Defined as “an object that can be handled by an individual in a sensory manner during which conscious and unconscious mathematical thinking will be fostered,” (2010, p. 14) manipulatives are used in mathematic classrooms all across the United States and other countries. Stein and Bovalino state that manipulatives provide a concrete way to link abstract information to already established knowledge thus giving new concepts a deeper meaning (2001). The purpose of this study is to compare concrete and virtual manipulatives to see if one fosters a deeper conceptual understanding of the FOIL Method. Students in a Middle Grades Cohort at Georgia College were given both a pre- and post-assessment to assess their level of understanding of the FOIL Method after a lesson using either virtual or concrete manipulatives. They then were taught using the other type of manipulative to assess whether students prefer virtual or concrete manipulatives.
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