A study of multi-representation of geometry problem solving with Virtual Manipulatives and Whiteboard system

Wu Yuin Hwang, Jia Han Su, Yueh Min Huang, Jian Jie Dong

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D space in which users could express their mathematic solutions and reasoning with a three dimensional model which can be viewed from any perspective. The purpose the VMW is to promote a multi-representative construction model with which users can easily organize their thinking manually and symbolically to solve geometry problems, based on the pedagogical theory which states: "Children would construct their geometry concepts from multiple representations like mapping the concrete items to abstract ideas through physical or mental manipulation". The proposed system was evaluated with one pilot study to investigate its perceived ease of use and usefulness. Furthermore, students' solving strategies were analyzed using their manipulations in the 3D space and solutions recorded in the whiteboards. The results showed that the proposed system was perceived as useful, and helped students to understand the processes of geometry problem solving, such as using various solving strategies, as well as exposing geometrical misconceptions. In the future, researchers also aim to apply the multi-representative construction model to knowledge construction in other domains.

Original languageEnglish
Pages (from-to)229-247
Number of pages19
JournalEducational Technology and Society
Issue number3
StatePublished - Jul 2009


  • Constructivism
  • Geometry problem solving
  • Multi-representative construction model
  • Virtual manipulatives
  • Web3D


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