Taxonomy of Manipulatives in STEM Learning

• In Event: Theoretical Perspectives and Empirical Evidence Relevant to Classroom Instruction With Manipulatives

Abstract

Much of what is known about manipulatives for teaching and learning comes from research in mathematics and early childhood education (Clements & McMillen, 1996; Friedman, 1978), but manipulatives (both concrete and virtual) are also a common learning aid for older children and adults across many STEM (science, technology, engineering, and mathematics) disciplines, including anatomy (Hopkins, Regehr, & Wilson, 2011), chemistry (Stull, Hegarty, Dixon, & Stieff, 2012), engineering (Potkonjak, Vukobratovic, Jovanovic, & Medenica, 2010), geology (Miller, Rivet, Kastens, & Lyons, 2013; Rivet & Kastens, 2012), and physics (Zacharia & Olympiou, 2011). However, these disciplines are diverse in the information they encompass and the methods they employ, therefore uses of manipulatives in these disciplines are also diverse, with even more diversity resulting from the flood of new technologies into the computer-enhanced classroom.
Perspectives: We define a manipulative as an actionable representation. By actionable, we mean that manipulatives can be modified, moved, or used in purposeful ways. Such action may support referential learning, skill development, concept development, or problem solving. As a representation, a manipulative encompasses a spectrum that includes entities depicting physical referents that may be visible or invisible at one end and those symbolizing abstract concepts at the other. They may also be a direct representation of a referent or the embodiment of an abstract idea, a representation of a process, or a modeling of scientific inference. They may be perceptually rich, such as a hand-held (concrete) object or perceptually poor, such as an on-screen (virtual) image of an object that is manipulated with a computer keyboard and mouse.
Objective: In this presentation, we will discuss results of recent research investigating the use of both physical and virtual manipulatives in a broad range of STEM disciplines and outline a taxonomy of manipulatives. This taxonomy will classify manipulatives according to the type of knowledge they target (factual, conceptual, or procedural), their perceptual fidelity, that is, visual and haptic congruence between the viewed object and the manipulated object, and the fidelity of the interface by which they are manipulated (direct control vs. technology-mediated control). We will review how these different aspects of physical and virtual manipulatives relate to their effectiveness, discuss our own research in chemistry, and then make prescriptions for the design of manipulatives to support different domains and instructional contexts.
Mode of Inquiry & Material: To build our taxonomy, we conducted a literature search on concrete and virtual manipulatives in the various STEM disciplines. These include studies that directly compare concrete and virtual manipulatives and those that compare either concrete or virtual against a control group.
Significance of the work: It is a common assumption in the education community that manipulatives are valuable tools in teaching and learning. However the breadth of the topics within which they are used and the purpose to which they are applied is broad. We argue that a categorization of these learning aids, beyond the general label of manipulative, is necessary to fully understand their value in education.

Authors

• Andrew T. Stull, University of California - Santa Barbara

• Mary Hegarty, University of California - Santa Barbara