Publication Date


Document Type



Master of Arts in Education (MA)

MA Concentration

Teaching Mathematics


Pierre van Hiele, geometry instruction, concrete manipulatives, virtual manipulatives, geometric understanding


Helen Hawley-Davis, Pamela A. Redmond, Jim O'Connor


This thesis study compared the effects of concrete and virtual manipulatives on the learning of perimeter and area, and was based on Pierre van Hiele's theories of geometry understanding and instruction. The convenience sample included 55 sixth-grade students in a suburban school, predominately white and affluent. The researcher used a mixed­ method, quasi-experimental group comparison design consisting of a one-group pretest­ posttest with two treatment groups; each of the researcher's two mathematics classes would comprise one treatment group, alternately receiving two different treatments. All students took a pretest and the van Hiele Geometry Test. One treatment group first used concrete manipulatives during the lesson; the other treatment group first used virtual manipulatives. After students took a posttest, treatments were reversed. Students took the perimeter and area test, took the Geometry Test, and completed a survey about the different manipulatives. The researcher used validated instruments for the quantitative data and criteria of trustworthiness for the qualitative data. She used descriptive statistics and constant comparative method to analyze the data. The results of the quantitative data showed both types of manipulatives increased student achievement, and manipulatives support students who need more concrete representations. For those who are ready for more abstraction, the differences in learning experiences and understandings [from the use of both types of manipulative] can support student's development of geometric understanding. For those lower-achieving students, concrete manipulatives work better than virtual manipulatives. The qualitative data showed that teachers need to consider their students' computer literacy, each student's learning goals, and mathematical content of a lesson when deciding on manipulative use. Teachers need to ensure students are comfortable with virtual manipulatives before using them for learning, and they need to choose the most appropriate manipulative for the learning goal.