How does the type of learning material impact what is learned? The current research investigates the nature of students' learning of math concepts when using manipulatives (Uttal, Scudder, & DeLoache, 1997). We examined how the type of manipulative (concrete, abstract, none) and problem-solving prompt (metacognitive or problem-focused) affect student learning, engagement, and knowledge transfer. Students who were given concrete manipulatives with metacognitive prompts showed better transfer of a procedural skill than students given abstract manipulatives or those given concrete manipulatives with problem-focused prompts. Overall, students who reported low levels of engagement showed better learning and transfer when getting metacognitive prompts, whereas students who reported high levels of engagement showed better learning and transfer when getting the problem-focused prompts. The results are discussed in regards to their implications for education and instruction. Keywords learning, engagement, transfer, problem solving, manipulatives, metacognition
Examining the Role of Manipulatives and Metacognition
103• volume 2, no. 2 (Fall 2009) Learning math can be hard. One way educators try to aid in math learning is by teaching new concepts using concrete examples. This has been hypothesized to be an effective instructional tactic because it reduces memory load (Sweller, 2006;Sweller, Merrienboer, & Paas, 1998), facilitates understanding by grounding new information in meaningful prior knowledge (Brown, Collins, & Duguid, 1989), and may increase students' motivation to learn and understand the instruction, task, or problem (Cordova & Lepper, 1996;Schraw, Flowerday, & Lehman, 2001). However, there are also potential downsides to this pedagogical strategy. Using highly realistic situations and materials may cause the knowledge to be tied to the particulars of that scenario, making transfer to other scenarios or into abstract terms more difficult (Goldstone & Sakamoto, 2003;Son & Goldstone, 2009a). The relevant features that are key to deep understanding may be less salient. Moreover, the concrete details may distract students from these features (Harp & Mayer, 1998;Son & Goldstone, 2009b). It appears that there are open questions as to the best way to use concrete materials in learning and whether learning with them is different than learning with more abstract materials. A second way in which teachers try to aid in math learning is by having students engage in valuable and productive activities with the learning materials. This sometimes manifests itself as students being "active" with the materials (Brown, Collins, & Duguid, 1989), such as giving students manipulatives so that they can get "hands-on" experience (Fuson & Briars, 1990). Manipulatives are physical objects that are supposed to help the student concretize his or her knowledge by expressing concepts and performing problem-solving steps with them. It has been hypothesized that being "active" facilitates learning by doing (Anzai & Simon, 1979) and i...