• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Journal of Creative Information Culture
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• v.5 no.3
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• pp.295-306
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• 2019

Despite the popularity and convenient accessibility of puzzles, the variety of puzzles have led to a lack of research on the nature of the puzzle itself. In guiding certain skills, such as abstractness, creativity, and logic, a teacher should have the thinking skill and strategy that appear in solving puzzles. In this study, the mathematical thinking that appears in solving puzzles from the perspective of experts is identified, and the strategies and characteristics are described and classified accordingly. For this purpose, we analyzed 85 math puzzles including the well-know puzzles to the public, plus puzzles from a popular book for the gifted student. The research analysis shows that there are 6 types of mathematics puzzles in which require mathematical thinking.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.619-640
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• 2011

The study aims the introducing the items for the assessment of mathematical thinking including mathematical reasoning, problem solving, and communication and the analyzing on the responses of the 5th grade pupils. We categorized the area of mathematical reasoning into deductive reasoning, inductive reasoning, and analogy; problem solving into external problem solving and internal one; and communication into speaking, reading, writing, and listening. And we proposed the examples of our items for each area and the 5th grade pupils' responses. When we assess on pupil's mathematical reasoning, we need to develop very appropriate items needing the very ability of each kind of mathematical reasoning. When pupils solve items requesting communication, the impact of the form of each communication seem to be smaller than that of the mathematical situation or sturucture of the item. We suggested that we need to continue the studies on mathematical assessment and on the constitution and utilization of cognitive areas, and we also need to in-service teacher education on the development of mathematical assessments, based on this study.

• Journal of the Korean Chemical Society
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• v.68 no.1
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• pp.40-53
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• 2024

The study investigates the number and proportion of questions in each area by examining Chemistry I questions from the College Scholastic Ability Test from 2019 to 2022. The analysis was conducted using a three-dimensional framework that included key concepts in chemistry, behavioral domains in chemistry, and behavioral domains in mathematics. The results indicated that Chemistry I questions on the College Scholastic Ability Test had a relatively even distribution of questions across core individual topics, but highly difficult questions were predominantly biased toward stoichiometry. In terms of the behavioral domains in chemistry, there was a remarkably low proportion of questions related to problem recognition and hypothesis establishment, as well as designing research and implementing research. Conversely, highly difficult questions were more inclined towards drawing conclusions and evaluations. Regarding behavioral domains in mathematics, there was a limited number of questions addressing heuristic reasoning and deductive reasoning. On the other hand, high-difficulty questions favored internal problem-solving ability. Additionally, certain key concepts in chemistry and behavioral domains in chemistry exhibited a strong correlation with specific behavioral domains in mathematics. This characteristic was particularly evident in questions that encompassed higher-dimensional behavioral domains in mathematics, which students tend to find challenging.

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.223-237
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• 2008

In this paper, We focus on grasping De Morgan's perspectives on mathematics education systematically. His perspectives can be summarized as followings. First, historico-genesis of mathematics must be considered in the teaching and learning of mathematics. Second, mathematical conception of students must be formulated progressively. Third, it is important to use errors which come out continually in the process of passing from inductive stage to deductive stage. Fourth, personal knowledge of students is important in the teaching and learning of mathematics. These De Morgan's four perspectives are the way of approach for experiencing moral certainty first of all to get to mathematical certainty. Moral certainty which he presented is a combination of rationality and humanity to fill up gaps between Platonism and general public education.

• 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.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.101-116
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• 2005

The purpose of this study is to survey mathematics teacher's cognition of proof along with their proof forms of expression and proof ability, and to explore the relationship between their proof scheme and teaching practice. This study shows that mathematics teachers tend to regard proof as a deduction from assumption to conclusion and that they prefer formal proof with mathematical symbols. Mathematics teachers also recognize that prof is an important area in school mathematics but they reveal poor understanding of teaching methods of proof. Teachers tend to depend on the proof style employed in mathematics textbooks. This study demonstrates that a proof scheme is a major factor of determining the teaching method of proof.

• School Mathematics
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• v.15 no.2
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• pp.289-314
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• 2013

Achievement profile by attribute in Korean students' mathematics was analyzed by applying cognitive diagnostic model, which is the newest measurement theory, to 2011 NAEA(National Assessment of Educational Assessment) results. The results are as follows. As the level of school is higher from 6th grade, 9th grade to 11th grade, the percentage of students mastering cognitive attribute 9(expressions using picture, table, graph, formula, symbol, writing, etc) drastically declined from 78%, 35% to 26%. It is necessary to have learning strategies to reinforce their abilities of expressing table, graph, etc. that higher graders in mathematics are more vulnerable to. Next, the property of mastering cognitive attributes according to gender, multi-cultural family was analyzed. In terms of mathematics, the percentage of girls mastering most of the attribute generally is higher than that of boys from 6th grade to 9th grade, however, boys show higher mastery in almost attributes than girls in the 11th grade. Compared to boys, the part where girls have the most trouble is attribute 9 in mathematics(expressions using picture, table, graph, formula, symbol, writing, etc). As international marriage, influx of foreign workers, etc. increase, the number of students from Korea's multi-cultural families is expected to be higher, therefore, identifying the characteristics of their educational achievement is significant in reinforcing Korea's basic achievement. In mathematics, gap of mastery level of attributes between multi-cultural group and ordinary group is more severe in higher grade and the type of multi-cultural group that needs supports for improving achievement most urgently changed in 6th grade, 9th grade and 11th grade respectively. In the 6th and 11th grade, migrant students from North Korea show the lowest level of mastering attributes, however, in the 9th grade, the mastery rate of immigrant students is lowest. Therefore, there is an implication that supporting plans for improving achievement of students from multi-cultural family should establish other strategies based on the characteristics of school level.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.1
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• pp.1-16
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• 2015

This study investigated the analysis of examples that gifted students' realizing the learning objectives through teaching method of the teacher's questions and advice. 6 gifted students were selected to be examined with 'magic square' in class. The teacher emphasized the learning objectives without directly proposing. Whereas, the teacher proposed the learning objectives by questioning and giving advice to students. After the class, the 6 gifted students were surveyed to answer about realizing the learning objectives of mathematics (about contents, process, and attitude in mathematics learning objectives). Mathematical gifted students thought about the process that consists of deductive thinking, analogic thinking, extensive thinking, creative thinking, and critical thinking. But, they underestimated the deductive thinking. So the teacher should develop the questions and advice to teach the mathematical gifted students according to the level of them. The high level of mathematical gifted students were able to realize the value and the importance of the mathematical attitude, while the low level of mathematical gifted students were able to realize them little. For this reason, the teacher should apprehend the level of the students, and propose materials and contents of the learning. The teacher should also make the gifted students realize value, will, and personality of mathematics by questions and advice. Lastly, like it is needed in general classes, there should be a constant researches and improvements about questions of the teacher that are appropriate to each student's learning abilities and cognition ability.

• Journal of the Korean School Mathematics Society
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• v.9 no.4
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• pp.459-479
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• 2006

The purpose of this study is to investigate the applicability of DGS(dynamic geometry software) for the assessment of reasoning ability and the influence of DGS on the process of assessing students' reasoning ability in middle school geometry. We developed items for assessing students' reasoning ability by using DGS in the connected form of 'construction - inductive reasoning - deductive reasoning'. And then, a case study was carried out with 5 students. We analyzed the results from 3 perspectives, that is, the assessment of students' construction ability, inductive reasoning ability, and justification types. Items can help students more precisely display reasoning ability Moreover, using of DGS will help teachers easily construct the assessment items of inductive reasoning, and widen range of constructing items.