The role of epistemic agency and progressive inquiry in the transfer of Mathematical thinking

Instructional design of inquiry-based classrooms need to regard learning as dynamically flexible and adaptive with opportunities for emergent teaching and learning strategies as well as assessments. Consequently, we argue that emergent instructional design and emergent learning systems should focus on the discovery of instructional principles, instructional strategies and technologies that promote the development of inquiry, with teacher beliefs as a key design factor. We scope our study to the inculcation of Mathematical thinking because Mathematical thinking focuses on the identification of similarities among instances, leading to the development of general principles. The ability to formulate principles grows alongside learners' search for abstract problem-solving methods and mental schemata. These serve as analogy-enhancing transfer between different task situations. Consequently, in this exploratory study, we aim to help learners to learn to inquire and to reason, to be able to identify patterns, describe patterns and apply patterns to solve problems. Furthermore, we aim to identify how teacher's beliefs influence the design of teaching-learning practices. Subsequently, we suggest implications to the design of creative inquiry-oriented-based curriculum, pedagogy and technologies for the learning of Mathematical thinking.