• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.607-622
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• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.

• The Mathematical Education
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• v.46 no.3
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• pp.331-349
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• 2007

This study aims to improve the teaching and learning method on the conic sections. To do that the researcher analyzed the impact of dynamic geometry software on students' problem solving of the conic sections. Students often say, "I have solved this kind of problem and remember hearing the problem solving process of it before." But they often are not able to resolve the question. Previous studies suggest that one of the reasons can be students' tendency to approach the conic sections only using algebra or analytic geometry without the geometric principle. So the researcher conducted instructions based on the geometric and historico-genetic principle on the conic sections using dynamic geometry software. The instructions were intended to find out if the experimental, intuitional, mathematic problem solving is necessary for the deductive process of solving geometric problems. To achieve the purpose of this study, the researcher video taped the instruction process and converted it to digital using the computer. What students' had said and discussed with the teacher during the classes was checked and their behavior was analyzed. That analysis was based on Branford's perspective, which included three different stage of proof; experimental, intuitive, and mathematical. The researcher got the following conclusions from this study. Firstly, students preferred their own manipulation or reconstruction to deductive mathematical explanation or proving of the problem. And they showed tendency to consider it as the mathematical truth when the problem is dealt with by their own manipulation. Secondly, the manipulation environment of dynamic geometry software help students correct their mathematical misconception, which result from their cognitive obstacles, and get correct ones. Thirdly, by using dynamic geometry software the teacher could help reduce the 'zone of proximal development' of Vigotsky.

• Journal of Educational Research in Mathematics
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• v.23 no.3
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• pp.389-406
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• 2013

The purpose of this study is to analyze eighth grade students' errors in the constructed-response items to improve teaching and learning of mathematics in schools. By analyzing 99 students' responses to nine constructed-response items, we found several types of students' errors in their responses to the assessment items involving with mathematical reasoning and representations, problems within realistic contexts, and mathematical connections. Not only a single error but also multiple errors (a combination of two or more types of errors) were discovered. In particular, high achieving students showed more simple errors than multiple errors while low achieving students had more multiple errors in various kinds.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.419-442
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• 2023

This study investigated fifth graders' understanding of variables from a generalized arithmetic and a functional perspectives of early algebra. Specifically, regarding a generalized perspective, we included the property of 1, the commutative property of addition, the associative property of multiplication, and a problem context with indeterminate quantities. Regarding the functional perspective, we covered additive, multiplicative, squaring, and linear relationships. A total of 246 students from 11 schools participated in this study. The results showed that most students could find specific values for variables and understood that equations involving variables could be rewritten using different symbols. However, they struggled to generalize problem situations involving indeterminate quantities to equations with variables. They also tended to think that variables used in representing the property of 1 and the commutative property of addition could only be natural numbers, and about 25% of the students thought that variables were fixed to a single number. Based on these findings, this paper suggests implications for elementary school students' understanding and teaching of variables.

• The Mathematical Education
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• v.63 no.2
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• pp.123-138
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• 2024

This study described the utilization of ChatGPT in teaching and students' learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at 'S' University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students' discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.

• Journal of Gifted/Talented Education
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• v.26 no.1
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• pp.211-230
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• 2016

The study aimed to investigate the characteristics of algebraic thinking of the mathematically gifted students and search for how to teach algebraic thinking. Research subjects in this study included 93 students who applied for a science gifted education center affiliated with a university in 2015 and previously experienced gifted education. Students' responses on an algebraic item of a creative thinking test in mathematics, which was given as screening process for admission were collected as data. A framework of algebraic thinking factors were extracted from literature review and utilized for data analysis. It was found that students showed difficulty in quantitative reasoning between two quantities and tendency to find solutions regarding equations as problem solving tools. In this process, students tended to concentrate variables on unknown place holders and to had difficulty understanding various meanings of variables. Some of students generated errors about algebraic concepts. In conclusions, it is recommended that functional thinking including such as generalizing and reasoning the relation among changing quantities is extended, procedural as well as structural aspects of algebraic expressions are emphasized, various situations to learn variables are given, and activities constructing variables on their own are strengthened for improving gifted students' learning and teaching algebra.

