• Education of Primary School Mathematics
• /
• v.16 no.2
• /
• pp.123-145
• /
• 2013

This study was expected to yield the meaningful conclusions from the experimental group who took lessons based on inductive activities using GeoGebra at the beginning of proof learning and the comparison one who took traditional expository lessons based on deductive activities. The purpose of this study is to give some helpful suggestions for teaching proof to mathematically gifted elementary students. To attain the purpose, two research questions are established as follows. 1. Is there a significant difference in proof abilities between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? 2. Is there a significant difference in proof attitudes between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? To solve the above two research questions, they were divided into two groups, an experimental group of 10 students and a comparison group of 10 students, considering the results of gift and aptitude test, and the computer literacy among 20 elementary students that took lessons at some education institute for the gifted students located in K province after being selected in the mathematics. Special lesson based on the researcher's own lesson plan was treated to the experimental group while explanation-centered class based on the usual 8th grader's textbook was put into the comparison one. Four kinds of tests were used such as previous proof ability test, previous proof attitude test, subsequent proof ability test, and subsequent proof attitude test. One questionnaire survey was used only for experimental group. In the case of attitude toward proof test, the score of questions was calculated by 5-point Likert scale, and in the case of proof ability test was calculated by proper rating standard. The analysis of materials were performed with t-test using the SPSS V.18 statistical program. The following results have been drawn. First, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in proof ability than the comparison group who took traditional proof lessons. Second, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in the belief and attitude toward proof than the comparison group who took traditional proof lessons. Third, the survey about 'the effect of inductive activities using GeoGebra on the proof' shows that 100% of the students said that the activities were helpful for proof learning and that 60% of the reasons were 'because GeoGebra can help verify processes visually'. That means it gives positive effects on proof learning that students research constant character and make proposition by themselves justifying assumption and conclusion by changing figures through the function of estimation and drag in investigative software GeoGebra. In conclusion, this study may provide helpful suggestions in improving geometry education, through leading students to learn positive and active proof, connecting the learning processes such as induction based on activity using GeoGebra, simple deduction from induction(i.e. creating a proposition to distinguish between assumptions and conclusions), and formal deduction(i.e. proving).

• Journal of the Korean School Mathematics Society
• /
• v.9 no.4
• /
• pp.521-538
• /
• 2006

The purpose of this study is to examine the effect of teaching mathematical proofs that made use of the 'proof assisted cards' at the second year of middle school and to investigate students' ability to geometric proofs as well as changes of mathematical attitudes toward geometric proofs. The subjects are seven students at the 2nd year of D Middle School in Daegu who made use of the 'proof assisted cards' during five class periods. The researcher interviewed the students to investigate learning questions made by students as well as the 'proof assisted cards' before and after use. The findings are as follows: first, the students made change of geometric proof ability by proof activity with the 'proof assisted cards' and second, the students made significant change of mathematical attitudes toward geometric proofs by proof activity using the cards.

• Journal of Educational Research in Mathematics
• /
• v.8 no.1
• /
• pp.291-298
• /
• 1998

This study deals with the problem of proof education in the middle school geometry bby examining van Hiele#s geometric thought level theory and Freudenthal#s mathematization teaching theory. The implications that have been revealed by examining the theory of van Hie이 and Freudenthal are as follows. First of all, the proof education at present that follows the order of #definition-theorem-proof#should be reconsidered. This order of proof-teaching may have the danger that fix the proof education poorly and formally by imposing the ready-made mathematics as the mere record of proof on students rather than suggesting the proof as the real thought activity. Hence we should encourage students in reinventing #proving#as the means of organization and mathematization. Second, proof-learning can not start by introducing the term of proof only. We should recognize proof-learning as a gradual process which forms with understanding the meaning of proof on the basic of the various activities, such as observation of geometric figures, analysis of the properties of geometric figures and construction of the relationship among those properties. Moreover students should be given this natural ground of proof.

• Research in Mathematical Education
• /
• v.13 no.3
• /
• pp.217-233
• /
• 2009

The purpose of this study is to describe how dynamic geometry systems can be useful in proof activity; teaching sequences based on the use of dynamic geometry systems and to analyze the possible roles of dynamic geometry systems in both teaching and learning of proof. And also dynamic geometry environments can generate powerful interplay between empirical explorations and formal proofs. The point of this study was to show that how using dynamic geometry software can provide an opportunity to link between empirical and deductive reasoning, and how such software can be utilized to gain insight into a deductive argument.

