This research focused on the development of geometric understanding in grades K-5, and on the role that technology-enhanced curriculum can play in the development of that thinking. The research investigated and documented how, and in which circumstances, technology-enhanced curricula allow students in grades K-5 to engage in learning challenges and experimentation that support the development and application of important geometric concepts and principles. The technology-enhanced curricula that were the focus of our research include conceptually-designed microworlds, research-based computer software, designed to embody specific mathematical concepts in age-appropriate ways. To ensure effective learning, technology-enhanced curricula incorporate a range of different software-based activities, along with use of concrete manipulatives, and a variety of activities supporting multiple learning modalities, examples and applications from students' daily lives, and especially, effective, reform-oriented instruction by knowledgeable teachers. Our research focused on classrooms in which the essential elements - curriculum, software, technology infrastructure, and prepared teachers - were present. The findings of our work are significant for informing future efforts to develop technology-enhanced learning environments and provide insights about changes in pedagogy that may be needed to support effective learning in such environments. Furthermore, the assessment tasks that we developed for the research can be adapted for use as classroom assessment tasks. "Big Ideas" in geometry Our research focused on the growth and development of student thinking about "big ideas" in geometry - concepts that underlie understanding and mastering these and other topics in mathematics, science and the arts. We have identified several such "big ideas" that can be addressed through technology-enhanced curricula. These include units, patterns and repetition; transformation of shapes; symmetries; composition and decomposition of shapes; similarity and scale; measurement and dimensionality; and three-dimensional/two-dimensional visualization. To make this research effort manageable, our proposed work focused on the first four of these "big ideas". Units, Patterns and Repetition: For the purpose of our research, we consider units, patterns and repetition to be one "big idea," which is critical for mathematical understanding and analysis of many geometric patterns as found in nature, many traditional arts and crafts, geometric art such as the work of M. C. Escher, and three-dimensional patterns in many engineered structures such as bridges or buildings. Using this idea, one starts with a unit, which could be a shape or group of shapes (a geometric/spatial unit) or a unit of measurement, and through a process of repetition, constructs a pattern, or builds a measuring tool. The idea can also be used in reverse - starting with a pattern, one uses a related conceptual process to define the units, or repeating elements, from which the pattern could be constructed. Transformations of Shapes: The ability to define, use, and visualize the effects of translations, rotations, reflections, and dilations, and understand the effects of repeated transformations including mathematically significant concepts of inverse, equivalent and identity transformations, forms a second big idea that unlocks the mathematics of geometric patterns. Symmetries: Symmetries involve the study of what remains the same after a transformation or series of transformations. This expands the common understanding of bilateral symmetry to include rotational and translational symmetries, supporting deeper analyses of geometric structures. Composition and Decomposition of Shapes: The ability to define, use, and visualize the effects of composing (putting together) and decomposing (taking apart) geometry shapes forms is another big idea of geometry. It corresponds with, and supports, children's ability to compose and decompose numbers. Our research is revealing that children move through levels in the composition and decomposition of 2-D figures. From lack of competence in composing geometric shapes, they gain abilities to combine shapes into pictures, then synthesize combinations of shapes into new shapes (composite shapes), eventually operating on and iterating those composite shapes.