Virtual manipulatives for mathematics

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In mathematics education, virtual manipulatives are a relatively new technology modeled after existing manipulatives such as base ten blocks, coins, blocks, tangrams, spinners[disambiguation needed], rulers, fraction bars, algebra tiles, geoboards, geometric plane, and solids figures. They are usually in the form of Java or Flash applets. Virtual manipulatives allow teachers to allow for efficient use of multiple representations and to 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).[1]

Many[who?] believe that virtual manipulatives can be particularly helpful to students with language difficulties, including English Language Learners (ELL). ELL students usually have trouble explaining what they are learning in mathematics classes. With virtual manipulatives, such students may be able to clarify their thoughts and demonstrate it to others in a much more effective way. For example, with base ten blocks, students may use the place-value layout to show their understanding.

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.

Although relatively new, virtual manipulatives can support learning mathematics for all students which includes those with learning disabilities and ELL learners. Virtual manipulatives can be included into the general academic curriculum and not just used as an extra student activity. If they are used wisely, virtual manipulatives can provide students with opportunities for guided discovery which can help them to build a better understanding of mathematical concepts and ultimately exhibit measurable learning skills.

Notable collections of virtual manipulatives[edit]

Wolfram Demonstrations Project

Wolfram Demonstrations Project contains around 10,000 Virtual manipulatives for math, science and engineering. They are provided in CDF format together with source code.

Shodor Interactivate Activities

Shodor is a national resource for computational science education. They have offered online education tools such as Interactivate and the Computational Science Education Reference Desk (CSERD) since 1994. The activities are sorted from Grade 3 through Undergraduate.

National Library of Virtual Manipulatives

Utah State University has offered this collection of internet-based manipulatives since 1999. The activities are sorted from Pre-Kindergarten through High School.

Illuminations: Activities

Illuminations has been found on a section of the website for the National Council of Teachers of Mathematics since 2000. Students and teachers from Pre-Kindergarten through High School can use these interactivities.

MSTE at the University of Illinois

According to their website, "Mathematics Materials for Tomorrow's Teachers (M2T2) are a set of mathematics modules created in the spring of 2000 by a team consisting of teachers, administrators, university researchers, mathematicians, graduate students, and members of the Illinois State Board of Education." They are five modules. Each module is connected to one of the goals for mathematics in the Illinois Learning Standards. The content is at a middle school level.


  • Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2000). What are virtual manipulatives? [Online]. Teaching Children Mathematics, 8(6), 372-377. Available: [1]
  • 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.

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