User:N.EDU5287/Interactive learning

Definition

Virtual Manipulates for Mathematics is an interactive, technology-enabled visual representation of a dynamic mathematical object, including all of the programmable features that allow it to be manipulated, that presents opportunities for constructing mathematical knowledge. All virtual manipulatives do not have to be “web-based,” in fact virtual manipulatives appear in a variety of forms. In the future it is very likely that virtual manipulatives will no longer be based in any technology. For example, they may be projected using 3D objects or holographic images (Moyer et al., 2016, 6 -13).

Virtual manipulatives allow teachers to efficiently use multiple representations and provide concrete models of abstract mathematical concepts for learners of mathematics. Research suggests that students may also develop more connected understandings of mathematical concepts when they use virtual manipulatives (Moyer, Niezgoda, & Stanley, 2005).

Manipulatives by themselves have little meaning. It is important for teachers to make the mathematical meaning of manipulatives clear and help the students to build connections between the concrete materials and abstract symbols. Virtual manipulatives usually have this built-in structure. Many virtual manipulative activities give students hints and feedback with pop-ups and help features. More traditional concrete manipulatives are not conducive to comprehension without direct instructor assistance. For example, in using tangrams, students can practically copy a design made from pattern blocks. When a block is near a correct location, it will snap into place. This virtual manipulative includes a hint function that will show the correct location of all the blocks.

Advantages & Disadvantages

Classroom studies were conducted which investigated virtual manipulatives. The studies compares virtual manipulatives to concrete manipulatives and discuss some of its implications.

Advantages

The advantages of virtual manipulatives include immediate feedback—you know when it’s right or wrong, It is easier to maneuver and keep together. They indicate that it is a lot quicker to grasp the concept. It offers a larger variety of experiences. Virtual manipulatives allows for more complex operations to be learned. It catches the attention of the “technology generation.” Learners must relate what they're doing with the manipulatives to the numbers. In addition, virtual manipulatives is more accessible at home than the concrete manipulatives. Virtual manipulatives gives a step-by-step instruction, allowing learners to see what they were actually attempting in a task. Furthermore, it makes integer subtraction a lot more clear and gives hints when students get answers wrong. Lastly, virtual manipulatives retain students’ attention and can often provide explicit connections between visual and symbolic representations (Hunts et al., 2011, 4).

Disadvantages

In comparison to concrete manipulatives, virtual manipulatives do not provide educators and learners with the opportunity to physically touch objects. Virtual manipulatives does not provide instructions on how to enter a problem, this can be difficult when trying to expand learning. Oftentimes, the models for some content not yet available. Moreover, virtual manipulates forces learners to think abstractly making it more suitable a student who’s already mastered the concept. Additionally, computers do the work for the students so they are able to guess the correct answer. This limits students learning abilities since it does not encourage the student to find the answer on their own. Ideally many teachers would prefer students to be guided to guess answers only when they find difficulty grasping or comprehending. Furthermore, virtual manipulatives in studies have shown to sometimes limit the teacher’s ability to follow the students’ thought processes. Lastly, learning mathematics through the use of virtual manipulatives feels more like a "do" experience rather than a learn and explore learning experience (Hunts et al., 2011, 5).

Students with Disabilities

Researchers have studied the use of virtual manipulatives for mathematics on students with disabilities. Research has shown that virtual manipulatives provides students with disabilities with flexible options for learning, promoting student autonomy, and offering educators a wider range of options to accommodate diverse groups of students.

Examples of Virtual Manipulatives for Mathematics

Examples of websites or apps pertaining to virtual manipulatives for mathematics that educators can use in their classrooms with students are

1. Math Playground Manipulatives
2. Math Learning Centre
3. Mathigon Manipulatives
4. Toy Theatre Manipulatives

References

Bouck, Emily C.; Park, Jiyoon; Stenzel, Kelly (2020-08-03). "Virtual manipulatives as assistive technology to support students with disabilities with mathematics". Preventing School Failure: Alternative Education for Children and Youth. 64 (4): 281–289.

Hunts, A., Nash, L., Nipper, K. (2011). Virtual vs. Concrete Manipulatives in Mathematics Teacher Education: Is One Type More Effective than the Other? Current Issues in Middle Level Education, 6, 1-6. Retrieved from https://files.eric.ed.gov/fulltext/EJ1092638.pdf

Long, Holly; Bouck, Emily; Domka, Anna (2021-05-27). "Manipulating Algebra: Comparing Concrete and Virtual Algebra Tiles for Students with Intellectual and Developmental Disabilities". Exceptionality. 29 (3): 197–214.

Moyer-Packenham P.S., Bolyard J.J. (2016) Revisiting the Definition of a Virtual Manipulative. In: Moyer-Packenham P. (eds) International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives. Mathematics Education in the Digital Era, vol 7. Springer, Cham.

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.

Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2000). What are virtual manipulatives? [Online]. Teaching Children Mathematics, 8(6), 372-377.

Rajiv Satsangi & Bridget Miller (2017) The case for adopting virtual manipulatives in mathematics education for students with disabilities, Preventing School Failure: Alternative Education for Children and Youth, 61:4, 303-310, DOI: 10.1080/1045988X.2016.1275505