Q: What are the feasibilities of replacing physical mathematics manipulatives with virtual mathematics manipulatives for mathematics teaching in the classroom? Will the students’ learning be affected if the teachers solely based on virtual mathematics manipulatives in their classroom mathematics teaching?
Research has demonstrated a positive impact of the use of virtual manipulatives on students‘ learning. The experience of students manipulating the on-screen objects to test hypotheses and experiment with ideas also promotes students‘ thinking and creativity. So the question, more importantly, is how does this fit into the local Concrete to Pictorial to Abstract (C-P-A) approach in concept development?
The C-P-A approach encourages teachers to use multiple forms of external representation to achieve the abstract conceptualisation of mathematics. The sequence in introducing these representations from concrete to pictorial to abstract ones helps the students to relate their concrete experiences with the abstract mathematical idea – narrowing the “cognitive gap” that exists between the two. The use of each of these three external representations further narrow the “cognitive gaps” that also exists between any two such representations in the sequence.
The virtual manipulative, though not a concrete manipulative, behaves much the same way as the concrete counterpart. The dynamism of the representation afforded by the virtual manipulative is certainly unlike a pictorial representation, which is basically static. The external representation afforded by the virtual manipulatives thus lies between that of concrete and pictorial. Virtual manipulatives may be viewed as further narrowing the “cognitive gap” between the concrete and pictorial representations.
A possible revision to the C-P-A approach could be the C-V-P-A approach, where V refers to the external representation. However, the C-V-P-A approach would require teachers to use and make available the comparison of all these four representations, a situation that might further complicate the mess and logistic involved in the development of abstract concepts using three representations in the actual classroom situation. Instead, the alternative integrative C-V and V-P-A approach is advocated.
References
Lee, N.H., & Ferrucci, B. (2012). Enhancing Learning Of Fraction Through The Use Of Virtual Manipulatives. The Electronic Journal of Mathematics and Technology, 6(2), 126-140 (https://repository.nie.edu.sg/bitstream/10497/18915/1/TEJMT-6-2-126.pdf)
Lee, N. H., & Tan, B. L. J. (2014). The Role Of Virtual Manipulatives On The Concrete-Pictorial-Abstract Approach In Teaching Primary Mathematics. The Electronic Journal of Mathematics & Technology, 8(Special), 102-121. (https://repository.nie.edu.sg/bitstream/10497/18917/1/TEJMT-8-2-102.pdf)
