While in some classrooms virtual manipulatives are used instead of physical manipulatives (Moyer-Packenham et al., 2013), virtual manipulatives can also be used in conjunction with traditional physical manipulatives. Their use does not need to be reserved for replacing physical manipulatives, as together they can provide different methods for student exploration, which can in turn support growth in relational thinking and algebraic reasoning (Moyer-Packenham et al., 2008). This combination of both physical and virtual manipulatives has been found to be more effective for student learning then using either type of manipulative by itself (Moyer-Packenham et al., 2008; Rosen & Hoffman, 2009).
Moyer-Packenham, P., Baker, J., Westenskow, A., Anderson, K., Shumway, J., Rodzon, K., &
Jordan, K. (2013). A study comparing virtual manipulatives with other instructional
treatments in third and fourth grade classrooms. Journal of Education, 193(2), 25–39.
Moyer-Packenham, P., Salkind, G., & Bolyard, J. J. (2008). Virtual manipulatives used by K-
8 teachers for mathematics instruction: Considering mathematical, cognitive, and
pedagogical fidelity. Contemporary Issues in Technology and Teacher Education (CITE
Journal), 8(3), 202–218.
Rosen D., & Hoffman J. (2009). Integrating concrete and virtual manipulatives in early
childhood mathematics. YC Young Children, 64(3), 26–33.