• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.491-510
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• 2017

This study analyzes on conjecturing tasks in elementary mathematics textbook. We adopted Peircean semiotic perspective and variation theory to analyze conjecturing tasks in elementary mathematics textbook. We specifically analyzed mathematical tasks designed to support students' inquiries into definitions and properties of quardrilaterals. As a result, we found that conjecturing tasks in textbooks do not focus on supporting students' diagrammatic reasoning and inductive verification on provisional abductions. These tasks were mainly designed to support students' conjecturing on commonalities of mathematical objects rather than differences between objects.

• School Mathematics
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• v.13 no.1
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• pp.107-125
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• 2011

In this paper, we investigated how the GSP environments impact students' conjecturing of geometric properties. And we wanted to draw some implication in teaching and learning geometry in dynamic geometric environments. As results, we conclude that when students were given the problem situations which almost has no condition, they were not successful, and rather when the problem situations had appropriate conditions students were able to generate many conditions which were not given in the original problem situations, and consequently they were more successful in conjecturing geometric properties. And the geometric properties conjectured in GSP environments are more complex and difficult to prove than those in paper and pencil environments. Also the function of moving screen with 'Alt' key is frequently used in conjecturing geometric properties with functions of measurement and calculation of GSP. And students felt happier when they discovered geometric properties than when they could prove geometric properties.

• School Mathematics
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• v.1 no.1
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• pp.7-17
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• 1999

The purpose of this note is to give insights into the role of parallelism to the middle school mathematics. According to NCTM(1998), the middle grades mathematics classroom should be a place in which students regularly engage in thoughtful activity that relates to their emerging capabilities of finding and imposing structure, conjecturing and verifying, and engaging in abstraction and generalization. In this aspect it is desirable to reinvestigate Euclidean Parallel Postulate in the axiomatic point of view in the level of the middle school mathematics. Reconstructing the contents Greenberg(1993), and we explain the statements which are logically equivalent to the Parallel Postulate for mathematics teachers in the middle school.

• Research in Mathematical Education
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• v.4 no.2
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• pp.63-77
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• 2000

The purpose of this article is to devise the activities based on van Hiele levels of geometric thought using computer software, Geometer\\\\`s Sketchpad(GSP) as a tool. The most challenging task facing teachers of geometry is the development of student facility for understanding geometric concepts and properties. The National Council of teachers of Mathematics(Curriculum and Evaluation Standards for School Mathematics, 1991; Principles and Standards for School Mathematics, 2000) and the National Re-search Council(Hill, Griffiths, Bucy, et al., Everybody Counts, 1989) have supported the development of exploring and conjecturing ability for helping students to have mathematical power. The examples of the activities built is GSP for students ar designed to illustrate the ways in which van Hiele\\\\`s model can be implemented into classroom practice.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.1
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• pp.145-156
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• 1998

In a classical clustering problem, grouping is done on the basis of similarities or distances (dissimilarities) among the elements. Therefore, the objective is to minimize the variance within each group while maximizing the between-group variance among all groups. In this paper, however, a new class of clustering problem is introduced. We call this a laydown grouping problem (LGP). In LGP, the objective is to minimize both the within-group and between-group variances. Furthermore, the problem is expanded to a multi-dimensional case where the two-way minimization process must be considered for each dimension simultaneously for all measurement characteristics. At first, the problem is assessed by analyzing its variance structures and their complexities by conjecturing that LGP is NP-complete. Then, the simulated annealing (SA) algorithm is applied and the results are compared against that from others.

• Biomedical Science Letters
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• v.16 no.3
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• pp.197-200
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• 2010

All citizens over 17 year old living in Korea have to be fingerprinted to obtain a certificate of resident registration. For this reason, human identification through fingerprints has been used actively in crime scene investigation. The fingerprint is so unique that it is one of the most certain ways to identify oneself and it can differentiate between genetically identical twins. Fingerprints gained in crime scene indicate a direction of criminal investigation in conjecturing a suspect. Fingerprints help a reunion of family got scattered for a long time and make it possible to get a personal identification for missing person who met with natural calamity. We developed a new fingerprinting method using safranine O, so as to develop fingerprints on the adhesive tapes and non-porous papers in various physical environments. Results were compared to the preexisting fingerprinting method, the minutiae numbers of fingerprints were greatly increased in our newly developed safranine O fingerprinting method. This newly developed safranine O method showed a quantity and quality comparable to the preexisting fingerprinting method routinely used in these days. In our hands, the safranine O fingerprinting method is another easy and obvious choice when the forensic case sample is available for fingerprints on the adhesive tapes and non-porous papers.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.69-88
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• 2017

One of the most important activities in the process of mathematical modeling is to build models by conjecturing mathematical rules and principles in the real phenomena and to validate the models by considering its validity. Due to uncertainty and ambiguity inherent real-contexts, various strategies and solutions for mathematical modeling can be available. This characteristic of mathematical modeling can offer a proper environment in which creativity could intervene in the process and the product of modeling. In this study, first we analyze the process and the product of mathematical modeling, especially focusing on the students' models and validating way, to find evidences about whether modeling can facilitate students'creative thinking. The findings showed that the students' creative thinking related to fluency, flexibility, elaboration, and originality emerged through mathematical modeling.

• The Journal of Industrial Distribution & Business
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• v.11 no.5
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• pp.7-16
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• 2020

Purpose: Prior studies empirically examine how financial flexibility is related to required returns by using realized returns and considering cash holdings as net debts, but they fail to find consistent results. Conjecturing that inappropriate proxy of required returns and aggregation of cash and debts caused the inconsistent results, this study revisits this topic by using a refined proxy of required returns and separating cash holdings from debts. Research design, data and methodology: This study uses a multivariate regression model to investigate the relationship between required returns on cash holdings and financial leverage. The required returns are estimated using the return decomposition method by vector autoregression model. Empirical tests use US stock market data from1968 to 2011. Results: Empirical results reveal that both cash holdings and leverage are positively related to required returns. The positive relation is stronger in economic downturns than in economic upturns. Conclusions: Three major findings are drawn. First, risky firms prefer large cash balance. Second, information shocks in the realized returns caused failure of prior studies to find consistent positive relationship between leverage and realized returns. Third, cash and leverage are related to required returns in the same direction; therefore, cash cannot be considered as negative debts.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.257-275
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• 2023

In this study, we designed and implemented a instruction emphasizing mathematical argument for fifth-grade students and analyzed the teaching practices. Through a literature review related to instruction emphasizing mathematical argument, we organized a teaching model of five phases that explain why the general claim that the sum of consecutive odd numbers equals a square number is true: 1) noticing patterns, 2) articulating conjectures, 3) representing through visual model, 4) arguing based on representation, 5) comparing and contrasting. Then, we analyzed the argumentation stream by phases to observe how the instruction emphasizing mathematical argument is implemented in the elementary classroom. Based on the results of this study, we discuss the implications of teaching a mathematical argument in elementary school.

• School Mathematics
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• v.15 no.2
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• pp.481-501
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• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.