Journal of Computers in Mathematics and Science Teaching
Association for the Advancement of Computing in Education
Both virtual and physical manipulatives are reported as effective learning tools when used with different groups of students in a variety of contexts to learn mathematical content. The use of multiple representations and the flexibility to translate among those representational forms facilitates students' learning and has the potential to deepen their understanding. This classroom project involved two groups of third-grade students in a week-long unit focusing on algebraic relationships. The purpose of the unit was to engage students with different algebraic models and encourage students to use informal strategies to represent their relational thinking. The paper highlights examples of these student representations as evidence of the children's developing algebraic thinking. Result from the pre- and post-test measures showed that students in the physical and virtual manipulative environments gained significantly in achievement and showed flexibility in translating and representing their understanding in multiple representations: manipulative model, pictorial, numeric and word problems. The researchers recorded field notes, interviewed students, and videotaped class sessions in order to identify unique features of the learning environments. The virtual environment had unique features that promoted student thinking such as: a) explicit linking of visual and symbolic modes; b) guided step-by-step support in algorithmic processes; and c) immediate feedback and self-checking system. In the physical environment, some unique features were: a) tactile features; b) opportunities for invented strategies; and c) mental mathematics. These results show that although the different manipulative models had different features, both the physical and virtual environments were effective in supporting students' learning and encouraging relational thinking and algebraic reasoning.
Suh, J., & Moyer, P. S. (2007). Developing Students' Representational Fluency Using Virtual and Physical Algebra Balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155-173.