This paper presents findings from a research study, which sought to illuminate the perceived notions of inclusion of four to five year old children in pedagogical activities, in the early years classes of two schools in the North of England. It employed a qualitative methodology to gather extensive data with forty children over a six-week period in each school. This included collecting fieldnotes; undertaking observations of children in pedagogical activities; and conducting group and individual interviews. Central to the research aim was the use of participative tools to engage with children's voices; these included photographs and drawings. Children's perceived notions of inclusion resonated with two dimensions: belonging and relationships (with practitioner and/or child) and democratic pedagogies. The findings advance the conceptualisation of the notion of inclusion and bring to the fore the voices of a young group of children that has not been studied before. Engaging with children in meaningful ways can enable practitioners to better understand young children's perceived, multi-faceted notions of inclusion as they experience it within pedagogical activities.
In this paper, we report an enquiry into elementary preservice teachers’ learning, as they engage in doing mathematics for themselves. As a group of researchers working in elementary Initial Teacher Education in English universities, we co-planned and taught sessions on growing pattern generalisation. Following the sessions, interviews of fifteen preservice teachers at two universities focused on their expressed awareness of their approach to the mathematical activity. Preservice teachers’ prospective planning and post-teaching evaluations of similar activities in their classrooms were also examined. We draw on aspects of enactivism and the notion of reflective “spection” in the context of teacher learning, tracing threads between preservice teachers’ retro-spection of learning and pro-spection of teaching. Our analysis indicates that increasing sensitivity to their own embodied processes of generalisation offers opportunities for novice teachers to respond deliberately, rather than to react impulsively, to different pedagogical possibilities. The paper contributes a new dimension to the discussion about the focus of novice elementary school teachers’ retrospective reflection by examining how deliberate retrospective analysis of doing mathematics, and not only of teaching actions, can develop awarenesses that underlie the growth of expertise in mathematics teaching. We argue that engaging preservice teachers in mathematics to support deliberate retrospective analysis of their mathematics learning and prospective consideration of the implications for teaching can enable more critical pedagogical choices.
Existing research suggests that young children can develop a partial understanding of the equal sign as an operator rather than as a relational symbol of equivalence. This partial understanding can be the result of overemphasis on canonical equation syntaxes of the type a + b = c in elementary school mathematics. This paper presents an examination of context and syntax nuances of relevant sections from the grade 1 Greek series of textbooks and workbooks. Using a conceptual framework of context variation, the analysis shows qualitative differences between equations of similar syntax and provides a nuanced determination of contextual and structural aspects of 'variation' in how the equal sign is presented in elementary mathematics. The paper proposes that since equations have contextspecific meanings, context variations should constitute a separate element of analysis when investigating how the equal sign is presented. The implication for practice and future research is that nuanced considerations of equation syntax within varied contexts are needed for elaborating analyses of the equal sign presentation that move beyond dichotomized categorizations of canonical/non-canonical syntaxes.
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