The researchers in the Children's Understanding of Functions project are studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers at University of Massachusetts at Dartmouth and Tufts University are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. Most research has focused on student development at the upper elementary and middle school levels, but this project will add information about early elementary learners.
The project's research methodology uses teaching experiments which allow researchers to talk directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization. Researchers have designed tasks that help students explain their thinking and solve problems where some quantities vary and others are constant. They are analyzing videos and students' written work as they build case studies about the development of algebraic thinking. External evaluation of this exploratory project is one of the responsibilities of its advisory board.
This project is connecting the algebraic thinking of younger children to what has been documented for older children. This process enables them to build an evidence-based learning trajectory about students' development of algebraic thinking. The products of this research can be used to build curricula and lessons that are aligned with what students know and can learn at various points in their development. Project findings, tasks and videos are being disseminated not only to researchers, but also to practitioners through professional publications and the DRK-12 Resource Network.