• Journal of Educational Research in Mathematics
• /
• v.19 no.4
• /
• pp.479-491
• /
• 2009

This paper researches the possibility of introducing Descartes' theorem to mathematically gifted students. Not only is Descartes' theorem logically equivalent to Euler's theorem but is hierarchically connected with Gauss-Bonnet theorem which is the core concept on differential geometry. It is possible to teach mathematically gifted students Descartes' theorem by generalizing mathematical property in solid geometry through analogical reasoning, that is, so in a polyhedrons the sum of the deficient angles is $720^\circ$ as in an polygon the sum of the exterior angles is $360^\circ$. This study introduces an alternative method of instruction that we enable mathematically gifted students to reinvent Descartes' theorem through analogical reasoning instead of deductive reasoning.

• The Mathematical Education
• /
• v.58 no.2
• /
• pp.161-185
• /
• 2019

This study aims to examine pre- and in-service mathematics teachers' reasoning and how they justify their reasoning. For this purpose, we developed a set of mathematical tasks that are based on mathematical contents for middle grade students and conducted the survey to pre- and in-service teachers in Korea. Twenty-five pre-service teachers and 8 in-service teachers participated in the survey. The findings from the data analysis suggested as follows: a) the pre- and in-service mathematics teachers seemed to be very dependent of the manipulation of algebraic expressions so that they attempt to justify only by means of procedures such as known algorithms, rules, facts, etc., rather than trying to find out a mathematical structure in the first instance, b) the proof that teachers produced did not satisfy the generality when they attempted to justify using by other ways than the algebraic manipulation, c) the teachers appeared to rely on using formulas for finding patters and justifying their reasoning, d) a considerable number of the teachers seemed to stay at level 2 in terms of the proof production level, and e) more than 3/4 of the participating teachers appeared to have difficulty in mathematical reasoning and proof production particularly when faced completely new mathematical tasks.

• Journal of Digital Convergence
• /
• v.12 no.6
• /
• pp.549-557
• /
• 2014

The learning application of the rotating object utilizing smart devices, it is possible by using the touch functionality and 3D graphics to enhance the realism and operational feeling, and to overcome the limitations of learning content existing. In this study, I designed a "rotation class" based on the learning contents of elementary and middle mathematics education and developed the learning application which driven by smart Android-based device by using Andoroid API class and the OpenGL ES Because this application is driven by the smart devices, learners easily can make the rotated objects and observe them. It can be utilized in various for elementary and middle education.

• Journal of the Korean School Mathematics Society
• /
• v.25 no.1
• /
• pp.1-17
• /
• 2022

The goal of this study was to analyze students' views about statistical themes in Mongolian secondary schools in Ulaanbaatar. To this end, 129 9th grade students were stratified random sampling at two secondary schools in Ulaanbaatar, Mongolia, and a survey was conducted on them. The attitude survey focused on six factors contributing to the attitude: affective, cognitive competency, value, difficulty, interest, and student effort. The results show that students believed their statistical knowledge and skills have increased compared to the beginning of the courses. Furthermore, the survey revealed that they perceived statistics as neither an easy nor a difficult subject. Students' interest in statistics was neutral in general. These results suggest a need to develop effective and innovative statistical teaching and learning methods that can attract attention to statistical topics.

• East Asian mathematical journal
• /
• v.34 no.4
• /
• pp.429-449
• /
• 2018

The purpose of this study is to investigate how the mathematical creativity of middle school mathematical gifted students is represented through the process of problem posing activities. For this goal, they were asked to pose real-world problems similar to the tasks which had been solved together in advance. This study demonstrated that just 2 of 15 pupils showed mathematical giftedness as well as mathematical creativity. And selecting mathematically creative and gifted pupils through creative problem-solving test consisting of problem solving tasks should be conducted very carefully to prevent missing excellent candidates. A couple of pupils who have been exerting their efforts in getting private tutoring seemed not overcoming algorithmic fixation and showed negative attitude in finding new problems and divergent approaches or solutions, though they showed excellence in solving typical mathematics problems. Thus, we conclude that it is necessary to incorporate problem posing tasks as well as multiple solution tasks into both screening process of gifted pupils and mathematics gifted classes for effective assessing and fostering mathematical creativity.

