Using Concreteness in Education: Real Problems, Potential Solutions

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The Enactive Roots of STEM: Rethinking Educational Design in Mathematics (2015, background): “…posed by symbolical objects on flat media that have afforded the development of semiotic systems and discursive forms critical to the evolution of the mathematical discipline (Brown et al. 2009; Kirsh 2010; Olson 1994; Schmandt-Besserat 1992; Smith and Gasser 2005; Uttal and O’Doherty 2008).”
A psychological perspective on augmented reality in the mathematics classroom (2013, background): “A common problem observed by researchers has been the fact that with physical manipulatives, students cannot easily see the instructional information represented by manipulative (M. C. Brown et al., 2009).”
Concreteness Fading in Mathematics and Science Instruction: a Systematic Review (2014, background): “Indeed, as Brown et al. (2009) note, " linking nonsymbolic conceptual understanding to more abstract, symbolic representations may be one of the most significant challenges teachers face today " (p. 162).”
An Embedded and Embodied Cognition Review of Instructional Manipulatives (2014, background): “…about the role of perceptual and interactive richness are warranted, which has been important for furthering our understanding of learning with manipulatives (Brown et al. 2009; Kaminski et al. 2009a, b; McNeil and Jarvin 2007; Sarama and Clements 2009; Sherman and Bisanz 2009; Uttal et al. 1997).”