You are here:

Third graders' mathematical thinking of place value through the use of concrete and virtual manipulatives

, University of Houston, United States

University of Houston . Awarded


As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with third grade students: tactile instruction with concrete or physical manipulatives, and visual instruction with computer-based or virtual manipulatives. The study was designed to analyze students' learning of place value using groupable concrete base ten blocks or virtual base ten blocks. The study addressed the following research question: In what ways do concrete and virtual manipulatives elicit mathematical thinking of place value among third grade students?

The study used qualitative methods and analysis procedures. Participants were 76 third grade students in an urban elementary school. Data were collected in the form of observations, digital videotapes and student work in order to describe the interactions and relationships among students and the mode of instruction. A video analysis protocol, based on research of student's conceptualization of place value, was utilized to interpret the videos.

Analysis of data revealed that students' conceptualization of place value using concrete or virtual manipulatives were similar. Strategies for constructing and counting quantities as well as writing numerals were consistent among students using the concrete or the virtual base ten blocks. Differences occurred in the construction of non-canonical numbers and the tools afforded to the virtual manipulatives for place value instruction. Students using the virtual base ten blocks conceptualized place value constructs and generated more diverse non-canonical representations. In addition, Dual Coding Theory provided a solid foundation to describe cognition regarding the use of virtual models and mathematical concepts. The study suggests that virtual manipulatives are a viable instructional tool for the instruction and learning of place value, as well as that student use of virtual manipulatives within place value instruction may "support and extend mathematical reasoning and sense making" (NCTM, 2008).


Burris, J.T. Third graders' mathematical thinking of place value through the use of concrete and virtual manipulatives. Ph.D. thesis, University of Houston. Retrieved June 20, 2019 from .

This record was imported from ProQuest on October 23, 2013. [Original Record]

Citation reproduced with permission of ProQuest LLC.

For copies of dissertations and theses: (800) 521-0600/(734) 761-4700 or