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Manipulatives are blocks, algebra tiles, cubes, rods, fraction pieces, and pattern blocks that are used in mathematics classes for students to make meaning of abstract ideas and symbols. (Manches, Claire, Benford, 2009)
Concrete Vs. Virtual Manipulatives Concrete Manipulatives are physical objects students can manipulate to explore and develop an understanding of mathematical concepts. Virtual Manipulatives are computer-based simulations of physical manipulatives that can be accessed through the internet or computer software.
Manches, A., Claire O., Malley, Benford S. (2009) The role of physical representations in solving number problems: A comparison of young children’s use of physical and virtual material. Computer and Education. 54, 622-640.
Moyer, P.S. (2001) Are we having fun yet? How teachers use Manipulatives to teacher mathematics . Educational Studies in Mathematics . 47(2), 175-197.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author