• School Mathematics
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• v.9 no.3
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• pp.353-373
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• 2007

The purpose of this study was to provide instructional suggestions by investigating the spatial sense and spatial reasoning ability of 6th grade students. The questionnaire consisted of 20 questions, 10 for spatial visualization and 10 for spatial orientation. The number of subjects for the survey was 145. The processes through which the students solved the problems were the basis for the assessment of their spatial reasoning. The result of the survey is as follows: First, students performed better in spatial visualization than in spatial orientation. With regard to spatial visualization, they were better in transformation than in rotation. With regard to spatial orientation, students performed better in orientation sense and structure cognitive ability than in situational sense. Second, the students that weren't excellent in spatial visualization tended to answer the familiar figures without using mental images. The students who lacked spatial orientation experienced difficulties finding figures observed from the sides. Third, students had high frequency rate on the cognition and use of transformation, the development and application of visualization methods and the use of analysis and synthesis. However they had a lower rate on a systematic approach and deductive reasoning. Further detailed investigation into how students use spatial reasoning, and apply it to actual teaching practice as a device for advancing their geometric thinking is necessary.

• Journal of Korean Elementary Science Education
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• v.40 no.3
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• pp.390-406
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• 2021

This study investigated how elementary students with different spatial ability constructed spatial thinking process about on volcanoes and earthquakes with GeoMapApp-based materials. Students' spatial thinking process was analyzed in terms of spatial concept recognized, tools of spatial representation, and their spatial reasoning to construct topographic structure. The student group with high-scored spatial ability showed the spatial reasoning based on internal representation of building mental images through sectional division of horizontal distance, directly connected with spatial concept, or distorting spatial concept. The student group with low-scored spatial ability built the spatial reasoning directly connected with spatial concept instead of transforming into internal representation, and partially recognized spatial concept on either distance or depth. Based on the results, we argued identifying spatial concepts such as distance, height, or depth from the GeoMapApp data would be funda- mental for the better spatial thinking.

• The Mathematical Education
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• v.60 no.2
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• pp.133-157
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• 2021

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.

• Annual Conference of KIPS
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• 2014.04a
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• pp.769-772
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• 2014

Jeopardy 퀴즈쇼와 같은 DeepQA 환경에서 인간을 대신해 컴퓨터가 효과적으로 답하기 위해서는 인물, 지리, 사건, 역사 등을 포함하는 광범위한 지식베이스와 이를 토대로 한 빠른 시공간 추론 능력이 필요하다. 본 논문에서는 대표적인 병렬 분산 컴퓨팅 환경인 하둡/맵리듀스 프레임워크를 이용하여 방향 및 위상 관계를 추론하는 효율적인 대용량의 공간 추론 알고리즘을 제시한다. 본 알고리즘에서는 하둡/맵리듀스 프레임워크의 특성을 고려하여 병렬 분산처리의 효과를 높이기 위해, 지식 분할 문제를 맵 단계에서 해결하고, 이것을 토대로 리듀스 단계에서 효과적으로 새로운 공간 지식을 유도하도록 설계하였다. 또한, 본 알고리즘은 초기 공간 지식베이스로부터 새로운 지식을 유도할 수 있는 기능뿐만 아니라 초기 공간 지식베이스의 불일치성도 미연에 감지함으로써 불필요한 지식 유도 작업을 계속하지 않도록 설계하였다. 본 연구에서는 하둡/맵리듀스 프레임워크로 구현한 대용량 공간 추론기와 샘플공간 지식베이스를 이용하여 성능 분석 실험을 수행하였고, 이를 통해 본 논문에서 제시한 공간 추론 알고리즘과 공간 추론기의 높은 성능을 확인 할 수 있었다.

• Journal of KIISE
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• v.42 no.5
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• pp.601-608
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• 2015

In order to answer questions successfully on behalf of the human contestant in DeepQA environments such as 'Jeopardy!', the American quiz show, the computer needs to have the capability of fast temporal and spatial reasoning on a large-scale commonsense knowledge base. In this paper, we present a hybrid spatial reasoning algorithm, among various efficient spatial reasoning methods, for handling directional and topological relations. Our algorithm not only improves the query processing time while reducing unnecessary reasoning calculation, but also effectively deals with the change of spatial knowledge base, as it takes a hybrid method that combines forward and backward reasoning. Through experiments performed on the sample spatial knowledge base with the hybrid spatial reasoner of our algorithm, we demonstrated the high performance of our hybrid spatial reasoning algorithm.

