Virtual manipulatives for mathematics
Encyclopedia
Virtual manipulatives are a relatively new technology and are modeled after existing manipulatives such as base ten blocks
Base ten blocks
Base ten blocks are a mathematical manipulative used by students to learn basic mathematical concepts including addition, subtraction, number sense, place value and counting. The student can manipulate the blocks in different ways to express numbers and patterns...

, coins
COinS
ContextObjects in Spans, commonly abbreviated COinS, is a method to embed bibliographic metadata in the HTML code of web pages. This allows bibliographic software to publish machine-readable bibliographic items and client reference management software to retrieve bibliographic metadata. The...

, blocks, tangrams, spinners
Spinners
Spinners can refer to:* The Spinners , an American R&B/soul group active from 1957 to the present* The Spinners , a British folk group active from 1959 to 1989...

, rulers, fraction bars
Fraction Bars
Fraction Bars are a type of mathematical manipulative, developed in the sixties by Albert B. Bennett, Jr. . They provide visual illustrations of mathematical operations with fractions to gain better understanding of these operations.- Overview :...

, algebra tiles, geoboard
Geoboard
A geoboard is a mathematical manipulative often used to explore basic concepts in plane geometry such as perimeter, area or the characteristics of triangles and other polygons...

s, geometric plane, and solids figures. They are usually in the form of Java
Java applet
A Java applet is an applet delivered to users in the form of Java bytecode. Java applets can run in a Web browser using a Java Virtual Machine , or in Sun's AppletViewer, a stand-alone tool for testing applets...

 or Flash
Adobe Flash
Adobe Flash is a multimedia platform used to add animation, video, and interactivity to web pages. Flash is frequently used for advertisements, games and flash animations for broadcast...

 applets. Virtual manipulatives allow teachers to allow for efficient use of multiple representations
Multiple representations (mathematics education)
Multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties...

 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).

Many 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 math 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 students 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

Shodor Interactivate Activities

http://www.shodor.org/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

http://nlvm.usu.edu/

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

http://illuminations.nctm.org/ActivitySearch.aspx

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.

External links

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