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Virtual manipulatives for mathematics

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Base Ten Blocks for math

Virtual math manipulatives are visual representations of concrete math manipulatives, accessed through a websites and apps.[1] These virtual manipulatives are modeled after concrete ones used in classrooms. They physically represent mathematical concepts and support students' understanding of mathematical concepts.[2][3]

Common manipulatives include: base ten blocks, coins, blocks, tangrams, rulers, fraction bars, algebra tiles, geoboards, geometric plane, and solids figures.

Advantages and disadvantages

Classroom studies were conducted that investigated virtual manipulatives. The studies compared virtual manipulatives to concrete manipulatives and discussed some of the implications.[4]

Advantages

An analysis of the educational advantages associated with virtual manipulatives reveals that they offer comprehensive instructional guidance and prompt evaluation for assigned tasks. Notably, students exhibit enhanced comprehension of concepts, given that this learning approach resonates particularly well with digital natives. Furthermore, virtual manipulatives frequently establish explicit connections between visual and symbolic representations, facilitating a deeper understanding.

A notable feature is the ability of virtual manipulatives to promptly alert students to errors, thereby fostering a reflective process and encouraging them to revisit and refine their answers. Additionally, the convenience of virtual manipulatives is underscored by their greater accessibility at home compared to traditional concrete manipulatives.[4]

Disadvantages

In comparison to concrete manipulatives, virtual manipulatives lack opportunities for learners and educators to physically touch objects, which is a disadvantage for kinesthetic learners. Educators are unable to follow the learners’ thought process, making it difficult to understand their comprehension levels. One of the drawbacks of digital learning is an increase in computer dependence as it limits students' learning abilities. It does not encourage learners to independently find answers and locate their mistakes. Teaching preferences often include guiding students through answers only when they are unable to grasp content or find difficulty comprehending questions. Lastly, Hunts et al. states that learning mathematics through the use of virtual manipulatives feels more like a "do" experience rather than a learning and exploring experience.[4]

Special education

Virtual manipulatives can be included into the general academic curriculum as assistive technology and should not just be used for their novelty.[5]

Studies [6][7][5] on the use of virtual manipulatives in mathematics for students with learning disabilities advocate the use of virtual manipulatives in mathematics for students with learning disabilities due to several benefits.

Practicality: Virtual manipulatives help where physical manipulation is not physically possible, it offers opportunities for repeated practice, it is accessible (i.e. accessed by phones, iPads, etc.) and cost-effective (i.e. free or low cost).[6][5]

Student independence: Virtual manipulatives allow for instant feedback and built-in scaffolding,[6] which allows for individualized instruction and for students to build on their learning skills independently and effectively, without the presence of a teacher. Virtual manipulatives offer students the opportunity to double-check their work and have visual representations of mathematical problems to solve.[7]  

Learning beyond the classroom: Virtual manipulatives provide opportunity for learning outside the classroom, as they are transportable.[6][7]  They can also allow students to share their results with their teacher beyond the classroom.

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: - MyNCTM
  • 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:[1]
  • 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.

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. 1884: 75–89. doi:10.1007/978-3-030-73988-1_6. ISBN 978-3-030-73987-4. S2CID 234959877.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  4. ^ a b c Hunt, Annita W. (2008-01-01). "Virtual vs. Concrete Manipulatives in Mathematics Teacher Education: A Call for Research". Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators. 2 (1). doi:10.20429/gamte.2008.020103. ISSN 2692-7721.
  5. ^ a b c 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. ^ a b c d 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.
  7. ^ a b c 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.
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