary statistics for the episodes of each of the two teachers. Details of the codes are beyond this chapter, although working definitions can be seen in Table 2.…”

“…When the quantitative data derived from Pauline's lessons are considered, it would seem that she placed greater emphasis on procedural knowledge and lower emphases on conceptual knowledge, structural knowledge and reasoning than her Flemish colleagues (Andrews 2009a). Moreover, in respect of her didactic emphases, she questioned and shared more rarely than her colleagues and this, coupled with a tendency to coach and assess more frequently, (Andrews 2009b) could be construed not only as distinguishing her practice from the Flemish collective but further evidence of a teacher who, through frequent checks that students were succeeding with the work set, places great value in procedural competence. In summary, the evidence highlights elements of Pauline's received curriculum that identify her with her colleagues and elements that suggest divergence from it.…”

“…The only criterion was the presence of a learning outcome or didactic strategy at some point during the episode. Several quantitative analyses have been undertaken and these have been effective in highlighting similarities and differences in the emphases found in the episodes of the countries under scrutiny (Andrews 2007b(Andrews , 2009a(Andrews , 2009b. However, much work has still to be done in respect of qualitative analyses and this chapter represents a first pass at that process.…”

“…In sum, the evidence suggests that Eva adhered closely to systemic expectations in respect of her presentation of both linear equations and generic learning outcomes. Table 2 Working definitions of the codes used in Andrews (2009aAndrews ( , 2009b. The abbreviation K. refers to knowledge…”