• Research in Mathematical Education
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• v.7 no.4
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• pp.211-222
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• 2003

Recursive thinking is iterative, self-referential, and building on itself continuously. Moreover, it is becoming a more prominent feature of the mathematical scope because of the availability of computers and languages like Logo, Excel, and Pascal that support recursion. This study investigates the way to create students' recursive thinking in mathematics classroom and to use various methods to solve problems using a spreadsheet, the Excel program where technology could be accessible.

• The Mathematical Education
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• v.58 no.2
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• pp.319-335
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• 2019

In this paper, we examine the effectiveness of calculation according to automation, which is one of Computational Thinking, by coding the conceptual process into Python language, focusing on the concept of divisibility in elementary school textbooks. The educational implications of these considerations are as follows. First, it is possible to make a field of learning that can revise the new mathematical concept through the opportunity to reinterpret the Conceptual Thinking learned in school mathematics from the perspective of Computational Thinking. Second, from the analysis of college students, it can be seen that many students do not have mathematical concepts in terms of efficiency of computation related to the divisibility. This phenomenon is a characteristic of the mathematics curriculum that emphasizes concepts. Therefore, it is necessary to study new mathematical concepts when considering the aspect of utilization. Third, all algorithms related to the concept of divisibility covered in elementary mathematics textbooks can be found to contain the notion of iteration in terms of automation, but little recursive activity can be found. Considering that recursive thinking is frequently used with repetitive thinking in terms of automation (in Computational Thinking), it is necessary to consider low level recursive activities at elementary school. Finally, it is necessary to think about mathematical Conceptual Thinking from the point of view of Computational Thinking, and conversely, to extract mathematical concepts from computer science's Computational Thinking.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.2
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• pp.75-79
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• 2017

This paper approaches the subject of consciousness and unconsciousness from a mathematical point of view. It sets up a hypothesis that when unconscious state becomes conscious state, high density energy is released. We argue that the process of transformation of unconsciousness into consciousness can be expressed using the infinite recursive Heaviside step function. We claim that differentiation of the potential of unconsciousness with respect to time is the process of being conscious in a world where only time exists, since the thinking process never have any concrete space. We try to attribute our unconsciousness to a special solution of the multi-dimensional advection partial differential equation which can be represented by the finite recursive Heaviside step function. Mathematical language explains how the infinitive neural process is perceived and understood by consciousness in a definitive time.

• English Language & Literature Teaching
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• v.11 no.2
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• pp.67-89
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• 2005

Writing is a difficult skill for many people, both for children and adult alike and generally most people find it difficult to write down their thoughts effectively. Numerous studies have revealed that teachers find it frustrating to teach writing and many failed to help ESL students develop their writing ability. The theoretical emphasis on process oriented writing instruction has, in general brought about positive changes in the way writing is taught and has become widely accepted in the teaching of English as a second or foreign language (ESL/EFL). Although the interpretation and implementation of the process approach varies considerably from instructor to instructor, nevertheless, the emphasis on process writing has brought about significant and beneficial changes in teachers' orientations to writing. Despite the theoretical recognition of writing as a recursive process, many ESL/EFL classrooms continue to teach writing as a linear sequence of planning, pre-writing, writing, revising and editing and has not enhanced ESL/EFL students writing ability to the desired level. There appears to be a missing link in helping students to crystallize their thoughts before writing. Studies have shown that incorporating visual thinking tools into the process approach of ESL writing can enhance students' ability to write. This paper reports the findings of an exploratory study on the effects of using visual thinking tools in enhancing ESL students writing.

• The Journal of Korean Association of Computer Education
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• v.21 no.6
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• pp.39-47
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• 2018

This paper dealt with investigating the number of minimal spanning ladders originated from ladder game and their properties as well as the related computational thinking aspects. The author modified the filtering techniques to enhance Mathematica project where a new type of graph was generated based on the algorithm using a generator of firstly found minimal spanning graph by repeatedly applying independent ladder operator to a subsequence of ladder sequence. The newly produced YC graphs had recursive and hierarchical graph structures and showed the properties of edge-symmetric. As the computational complexity increased the author divided the whole search space into the each floor of the newly generated minimal spanning graphs for the (5, 10) YC graph and the higher (6, 15) YC graph. It turned out that the computational thinking capabilities such as data visualization, abstraction, and parallel computing with Mathematica contributed to enumerating the new YC graphs in order to investigate their structures and properties.

• School Mathematics
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• v.18 no.4
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• pp.793-818
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• 2016

The purpose of this study is to explore in detail $5^{th}$ grade students' understanding on the big ideas related to addition of fraction with different denominators: fixed whole unit, necessity of common measure, and recursive partitioning connected to algorithms. We conducted teaching experiments on 15 fifth grade students who had learned about addition of fractions with different denominators using the current textbook. Most students approached to the big ideas related to addition of fractions in a procedural way. However, some students were able to conceptually understand the interpretations and algorithms of fraction addition by quantitatively thinking about the context and focusing on the structures of units. Building on these results, this study is expected to suggest specific implications on instruction methods for addition of fractions with different denominators.

• Journal of Science Education
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• v.33 no.1
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• pp.12-30
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• 2009

The purpose of this study was to analyze recognition characteristics of science gifted students on the earth system based on their thinking style. The subjects were 24 science gifted students at the Science Institute for Gifted Students of a university located in metropolitan city in Korea. The students' thinking styles were firstly examined on the basis of the Sternberg's theory of mental self-government. And then, the students were divided into two groups: Type I group(legislative, judicial, global, liberal) and Type II group(executive, local, conservative) based on Sternberg's theory. Data was collected from three different type of questionnaires(A, B, C types), interview, word association method, drawing analyses, concept map, hidden dimension inventory, and in-depth interviews. The findings of analysis indicated that their thinking styles were characterized by 'Legislative', 'Executive', 'Anarchic', 'Global', 'External', 'Liberal' styles. Their preference were conducting new projects and using creative problem solving processes. The results of students' recognition characteristics on earth system were as follows: First, though the two groups' quantitative value on 'System Understanding' was very similar, there were considerable distinctions in details. Second, 'Understanding the Relationship in the System' was closely connected to thinking styles. Type I group was more advantageous with multiple, dynamic, and recursive approach. Third, in the relation to 'System Generalization' both of the groups had similar simple interpretational ability of the system, but Type I group was better on generalization when 'hidden dimension inventory' factor was added. On the system prediction factor, however, students' ability was weak regardless of the type. Consequently, more specific development strategies on various objects are needed for the development and application of the system learning program. Furthermore, it is expected that this study could be practically and effectively used on various fields related to system recognition.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2022.05a
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• pp.22-24
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• 2022

Recently, Graph Database (GDB) is being used in wide range of industrial fields. GDB is a database system which adopts graph structure for storing the information. GDB handles the information in the form of a graph which consists of vertices and edges. In contrast to the relational database system which requires pre-defined table schema, GDB doesn't need a pre-defined structure for storing data, allowing a very flexible way of thinking about and using the data. With GDB, we can handle a large volume of heavily interconnected data. A network service provider provides its services based on the heavily interconnected communication network facilities. In many cases, their information is hosted in relational database, where it is not easy to process a query that requires recursive graph traversal operation. In this study, we suggest a way to store an example set of interconnected network facilities in GDB, then show how to graph-query them efficiently.