• Journal of The Korean Association For Science Education
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• v.41 no.5
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• pp.371-390
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• 2021

The purpose of this study is to develop a neuropsychological model for the spatial ability factor and to divide the brain active area involved in the light & shadow problem solving process into the domain-general ability and the domain-specific ability based on the neuropsychological model. Twenty-four male college students participated in the study to measure the synchronized eye movement and electroencephalograms (EEG) while they performed the spatial ability test and the light & shadow tasks. Neuropsychological model for the spatial ability factor and light & shadow problem solving process was developed by integrating the measurements of the participants' eye movements, brain activity areas, and the interview findings regarding their thoughts and strategies. The results of this study are as follows; first, the spatial visualization and mental rotation factors mainly required activation of the parietal lobe, and the spatial orientation factor required activation of the frontal lobe. Second, in the light & shadow problem solving process, participants use both their spatial ability as a domain-general thought, and the application of scientific principles as a domain-specific thought. The brain activity patterns resulting from a participants' inferring the shadow by parallel light source and inferring the shadow when the direction of the light changed were similar to the neuropsychological model for the spatial visualization factor. The brain activity pattern from inferring an object from its shadow by light from multiple directions was similar to the neuropsychological model for the spatial orientation factor. The brain activity pattern from inferring a shadow with a point source of light was similar to the neuropsychological model for the spatial visualization factor. In addition, when solving the light & shadow tasks, the brain's middle temporal gyrus, precentral gyrus, inferior frontal gyrus, middle frontal gyrus were additionally activated, which are responsible for deductive reasoning, working memory, and planning for action.

• Journal of KIISE
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• v.43 no.12
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• pp.1365-1375
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• 2016

One of the most important capabilities for autonomous service robots working in living environments is to recognize and understand the correct context in dynamically changing environment. To generate high-level context knowledge for decision-making from multiple sensory data streams, many technical problems such as multi-modal sensory data fusion, uncertainty handling, symbolic knowledge grounding, time dependency, dynamics, and time-constrained spatio-temporal reasoning should be solved. Considering these problems, this paper proposes an effective dynamic context management and spatio-temporal reasoning method for intelligent service robots. In order to guarantee efficient context management and reasoning, our algorithm was designed to generate low-level context knowledge reactively for every input sensory or perception data, while postponing high-level context knowledge generation until it was demanded by the decision-making module. When high-level context knowledge is demanded, it is derived through backward spatio-temporal reasoning. In experiments with Turtlebot using Kinect visual sensor, the dynamic context management and spatio-temporal reasoning system based on the proposed method showed high performance.

• KIPS Transactions on Software and Data Engineering
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• v.3 no.10
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• pp.397-406
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• 2014

In order to answer the questions successfully on behalf of the human in DeepQA environments such as Jeopardy! of the American quiz show, the computer is required to have the capability of fast temporal and spatial reasoning on a large-scale commonsense knowledge base. In this paper, we present a scalable spatial reasoning algorithm for deriving efficiently new directional and topological relations using the MapReduce framework, one of well-known parallel distributed computing environments. The proposed reasoning algorithm assumes as input a large-scale spatial knowledge base including CSD-9 directional relations and RCC-8 topological relations. To infer new directional and topological relations from the given spatial knowledge base, it performs the cross-consistency checks as well as the path-consistency checks on the knowledge base. To maximize the parallelism of reasoning computations according to the principle of the MapReduce framework, we design the algorithm to partition effectively the large knowledge base into smaller ones and distribute them over multiple computing nodes at the map phase. And then, at the reduce phase, the algorithm infers the new knowledge from distributed spatial knowledge bases. Through experiments performed on the sample knowledge base with the MapReduce-based implementation of our algorithm, we proved the high performance of our large-scale spatial reasoner.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.03a
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• pp.99-102
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• 1998

본 논문에서는 복잡하고 비선형적인 시스템의 최적 모델링을 우해서 지능형 퍼지-뉴럴네트워크의 최적 모델 구축을 위한 방법을 제안한다. 기본 모델은 퍼지 추론 시스템의 언어적인 규칙생성의 장점과 뉴럴 네트워크의 학습기능을 결합한 FNNs 모델을 사용한다. FNNs 모델의 퍼지 추론부는 간략추론이 사용되고, 학습은 요류 역전파 알고리즘을 사용하여 다른 모델들에 비해 학습속도가 빠르고 수렴능력이 우수하다. 그러나 기본 모델은 주어진 시스템에 대하여 퍼지 공간을 균등하게 분할하여 퍼지 소속을 정의한다. 이것은 비선형 시스템의 모델링에 있어어서 성능을 저하시켜 최적의 모델을 얻기가 어렵다. 논문에서는 주어진 데이터의 특성을 부여한 공간을 설정하기 위하여 클러스터링 알고리즘을 사용한다. 클러스터링 알고리즘은 주어진 시스템에 대하여 상호 연관성이 있는 데이터들끼리 특성을 나누어 몇 개의 클래스를 이룬다. 클러스터링 알고리즘을 사용하여 초기 FNNs 모델의 퍼지 공간을 나누고 소속함수를 정의한다. 또한, 최적화 기법중의 하나로 자연선택과 자연계의 유전자 메카니즘에 바탕을 둔 탐색 알고리즘인 유전자 알고리즘을 사용하여 주\ulcorner 진 모델에 대하여 최적화를 수행한다. 또한 본 연구에서는 학습 및 테스트 데이터의 성능 결과의 상호 균형을 얻기 위한 하중값을 가긴 성능지수가 제시된다.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.