• School Mathematics
• /
• v.4 no.1
• /
• pp.1-13
• /
• 2002

The purpose of this study is to investigate the reasons and backgrounds of drawing auxiliary lines in the proof of geometry. In most of proofs in geometry, drawing auxiliary lines provide important clues, thus they play a key role in deductive proof. However, many student tend to have difficulties of drawing auxiliary lines because there seems to be no general rule to produce auxiliary lines. To alleviate such difficulties, informal activities need to be encouraged prior to draw auxiliary lines in rigorous deductive proof. Informal activities are considered to be contrasting to deductive proof, but at the same time they are connected to deductive proof because each in formal activity can be mathematically represented. For example, the informal activities such as fliping and superimposing can be mathematically translated into bisecting line and congruence. To elaborate this idea, some examples from the middle school mathematics were chosen to corroborate the relation between informal activities and deductive proof. This attempt could be a stepping stone to the discussion of how to teach auxiliary lines and deductive reasoning.

• Fashion & Textile Research Journal
• /
• v.21 no.5
• /
• pp.665-676
• /
• 2019

This study provides basic data for future design proposals aimed at improving the uniforms and bullet/stab proof garments of local police. An analysis was conducted on various aspects of the uniforms used until 2015 and those newly introduced in 2016. Current bullet/stab proof garments were compared with old stab proof garments; in addition, police force posting on the internal SNS were analyzed in regards to the improvement needs for uniforms. Analyses results are as follows. As for the uniforms, convenience was improved by eliminating the necktie, and the four trigrams embroidery was added to emphasize the Korean identity. Cargo-style pants were added for enhanced activity, and the color of the top was changed to turquoise to improve discrimination. In terms of material, durable polyester was used heavily in outside uniforms that were likely to be damaged during work; consequently, the percentage of elastic materials was increased for improved activity. The price showed a high increase rate due to inflation and the use of functional new materials. Complaints and demands for improvement continued despite various modifications made to uniforms and suggested a strong need for further improvements that reflected the opinions of wearers. As for the protective garments, there was a limit to reducing the final weight despite the use of lightweight material because of protection performance enhancements made from expanding the protection surface area. Also, considering further decrease in supply rate, it was deemed necessary to secure budget for full supply of bullet/stab proof garments.

• East Asian mathematical journal
• /
• v.31 no.4
• /
• pp.459-481
• /
• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.

• School Mathematics
• /
• v.13 no.3
• /
• pp.501-524
• /
• 2011

The purpose of this study was to develop teaching-learning materials for informal activities geared toward teaching the nature and structure of proof, to make a case analysis of the application of the developed instructional materials to students in an elementary gifted class, to discuss the feasibility of proof education for gifted elementary students and to give some suggestions on that proof education. It's ultimately meant to help improve the proof abilities of elementary gifted students. After the characteristics of the eight selected gifted elementary students were analyzed, instructional materials of nine sessions were developed to let them learn about the nature and structure of proof by utilizing informal activities. And then they took a lesson two times by using the instructional materials, and how they responded to that education was checked. An analysis framework was produced to assess how they solved the given proof problems, and another analysis framework was made to evaluate their understanding of the structure and nature of proof. In order to see whether they showed any improvement in proof abilities, their proof abilities and proof attitude were tested after they took lessons. And then they were asked to write how they felt, and there appeared seven kinds of significant responses when their writings were analyzed. Their responses proved the possibility of proof education for gifted elementary students, and seven suggestions were given on that education.

• Journal of the Korean Society of Physical Medicine
• /
• v.13 no.2
• /
• pp.1-9
• /
• 2018

PURPOSE: This study investigated the relationship between the daily physical activity level and fall-proof-related fitness in older female adults. METHODS: This study promoted and sampled the subjects who participated in the study for 2 weeks, and developed a basic information questionnaire to select the subjects to be excluded from the research. The amount of energy expenditure through daily physical activity was examined, and the elderly physical fitness, and balance test were analyzed. The subjects were divided into group A (${\geq}1,500kcal/week$), group B (<$1,500-{\geq}1,000kcal/week$), and group C (<1,000 kcal/week) according to their daily physical activity level. RESULTS: A significant difference in the daily physical activity level (energy expenditure), Chair Stand Test (lower body strength), 8-Foot Up-and Go Test (dynamic balance), and CTSIB-M (modified Clinical Test of Sensory Interaction in Balance) was observed among groups A, B, and C (p<.5), but there was no significant difference in the Chair Sit-and-Reach Test (lower body flexibility) (p>.5). CONCLUSION: The increase in physical activity is an essential factor for preventing falls and it provides many health benefits for the elderly. On the other hand, considering that elderly people cannot access exercise programs easily in Korea, it can be predicted that increasing elderly people's physical activity in daily life rather than specific exercises may help prevent falls.

• Journal of Educational Research in Mathematics
• /
• v.21 no.2
• /
• pp.105-120
• /
• 2011

This research intends to analyse how mathematically gifted 8th graders (age 14) discover and proof the properties on the sum of face angles of polyhedron. In this research, the problems on the sum of face angles of polyhedrons were given to 36 gifted students, and their discovery and proof processes were analysed on the basis of their the activity sheets and the researcher's observation. The discovery and proof processes the gifted students made were categorized, and levels revealed in their processes were analysed.