1 CHILDREN’S GRAPHICAL CONCEPTIONS Constantia Hadjidemetriou and Julian Williams University of Manchester In this paper we report the development and validation of a ‘graphical assessment’ tool and attainment hierarchy, based on a previous pilot and a main study (n=425) of 14 to 15 year old children. The items were developed from the research literature to suit the UK National Curriculum, and scaled using Rasch methodology. The result is a single dimension measuring ‘graphicacy’, which updates and extends Kerslake’s CSMS hierarchy. Each level is described as a characteristic performance but now includes errors which diagnose significant misconceptions. The items and diagnoses (drawn a priori from the literature) were validated in group discussions and in general were consistent with previous work. We provide an analysis of one exception, i.e. Janvier's and Clement’s ‘slope-height’ confusion, which we attribute to a new form of Leinhardt’s 'Interval-point' confusion. Finally we argue that creating valid diagnostic tools is a prerequisite for the transformation of previous research findings into pedagogical content knowledge and hence of practice. INTRODUCTION AND BACKGROUND This study builds on previous work on misconceptions in children's graphical thinking, and especially in their interpretations of graphs (Clement, 1985; Janvier, 1981; Kerslake, 1993; Sharma, 1993). It is widely believed that effective teaching should benefit from diagnostic assessment (see e.g. Bell, Swan, Onslow, Pratt and Purdy, 1985); that is, effective teachers must understand their pupils’ ways of thinking, their alternative frameworks, misconceptions, prototypes and so on. We draw a distinction between an error, i.e. erroneous responses to a question, and a misconception which may be part of a faulty cognitive structure that causes, lies behind, explains or justifies the error. Some errors may be symptomatic of a misconception, a prototypical way of thinking or an intuition. Others may not: they may simply be the result of faulty memory, a cognitive overload, etc. But misconceptions may sometimes be more than simply a justification for an error. They can be general features of students' learning of mathematics, such as students' tendency to over-generalize a correct conception or to be influenced due to interference from everyday knowledge and experience. They lead pupils to construct some well-formulated alternative frameworks of ideas which are not appropriate (Leinhardt, Zaslavsky and Stein, 1990). However, all this research knowledge is widely known to be underused in practice: this is not just a matter of ‘dissemination’, the research knowledge does not seem to address practical concerns, the nature of the curriculum, or the reality of teachers’ lives in and out of classrooms. It seems that researching and developing the transformation of research knowledge into practice is a major task in itself. Williams and Ryan (2000) argued that research knowledge about students’