• The Mathematical Education
• /
• v.47 no.4
• /
• pp.519-543
• /
• 2008

The study has been conducted with 29 children from 4th to 6th grades to realize how they understand addition, subtraction, multiplication, and division of whole numbers, and how their understanding influences solving of one-step word problems. Children's understanding of operations was categorized into "adding" and "combination" for additions, "taking away" and "comparison" for subtractions, "equal groups," "rectangular arrange," "ratio," and "Cartesian product" for multiplications, and "sharing," "measuring," "comparison," "ratio," "multiplicative inverse," and "repeated subtraction" for divisions. Overall, additions were mostly understood additions as "adding"(86.2%), subtractions as "taking away"(86.2%), multiplications as "equal groups"(100%), and divisions as "sharing"(82.8%). This result consisted with the Fischbein's intuitive models except for additions. Most children tended to solve the word problems based on their conceptual structure of the four arithmetic operations. Even though their conceptual structure of arithmetic operations helps to better solve problems, this tendency resulted in wrong solutions when problem situations were not related to their conceptual structure. Children in the same category of understanding for each operations showed some common features while solving the word problems. As children's understanding of operations significantly influences their solutions to word problems, they needs to be exposed to many different problem situations of the four arithmetic operations. Furthermore, the focus of teaching needs to be the meaning of each operations rather than computational algorithm.

• Honam Mathematical Journal
• /
• v.1 no.1
• /
• pp.21-25
• /
• 1979

Abelian군(群)의 presheaf에 관한 직적(直積)과 직화(直和)를 Category 입장에서 정의(定義)하고 presheaf $F_{\lambda}\;({\lambda}{\epsilon}{\Lambda})$들의 두 직적(直積)(또는 直和)은 서로 동형적(同型的) 관계(關係)에 있으며, 특히 ${\phi}:X{\rightarrow}Y$가 homeomorphism이라 하고 ${\phi}_*F$를 X상(上)의 presheaf F의 direct image이라 하면 (1) $({\phi}_*F, \;{\phi}_*(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직적(直積)일 때 오직 그때 한하여 $(F,\;(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직적(直積)이다. (2) $({\phi}_*F,\;{\phi}_*(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직화(直和)일 때 오직 그때 한하여 $(F,\;(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직화(直和)이다. Let $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ be an indexed set of presheaves of abelian group on topological space X. We can define the cartesian product $$\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda}$$ of $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ by $$(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U)=\prod_{{\lambda}{\epsilon}{\Lambda}}(F_{\lambda}(U))$$ for U open in X $${\rho}_v^u:\;(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U){\rightarrow}(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(V)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}(_{\lambda}{\rho}_v^u(s_{\lambda}))_{{\lambda}{\epsilon}{\Lambda}})$$ for $V{\subseteq}U$ open in X where $_{\lambda}{\rho}^U_V$ is a restriction of $F_{\lambda}$, And we have natural presheaf morphisms ${\pi}_{\lambda}$ and ${\iota}_{\lambda}$ such that ${\pi}_{\lambda}(U):\;({\prod}_\;F_{\lambda})(U){\rightarrow}F_{\lambda}(U)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}s_{\lambda})$ ${\iota}_{\lambda}(U):\;F_{\lambda}(U){\rightarrow}({\prod}\;F_{\lambda})(U)(s_{\lambda}{\rightarrow}(o,o,{\cdots}\;{\cdots}o,s_{\lambda},o,{\cdots}\;{\cdots}o)$ for $(s_{\lambda}){\epsilon}{\prod}_{\lambda}\;F_{\lambda}(U)$ and $(s_{\lambda}){\epsilon}F_{\lambda}(U)$.

