Inculcating Mathematical thinking through Epistemic Agency

Abstract

The ability to formulate and apply principles are crucial 21st Century skills. These skills are inherent in Mathematical thinking processes, which require learners to search for abstract problem-solving methods that would serve as analogy-enhancing bridges enabling transfer between different task situations. Consequently, two component skills that need to be mastered are pattern recognition and reasoning. In this exploratory study, we adopted an inquiry- based approach to design technological scaffolds. Wre aimed to investigate the relation between the teacher's beliefs, his design of instructional practices, the design of technology and students' learning outcomes. We discovered that epistemic agency can be used as the core design factor, redefining earlier definitions of context. Furthermore, teachers' beliefs clearly influenced how he sequenced the classroom curriculum, how he relates Mathematical problems with real life, how he identifies, interprets and addresses students' misconceptions (especially with regards to the lower-performing students) and how students should be motivated to learn. From the students' perspective, based on the Technology Acceptance Model, the highest score was for satisfaction when using the system, followed by usefulness (i.e., the system helped them to reason and think), ease of use and opportunities to practice. We inferred from this high score that students liked being challenged by diverse problems of increasing difficulty. comparisons between their pattern recognition and fill in the blanks answers eshowed that our system was able to identify implicitly how students actually think, areas students need further help with and most importantly, may be able to utilize students’s thinking strategies to implicitly predict student performance in Mathematics. Based on these findings, we suggest implications to teacher professional development/TPACK.