• The Mathematical Education
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• v.59 no.1
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• pp.63-80
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• 2020

This study analyzed 3,114 articles published in KCI journals and 1,636 articles published in SSCI journals from 2000 to 2019 in order to compare domestic and international research trends of mathematics education using a topic modeling method. Results indicated that there were 16 similar research topics in domestic and international mathematics education journals: algebra/algebraic thinking, fraction, function/representation, statistics, geometry, problem-solving, model/modeling, proof, achievement effect/difference, affective factor, preservice teacher, teaching practice, textbook/curriculum, task analysis, assessment, and theory. Also, there were 7 distinct research topics in domestic and international mathematics education journals. Topics such as affective/cognitive domain and research trends, mathematics concept, class activity, number/operation, creativity/STEAM, proportional reasoning, and college/technology were identified from the domestic journals, whereas discourse/interaction, professional development, identity/equity, child thinking, semiotics/embodied cognition, intervention effect, and design/technology were the topics identified from the international journals. The topic related to preservice teacher was the most frequently addressed topic in both domestic and international research. The topic related to in-service teachers' professional development was the second most popular topic in international research, whereas it was not identified in domestic research. Domestic research in mathematics education tended to pay attention to the topics concerned with the mathematical competency, but it focused more on problem-solving and creativity/STEAM than other mathematical competencies. Rather, international research highlighted the topic related to equity and social justice.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.139-170
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• 2022

In relation to differentiated mathematics education, Russia has a longer experience in research and practice than Korea. The mathematics curriculum for 10-11 grades currently in use in Russia is a level-specific curriculum and consists of a basic level and an advanced level. And in Russia mathematics textbooks for 10-11 grades are also textbooks for each level. In this study, we analyzed basic level textbook and advanced level textbook written by the same author group among the textbooks 'Algebra and Introduction of Mathematical Analysis' of the 10th grade in Russia. To analyze the main learning contents and textbook descriptions that were added in advanced level the 'real numbers' and 'complex numbers' sections were studied. The main contents of basic and advanced level textbooks for 'functions', 'trigonometric functions', 'trigonometric equations', 'conversions of trigonometric expressions', and 'derivatives', which are included in both basic and advanced textbooks were compared and analyzed, and the descriptive characteristics of the definitions and theorems presented in the two levels of textbooks were also compared and analyzed. From the results of this study, it is expected that various information on the contents of various level textbooks of mathematics, the differences between textbooks for each level, and strategies for the composition of textbooks for various level can be accumulated.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.977-998
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• 2009

In this article, we give a comparative study on the last 300 years of USA and Korean tertiary mathematics. The first mathematics classes in United States were offered before July, 1638, but the real founding of tertiary mathematics courses was in 1640 when Henry Dunster assumed the duties of the presidency at Harvard. President Dunster read arithmetics and geometry on Mondays and Tuesdays to the third year students during the first three quarters, and astronomy in the last quarter. So tertiary mathematics education in United States began at Harvard which is the oldest college in USA. After 230 years since then, Benjamin Peirce in 1870 made a major and first American contribution to mathematics and got an attention from European mathematicians. Major change on the role of Harvard mathematics from teaching to research made by G.D. Birkhoff when he joined as an assistant professor in 1912. Tertiary mathematics education in Korea started long before Chosun Dynasty. But it was given to only small number of government actuarial officers. Modern mathematics education of tertiary level in Korea was given at Sungkyunkwan, Ewha, Paichai, and Soongsil. But all college level education opportunity, particularly in mathematics, was taken over by colonial government after 1920. And some technical and normal schools offered some tertiary mathematics courses. There was no college mathematics department in Korea until 1945. After the World War II, the first college mathematics department was established, and Rimhak Ree in 1949 made a major and first Korean contribution to modern mathematics, and later found Ree group. He got an attention from western mathematicians for the first time as a Korean. It can be compared with Benjamin Peirce's contribution for USA.