Should you show me the money? Concrete objects both hurt and help performance on mathematics problems

McNeil, Nicole M.; Uttal, David H.; Jarvin, Linda; Sternberg, Robert J.

doi:10.1016/j.learninstruc.2008.03.005

Cited by 132 publications

(137 citation statements)

References 40 publications

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“…Some studies report beneficial effects of visual representations (e.g., Hegarty & Kozhevnikov, 1999); others report detrimental effects (e.g., Berends & van Lieshout, 2009), and still others report no effects (Dewolf, van Dooren, Ev Cimen, & Verschaffel, 2014) or mixed effects (e.g., Magner, Schwonke, Aleven, Popescu, & Renkl, 2014;McNeil, Uttal, Jarvin, & Sternberg, 2009). In many studies, findings differ across subgroups of students, particularly subgroups based on student ability (e.g., Berends & van Lieshout, 2009;Booth & Koedinger, 2012).…”

mentioning

confidence: 99%

Who Benefits from Diagrams and Illustrations in Math Problems? Ability and Attitudes Matter

Cooper

Sidney

Alibali

2017

Applied Cognitive Psychology

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confidence: 99%

Who Benefits from Diagrams and Illustrations in Math Problems? Ability and Attitudes Matter

Cooper

Sidney

Alibali

2017

Applied Cognitive Psychology

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“…This work adds to a growing body of research that points to weaknesses in the pedagogical assumption that making materials as concrete and real-world as possible will automatically increase student learning. Research on text-based interest (Harp & Mayer, 1998), perceptual richness (Sloutsky, Kaminski, & Heckler, 2005;McNeil, Uttal, Jarvin, & Sternberg, 2009) and narrative voice (Son & Goldstone, 2009b) have all pointed to the limitations of such a view. In many of these cases, manipulations are made to instructional materials and the effect on student learning is observed.…”

Section: Discussionmentioning

confidence: 99%

Examining the Role of Manipulatives and Metacognition on Engagement, Learning, and Transfer

Belenky¹,

Nokes²

2009

The Journal of Problem Solving

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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...

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“…Some scholars have argued that under certain conditions, concrete representations are best presented after abstract representations. Abstract representations do not resemble their referents (Schnotz et al, 2010) [17] and are devoid of superficial features that may distract the learner from abstracting the underlying principle or concept (Kaminski, Sloutsky & Heckler, 2013;McNeil, Uttal, Jarvin & Sternberg, 2009) [25,26]. Presenting abstract representations first can reduce cognitive load and allow the learner to focus on important conceptual principles before introducing contextual elements later (van Merriënboer & Sluijsmans, 2009) [27].…”

Section: Representational Sequencing In Instructionmentioning

confidence: 99%

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

2017

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Concrete objects used to illustrate mathematical ideas are commonly known as manipulatives. Manipulatives are ubiquitous in North American elementary classrooms in the early years, and although they can be beneficial, they do not guarantee learning. In the present study, the authors examined two factors hypothesized to impact second-graders' learning of place value and regrouping with manipulatives: (a) the sequencing of concrete (base-ten blocks) and abstract (written symbols) representations of the standard addition algorithm; and (b) the level of instructional guidance on the structural relations between the representations. Results from a classroom experiment with second-grade students (N = 87) indicated that place value knowledge increased from pre-test to post-test when the base-ten blocks were presented before the symbols, but only when no instructional guidance was offered. When guidance was given, only students in the symbols-first condition improved their place value knowledge. Students who received instruction increased their understanding of regrouping, irrespective of representational sequence. No effects were found for iterative sequencing of concrete and abstract representations. Practical implications for teaching mathematics with manipulatives are considered.

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Should you show me the money? Concrete objects both hurt and help performance on mathematics problems

Cited by 132 publications

References 40 publications

Who Benefits from Diagrams and Illustrations in Math Problems? Ability and Attitudes Matter

Who Benefits from Diagrams and Illustrations in Math Problems? Ability and Attitudes Matter

Examining the Role of Manipulatives and Metacognition on Engagement, Learning, and Transfer

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

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