• School Mathematics
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• v.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

• Korean Journal of Child Education & Care
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• v.18 no.4
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• pp.199-211
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• 2018

Objective: The purpose of this study is to examine the relative effects of young children's mathematical abilities and scientific abilities on intelligence. Methods: The object of this study is 100 five or six-years-old children in a kindergarten of S district in S city. I conducted analysis of partial correlation after controlled young children's age and sex to examine correlation between young children's mathematical abilities, scientific abilities and intelligence, also I used stepwise multiple regression analysis for inspecting the relative effects of young children's mathematical abilities and scientific abilities on intelligence. Results: Young children's intelligence is relative with mathematical abilities and scientific abilities, this relation is higher in 'measurement' and 'algebra' factors of mathematical abilities and 'predicting' factor of scientific abilities. Mathematical abilities bigger impact to the relative effects on young children's intelligence. Conclusion/Implications: On this, it is necessary that evenly providing the math and science activities in early childhood education field and home, and we have to consider the integrations of the process when provide the math and science integrated activities. This study has the significance to use basic line data when people plan the integrated math-science activities and develop program associated those by finding the relationship between mathematical abilities, scientific abilities and intelligence and evaluating the relative effects on intelligence.

• 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.