• Korean Journal of Childcare and Education
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• v.19 no.6
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• pp.79-95
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• 2023

Objective: This study examines the relationships among four-year-olds' counting skills, their use of number words, and their mothers' use of number words during mother-child free play. Specifically, we assess whether children's use of number words mediates the relationship between their counting skills and their mothers' use of number words during play. Methods: Forty-two 4-year-old children and their mothers were asked to play freely with a given set of toys at their home for 10 minutes. Children also completed a counting skill test. Frequencies of number word use were calculated for mothers and children from transcriptions of the free play. Results: Children's counting skills, the frequency of their number word use, and their mothers' frequency of number word use were positively correlated with each other. Additionally, the frequency of children's number-word use completely mediated the relationship between their counting skills and their mothers' frequency of number-word use. Conclusion/Implications: The results suggest that children's use of number language may play a crucial role in the provision of number-related language input by parents, based on their children's math skills. Practical implications of the findings are discussed.

• Education of Primary School Mathematics
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• v.4 no.1
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• pp.43-49
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• 2000

The purpose of this paper is to address the theory of counting and the development of number concepts. Leslie Steffe and his colleagues developed the theory of children's counting types using the teaching experiment. As the results of their research, they published two books： "Children's counting types" (Steffe, von Glasersfeld, Richards, '||'&'||' Cobb, 1983) and "Construction of arithmetic meanings and strategies" (Steffe, Cobb, ＆ von Glasersfeld, 1988). They classified children's counting types into five categories： Perceptual Counting Stage, Figural Counting Stages, Initial Number Sequence Stage, Tacitly Nested Number Sequence Stage, and Explicitly Nested Number Sequence Stage. The meaning of this theory is added in the last part of this paper. this paper.

• Journal of the Optical Society of Korea
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• v.14 no.4
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• pp.388-394
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• 2010

In this paper the object recognition performance of a photon counting integral imaging system is quantitatively compared with that of a conventional gray scale imaging system. For 3D imaging of objects with a small number of photons, the elemental image set of a 3D scene is obtained using the integral imaging set up. We assume that the elemental image detection follows a Poisson distribution. Computational geometrical ray back propagation algorithm and parametric maximum likelihood estimator are applied to the photon counting elemental image set in order to reconstruct the original 3D scene. To evaluate the photon counting object recognition performance, the normalized correlation peaks between the reconstructed 3D scenes are calculated for the varied and fixed total number of photons in the reconstructed sectional image changing the total number of image channels in the integral imaging system. It is quantitatively illustrated that the recognition performance of the photon counting integral imaging system can be similar to that of a conventional gray scale imaging system as the number of image viewing channels in the photon counting integral imaging (PCII) system is increased up to the threshold point. Also, we present experiments to find the threshold point on the total number of image channels in the PCII system which can guarantee a comparable recognition performance with a gray scale imaging system. To the best of our knowledge, this is the first report on comparisons of object recognition performance with 3D photon counting & gray scale images.

• East Asian mathematical journal
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• v.34 no.2
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• pp.85-101
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• 2018

The purpose of this paper is to investigate counting-based and collection-based computation of the elementary mathematics textbook in Korea and United States of America. As a results, we will provide some suggestive points through how to use and activity of number line, decomposing number, counting, grouping and so on by analyzing counting and collection-based computation in the elementary mathematics textbook of Korea and United States of America.

• The Mathematical Education
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• v.49 no.4
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• pp.437-462
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• 2010

The purpose of this research is to analyze the textbook contents about the natural number concepts in the Korean National Elementary Mathematics Curriculum. Understanding a concept of natural number is crucial in school mathematics curriculum planning, since elementary students start their basic learning with natural number system. The concepts of natural number have various meaning from the perspectives of pedagogical research, and the philosophy of mathematics. The natural number concepts in the elementary math curriculum consist of four aspects; counting numbers, cardinal numbers, ordinal numbers, and measuring numbers. Two research questions are addressed; (1) How are the natural number concepts focusing on counting, cardinal, ordinal, measuring numbers are covered in the national math curriculum? ; (2) What suggestions can be made to enhance the teaching and learning about the natural number concepts? Findings reveal that (1) the national mathematics curriculum properly reflects four aspects of natural number concepts, as the curriculum covers 50% of the cardinal number system; (2) In the aspect of the counting number, we hope to add the meaning about 'one, two, three, ......, and so on' in the Korean Mathematics curriculum. In the ordinal number, we want to be rich the related meaning in a set. Further suggestions are made for future research to include them ensuing number in the curriculum.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.12
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• pp.4866-4888
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• 2020

