• Communications for Statistical Applications and Methods
• /
• v.31 no.3
• /
• pp.309-322
• /
• 2024

Identifying algae in water is important for managing algal blooms which have great impact on drinking water supply systems. There have been various microscopic approaches developed for algae classification. Many of them are based on the morphological features of algae. However, there have seldom been mathematical frameworks for comparing the shape of algae, represented as a planar continuous curve obtained from an image. In this work, we describe a recent framework for computing shape distance between two different algae based on the elastic metric and a novel functional representation called the square root velocity function (SRVF). We further introduce statistical procedures for multiple shapes of algae including computing the sample mean, the sample covariance, and performing the principal component analysis (PCA). Based on the shape distance, we classify six algal species in watersheds experiencing algal blooms, including three cyanobacteria (Microcystis, Oscillatoria, and Anabaena), two diatoms (Fragilaria and Synedra), and one green algae (Pediastrum). We provide and compare the classification performance of various distance-based and model-based methods. We additionally compare elastic shape distance to non-elastic distance using the nearest neighbor classifiers.

• School Mathematics
• /
• v.10 no.4
• /
• pp.603-623
• /
• 2008

The purpose of this research was to gain a better understanding of the characteristics of students' mathematical representations using additive strategy in ratio and proportion tasks. The additive strategy is the erroneous one used most often among the strategies reported in solving ratio and proportion tasks. It is a problem solving strategy that preserves the difference from one ratio to another. Students' additive strategies were categorized into four parts: subtracting without considering units of quantities, comparing the numbers that represent the whole subtracted from the part and same part, adding the difference, and subtracting the difference. In order to change from additive strategy to multiplicative strategy, the researcher asked to find out the unit quantity and found the characteristics of students' mathematical notations in the following: Firstly, the students made the number which they wanted by multiplying and adding same numbers. Secondly, they represented the mid-points between natural numbers. Thirdly, they related $a{\div}b$ to decimal number, not $\frac{a}{b}$. Fourthly, they were inclined to divide the larger number with the smaller number without understanding the context of the problem. These results are interpreted as showing that lower level of performance in the dividing operation with the notations of fraction hinders the transformation from additive strategy to multiplicative strategy.

• Communications of Mathematical Education
• /
• v.38 no.2
• /
• pp.121-144
• /
• 2024

This study analyzes how the academic achievement of students in Korea changes as they transition from 4th grade of elementary school to 2nd grade of middle school, considering that the 4th graders in the previous TIMSS cycle become 2nd graders in the next cycle. In particular, this study selects and compares the eight main countries in the TIMSS math evaluation (Korea, Singapore, Taiwan, Japan, USA, UK, Australia, and Russia) to analyze the trend of change in academic achievement of Korean students according to school grade transition. The trend of change in academic achievement of students was analyzed not only overall but also by content area (number, geometry and measurement, data representation (data and probability/data and probability), gender, and regional scale. The analysis focused on the average score and the proportion of students by achievement level. The results of the study are as follows. First, there was no significant change in the average score of Korean students' academic achievement as the school grade transitioned, but the achievement gap widened in terms of the proportion by achievement level. Second, there were differences in students' academic achievement by content area according to school grade transition, and the pattern differed depending on the evaluation cycle. Third, there was a significant gap in students' math academic achievement depending on gender and regional scale of school location. This study reveals that the achievement gap among students in our country widens as they transition between school levels. The gap is found to vary in terms of achievement level, math content area, student gender, and school location. To alleviate these disparities, more substantial research and support are proposed in addition to policy implementation by the government or provincial offices of education.

• Journal of Educational Research in Mathematics
• /
• v.23 no.2
• /
• pp.213-235
• /
• 2013

The purpose of this study is to analyze how the teaching activities which used EXCEL influence the specialized high school underachieved students. They have difficulties in making use of various representations for better understanding of function. EXCEL is helpful for learning function because it enables the students to use real life materials in math learning as well as formulates Tabular, Algebraic and Graphical which represent function. Furthermore, the students in specialized high school also have the experience of using EXCEL while studying other subjects. For that reason they have no burdens and fears on using EXCEL in learning activities. Utilizing EXCEL in the classroom gives an expectation that it helps to have interests on studying function and prepare for the next learning in the end. Research classes were conducted in a group of five students who have different hopes of career and a variety of mathematical interests. Though the students couldn't transfer Algebraic to Graphical in the diagnostic evaluation, they could resolve the problem of connections between Graphical, Tabular and Algebraic in the process perspectives, and could also express graphical representation by linking object perspectives with process perspectives. Therefore, they solved the connection problem of Tabular, Algebraic and Graphical in the object perspectives. As a result, the students could make transitions between Algebraic and Graphical in object perspectives through the classes applying EXCEL. Consequently, teaching the students with underachievement utilizing EXCEL enables them to recover their interests on math and it helps them to complete their following curriculum.

• Journal of Educational Research in Mathematics
• /
• v.16 no.4
• /
• pp.367-386
• /
• 2006

There are two strands for considering tile relationships between education and technology. One is the viewpoint of 'learning from computers' and the other is that of 'learning with computers'. In this paper, we call mathematics education with computers as 'computers and mathematics education' and this computer environments as microworlds. In this paper, we first suggest theoretical backgrounds ai constructionism, mathematization, and computer interaction. These theoretical backgrounds are related to students, school mathematics and computers, relatively As specific strategies to design a microworld, we consider a physical construction, fuctiionization, and internet interaction. Next we survey the different microworlds such as Logo and Dynamic Geometry System(DGS), and reform each microworlds for mathematical level-up of representation. First, we introduce the concept of action letters and its manipulation for representing turtle actions and recursive patterns in turtle microworld. Also we introduce another algebraic representation for representing DGS relation and consider educational moaning in dynamic geometry microworld. We design an integrating microworld between Logo and DGS. First, we design a same command system and we get together in a microworld. Second, these microworlds interact each other and collaborate to construct and manipulate new objects such as tiles and folding nets.

