• Research in Mathematical Education
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• v.25 no.1
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• pp.65-89
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• 2022

Despite its recognition in the field of mathematics education and mathematics, students' understanding about proof and performance on proof tasks have been far from promising. Research has documented that teachers tend to accept empirical arguments as proofs. In this study, an online survey was administered to examine how Korean secondary mathematic teachers make judgements on mathematical arguments varied along representations. The results indicate that, when asked to judge how convincing to their students the given arguments would be, the teachers tended to consider how likely students understand the given arguments and this surfaces as a controversial matter with the algebraic argument being both most and least convincing for their students. The teachers' judgements on the algebraic argument were shown to have statistically significant difference with respect to convincingness to them, convincingness to their students, and validity as mathematical proof.

• Research in Mathematical Education
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• v.14 no.3
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• pp.219-231
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• 2010

Mathematically, a proof is to create a convincing argument through logical reasoning towards a given proposition or a given statement. Mathematics educators have been working diligently to create environments that will assist students to perform proofs. One of such environments is the use of dynamic-geometry-software in the classroom. This paper reports on a case study and intends to probe into students' own thinking, patterns they used in completing certain tasks, and the extent to which they have utilized technology. Their tasks were to explore the shape-to-shape, shape-to-part, and part-to-part interrelationships of geometric objects when dealing with certain geometric problem-solving situations utilizing dissection-motion-operation (DMO).

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• Korean Journal of Logic
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• v.13 no.1
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• pp.83-100
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• 2010

In his recent paper "Early Wittgenstein, Logic, and Metaphysics" Professor Jinho Kang argues that there has been an important change in Wittgenstein's view on the nature of logic between October 1913 and December 1916, which resulted in his change of attitude toward metaphysics. In my paper, raising some questions regarding his basic assumptions and arguments, I attempt to show that Professor Kang's paper fails to provide convincing solution to the points at issue.

• Journal of Korean Philosophical Society
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• v.116
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• pp.207-224
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• 2010

Belief is generally understood as a mental phenomenon which is aimed to attain objective information of the world. Thus, the content of belief is not something that can be manipulated or created by men. The primary function of belief in a word is to represent the world correctly. Now, William James in his "The Will to Believe" challenges this view. According to James, one can come to believe something by choosing to believe it. And he argues for his position by criticizing W. K. Clifford who wrote an essay entitled "The Ethics of Belief". In this paper, I examine both arguments given by them and show whose position is more convincing.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2016.10a
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• pp.838-839
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• 2016

IEEE 802.15.4 is the standard wireless link technology for low power, low cost, but long lifetime applications including wireless sensor network (WSN). Currently, whether or not IP architecture should be used in WSN over its 802.15.4 link is under dispute. Such kind of arguments may last for a long time without some convincing experimental measurements of real case performances of IP over 802.15.4 implementation, and thus prevent the advance of related research. In RFC4944, IETF proposed the 6LoWPAN specification to enable IPv6 communication over low power, wireless personal area networks. We try to alleviate the dispute and make the direction clearer to the community so as to promote further valuable research in this topic.

• Asian review of World Histories
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• v.1 no.1
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• pp.5-44
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• 2013

This essay offers a historically based critique of the idea of "alternative modernities" that has acquired popularity in scholarly discussions over the last two decades. While significant in challenging Euro/American-centered conceptualizations of modernity, the idea of "alternative modernities" (or its twin, "multiple modernities") is open to criticism in the sense in which it has acquired currency in academic and political circles. The historical experience of Asian societies suggests that the search for "alternatives" long has been a feature of responses to the challenges of Euromodernity. But whereas "alternative" was conceived earlier in systemic terms, in its most recent version since the 1980s cultural difference has become its most important marker. Adding the adjective "alternative" to modernity has important counter-hegemonic cultural implications, calling for a new understanding of modernity. It also obscures in its fetishization of difference the entrapment of most of the "alternatives" claimed--products of the reconfigurations of global power--within the hegemonic spatial, temporal and developmentalist limits of the modernity they aspire to transcend. Culturally conceived notions of alternatives ignore the common structural context of a globalized capitalism which generates but also sets limits to difference. The seeming obsession with cultural difference, a defining feature of contemporary global modernity, distracts attention from urgent structural questions of social inequality and political injustice that have been globalized with the globalization of the regime of neoliberal capitalism. Interestingly, "the cultural turn" in the problematic of modernity since the 1980s has accompanied this turn in the global political economy during the same period. To be convincing in their claims to "alterity", arguments for "alternative modernities" need to re-articulate issues of cultural difference to their structural context of global capitalism. The goal of the discussion is to work out the implications of these political issues for "revisioning" the history and historiography of modernity.

• Education of Primary School Mathematics
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• v.4 no.2
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• pp.111-125
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• 2000

This paper presents cross-national perspectives on challenges in implementing current mathematics education reform ideals. This paper includes detailed qualitative descriptions of mathematics instruction from unevenly successful second-grade classrooms both in Koran and in the U. S with regared to reform recommendations. Despits dramatic differences in mathematics achivement between Korean and the U.S student. problems in both countries with regard to mathematics education are perceived to be very similar. The shared problems have a common origin in teacher-centered instruction. Educational leaders in both countries have persistently attempted to change the teacher-centered pedagogy to a student-centered approach. Many teachers report familiarity with and adherence to reform ideas, but their actual classroom teaching practices do not reflect the full implications of the reform ideals. Given the challenges in implementing reform, this study explored the breakdown that may occur between teachers adoption of reform objectives and their successful incorporation of reform ideals by comparing and contrasting two reform-oriented classrooms in both countries. This comparison and contrast provided a unique opportunity to reflect on possible subtle but crucial issues with regard to reform implementation. Thus, this study departed from past international comparisons in which the common objective has been to compare general social norma of typical mathematics classes across countries. This study was and exploratory, qualitative, comparative case study using grounded theory methodology based on constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The Korean portion of this study was conducted by the team of four researchers, including the author. The U.S portion of this study and a brief joint analysis were conducted by the author. This study compared and contrasted the classroom general social norms and sociomathematical norms of two Korean and two U.S second-grade teachers who aspired to implement reform. The two classrooms in each country were chosen because of their unequal success in activating the reform recommendation. Four mathematics lessons were videotaped from Korean classes, whereas fourteen lessons were videotaped from the U.S. classes. Intensive interviews were conducted with each teacher. The two classes within each country established similar participation patterns but very different sociomathematical norms. In both classes open-ended questioning, collaborative group work, and students own problem solving constituted the primary modes of classroom participation. However in one class mathematical significance was constituted as using standard algorithm with accuracy, whereas the other established a focus on providing reasonable and convincing arguments. Given these different mathematical foci, the students in the latter class had more opportunities to develop conceptual understanding than their counterparts. The similarities and differences to between the two teaching practices within each country clearly show that students learning opportunities do not arise social norms of a classroom community. Instead, they are closely related to its sociomathematical norms. Thus this study suggests that reform efforts highlight the importance of sociomathematical norms that established in the classroom microculture. This study also provides a more caution for the Korean reform movement than for its U.S. counterpart.