• Education of Primary School Mathematics
• /
• v.20 no.1
• /
• pp.53-68
• /
• 2017

Although the table, as one of the representations for helping mathematics understanding, steadily has been shown in the mathematics textbooks, there have been little studies that focus on the table and analyze how the table may be used in understanding students' functional thinking. This study investigated the elementary school 5th graders' abilities to design function tables. The results showed that about 75% of the students were able to create tables for themselves, which shaped horizontal and included information only from the problem contexts. And the students had more difficulties in solving geometric growing pattern problems than story problems. Building on these results, this paper is expected to provide implications of instructional directions of how to use the table as 'function table'.

• Research in Mathematical Education
• /
• v.14 no.3
• /
• pp.219-231
• /
• 2010

Mathematically, a proof is to create a convincing argument through logical reasoning towards a given proposition or a given statement. Mathematics educators have been working diligently to create environments that will assist students to perform proofs. One of such environments is the use of dynamic-geometry-software in the classroom. This paper reports on a case study and intends to probe into students' own thinking, patterns they used in completing certain tasks, and the extent to which they have utilized technology. Their tasks were to explore the shape-to-shape, shape-to-part, and part-to-part interrelationships of geometric objects when dealing with certain geometric problem-solving situations utilizing dissection-motion-operation (DMO).

• Journal of Educational Research in Mathematics
• /
• v.11 no.1
• /
• pp.89-102
• /
• 2001

Computer has been regarded as an alternative that could overcome the difficulties in the teaching and learning of mathematics. But the didactical problems of the computer-based environment for mathematics education could give us new obstacles. In this paper, first of all, we examined the application of the learning theories of mathematics to the computer environment. If the feedbacks of the computer are too immediate, students would have less opportunity to reflect on their thinking and focus their attention on the visual aspects, which leads to the simple abstraction rather than the reflective abstraction. We also examined some other Problems related to cognitive obstacle to learn the concepts of geometric figure and the geometric knowledge. Based on the analysis on the problems related to the computer-based environment of mathematics teaching and learning, we tried to find out the direction to use computer more adequately in teaching and learning geometry.

• School Mathematics
• /
• v.4 no.3
• /
• pp.347-360
• /
• 2002

This study analyzed the mathematical and didactical contexts of the Euclid's proof about Pythagorean theorem and compared with the teaching methods about Pythagorean theorem in school mathematics. Euclid's proof about Pythagorean theorem which does not use the algebraic methods provide students with the spatial intuition and the geometric thinking in school mathematics. Furthermore, it relates to various mathematical concepts including the cosine rule, the rotation, and the transfor-mation which preserve the area, and so forth. Visual demonstrations can help students analyze and explain mathematical relationship. Compared with Euclid's proof, Algebraic proof about Pythagorean theorem is very simple and it supplies the typical example which can give the relationship between algebraic and geometric representation. However since it does not include various spatial contexts, it forbid many students to understand Pythagorean theorem intuitively. Since both approaches have positive and negative aspects, reciprocal complementary role is required in pedagogical aspects.

• Journal of Educational Research in Mathematics
• /
• v.15 no.3
• /
• pp.273-286
• /
• 2005

We teach students to explore geometric figures by its properties and establish relationships between some basic figures. The concept of parallel line play very im-portant roles in such geometry learning process. In this study, 1 investigate the con-cept of parallel line we teaching in elementary school. Students have wrong concept images for parallel line, which is the result of the elementary school mathematics text books, where only typical cases for parallel line Is presented and there is no method to find if two lines is parallel or not. Therefore, we should teach explicitly students to find if two lines is parallel or not. The depth study on it is needed to develope students' geometric thought level.

• Journal of the Architectural Institute of Korea Planning & Design
• /
• v.35 no.5
• /
• pp.107-116
• /
• 2019

Non-geometric shapes in contemporary architecture was explained from the transcendental schema of Deleuze with his abstraction theory. In this explanation, the intensity, the movement and change and the sublime were suggested as the expressional elements of the transcendental abstraction related with the artistic sensation of architecture. First, the intensity as a power of sensation which acts to the body before the recognition of brain is mainly expressed with the movement of curved lines of architectural space. Second, the movement of change is expressed as the de-centralized and de-formalized nomadic curve as the line in architectural 'smooth space' which has unrestrained orientations. Third, the sublime is expressed in the hugeness, enormousness or sometimes uncanny in void space, which could be contradictively mixed with senses of displeasure and pleasure. The sublime feelings in architecture can be emerging by rationally overcoming the unpleasant senses of contradictive spaces in architecture or urban fabric. This study has explained those expressional elements with the architectural works of Steven Holl, Frank Gehry and Zaha Hadid.

• The Mathematical Education
• /
• v.60 no.4
• /
• pp.543-554
• /
• 2021

The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method. In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students. The continuous spectrum can be used in the 'Understand the problem' of Polya(1957)'s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the 'Devise a plan' stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis. The continuous spectrum can be used in the 'Review/Extend' stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem. Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students' geometric learning.

• School Mathematics
• /
• v.14 no.4
• /
• pp.409-429
• /
• 2012

This paper reports the process two 11th grade students went through in reinventing derivatives on their own via a context problem involving the concept of velocity. In the reinvention process, one of the students conceived a tangent line as the limit of a secant line, and then the other student explained to a peer that the slope of a tangent line was the geometric mean of derivative. The students also used technology to concentrate on essential thinking to search for mathematical concepts and help visually understand them. The purpose of this study was to provide meaningful implications to school practices by describing students' process of reinvention of derivatives. This study revealed certain characteristics of the students' reinvention process of derivatives and changes in the students' thinking process.

• Journal of the Korea Furniture Society
• /
• v.25 no.3
• /
• pp.188-197
• /
• 2014

This study aimed to develop organic design and propose references on an origin and developing factors of the organic design as looking into previous researches on furniture design. Expressive features with curves observed in the furniture design have been interpreted as organic meanings, and the study also approached grounds for the organic design elements while talking about developments of new materials and digital technology. In addition, the study presented a possibility explaining that these organic design elements might have been derived and developed from Art Nouveau. State-of-the art technology of the digital era in the 21st century has been built upon more creative concepts, and as this technology gets combined with the digital technology, it is, now, changing but also improving both morphological aspects and design methodologies. In the midst of this change, when it comes to factors to develop the organic design, creation of various new materials and state-of-the art digital technology are considered to be immediate factors to changes in the design. As morphological thinking using digital media develops, geometric thinking and such form are realized which eventually would lead us to furniture design of a new concept.

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