Transfer of Mathematical Knowledge: The Portability of Generic Instantiations

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An Embedded and Embodied Cognition Review of Instructional Manipulatives (2014, background): “For example, although concrete (cupcakes) in comparison to abstract (circles) instantiations were better for learning a mathematical relation (fractions), transfer of learning was higher for kindergartners who learned with the arbitrary symbolic instantiations (Kaminski et al. 2009a, b).”
Using Concreteness in Education: Real Problems, Potential Solutions (2009, background): “This differs from Kaminski et al. (2009) account, in which the distracting or misaligned object features themselves hinder learning.”
Concreteness Fading in Mathematics and Science Instruction: a Systematic Review (2014, background): “Abstract materials offer increased portability and generalizability to multiple contexts (Kaminski et al. 2009; Son et al. 2008).”
A Theory of Physically Distributed Learning: How External Environments and Internal States Interact in Mathematics Learning (2009, background): “one reason participants did not learn well with the high distractor materials in Kaminski et al.’s and Uttal et al.’s (2009) studies”