One major and time-consuming task in fish production is obtaining an accurate estimate of the number of fish produced. In most Nigerian farms, fish counting is performed manually. Digital image processing (DIP) is an inexpensive solution, but its accuracy is affected by noise, overlapping fish, and interfering objects. This study developed a catfish recognition and counting algorithm that introduces detection before counting and consists of six steps: image acquisition, pre-processing, segmentation, feature extraction, recognition, and counting. Images were acquired and pre-processed. The segmentation was performed by applying three methods: image binarization using Otsu thresholding, morphological operations using fill hole, dilation, and opening operations, and boundary segmentation using edge detection. The boundary features were extracted using a chain code algorithm and Fourier descriptors (CH-FD), which were used to train an artificial neural network (ANN) to perform the recognition. The new counting approach, based on the geometry of the fish, was applied to determine the number of fish and was found to be suitable for counting fish of any size and handling overlap. The accuracies of the segmentation algorithm, boundary pixel and Fourier descriptors (BD-FD), and the proposed CH-FD method were 90.34%, 96.6%, and 100% respectively. The proposed counting algorithm demonstrated 100% accuracy.

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.415-430
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• 2018

The purpose of this study was to get reflections on teaching numbers and operations for special education from analyzing lessons for counting, addition and subtraction of natural number with counting board for students with autism. In order to attain these purposes, this study analyzed the lessons for counting, addition and subtraction of natural number to students with autism in 4th and 6th graders in special class at regular elementary school using counting board for one hour per week for 30 weeks. According to the analysis, counting board that reveals the structure of numbers becomes an effective mathematical materials, and using the counting strategy and computation strategy can be an effective method of teaching, and it is possible to teach mathematical communication to students with autism. From this result, this study presented suggestions for teaching counting, addition and subtraction for students with disabilities.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.10a
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• pp.35-40
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• 2021

People counting data is crucial for most business owners, since they can derive meaningful information about customers movement within their businesses. For example, owners of the supermarkets can increase or decrease the number of checkouts counters depending on number of occupants. Also, it has many applications in smart buildings, too. Where it can be used as a smart controller to control heating and cooling systems depending on a number of occupants in each room. There are advanced technologies like camera-based people counting system, which can give more accurate counting result. But they are expensive, hard to deploy and privacy invasive. In this paper, we propose a method and a hardware sensor for counting people passing through a passage or an entrance using IR Infrared sensors. Proposed sensor operates at low voltage, so low power consumption ensure long duration on batteries. Moreover, we propose a new method that distinguishes human body and other objects. Proposed method is inexpensive, easy to install and most importantly, it is real-time. The evaluation of our proposed method showed that when counting people passing one by one without overlapping, recall was 96% and when people carrying handbag like objects, the precision was 88%. Our proposed method outperforms IR Infrared based people counting systems in term of counting accuracy.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.281-292
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• 1997

In this paper we are concered with the counting processes with intersity function $g_n(t)$, where $g_n(t)$ not only depends on t but n. It is shown that under certain conditions the number of events in [0, t] follows a generalizes Poisson distribution. A counting process is also provided such that $g_i(t)$$\neq$$g_i(t)$ for i$\neq$j and the number of events in [0, t] has a transformed geometric distribution.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.469-486
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• 2022

Counting occupies a fundamental and important position in mathematical learning due to its relation to number concepts and numeral operations. In particular, counting up to large numbers is an essential learning element in that it is structural counting that includes the understanding of place values as well as the one-to-one correspondence and cardinal principles required by counting when introducing number concepts in the early stages of number learning. This study aims to derive didactical implications by investigating the possibility of and the strategies for counting large numbers that is expected to have no students' experience because it is not composed of current textbook activities. To do this, 89 second-grade elementary school students who learned the three-digit numbers and experienced group-counting and skip-counting as textbook activities were provided with questions asking how many penguins were in a picture where 260 penguins were irregularly arranged and how to count. As a result of analyzing students' responses in terms of the correct answer rate, the strategy used, and their cognitive characteristics, the incorrect answer rate was very high, and the use of decimal principles, group-counting, counting by one, and partial sum strategies were confirmed. Based on these analysis results, several didactical implications were derived, including the need to include counting up to large numbers as textbook activities.