• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권1호
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• pp.31-50
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• 2012

The present study explored whether the implementation of focused activities (intervention programme) can enhance 22 pre-service mathematics teachers' proficiency in solid geometry thinking level as well as change for the better their feelings in this discipline. Over a period of 6 weeks the pre-service teachers participated in activities and diversified experiences with 3D shapes, using illustration aids and actual experience of building 3D shapes in relation to the various spatial thinking levels. The research objectives were to investigate whether the intervention programme, comprising task-oriented activities of solid geometry, enhance mathematics pre-service teachers' mastery of their geometric thinking levels as well as examine their feelings towards this discipline before and after the intervention programme. The findings illustrate that learners' levels of geometric thinking can be promoted, entailing control on higher thinking levels as well as a more positive attitude towards this field.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권2호
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• pp.275-290
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• 2014

This study investigated the types of the 3D geometric thinking and spatial reasoning through the observation of the 2D representing activities for representing the 3D geometrical objects with preservice secondary mathematics teachers. For this purpose, the 43 sophomoric students in college of education were divided into 10 groups and observed their group task performance on the basis of the representation they used. Observed processes were all recorded and the participants were interviewed based on the task. As a result, the role of physical object that becoming the object of geometric thinking and spatial reasoning, and diverse strategies and phenomena of the process that representing the 3D geometric figures in 2D were discovered. Furthermore, these processes of representing were assumed to be influenced by experience and study practice of students, and various forms of representing process were also discovered in the process of small group activities.

• 한국수학교육학회지시리즈A:수학교육
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• 제52권4호
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• pp.531-547
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• 2013

The purpose of the study is to examine how effects of activities using Google SketchUp on students' spatial ability and 3D geometric thinking in measuring the volume of solid figures. By comparing the results from pre- and post-tests between the experimental group and control group, we found that activities using Google SketchUp help students improve their spatial ability in the spatial orientation and visualization. In addition, more than half students in the experimental group moved from level 4 up to level 7 in thinking process of measuring the volume in terms of Battista(2004)'s levels. This study suggests that the instruction with Google SketchUp can help to improve students' spatial ability and 3D geometric thinking in the regular class in middle school. In addition, SketchUp can be an advanced technological tool to support students' self-directed learning, which create an efficient educational environment and a great opportunity to learn geometry in an effective manner.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권1호
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• pp.81-91
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• 2011

The aim of this study was to explore the grade 1-3 students' geometrical thinking level descriptors based on van Hiele level descriptors. The data were collected through collection of geometric curriculum materials such as indicators and learning standards in Basic Education Core Curriculum and mathematics textbook for grades 1-3. The findings were found that 1) Inconsistency between descriptors appeared on mathematics curriculum and Thai mathematics textbooks. 2) Using topics on textbooks as criterion for exploring 5 of 7 descriptors appeared on Thai mathematics textbook indicated geometrical thinking levels based on van Hiele's model merely level 0 (Visualization) across textbooks for grades 1-3.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권1호
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• pp.41-54
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• 2014

This study investigated the visual-mental capability of pre-service and in-service mathematics teachers as well as academicians making a career change to mathematics teachers with regard to manipulations of two geometric shapes (from 2- to 3-dimensional). Moreover, it investigated whether there are differences between the visual-mental capability of these participant groups. Findings illustrate that most of the participants demonstrate an adequate visual capability relating to the task dealing with a cube. Conversely, very low percentage of participants manifested a visual-mental capability in a task requiring the identification of a solid resulting from rotation of a square page, whose diagonal serves as the rotation axis. The study indicates that learners' high visual view should be developed in order to enhance their visual-mental capability.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제25권3호
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• pp.201-225
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• 2022

This paper details case study vignettes that focus on enhancing the teaching and learning of geometry and measurement in the elementary grades with attention to pedagogical practices for teaching through problem solving with rigor and centering equitable teaching practices. Rigor is a matter of equity and opportunity (Dana Center, 2019). Rigor matters for each and every student and yet research indicates historically disadvantaged and underserved groups have more of an opportunity gap when it comes to rigorous mathematics instruction (NCTM, 2020). Along with providing a conceptual framework that focuses on the importance of equitable instruction, our study unpacks ways teachers can leverage their deep understanding of geometry and measurement learning trajectories to amplify the mathematics through rigorous problems using multiple approaches including learning by doing, challenged-based and mathematical modeling instruction. Through these vignettes, we provide examples of tasks taught through rigorous problem solving approaches that support conceptual teaching and learning of geometry and measurement. Specifically, each of the three vignettes presented includes a task that was implemented in an elementary classroom and a vertically articulated task that engaged teachers in a professional learning workshop. By beginning with elementary tasks to more sophisticated concepts in higher grades, we demonstrate how vertically articulating a deeper understanding of the learning trajectory in geometric thinking can add to the rigor of the mathematics.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제14권3호
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• pp.219-231
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• 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).

• 과학교육연구지
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• 제47권3호
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• pp.263-272
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• 2023

예비교사가 비유클리드 기하학에서 수학적 정의를 이용한 이차곡선의 학습으로 유클리드 기하학의 다양한 개념을 어떻게 이해하고 활용할 수 있는지를 살펴본다. 본 연구에서는 D 대학교 수학교육과 3학년 수업에서 수학적 정의를 이용하여 택시기하, 민코프스키 거리공간과 같은 비유클리드 공간의 이차곡선 학습이 예비교사들에게 새로운 기하학적 개념을 습득하고 수용하는 능력 향상에 도움을 줄 수 있음을 보였다. 이러한 결과로부터 택시기하와 민코프스키 거리공간에서의 정의를 활용한 이차곡선 학습이 창의적이고 유연한 사고를 유도하여, 예비교사들의 유클리드 기하학 교육 전문성 향상에 기여할 것으로 기대된다.