Ji-eun Lee , Mi Yeon Lee

DOI: Vol.21(No.1) 1-13, 2018

While the utility of the number line is considerable, articulating its conceptual foundation is often neglected in school mathematics. We suggest that it is important to build up strong conceptual foundations in the earlier grades so that number lines can be used in a more meaningful way and that any misconceptions associated with the number line can be prevented or intervened. This paper addresses unit, direction, and origin as the key elements of number lines and presents activities from Davydov’s curriculum for early grades that promote exploration of those key elements and may resolve some students’ misconceptions. As shown in sample activities from Davydov’s curriculum, this paper suggests that students can broaden their perspectives on the number line and use it versatilely in various areas of mathematics learning when they deeply engage in the construction of a number line and have flexibility in interpreting the relationships between key number line elements.

number line, Davydov’s elementary curriculum, unit, direction, origin

Sheunghyun Yeo

DOI: Vol.21(No.1) 15-34, 2018

This paper describes how communicative technology between two classrooms located in different sociocultural contexts was used to support mathematics instruction. I analyzed what interactions emerged using the communicative technology, how sociocultural differences were leveraged to construct mathematical knowledge, and how students built this knowledge together across urban and rural classrooms. The results show that reciprocal interactions emerged. Teachers co-designed lesson plans and tasks with consideration of the different classroom social contexts. Based on those teachers’ interactions, students had opportunities to justify their ideas and to prepare answers before the connected discussions, and a wide spectrum of ideas was synthesized as collaborative knowledge. These findings suggest that communicative technology has the potential to enhance learning opportunities for students across different social contexts.

Communicative technology, interactions in mathematics instruction, knowledge building, Skype

Jinho Kim , Woong Lim

DOI: Vol.21(No.1) 35-46, 2018

In this perspective paper, we present seven elements of the appropriate educator mindset for teaching in the constructivist elementary mathematics classroom. The elements include supporting students as they construct their own understanding, eliminating deficit view of slow learners, setting new understanding and growth as the learning objective, providing opportunities to co-construct meaning with peers, using student contributions as the source of curricular material, encouraging all students to participate in learning, and providing instruction not bounded by time. In our struggles to provide authentic, inclusive elementary classrooms, we hope that our discussion of the educator mindset can increase discourse on constructivism from philosophy to practice in the community of mathematics education and policy makers.

open task, constructivism, elementary mathematics, teacher mindsets, intellectual development