• Economic and Environmental Geology
• /
• v.46 no.4
• /
• pp.301-312
• /
• 2013

Landslides are caused by complex interaction among a large number of interrelated factors such as topography, geology, forest and soils. In this study, a comparative study was carried out using fuzzy relationship method and artificial neural network to evaluate landslide susceptibility. For landslide susceptibility mapping, maps of the landslide occurrence locations, slope angle, aspect, curvature, lithology, soil drainage, soil depth, soil texture, forest type, forest age, forest diameter and forest density were constructed from the spatial data sets. In fuzzy relation analysis, the membership values for each category of thematic layers have been determined using the cosine amplitude method. Then the integration of different thematic layers to produce landslide susceptibility map was performed by Cartesian product operation. In artificial neural network analysis, the relative weight values for causative factors were determined by back propagation algorithm. Landslide susceptibility maps prepared by two approaches were validated by ROC(Receiver Operating Characteristic) curve and AUC(Area Under the Curve). Based on the validation results, both approaches show excellent performance to predict the landslide susceptibility but the performance of the artificial neural network was superior in this study area.

• School Mathematics
• /
• v.7 no.2
• /
• pp.103-121
• /
• 2005

This article compares and analyzes mathematics textbooks of North Korea, South Korea, China and Japan and draws meaningful ways for introducing the division algorithm of fractions. The analysis is based on the five contexts: 'measurement division', 'determination of a unit rate', 'reduction of the quantities in the same measure', 'division as the inverse of multiplication or Cartesian product', 'analogy with multiplication algorithm of fractions'. The main focus of the analysis is what context is used to introduce the algorithm and how much it can appeal to students. This analysis supports that there is a few differences of introducing methods the division algorithm of fractions among those countries and more meaningful way can be considered than ours. It finally suggests that we teach the algorithm in a way which can have students easily see the reason of multiplying the reciprocal of a divisor when they divide with fractions. For this, we need to teach the meaning of a reciprocal of fraction and consider to use the context of determination of a unit rate.

• Journal of Biosystems Engineering
• /
• v.28 no.6
• /
• pp.517-524
• /
• 2003

There have been worldwide research and development efforts to automate various processes of bio-production and those efforts will be expanded with priority given to tasks which require high intensive labor or produce high value-added product and tasks under hostile environment. In the field of bio-production capabilities of the versatility and robustness of automated system have been major bottlenecks along with economical efficiency. This paper introduces a new concept of automation based on tole-operation, which can provide solutions to overcome inherent difficulties in automating bio-production processes. Operator(farmer), computer, and automatic machinery share their roles utilizing their maximum merits to accomplish given tasks successfully. Among processes of greenhouse watermelon cultivation tasks such as pruning, watering, pesticide application, and harvest with loading were chosen based on the required labor intensiveness and functional similarities to realize the proposed concept. The developed system was composed of 5 major hardware modules such as wireless remote monitoring and task control module, wireless remote image acquisition and data transmission module, gantry system equipped with 4 d.o.f. Cartesian type robotic manipulator, exchangeable modular type end-effectors, and guided watermelon loading and storage module. The system was operated through the graphic user interface using touch screen monitor and wireless data communication among operator, computer, and machine. The proposed system showed practical and feasible way of automation in the field of volatile bio-production process.

• Journal of KIISE:Databases
• /
• v.35 no.1
• /
• pp.54-66
• /
• 2008

A spatio-temporal join is an expensive operation that is commonly used in spatio-temporal database systems. In order to generate an efficient query plan for the queries involving spatio-temporal join operations, it is crucial to estimate accurate selectivity for the join operations. Given two dataset $S_1,\;S_2$ of discrete data and a timestamp $t_q$, a spatio-temporal join retrieves all pairs of objects that are intersected each other at $t_q$. The selectivity of the join operation equals the number of retrieved pairs divided by the cardinality of the Cartesian product $S_1{\times}S_2$. In this paper, we propose aspatio-temporal histogram to estimate selectivity of spatio-temporal join by extending existing geometric histogram. By using a wide spectrum of both uniform dataset and skewed dataset, it is shown that our proposed method, called Spatio-Temporal Histogram, can accurately estimate the selectivity of spatio-temporal join. Our contributions can be summarized as follows: First, the selectivity estimation of spatio-temporal join for discrete data has been first attempted. Second, we propose an efficient maintenance method that reconstructs histograms using compression of spatial statistical information during the lifespan of discrete data.