• Journal of Elementary Mathematics Education in Korea
• /
• v.21 no.4
• /
• pp.663-686
• /
• 2017

The purpose of this study was to identify the effects of convergent approach of mathematics education on students' problem-solving ability and self-efficacy by designing and applying mathematics curriculum based on STEAM. The results are as follows. First, the test results between the two groups did not show any statistically significant difference in terms of problem solving ability, but the experimental group showed a higher average score than the comparative group. Compared with the standard deviation of the experimental group, It can be seen that the level of difference between students is great. This suggests that STEAM-based mathematics lessons have a positive effect on the problem solving ability of low-level students. Second, the results of the self-efficacy t-test of STEAM-based mathematics class showed statistically significant results at a 5% significance level. In the sub-domain, the preference for the difficulty of the mathematics task, except math self-confidence and the math self-regulation efficacy, were statistically significant at a 5% significance level. This study shows that STEAM-based mathematics classes have a positive effect on the students' positive aspects. Through the STEAM program, students learn that mathematics is connected with other fields, and it provides an opportunity to explore on their own, and they more became interested, motivated, and achievement. Also, through the results of the STEAM-based mathematics class, it can be seen that the expressive power and self-confidence are increased by using the non-formal representation outside of the existing formal representation center. The result of this study can be summarized as follows: A STEAM-based mathematics class has a positive effect on problem solving ability and self-efficacy. Therefore, it is interpreted that the application of the STEAM program focusing on mathematics accounts for education effectives.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.49 no.2
• /
• pp.1-16
• /
• 2021

The act of design in landscape architecture consists of a concept within a designer's mind, technical representations, and finally, a process of construction. In the 4th Industrial Revolution, the design process is facing many changes due to the rapid development of computer technology and the IT ecosystem. Computer technology was initially developed for simple functions, such as mathematical calculation and graphic representation. However, after the spread of Personal Computers, starting with IBM and Macintosh, programming languages and hardware rapidly developed, algorithms and applications became specialized, and the purpose of using computers became very diverse. This study diagnoses issues concerning the functions and roles that new design methods, such as computational design, parametric design, and algorithmic design, can play in landscape architecture based on changes in the digital society. The study focused on the design methodology using parametric technology, which has recently received the most attention. First, the basis for discussion was developed by examining the main concepts and characteristics of parametric design in modern landscape architecture. Prior research on the use of parametric design in landscape architecture was analyzed, as were the case studies conducted by landscape design firms. As a result, it was confirmed that parametric design has not been sufficiently discussed in terms of the number and diversity of studies compared to other techniques investigated by landscape design firms. Finally, based on the discussion, the study examined specific cases and future possibilities of the parametric design in landscape architecture.

• Journal of Korea Water Resources Association
• /
• v.32 no.5
• /
• pp.565-577
• /
• 1999

The geometric patterns of a stream network in a drainage basin can be viewed as a "fractal" with fractal dimensions. Fractals provide a mathematical framework for treatment of irregular, ostensively complex shapes that show similar patterns or geometric characteristics over a range of scale. GIUH (Geomorphological Instantaneous Unit Hydrograph) is based on the hydrologic response of surface runoff in a catchment basin. This model incorporates geomorphologic parameters of a basin using Horton's order ratios. For an ordered drainage system, the fractal dimensions can be derived from Horton's laws of stream numbers, stream lengths and stream areas. In this paper, a fractal approach, which is leading to representation of a 2-parameter Gamma distribution type GIUH, has been carried out to incorporate the self similarity of the channel networks based on the high correlations between the Horton's order ratios. The shape and scale parameter of the GIUH-Nash model of IUH in terms of Horton's order ratios of a catchment proposed by Rosso(l984J are simplified by applying the fractal dimension of main stream length and channel network of a river basin. basin.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.19 no.3
• /
• pp.40-45
• /
• 2018

Intelligent monitoring and diagnosis of production processes based on multivariate statistical methods has been one of important tasks for safety and quality issues. This is due to the fact that faults and unexpected events may have serious impacts on the operation of processes. This study proposes a diagnostic scheme based on effective representation of process measurement data and is evaluated using simulation process data. The effects of utilizing a preprocessing step and nonlinear statistical methods are also tested using fifteen faults of the simulation process. Results show that the proposed scheme produced more reliable results and outperformed other tested schemes with none of the filtering step and nonlinear methods. The proposed scheme is expected to be robust to process noises and easy to develop due to the lack of required rigorous mathematical process models or expert knowledge.

• Journal of KIISE
• /
• v.44 no.4
• /
• pp.392-398
• /
• 2017

The point-cloud representation of an object is performed by scanning a space through a laser scanner that is extracting a set of points, and the points are then integrated into the same coordinate system through a registration. The set of the completed registration-integrated point clouds is classified into meaningful regions, shapes, and noises through a mathematical analysis. In this paper, the aim is the matching of a curved area like a cylinder shape in 3D point-cloud data. The matching procedure is the attainment of the center and radius data through the extraction of the cylinder-shape candidates from the sphere that is fitted through the RANdom Sample Consensus (RANSAC) in the point cloud, and completion requires the matching of the curved region with the Catmull-Rom spline from the extracted center-point data using the Principal Component Analysis (PCA). Not only is the proposed method expected to derive a fast estimation result via linear and curved cylinder estimations after a center-axis estimation without constraint and segmentation, but it should also increase the work efficiency of reverse engineering.