Instructional Manipulatives

Overview

Instructional manipulatives are physical and virtual objects/mechanisms designed to help reinforce learning material. A student rotating a globe to increase their understanding of where the Northern hemisphere meets the Southern hemisphere at the equator is an example of a physical manipulator. Interactions with manipulators involve relations between the mind, body, and environment. Thus, an embedded embodied perspective on manipulatives is of interest to cognitive scientists, as this approach could help them discover new ways to enhance knowledge acquisition and transfer of learners.

Evidence

Embedded

In one of a number of studies conducted by Manches et al.(2010) to test whether qualitative differences in manipulation led to problem solving studies in children, children ages 5-7 were tasked to solve a partitioning problem. Groups were first asked to solve a problem with no materials. Afterwards, the children were asked to solve additional problems with either paper and pen, or with blocks. Results showed that participants who used the blocks came up with significantly more creative solutions than children in the paper and no material conditions. One conclusion was that in the context of blocks, two hands allowed participants to be able to move multiple blocks at a time, while keeping track of their locations via haptic sensation.

Embodied

A study by Hatano et al; 1977; Hatano & Osawa 1983, done to test transfer through the internalization of sensorimotor information, found that advanced abacus users, are able to utilize strong arithmetic abilities including mental calculation even without an abacus, by manipulating a mental projection of an abacus. Transfer tests showed that expert abacus users performed better when manipulating a mental projection of an abacus over a physical one.

Design Implications

Pouw, et al. (2014) suggest upon reflection of Diane (2010) where participants that used blocks as manipulators to understand powers of 10 had failure of transfer when tested in the absence of the manipulators, “Design of manipulatives should at times allow for self-discovery rather than pre-constrained problem solving when transfer of learning is the goal.” Pouw, et al. (2014) continue to propose that embedded learning might be able to flourish when it is learner centered, instead of it being primarily integrated into the environment.

Challenges

Challenges to the beneficial prospects of instructional manipulatives are voiced by researchers in Uttal et al. 1997; McNeil & Jarvin 2007; Sarama and Clements 2009; Kaminski et al 2009 a&b. These critiques come from claims that manipulatives which focus on the concrete to the symbolic can lower transfer of learning because of perceptual and interactive richness,and that perceptual and interactive richness can inflict a high cognitive load on learners, which can lessen learning outcomes.

References

• Manches, A., O’Malley, C., & Benford, S. (2010). The role of physical representations in solving number problems: a comparison of young children’s use of physical and virtual materials. Computers & Education,54(3), 622–640.

• Hatano, G., Miyake, Y., & Binks, M. G. (1977). Performance of expert abacus operators. Cognition, 5(1), 47–55.Hauk, O., Johnsrude, I., & Pulvermüller, F. (2004). Somatotopic representation of action words in human motor and premotor cortex. Neuron, 41,301–307

• Hatano, G., & Osawa, K. (1983). Digit memory of grand experts in abacus-derived mental calculation. Cognition, 15(1), 95–110

• Pouw, W., Gog, T.,Paas, F. (2014). An Embedded and Embodied Cognition Review of Instructional Manipulatives. Educational Psychology Review, 26(1), 51-72

• Dienes, Z. P. (1973).The six stages in the process of learning mathematics. Slough: National Foundation for Education Research/Nelson

• Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: a new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18(1), 37–54

• McNeil, N. M., & Jarvin, L. (2007). When theories don’t add up: disentangling the manipulatives debate. Theory Into Practice, 46(4), 309–316

• Sarama, J., & Clements, D. H. (2009).‘Concrete Computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145–150.

• Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2009a). Transfer of mathematical knowledge: the portability of generic instantiations. Child Development Perspectives, 3(3),

• 151–155.Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2009b). The devil is in the superficial details: why generic instantiations promote portable mathematical knowledge. Child Development Perspectives, 3, 151–155.