The goal of Spatial Mathematics, Engineering, and Science: Toward an Integrated STEM Education is to develop a provisional learning progression spanning grades K-5 that articulates and tests the potential of experiencing, describing, and representing space as the core of an integrated STEM education. The science of space has an extensive scope within and across disciplinary boundaries of science, mathematics and engineering, the project will create a coherent approach to elementary instruction in which mathematical reasoning about space is systematically cultivated. Simultaneously, researchers are exploring the potential of spatial mathematics as a resource for engineering design of kinematic machines and for the development of mechanistic reasoning about the behavior of these machines. Work across these disciplines situates and motivates the mathematical work and also provides opportunities to investigate the intersections and contrasts among signature disciplinary practices, such as definition and proof in mathematics, design in engineering, and modeling in science. The research and development is being conducted in a middle school which is a full partner in the project.
In partnership, researchers and participating teachers are designing and implementing curricular approaches intended to support spatial knowledge and reasoning. Professional development will enhance and capitalize on teachers' roles as specialists in student thinking. The research consists of design studies conducted in 12 participating classrooms, K-5, and small-scale teaching experiments conducted with children across the same grade span. The research will establish provisional pathways and landmarks in learning about space, as well as the curricular activities and teacher practices necessary to support integrated STEM learning.
The project is novel in three ways. First, it provides children with early and systematic access to multiple geometries (e.g., plane, cylinder, sphere) to develop sophisticated understandings of powerful, yet experientally accessible concepts, such as straight, and STEM-related practices, such as model, definition and proof. Second, both the National Research Council Science/Engineering and the Common Core State Standards Mathematics highlight the role of practices in the development of disciplinary knowledge, and this project is providing a practical avenue for coordinating the co-development of disciplinary practices and knowledge. Third, the unifying theme of space is threaded through problems and contexts in mathematics, science and engineering, which provide a sound basis for generative STEM integration-integration that does not lose sight of the distinctive practices in different disciplines, but, instead, leverages these distinctions to produce multiple ways of knowing about space. Research and development is being conducted with underrepresented populations of students who are typically underserved in STEM education. Although the numbers of students reached in this phase of the work are relatively modest, the longer-term potential is great, because instruction anchored in space may be more accessible to students who struggle with traditional forms of mathematics education. The increased attention to integrated STEM education at the national level also ensures that this effort is likely to contribute to the knowledge base required to advance interdisciplinary forms of schooling.
During the two years of the project, learning researchers, mathematicians, and 18 K-5 teachers in an elementary school that serves children predominantly from underrepresented populations (e.g., Latino, Marshall Islanders, rural White) collaborated to explore productive ways to engage children in the mathematics of measure (e.g., the construction and use of units) and space (e.g., symmetries in 2 and 3 dimensions). These mathematical underpinnings are often neglected in children’s early education, an oversight that potentially damages students’ capacity to participate in science, engineering, and technology. Teachers and the project team developed approaches to instruction, classes of problems and contexts, and forms of assessment that foster cumulative development across grades.. For example, kindergarten children ordered the heights and circumferences of a group of pumpkins by first establishing representations of these measures (i.e., with strips of adding machine tape) and then directly comparing the representations. First graders constructed their own measuring tools, exploring and mastering ideas of unit iteration, symbolization, and origin of a scale of measure. Children explored effects of changes in unit length on the resulting measure of the magnitude of a length. Second grade students extended these activities by splitting units to create partial units, resulting in new issues of symbolization and measure. This exploration tied measurement to developing meanings of fractions and to operations with fractions, such as multiplication and addition. Children again considered effects of changes in unit on the resulting measure of a fixed length. Third graders reverse-engineered conventional rulers, and along the way, explored ideas of factoring, symbolizing, and operating with fractions and fractional quantities. They also constructed areas by sweeping one length through another and dissected the resulting shapes with units of measure. While children were exploring length measures in the early grades, they also began to consider angles and the role that angles play in shapes. These foundations secure further opportunties to explore measure and geometry in the late elementary grades, such as area swept through length to generate volume and and consideration of how to measure angle in three dimensional structures. Teachers played a critical role in all of children’s mathematical investigations, asking students to explain and compare their thinking and to consider how their thinking was changing over time. Teachers used the results of embedded and formative assessments to guide learning and to modify instruction and instructional materials, as needed. Results of interview studies with children in grades K-3 suggested that their understandings met or exceeded those advocated in the Common Core standards. Teachers responded to interviews at the outset and near the end of the two years of the project. Their responses indicated considerable shifts in their interpretations of what teaching to "big ideas" in measurement implied about the conduct of instruction. The unit lessons, assessment constructs, and formative assessments are available on a secure website.
