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The Best Practice in Mathematics Education project was funded by the Australian Office of the Chief Scientist, to examine promotion of students' learning, engagement and aspirations in this core learning domain. We draw upon cross-sectional survey data from 551 students in grades three to nine to examine how students' mathematics engagement relates to key dimensions of their learning climate (mastery or performance focused classrooms), teacher enthusiasm, and school caring. Engagement is known to be associated with positive school outcomes and influenced by environmental factors. Less known is whether, and the extent to which, students have different profiles of engagement across component dimensions (Fredricks, Blumenfeld, & Paris, 2004); and, how profiles may differ according to experienced environment dimensions. We first develop profiles of adolescents' behavioral, emotional, and cognitive engagement using multilevel latent class analysis, educing three profiles of 'engaged', 'compliant', and 'disengaged' students, who systematically differed on experienced environmental factors. Mastery focused classrooms, enthusiastic teachers and caring school environment were experienced most by engaged, and least by disengaged students; performance focused

The aim of this study was, first, to provide evidence to support the notion of statistical literacy as a hierarchical construct and, second, to identify levels of this hierarchy across the construct. The study used archived data collected from two large-scale research projects that studied aspects of statistical understanding of over 3000 school students in grades 3 to 9, based on 80 questionnaire items. Rasch analysis was used to explore an hypothesised underlying construct associated with statistical literacy. The analysis supported the hypothesis of a unidimensional construct and suggested six levels of understanding: Idiosyncratic, Informal, Inconsistent, Consistent non-critical, Critical, and Critical mathematical: These levels could be used by teachers and curriculum developers to incorporate appropriate aspects of statistical literacy into the existing curriculum.  First published November 2003 at Statistics Education Research Journal: Archives

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers' knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers' confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.

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Average is a concept encountered in a wide variety of situations. In this paper, responses of 136 pre-and in-service teachers to a series of graded questions about average are analysed. The theoretical model used as the basis of the analysis is the SOLO Taxonomy with multimodal functioning developed by Biggs and Collis (1991).Information presented in graphical form requiring respondents to compare data sets induced responses in ikonic and concrete symbolic modes, demonstrating multimodal functioning. These responses are mapped onto a model of problem solving proposed by Collis and Romberg (1990). Cycles of response in relation to the concept of average are propósed.