Online Appendix to: Peace through Cooperation or Peace through Strength? How to Achieve Peace in the Very Intractable Conflict Society

The Korean War, having started on June 25, 1950, has never formally ended. As the two Koreas are technically still at war, the conflict on the Korean Peninsula has become intractable. The goal of this study is to explore the attitudes of South Koreans living in the intractable conflict about how to achieve peace. To fulfill this goal, we conducted a nation-wide survey to investigate attitudes toward militant and cooperative internationalism. We also measured various variables involved with the intractable conflict. Our results indicate that the value of international harmony and equality as well as attitudes toward peace are the best predictors of cooperative internationalism, while the value of international harmony and equality as well as the attitudes toward war were the strongest predictors of militant internationalism. Our results also suggest that the tendency to regard inter-Korean relations as zero-sum relations and the attitudes toward peace mediated the relationship between international harmony and cooperative internationalism, while the zero-sum perception and attitudes toward war on the Korean Peninsula mediated the same value factor and the cooperative internationalism. Possible implications are discussed

The Persistent Difficulty of Early Fraction Ideas in Early Secondary School Mathematics

This study explored the nature of difficulties of seventh and eighth grade students who struggled building their conceptual understanding of early fraction ideas, in particular ordering fractions. The participants engaged in a sequence of lessons that involved the use of fraction circles. The intervention of four weekly class sessions was adapted from the Rational Number Project (RNP) curriculum that has been created for and refined through teaching experiments in the RNP research since 1979. Pre and post group interviews were conducted with each student group for a sufficient identification of the nature of the students’ difficulties. This study identified the whole number dominance strategies used by the students for ordering fractions before and even after the intervention. The students also revealed minimal use of informal ordering strategies that involve more conceptual than procedural understanding of the concept of initial fraction ideas. Considering the short intervention, there was subtle (but meaningful) evidence for a positive influence of the fraction circle model developed within the RNP on students’ developing understanding of early fraction ideas. This study suggests the need of a remedial intervention for early secondary students showing the persistent difficulty with early fraction ideas. Students need to be given enough time with not only concrete models but also appropriate usage of language to support a complete understanding of how to use the models. Keywords: Rational Number Project (RNP), fraction circle model, initial fraction ideas, ordering fraction

Creating a Virtual World for Mathematics

A virtual world was created using the popular sandbox game Minecraft to support the development of preservice teachers’ knowledge for teaching mathematics. Preservice teachers explored the virtual world for a geometry activity involving area and volume problems. They then discussed how this integration of technology could support students’ effective learning of mathematics in a meaningful way. The findings of the study demonstrated that to a certain extent the Minecraft activity supported the transfer of knowledge from preservice teachers’ mathematics content knowledge to their mathematics pedagogical and instructional practice knowledge. Preservice teachers appreciated the usefulness and effectiveness of the Minecraft activity in enhancing the teaching and learning of mathematics by visualizing mathematical concepts in the virtual world. This integration of technology also gave them an opportunity for professional growth. Although this study focuses on preservice teachers’ perspectives on the Minecraft activity, the technology integration using Minecraft will also be beneficial for students because it engages them in active and discovery learning