J. Korean Soc. Math. Educ., Ser. D, Res. Math. Educ. http://dx.doi.org/10.7468/jksmed.2019.22.1.35 Vol. 22, No. 1, 35-46, March, 2019 ⓒ 2019 Korean Society of Mathematical Education 35 Reconceptualizing Learning Goals and Teaching Practices: Implementation of Open-Ended Mathematical Tasks Jinho Kim (Professor) 1 , Sheunghyun Yeo (Graduate Student) 21* 1 Daegu National University of Education, jk478kim@dnue.ac.kr 2 University of Missouri, syhw6@mail.missouri.com (Received March 4, 2019; Accepted March 18, 2019) This study examines how open-ended tasks can be implemented with the support of redefined learning goals and teaching practices from a student-centered perspective. In order to apply open-ended tasks, learning goals should be adopted by individual student’s cognitive levels in the classroom context rather than by designated goals from curriculum. Equitable opportunities to share children’s mathematical ideas are also attainable through flexible management of lesson-time. Eventually, students can foster their meta-cognition in the process of abstraction of what they’ve learned through discussions facilitated by teachers. A pedagogical implication for professional development is that teachers need to improve additional teaching practices such as how to tailor tasks relevant to their classroom context and how to set norms for students to appreciate peer’s mathematical ideas in the discussions. Keywords: open-ended mathematical tasks, learning goals, teaching practices, student- centered MESC Classification: C32, C72 MSC2010 Classification: 97C32, 97C92 I. INTRODUCTION Researchers have called for the use of open-ended tasks to implement good mathematics instruction (Sullivan, Warren, & White, 2000). Rather than listening to teachers’ explanations or engaging passively in a provided activity, learning actually takes place by discussing mathematical ideas followed by the activity (Bransford, Brown, & Cocking, 1999; Chapin, O’Connor, & Anderson, 2013). When students construct their own ideas regardless of their levels of knowledge and participate in discussions built on * Corresponding author: syhw6@mail.missouri.com