• Journal of the Korean School Mathematics Society
• /
• v.15 no.1
• /
• pp.183-197
• /
• 2012

Geometry having long history of mathematics have important role for thinking power and creativity progress in middle school. The regular polygon included in plane geometry was mainly taught convex regular polygon in elementary school and middle school. In this study, we investigated the denotation's extension of regular polygon by mathematical basic knowledge included in school curriculum. For this research, first, school mathematical knowledge about regular polygon was analyzed. And then, basic direction of research was established for inquiry. Second, based on this analysis inductive inquiry activity was performed with research using geometry software(Cabri Geometry II). Through this study the development of enriched learning material and showing the direction of geometry research is expected.

• School Mathematics
• /
• v.18 no.1
• /
• pp.43-59
• /
• 2016

The purpose of this qualitative case study is to investigate differences among two gifted middle school students emerging through the process of algebra word problem solving from the covariational perspective. We collected the data from four middle school students participating in the mentorship program for gifted students of mathematics and found out differences between Junghee and Donghee in solving problems involving varying rates of change. This study focuses on their actions to solve and to generalize the problems situations involving constant and varying rates of change. The results indicate that their covariational reasoning played a significant role in their algebra word problem solving.

• Journal for History of Mathematics
• /
• v.21 no.4
• /
• pp.105-126
• /
• 2008

This article summarizes the historical changes of the secondary school geometry to give insights into the new direction of geometry education for the 21th century. Geometry has been considered as an essential subject in high school since mid-nineteen century in accordance with the social changes. Since the development of computer softwares such as CAD effects on the role of geometry in work and professional societies, the knowledge and skills the contemporary world require to school geometry have being changed. More focus on applications and modeling aspects, expansion of reasoning and problem solving, emphasis on design-related elements are features of the school geometry for the new century.

• East Asian mathematical journal
• /
• v.39 no.2
• /
• pp.141-166
• /
• 2023

The purpose of this study is to confirm the MKT(Mathematical Knowledge for Teaching) of the in-service mathematics teachers on the statistics(Representative value, Degree of scattering) through the comparative analysis between the sub-elements of the MKT. In addition, it is to examine the factors that cause the difference of the subjects' MKT. To accomplish this, by the subject of 12 secondary in-service mathematics teachers, in this study the test items of the MKT on the statistics were developed and data were collected and analyzed. As a result of the analysis of the MKT test sheet, the CCK(Common Content Knowledge) and SCK(Specialized Content Knowledge) of the mathematics teacher was confirmed as a high score, whereas the and KCS(Knowledge of Content and Students) and KCT(Knowldge of Curriculum and teaching) were confirmed as low scores. In addition, through these results, it was shown that the difference in MKT's elements the middle school and high school teachers obtain occurred slightly.

• Journal of Educational Research in Mathematics
• /
• v.25 no.4
• /
• pp.599-615
• /
• 2015

Teachers' philosophies have not been emphasized enough in the current teacher education curriculum even though teacher's philosophy palys a critical role in schools and classrooms. The examination on pre-service teachers' teaching philosophies is necessary to improve teacher education curriculum so that teaching philosophies are often discussed in the courses of 'pedagogical content knowledge' as well as 'general education.' Therefore, the current study investigated 44 pre-service teachers' teaching philosophies, their sub domains, and relationships among the sub domains. The previous studies regarding mathematics teacher's teaching philosophy were more about 'teacher's belief' and employed deductive inference approach using surveys or questionnaires. These studies commonly pointed out that there were three major domains of 'belief on mathematics itself,' 'belief on teaching mathematics,' and 'belief on learning mathematics.' As these three domains of teacher's philosophy has been strengthened, there were very few studies examining the other potential domains of teacher's teaching philosophy. According to the findings of the present study, which employed inductive inference approach and pre-service teachers' free essay writing assignment, 'belief on teacher's role in mathematics classroom,' 'belief on the purpose of mathematics education,' and 'motivation to be a mathematics teacher' were additionally illuminated as sub domains of teacher's teaching philosophy. Moreover, the interrelationship among the sub-areas of teacher's teaching philosophy was disclosed. Specifically, 'belief on the purpose of mathematics education' and 'motivation to be a mathematics teacher' influenced the other sub domains. This implies that the relationships among the sub domains of teacher's teaching philosophy were more likely to be causal and vertical relationships rather than independent and parallel relationships. Finally, the findings from the current study provide implications indicating how pre-service teachers' teaching philosophies might be established in mathematics education courses for future research and education.