Objects, actions, and images: a perspective on early number development

By Eddie M. Gray, Demetra Pitta, David Tall. 2000

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Case Studies of Children's Development of Structure in Early Mathematics: A Two-Year Longitudinal Study. (2005, methodology): “Current analyses have also been influenced from two other perspectives: the study of spatial structuring in two and three dimensional situations (Battista, Clements, Arnoff, Battista & Borrow, 1998); and the role of imagery in the cognitive development of elementary arithmetic ( Gray, Pitta & Tall, ”
Towards understanding the origins of children's difficulties in mathematics learning (2011, background): “Studies of arithmetic indicate qualitative differences in low-achieving students’ use of imagery and concept development (Gray et al., 2000; Pitta-Pantazzi et al., 2004).”
Concept image revisited (2008, background): “This is clearly a potentially fruitful area of application as definitions are arguably more widely used in high school and undergraduate mathematics than they are in the early years of schooling, but the construct has been applied to early learners too (Gray et al. 2000).”
Awareness of pattern and structure in early mathematical development (2009, background): “Studies focused on imagery and arithmetic have indicated that students who recognise the structure of mathematical processes and representations acquire deep conceptual understanding (Pitta-Pantazzi, Gray & Christou, 2004; Gray, Pitta, & Tall, 2000; Thomas & Mulligan, 1995).”