When Theories Don't Add Up: Disentangling he Manipulatives Debate

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What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education (2015, background): “Finally, with even the best designed manipulatives, it is unreasonable to expect young children to make the relation between the concrete material and the mathematics concept it represents without explicit guidance (Ball, 1992; McNeil & Jarvin, 2007).”
A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives (2013, methodology): “Potential instructional moderators of the efficacy of teaching with manipulatives can be derived from contemporary human development and cognitive theories (McNeil & Jarvin, 2007).”
A Comparative Analysis of the Distributive Property in U.S. and Chinese Elementary Mathematics Textbooks (2010, background): “For example, graphics can be added to text presentations to enhance student learning ( Mayer, 2001 ; Moreno & Mayer, 1999 ; Sweller, 1999 ).”
Putting Education in “Educational” Apps (2015, background): “…blocks that are designed to help children learn mathematical concepts through hands-on manipu-lation—is commonplace and has some empirical support (see Lillard, 2005; Pouw, van Gog, & Paas, 2014; and see Sowell, 1989, for a review; but see McNeil & Jarvin, 2007; Uttal, Scudder, & DeLoache, 1997).”