This thesis intends to advance educational research by providing exploratory insights about the roles of, and relationships between, the actions, language, and gestures of college and elementary-aged students surrounding measurement estimation. To the best of my knowledge, prior research has examined the role of speech and gestures as they relate to areas of mathematics such as algebra and geometry, however, this work has not been extended to the area of measurement. Similarly, language and gesture have been explored but the three-way interplay between actions during problem-solving, and the language and gestures observed during explanations after problem solving has not been investigated in mathematics. To actualize the findings from this research in practice, this thesis uses the findings from two studies on behavior during measurement tasks to propose text and image support for an elementary-aged measurement game, EstimateIT!, to support students as they practice how to measure objects and develop conceptual skills through embodied game play. Specifically, this thesis intends to provide 1) a synthesis of the work on gestures in mathematics as well as the research methods used to study gestures, 2) a coding guide to analyze the gestures of mathematics learners, as well as their actions and language, 3) an application of the coding guide to explore the behavior of college and elementary students during measurement estimation tasks, and 4) proposals for action-guiding support for EstimateIT! to help elementary students develop and reinforce an understanding of measurement during gameplay based on the more mature strategies demonstrated by college students as they complete similar tasks.

Children are born with an intrinsic motivation to play games. Over the past decade, educational video games have invaded mainstream classroom instruction and researchers are “considering how games might be used in pursuit of engaging, effective learning experiences� (Squire and Jenkins, 2003). This research encompasses designing math games using a constructivist and embodied cognition pedagogy in an effort to answer the question: “Will overlapping wearable technology and mathematical objectives with traditional children’s games show improved efficacy in students’ math skills and increase students’ motivation to learn math in 4th thru 6th grade students?� Methods of research include a usability study and four subsequent iterative studies to improve the game and the technology, measuring students’ math self-efficacy and motivation to learn math. The final goal of this thesis is to design, test and document an engaging children’s math learning game using wearable technology that requires active physical experiences while involved in deep thinking and complex problem solving (Gee, 2003) within real world environments, beyond classrooms, pencil and paper, and even beyond traditional computer games in front of a computer screen.