Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Integrating engineering design into K-12 curricula is increasingly important as engineering has been incorporated into many STEM education standards. However, the ill-structured and open-ended nature of engineering design makes it difficult for an instructor to keep track of the design processes of all students simultaneously and provide…

The basis for individual students' instructional support by teachers is an individual diagnosis of one's learning advances and difficulties. Even though sophisticated diagnostic tools exist, it remains an open question how diagnosis and learning can be merged into a consistent pedagogical method to support both teachers and students with feedback…

Evaluating the impact of instructional innovations and coordinating instruction, assessment, and testing present complex tensions. Many evaluation and coordination efforts aim to address these tensions by using the coherence provided by modern cognitive science perspectives on domain-specific learning. This paper introduces an alternative…