• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.483-498
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• 2010

The purpose of this paper is to investigate the dispositions of university students' understanding and reasoning about rational number concept. For this, we surveyed for the subject groups of prospective math teachers(33), engineering major students(35), American engineering and science major students(28). The questionnaire consists of four problems related to understanding of rational number concept and three problems related to rational number operation reasoning. We asked multi-answers for the front four problem and the order of favorite algorithms for the back three problems. As a result, we found that university students don't understand exactly the facets of rational number and prefer the mechanic approaches rather than conceptual one. Furthermore, they reasoned illogically in many situations related to fraction, ratio, proportion, rational number and don't recognize exactly the connection between them, and confuse about rational number concept.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.581-609
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• 2013

Students' learning processes and mathematical levels should be correctly diagnosed in many different methods of assessment to help students learn mathematics. The study developed the model for the process-based assessment while using manipulatives in the middle school in order to improve problem solving, reasoning and communication which are emphasized in 2009 reformed curriculum as the areas of mathematical process. Identifying the principles of assessment, we created the assessment model for each area and carried out a preliminary study. Based on this, we revised the representative items and the observation checklist and then conducted a main study. Through the results of assessment, we found that students' thinking processes were well presented in scoring rubric for their responses on each item. It meant that the purpose of the assessment as a criterion-referenced test was achieved.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.1-15
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• 2011

Approximation is a very useful approach in mathematics research. It was the same in traditional Chinese and Chosun mathematics. This study derived five characteristics from approximation approaches which were found in Chinese and Chosun mathematical books: improvement of approximate values, common and inevitable use of approximate values, recognition of approximate values and their reasons, comparison of their exactness, application of approximate principles. Through these characteristics, we can infer what Chinese and Chosun mathematicians recognized approximate values and how they manipulated them. They took approximate approaches by necessity or for the sake of convenience in mathematical study and its applications. Also, they tried to improve the degree of exactness of approximate values and use the inverse calculations to check them.

• Journal of Sensor Science and Technology
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• v.9 no.6
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• pp.440-447
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• 2000

This paper describes a practical system to classify material temperature responses by composition of curve fitting and neuro-fuzzy inference. There are problems with a classification system which utilizes temperature responses. It requires too much time to approach the steady state of temperature response and it has to be filtered to remove the noise which occurs in experiments. Thus, this paper proposes a practical method using curve fitting only for transient state to remove the above problems of time and noise. Using the neuro-fuzzy system, the thermal conductivity of the material can be inferred on various ambient temperatures. So the material can be classified via its inferred thermal conductivity. To realize the system, we designed a contact sensor which has a similar structure with human finger, implemented a hardware system, and developed a classification software of curve fitting and neuro-fuzzy algorithm.

• The Mathematical Education
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• v.61 no.3
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• pp.499-519
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• 2022

Ratio and rate are key topics in the area of 'Patterns', but there are various perspectives on them. This study compared and analyzed the perspectives of Korean and Singaporean mathematics textbooks on ratio and rate, and explored how teaching and learning methods develop according to each perspective in terms of quantitative reasoning. To this end, we reorganized the analysis criteria based on some studies, and analyzed the textbooks of the two countries in relation to context, relationship, and representation. The results of the study are as follows. Regarding the context, there were differences in the situations, types of units and use of units of the problems presented in textbooks. In terms of relationship, there were differences in the types of two quantities and relationship of quantities. Lastly, there were differences in the representation of ratio and rate. Through these results, we found that elementary mathematics textbooks in Korea and Singapore take different perspectives on ratio and rate. In particular, the perspective taken by Korean textbooks on ratio and rate had unique points different from that of other previous studies. Considering this Korean perspective, we suggested some implications that could help improve textbooks related to ratio and rate and teach them meaningfully.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1998.05a
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• pp.300-307
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• 1998

인간의 몸에서 발생하는 여러 생체반응을 이해하고 계측한다는 것은 매우 힘든 일이다. 그러나 분명히 존재하고 있는 물리화학적 변수들간의 상호관계를 정성적으로 묘사함으로써 생체반응을 설명한다. 본 논문에서는 인체의 기능을 추론 및 공학적 이론을 토대로 생체변수간의 관계를 수학적으로 표현하고 컴퓨터 시뮬레이션을 수행해 수리적으로 해석함으로써 인체의 각종현상을 정량적으로 예측한다.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.157-177
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• 2006

The concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this development process. One fourth student, Kyungsu, was encourage to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Kyungsu made during the teaching experiment and analyzes the challenges Kyungsu faced in attempting to schematize his method. Finally, the mathematical knowledge Kyungsu needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

• Proceedings of the Korea Information Processing Society Conference
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• 2023.11a
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• pp.23-26
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• 2023

본 논문에서는 서술형 수학 문제 풀이 모델의 숫자 대소관계 파악을 위한 명시적 자질추출방식 Explicit Feature Extraction(EFE) Reasoner 모델을 제안한다. 서술형 수학 문제는 자연현상이나 일상에서 벌어지는 사건을 수학적으로 기술한 문제이다. 서술형 수학 문제 풀이를 위해서는 인공지능 모델이 문장에 함축된 논리를 파악하여 수식 또는 답을 도출해야 한다. 때문에 서술형 수학 문제 데이터셋은 인공지능 모델의 언어 이해 및 추론 능력을 평가하는 지표로 활용되고 있다. 기존 연구에서는 문제를 이해할 때 숫자의 대소관계를 파악하지 않고 문제에 등장하는 변수의 논리적인 관계만을 사용하여 수식을 도출한다는 한계점이 존재했다. 본 논문에서는 자연어 이해계열 모델 중 SVAMP 데이터셋에서 가장 높은 성능을 내고 있는 Deductive-Reasoner 모델에 숫자의 대소관계를 파악할 수 있는 방법론인 EFE 를 적용했을 때 RoBERTa-base 에서 1.1%, RoBERTa-large 에서 2.8%의 성능 향상을 얻었다. 이 결과를 통해 자연어 이해 모델이 숫자의 대소관계를 이해하는 것이 정답률 향상에 기여할 수 있음을 확인한다.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.573-588
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• 2014

How will the field of education react to the big data craze that has recently seeped into every aspect of society? To search for ways to use big data in mathematics education, this study first examined the concept of big data and examples of its application, and then pursued directions for future research in two ways. First, changes in the representation and acceptance of data are required because of changes in technology and the environment. In other words, the learning content and methodology of data treatment need to be changed by describing a myriad amount of data visually or by 'analyzing and inferring' data to provide data efficiently and clearly. Additionally, the mathematics education field needs to foster changes in curricula to facilitate the improvement of students' learning capacity in the 21st century. Second, it is necessary to more actively collect data on general education and not merely on teaching or learning to identify new information, pursue positive changes in the teaching and learning of mathematics, and stimulate interest and research in the field so that it can be used to make policy decisions regarding mathematics education.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.281-302
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• 2015

In the current study, answer sheets from 8007 students in 236 Korean schools were selected and analyzed to examine errors that emerge in the process of solving descriptive questions of the National Educational Achievement Assessment in mathematics. Questions used in the analysis were response assessment covering middle school mathematics topics: "mathematical symbols and equations" and "functions." The behavioral domain of the questions was that of "problem solving and computation," which requires establishing an equation for a word problem and allows the calculation of an answer that meets a certain condition. The analysis results revealed various errors in each stage of each question, from understanding to solving; the study attempts to conjecture causes for these errors and draw pedagogical implications.