International Journal for Research in Mathematics Education
The purpose of this study was to examine how the affordances and constraints of physical and virtual manipulatives influence the development of students’ algorithmic thinking when learning algebra and rational number concepts. Thirty-six third-grade students participated in two weeks of instruction using physical and virtual manipulatives as instructional tools. The primary design of the study was a teaching experiment in which quantitative and qualitative data were collected to provide a holistic examination. Pre- and post-test items were used in the quantitative analysis following a within-subjects crossover repeated measures design. Students’ written work, a user survey, student interviews, field notes, and classroom videotapes were used in a qualitative analysis by coding the text data for evidence of major themes. Quantitative results indicated a significant difference between the physical and virtual manipulatives teaching episodes on students’ pre- and post-test performance that was mediated by mathematics content type (fractions vs. algebra). Qualitative results confirmed that the affordances and constraints of the virtual manipulative fraction applets supported students’ development of algorithmic thinking.
Suh, J. M., & Moyer-Packenham, P. S. (2016). How affordances and constraints of physical and virtual manipulatives support the development of procedural fluency and algorithmic thinking in mathematics. International Journal for Research in Mathematics Education, 6(2), 245-265.