Abstract
Digital multimodal technologies, combining multiple modes of input and output interaction, are cultural symbolic-embedded tools that can foster young children mathematical thinking in the 21st century. The purpose of the study was to design and implement an educational strategy to foster small groups of young children's intuitive meanings about congruence and similarity. The educational strategy entailed a sequence of six inquiry-based activities with dynamic congruent and similar triangles, utilizing Sketchpad on the iPad. I investigated how the young children's ways of thinking about congruence and similarity emerged and how these ways of thinking developed across the sequence of exploratory and problem-solving situations as mediated by the technological environment and collaboration of the small groups. Congruence and similarity are important ideas for students' development of advanced mathematical thinking and knowledge. However, prior research has shown that students have difficulties in making sense of these concepts at different grade levels. Researchers have suggested the importance of nurturing young children's foundations on congruence and similarity. However, little is known about what type of educational strategies can foster young children's thinking about these concepts and help them overcome the challenges they face at these early ages. This study seeks to contribute to address this need in mathematics education. A qualitative multiple-case study method of inquiry was utilized, based on the description of three individual cases, and a cross-case analysis to draw commonalities and differences across cases. Nine 7-year-old-children (second-grade) participated in the study. The learning sequence involved four exploratory activities and two problem-solving situations with varied levels of complexity, and was implemented across four 1-hour sessions. Transcriptions from task-based interviews, observation of videotapes and students' digital and written artifacts were the data sources. Discourse analysis of the children's conversations was the method to analyze data. Findings from the study revealed six main assertions regarding how the children's ways of thinking about congruence and similarity were mediated: (a) Dynamism of the geometric objects and tools from the technological environment facilitated the emergence of the children's ways of thinking about the congruent and similar triangles across the learning sequence, (b) the children drew upon their prior experiences as means to mathematize the congruence and similarity activities, (c) Peer collaboration played a critical role in supporting the development of children's ways of thinking within and across activities, (d) my collaboration as researcher through my questions and my design of the sequence of activities fostered the development of children's ways of thinking, (e) hand gestures and hand-gesture sequences allowed the children to communicate relationships related to congruence and similarity, and were socially exploited and enriched within the collaborative-technological environment, and (f) Development of ways of thinking widely varied across cases, based on the target concept, as similarity activities were more complex for the children than congruence activities. These findings have several implications for mathematics education and future research..