Igniting and sustaining mathematical proficiency: a poststructuralist analysis of the pitfalls and essentials of classroom practice

Nationally we face a serious problem in that over the last twenty years the quality of Australian students' mathematical knowledge and abilities has "deteriorated to a dangerous level" (Brown, 2009, p. 3). Too few students want to study further mathematics (Willoughby, 2000) or pursue careers where high levels of mathematical proficiency are needed. In this paper I make use of the poststructuralist notion that 'proficiency' is a state of being daily constituted in classroom practice to (a) at a theoretical level, rethink how it might be ignited and sustained, (b) analyse contemporary interactional strategies that commonly interrupt proficiency in participation and (c) nominate three (3) key indicators of instructional practice necessary for students to achieve and maintain a state of being 'proficient' as defined in the Australian curriculum: mathematics (ACARA, 2010). An alternative, poststructuralist reading of how the learning process impacts engagement and ultimately proficiency may interrupt taken-far-granted humanist assumptions that currently inform the teaching and learning of mathematics. Lauren Resnick (2010), in the Wallace Foundation Distinguished Lecture Series made the chilling claim: "The evidence is now pretty clear. We seem to have figured out how to teach the 'basics' to just about everyone ... but we are deeply unsuccessful at out 21" century agenda of moving beyond basic competencies to proficiencies" (p. 183). For Resnick, and indeed for contemporary mathematics education in Australia proficiency is key in postmodern times (ACARA, 2010), as basic skills are necessary but not sufficient for sustainable engagement and achievement [with/in mathematics] (Luke, 2010). The emphasis on proficiency, a state of being proficient, introduces an ontological dimension to mathematics education, not yet carefully enough delineated and understood; it raises an urgent and pressing question about the nature of the pedagogic processes and strategies that might render each student proficient, that is, in having an appreciation of mathematics and the confidence to creatively use, investigate and communicate mathematical ideas (ACARA, 2010). Clearly, instructional strategies are needed that mobilise students as active and engaged doers and users of mathematics, sustaining and extending interest and confident engagement in mathematical tasks and investigations in, and after, schooling. It may be useful to try to think again about what sorts of interactional strategies might have some effect in enabling students to creatively use and apply constructed knowledge