Improving learners' productive disposition through realistic mathematics education, a teacher's critical reflection of personal pedagogy.

This paper reports an action research study I conducted into the mathematical productive disposition of 29 tenth grade learners in the Philippines by analyzing their metaphorical conceptualizations of mathematics in a series of lessons following principles of Realistic Mathematics Education. Analysis of participants' pre-intervention metaphors of mathematics revealed four conceptualizations that capture learners' perceptions of mathematics reflective of their productive disposition: mathematics as a process, mathematics as a puzzle, mathematics as a problem, and mathematics as a difficulty. Insightful changes in the learners' metaphors of mathematics support the argument that making mathematics matter to students can be achieved if teachers make considerable and devoted attempts at making what matters to students mathematical. Several challenges in the implementation of realistic mathematics lessons on Permutation included developing and enabling students' awareness of their social and cultural environment and encouraging critical thinking. Reflecting on my experience, I argue that constant exposure to lessons that present mathematics as contextually and socially relevant can potentially improve students' mathematical productive disposition together with other strands of their mathematical proficiency. [ABSTRACT FROM AUTHOR]