1 Credible Tools for Formative Assessment: Measurement AND Qualitative Research Needed for Practice Julian Williams, Julie Ryan, Constantia Hadjidemetriou, Christina Misailidou, Thekla Afantiti-Lamprianou Keywords: assessment, mathematics education, mixed methods Abstract The historical schism between quantitative and qualitative research parallels a divide in assessment theory and practice, in which measurement is associated with summative assessment against normative expectations, while formative assessment rests on interpretivist, qualitative research designed to reveal learners’ understandings and developmental needs. In our group’s approach to formative and diagnostic assessment over more than 6 years, however, we have brought the two strands together. We will describe these researches in mathematics education, based on various data sets of usually at least hundreds of students, in which the literature on the psychology of learning mathematics, Rasch measurement scaling, and dynamic group interviews are all used to develop and evaluate tools for formative assessment practices. These tools have now also been evaluated with teachers in practice, and this leads us to conclude that teaching without such tools is sometimes dangerous, like going mountain climbing without the necessary kit. We conclude that teacher knowledge and practice are best understood within a distributed, socio-cultural perspective, and that academic research activity that aims to support practice may need to be conceived and carried out in more complex ways than is traditionally the case. Introduction We have been working on research and development of diagnostic assessment in mathematics education for over 6 years now. This has involved the integration of summative and formative aspects of assessment and has drawn on qualitative and measurement research methods. For many years researchers have argued that formative assessment is a royal road to improving teaching practice, yet schools and teachers have found it difficult to develop such practices (Black and Wiliam, 1998). We believe this is because research typically does not provide adequate tools for classroom practice (see Ryan & Williams, 2000). This paper will describe some of our Research and Development (R&D) work designed to fill the gap between research and practice, and discuss the development of a socio-cultural perspective on this activity which can ground this work theoretically. The significance of this paper is that we: • inform the nature of assessment for learning, i.e. Formative Assessment (FA) in middle school mathematics; • describe a methodology for developing and evaluating the formative assessment tools teaching practice and practitioners need, and • develop an associated socio-cultural perspective on our R&D activity: e.g. we conceptualise pedagogical knowledge as socio-culturally distributed in tools and systems as well as ‘in teachers’.