• School Mathematics
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• v.7 no.4
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• pp.427-444
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• 2005

The Purpose of this study is to explore he mathematical discovery and justification of six 10th grade students through mathematical modeling activities in spreadsheet environments. The students investigated problem situations with a spreadsheet, which seem to be difficult to solve in paper and pencil environment. In spreadsheet environments, it is easy for students to form a data table and graph by inputting and copying spreadsheet formulas, and to make change specific variable by making a scroll bar. In this study those functions of spreadsheet play an important role in discovery and justification of mathematical rules which underlie in the problem situations. In modeling activities, the students could solve the problem situations and find the mathematical rules by using those functions of spreadsheets. They used two types of trial and error strategies to find the rules. The first type was to insert rows between two adjacent rows and the second was to make scroll bars connecting specific variable and change the variable by moving he scroll bars. The spreadsheet environments also help students to justify their findings deductively and convince them that their findings are true by checking various cases of the Problem situations.

• Journal of the Korean School Mathematics Society
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• v.24 no.3
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• pp.261-282
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• 2021

This study identified the meaning of mathematical justification and its characteristics for middle school math gifted students. 17 middle school math gifted students participated in questionnaires and written exams. Results show that the gifted students recognized justification in various meanings such as proof, systematization, discovery, intellectual challenge of mathematical justification, and the preference for deductive justification. As a result of justification exams, there was a difference in algebra and geometry. While there were many deductive justifications in both algebra and geometry questionnaires, the difference exists in empirical justifications: there were many empirical justifications in algebra, but there were few in geometry questions. When deductive justification was completed, the students showed satisfaction with their own justification. However, they showed dissatisfaction when they could not deductively justify the generality of the proposition using mathematical symbols. From the results of the study, it was found that justification education that can improve algebraic translation ability is necessary so that gifted students can realize the limitations and usefulness of empirical reasoning and make deductive justification.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.75-88
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• 2009

In this article it is investigated what role analysis play in the reasoning. The author suggests that the mathematical statements should be reformulated so that analysis can be activated in the reasoning.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.405-422
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• 2017

Nim games were divided into three stages : one file, two files and three files game, and inquiry activities were conducted for middle school mathematically gifted students. In the first stage, students easily found a winning strategy through deductive reasoning. In the second stage, students found a winning strategy with deductive reasoning or inductive reasoning, but found an error in inductive reasoning. In the third stage, no students found a winning strategy with deductive reasoning and errors were found in the induction reasoning process. It is found that the tendency to unconditionally generalize the pattern that is formed in the finite number of cases is the cause of the error. As a result of visually presenting the binary boxes to students, students were able to easily identify the pattern of victory and defeat, recognize the winning strategy through game activities, and some students could reach a stage of justifying the winning strategy.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.695-715
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• 2016

This study is on the teaching method for the students who belong to the same school (one, the gifted class, passed gifted education of Science High school ), 1-1, face-to-face learning (two, good students in regular classroom) with a teacher, paired learning teams (4 people, gifted classes), and group lessons (20 people, gifted classes) and using the justification analysis framework tool(PIRSO) of Kim(2010) analyzes the justification element of the students in the group classes regular polygons paper was to explore ways to improve the justification of the folding maps activities. As a result, the width of the largest polygon difficulty level appropriate to the class for gifted elementary school classes but the individual learning style of the 1-1 face-to-face with a teacher or discussion with colleagues and cooperative approach is justified, rather than the material of the study of origami activities it turned out to be more effective in improving the level of justification. Unlike the individual learning activities, the exploration for class is the need to strain in parallel to the student is selected as needed, rather than serial manner was confirmed that it is necessary to clearly present problems even from the beginning. Development of teaching through the implications obtained from this method of reconstruction activities and proposed improvement measures for questioning.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.927-941
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• 2013

In this paper, we investigate and analysis high school students' generalization of cosine rule using analogy, and we study teaching and learning methods improving students' analogical thinking ability to improve mathematical thinking process. When students can reproduce what they have learned through inductive reasoning process or analogical thinking process and when they can justify their own mathematical knowledge through logical inference or deductive reasoning process, they can truly internalize what they learn and have an ability to use it in various situations.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.

• School Mathematics
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• v.11 no.1
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• pp.55-70
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• 2009

The purpose of this study is to implement Lakatos method in the teaching and learning of geometry for middle school students. In his landmark book , Lakatos suggested the following instructional approach: an initial conjecture was produced, attempts were made to prove the conjecture, the proofs were repeatedly refuted by counterexamples, and finally more improved conjectures and refined proofs were suggested. In the study, students were selected from the high achieving students who participated in the special mathematics and science program offered by the city council of Seoul. The students were given a contradictory geometric proposition, and expected to find the cause of the fallacy. The students successfully identified the fallacy following the Lakatos method. In this process they also set up a primitive conjecture and this conjecture was justified by the proof and refutation method. Some implications were drawn from the result of the study.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.567-580
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• 2013

As integrated essay writing is performed in university entrance examinations, teachers and students recognize the importance of integrated essay, but teachers have still difficulties of teaching methods. The purpose of this study is to derive educational implications through case of mathematics instruction for integrated essay education to pre-service mathematics teachers. The content knowledge of this class is a definition of conic section in mathematics and properties of conic section in an antenna reflector. The students have to discover them using the history of math, manipulative material, paper-folding and computer simulation. In this teaching and learning process the students can realize mathematical knowledge invented by humans through history of mathematics. The students can evaluate the validity of that as create and justify a mathematical proposition. Also, the students can explain the relation between them logically and descript cause or basis convincingly in the process of justifying. We should keep our study to instructional materials and teaching methods in integrated essay education.