‘Concrete’ Manipulatives, Concrete Ideas

By Douglas H. Clements. 2000

320 citations recorded by the source corpus.

The notion of ‘concrete,’ from concrete manipulatives to pedagogical sequences such as ‘concrete to abstract,’ is embedded in educational theories, research, and practice, especially in mathematics education. In this article, the author considers research on the use of manipulatives and offers a critique of common perspectives on the notions of concrete manipulatives and concrete ideas. He offers a reformulation of the definition of ‘concrete’ as used in psychology and education and provides illustrations of how, accepting that reformulation, computer manipulatives may be pedagogically efficacious.

View Paper: https://www.semanticscholar.org/paper/9ae724044f6a7e26b6cd809bc99e7dbeb4a3c4db

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Citations in the corpus

Hands on What? The Relative Effectiveness of Physical versus Virtual Materials in an Engineering Design Project by Middle School Children (2007, background): “There are a few exceptions to this tendency to confound changes in medium with curricular changes, such as the study by Johnson-Gentile, Clements, and Battista (1994) comparing the effectiveness of physical manipulatives and LOGO programs for teaching geometric motion and Marshall’s (2005) compariso”
Comparing and combining real and virtual experimentation: an effort to enhance students' conceptual understanding of electric circuits (2007, background): “Therefore, the suggestion by Clements (1999) to redefine ‘concrete’ manipulatives to include digital manipulatives deserves to be given more careful thought by the science education community.”
An Embedded and Embodied Cognition Review of Instructional Manipulatives (2014, background): “…trend towards minimizing perceptual and interactive richness of manipulatives, as evidenced by the upsurge of mouse-based virtual manipulatives (e.g., Clements 2000; Moyer et al. 2002) that compared to their physical counterparts differ in perceptual aspects (e.g., information gained from touching…”
Fostering At-Risk Preschoolers' Number Sense (2009, background): “…preschoolers can discover that adding items to a collection makes it larger, that the outcome of addition (whole) is larger than either part, and (with sufficient practice) that “two and one more is three” (Baroody, 1987, 2006; Baroody, Lai, et al., 2006; Baroody & Rosu, 2006; Clements, 1999b).”
Representation in Teaching and Learning Mathematics (2020, background): “Several research studies reported that representations can be powerful tools to students learning (Bruner, 1966; Clements, 1999; Cuoco & Curcio, 2001; Fennema & Franke, 1992; Goldin & Shteingold, 2001; Greeno & Hall, 1997; Kilpatrick, Swafford, & Findell, 2001).”
Do tangible interfaces enhance learning? (2007, background): “…interfaces reported here, the view that cognitive benefits will result from manipulating physical materials and that the mental processing of children in the Piagetian stage of concrete operations will benefit from using concrete physical objects rely largely on untested assumptions [11, 30].”