updated September 3 2020
Although I believe nothing replaces the physical and sensory interaction with materials such as math manipulatives, in this time of COVID-19 and its many health and safety precautions and protocols, we are turning to the use of virtual manipulatives or e-manipulatives more then ever. Students can use them on their computers or devices at home or in-school so that students do not need to physically share and use materials that would need to be regularly sanitized.
The use of widely-used commercial mathematically structured manipulatives originated with the design and creation of Cuisenaire Rods in the early 1950s , although many other math materials, such as Froebel’s gifts and some Montessori math materials had been in use before this. Unifix Cubes were developed soon after this in 1953, by a family of educational suppliers who had worked with both Froebel and Montessori. Over time there have been “overhead projector” and magnetic versions of these manipulatives and since the 1990s virtual manipulatives have been developed using flash or java apps or applets.
One of the first collections of virtual manipulatives was the National Library of Virtual Manipulatives hosted by Utah State University, launched in 1999. You can find manipulatives sorted by math topic and grade band. The site can be accessed HERE.
A book sharing ways to teach mathematics with the manipulatives from the NLVM was published in 2010. I found it still available for purchases HERE.
The following are suites of free, accessible virtual manipulatives:
(please note that all image below are screenshots from the websites and do not link to the apps/sites. there is a link for each website embedded in the description)
The Math Learning Center
The Math Learning Center provides a suite of virtual manipulatives that are available as web-based apps, iOS apps and are also available in the Chrome Store. The Math Learning Center iOS apps have been loaded to our district-configured sets of iPad devices. Some of the apps have a new sharing features that allows teachers to pose problems or design investigations specific to their class of students. The pages hosting the apps and more information about them can be found HERE. Some of the apps available are pictured below.
Didax Education has created virtual manipulatives of their widely used physical manipulatives such as Unifix Cubes. The manipulatives, instructions, learning activities, and ways to embed the manipulatives in online platforms can be found HERE. Some of the virtual manipulatives that can be found on the Didax site are pictured below.
Mathies Learning Tools have been developed in Ontario, including Canadian money manipulatives. Information is available in English and French and the tools are available for different platforms. The pages hosting their virtual manipulatives and other tools can be found HERE.
Mathigon hosts a “polypad” which is like a web-based whiteboard screen that their suite of virtual manipulatives can be used on. The page can be accessed HERE.
Toy Theater hosts a page of virtual manipulatives. The site also includes a range of number charts like 100 and 120 chart and Canadian money manipulatives. The page of virtual manipulatives can be found HERE.
The following suites of virtual manipulative are added from Twitter suggestions. With thanks to Karla Pearce, Alistair Carratt and Sean K for their suggestions.
Mathsbot hosts a page of virtual manipulatives within their site found HERE. There are standard math manipulatives like tangrams, pattern blocks and Cuisenaire rods but also tools like discs, dice, counters, a visual fraction wall, geoboards and many other visual supports for learning, doing and thinking about mathematics. It is the only suite that I have found that includes prime factor tiles, number frames and Hungarian frames.
Geogebra create a specific page to host tools to support remote learning, including an array of whiteboards (dots, grids, isometric, etc) as well as virtual manipulatives such as algebra tiles, protractors, fraction circles, prism creators, and many others that can be used across the grades. This page can be found HERE.
The Geogebra home page also takes you to several math apps, tasks, simulations, games and other classroom resources.
Some online resources on the research and use of virtual manipulatives:
As part of the NCTM 100 Days of Learning series, Chrissy Newell presented a webinar, sharing different ways to use virtual manipulatives. The recorded webinar can be accessed HERE. And the presentation slides can be downloaded here:
What are Virtual Manipulatives? article published in Teaching Children Mathematics, NCTM, 2002
A meta-analysis of the effects of virtual manipulatives on student achievement and mathematics learning, 2013