Virtual manipulatives for mathematics

Base Ten blocks for math

Virtual manipulatives for mathematics are digital representations of physical mathematics manipulatives used in classrooms. ^[1] The goal of this technology is to allow learners to investigate, explore and derive mathematical concepts using concrete models. ^{[2] [3]}

Common manipulatives include base ten blocks, coins, 3D blocks, tangrams, rulers, fraction bars, algebra tiles, geoboards, geometric planes, and solid figures.

Advantages and educational efficacy

Research indicates that virtual manipulatives can offer distinct advantages over physical equivalents, particularly in the areas of accessibility and classroom management. Unlike physical objects, digital tools are not subject to wear and tear, do not require time-consuming distribution or cleanup, and provide an unlimited supply of materials for students. ^[4]

Furthermore, virtual environments often include features that are impossible in the physical world, such as linking symbolic notation dynamically with visual changes.

Use in special education

Virtual math manipulatives are sometimes included in the general academic curriculum as assistive technology for students with physical or mental disabilities. ^[5] Students with disabilities are often able to still participate in activities using virtual manipulatives even if they are unable to engage in physical activity. ^{[6] [7]}

Technological platforms

Early versions of virtual manipulatives were primarily Java-based applets available through web browsers. Modern iterations are typically developed using HTML5, allowing for cross-platform compatibility on tablets, Chromebooks, and interactive whiteboards. This shift has facilitated the integration of virtual manipulatives into flipped classroom models and remote learning environments.

Further reading

• Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2000). What are virtual manipulatives? [Online]. Teaching Children Mathematics, 8(6), 372-377. Available: - My NCTM
• Moyer, P. S., Niezgoda, D., & Stanley, J. (2005). Young children's use of virtual manipulatives and other forms of mathematical representations. In W. J. Masalaski & P. C. Elliot (Eds.), Technology-Supported Mathematics Learning Environments (pp. 17–34). Reston, VA: National Council of Teachers of Mathematics.
• Ortiz, Enrique (2017).Pre-service teachers’ ability to identify and implement cognitive levels in mathematics learning. Issues in the Undergraduate Mathematics Preparation of School Teachers (IUMPST): The Journal (Technology), 3, pp. 1–14. Retrieved from Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal -- Volume 1. pdf:
• Ortiz, Enrique, Eisenreich, Heidi & Tapp, Laura (2019). Physical and virtual manipulative framework conceptions of undergraduate pre-service teachers. International Journal for Mathematics Teaching and Learning, 20(1), 62-84. Retrieved from Physical and Virtual Manipulative Framework Conceptions of Undergraduate Pre-service Teachers.

External links

• Pre-service teachers’ ability to identify and implement cognitive levels in mathematics learning. or Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal -- Volume 1
• Physical and virtual manipulative framework conceptions of undergraduate pre-service teachers.

References

1. Moyer, P.S. (2002). "What are Virtual Manipulatives?". Teaching Children Mathematics. 8 (6): 372–377. doi:10.5951/TCM.8.6.0372.
2. Carbonneau, K.J. (2013). "A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives". Journal of Educational Psychology. 105 (2): 380–400. doi:10.1037/a0031084.
3. Silva R., Costa C., Martins, F. (2021). "Using Mathematical Modelling and Virtual Manipulatives to Teach Elementary Mathematics". Technology and Innovation in Learning, Teaching and Education. Communications in Computer and Information Science. Vol. 1884. pp. 75–89. doi:10.1007/978-3-030-73988-1_6. ISBN   978-3-030-73987-4. S2CID   234959877.
4. Reimer, K.; Moyer, P.S. (2005). "Third-Graders Learn About Fractions Using Virtual Manipulatives: A Classroom Study". Journal of Computers in Mathematics and Science Teaching. 24 (1): 5–25.
5. Bouck, Emily C.; Anderson, Rubia D.; Long, Holly; Sprick, Jessica (2021-02-26). "Manipulative-Based Instructional Sequences in Mathematics for Students With Disabilities" . TEACHING Exceptional Children. 54 (3): 178–190. doi:10.1177/0040059921994599. ISSN   0040-0599. S2CID   233907400.
6. Satsangi, Rajiv; Hammer, R.; Evmenova, A. (2018). "Teaching Multistep Equations with Virtual Manipulatives to Secondary Students with Learning Disabilities". Learning Disabilities Research & Practice. 33 (2): 99–111. doi:10.1111/ldrp.12166. S2CID   149871579.
7. Satsangi, Rajiv; Miller, Bridget (2017). "The Case for Adopting Virtual Manipulatives in Mathematics Education for Students with Disabilities" . Preventing School Failure. 61 (4): 303–310. doi:10.1080/1045988X.2016.1275505. ISSN   1045-988X. S2CID   152099008.