Development and Testing of Achievement from Multiple Modes of Mathematical Representation: Audio, Audio-Visual, and Kinesthetic

This dissertation is comprised of three articles that build on and support each other. The first article is an extensive literature review, and the other two are empirical studies. In this literature review, the author discussed major theories about human learning processes to guide instructional designers about effective integration of multiple modes in interactive learning environments and explored the knowledge base on representations and manipulatives in mathematics education. The first empirical study?s purpose was to investigate effects of affordances provided with virtual learning environments at different treatment durations. Students from multiple sixth-grade classes were randomly assigned to one of three treatment groups differed by allocated session time (10-, 20-, and 30-minute). The online manipulative tool (OMT), which was designed to scaffold learning in operations with rational numbers, allowed students to use the following three components in any order: (a) audio, (b) audio-visual, and (c) manipulatives. Analyses showed that students who used manipulatives most achieved highest; whereas, students who used audio-visual most achieved the second highest. Additionally, the 30-minute group used each component of OMT the least. A meaningful increase in standard algorithm use over manipulatives suggested a transition from concrete to abstract thinking. The second empirical study's purpose was to compare OMT's different representational aspects and to estimate OMT's effects on achievement and technology acceptance when compared to those of traditional classroom activities. Elementary- and middle-grade students were randomly assigned to the control group or one of three treatment groups: (a) audio-visual, (b) virtual-kinesthetic, and (c) dual-mode (virtual-kinesthetic and audio-visual combined). When the control group was compared with experimental groups, pre- and post-test results suggested that OMT was more effective than traditional classroom activities in improving students' understanding of operations with rational numbers. When the students' achievement on pre- and post-tests among experimental groups was compared, no substantial difference was found. However, students in the dual-mode group scored the highest on the technology acceptance survey. Students' technology acceptances also differed among different SES levels but not genders. The results suggested that virtual manipulatives provided additional affordances for conceptual understanding. However, students' acceptances of technology should be considered when implementing new technologies.