수학교육에서 인공지능 활용 가능성

박만구 ( Park¸ Mangoo ) 한국수학교육학회 2020 수학교육논문집 Vol.34 No.4

이 연구의 목적은 국내외 인공지능을 활용한 수학교육 서비스의 주요 기능과 인공지능의 활용 가능성을 알아보는 것이다. 이 연구를 위해 최근 5년 이내에 발행한 자료를 중심으로 출판물 및 인터넷에서 “인공지능”, “人工知能”, “Artificial Intelligence” “AI”. “수학교육”의 키워드를 독립적으로 또는 조합하여 검색하면서 관련 논문 및 보고서 그리고 인터넷 자료 등을 수집하여 분석하였다. 연구 결과, 수학교육을 위한 인공지능 서비스는 대부분 학습자의 개인별 수학 맞춤형 학습을 지원하고, 인간 수학 교사를 지원하기 위한 보조적인 역할로 규정하며, 인지적인 측면뿐만 아니라 정의적인 측면의 기술을 고도화하고 있었다. 제언으로, 정교한 수학 계통체계의 구축을 위한 연구, 인공지능 기술을 발굴하여 수학교육에 활용하는 방안, 인공지능 활용을 위한 양질의 수학 콘텐츠를 개발, 수학교육을 위한 클라우드 기반의 종합 시스템 구축과 운영이 필요함을 주장하였다. The purpose of this study is to investigate the applications and possibilities of major programs that provide services using artificial intelligence in mathematics education. For this study, related papers, reports, and materials were collected and analyzed, focusing on materials mostly published within the last five years. The researcher searched the keywords of "artificial intelligence", "artificial intelligence", "AI" and "mathematics education" independently or in combination. As a result of the study, artificial intelligence for mathematics education was mostly supporting learners' personalized mathematics learning, defining it as an auxiliary role to support human mathematics teachers, and upgrading the technology of not only cognitive aspects but also affective aspects. As suggestions, the researcher argued that followings are necessary: Research for the establishment of an elaborate artificial intelligence mathematical system, discovery of artificial intelligence technology for appropriate use to support mathematics education, development of high quality of mathematics contents for artificial intelligence, and the establishment and operation of a cloud-based comprehensive system for mathematics education. The researcher proposed that continuous research to effectively help students study mathematics using artificial intelligence including students' emotional or empathetic abilities, and collaborative learning, which is only possible in offline environments. Also, the researcher suggested that more sophisticated materials should be developed for designing mathematics teaching and learning by using artificial intelligence.

The Possibilities and Limitations of Using ChatGPT in Mathematics Education

Mangoo Park(Mangoo Park) 한국아세아태평양교육문화융복합학회 2023 Asia Pacific Journal of Teaching and Learning Vol.3 No.2

Purpose : The purpose of this paper is to present the possibilities and limitations of using ChatGPT, a generative artificial intelligence model, that learners and instructors can use for mathematics education, and to make suggestions for mathematics education. Method : For this purpose, I analyzed previous research data on the use of ChatGPT in various documents in each area. Results : As a result of the study, in mathematics education, learners use ChatGPT to solve mathematics problems, learn mathematics study plans and study methods, receive creative problems, become questioners, become proactive learners, and become owners of their own mathematics learning through reflection on the learning process, resulting in in-depth learning. Instructors can use ChatGPT to improve the quality of mathematics education, including preparation for classes, creation of class materials, class delivery, post-class evaluation and reporting, and sharing experiences among teachers. Limitations of using ChatGPT in mathematics education include the risk of superficial knowledge, lack of interaction between teachers and peers, problems with the Internet environment, absence of real-time feedback for individual students, risk of biased knowledge and inaccurate information, limitations in communication through text, and teacher Difficulty of independent use without supervision, deepening dependence on ChatGPT and ethical issues. Conclusion : In conclusion, for effective utilization of ChatGPT, both teachers and students need to be aware of the system's limitations and ethical considerations in mathematics education.

The Perceptions of AI of Teachers in Mathematics Education

Mangoo Park 한국아세아태평양교육문화융복합학회 2022 Asia Pacific Journal of Teaching and Learning Vol.2 No.1

Purpose The purpose of this paper is to investigate the perceptions of AI(artificial intelligence) of Korean teachers in mathematics education. It is important to maximize the effectiveness of mathematics education when considering the fusion of mathematics education and artificial intelligence. In this study, the perceptions of teachers in elementary and secondary schools on how each function of AI can be fused into mathematics education was analyzed, and suggested implications to construct an AI system. Method Researcher employed a survey to investigate the perceptions of AI of teachers in mathematics education. Researcher conducted a survey with 174 teachers from October 16 to October 24 in 2020. The questionnaire consisted of 11 questions on the difficulty of mathematics teaching, the actual status of online and offline mathematics teaching, the effect and necessity of online teaching, and the functions to recommend. The survey results were categorized by Likert scale. Results In the difficulty of mathematics teaching, the teachers who participated in the survey felt a little less difficult to teach mathematics as a whole. In the reasons of difficulties, there are relatively few responses that they had difficulty in teaching mathematics due to the level and quantity of mathematics and content that they had to teach at school. The preferred teaching is offline teaching due to lack of equipment and proper online mathematics programs. In the descriptive opinions of AI functions of AI systems, teachers suggested various diagnostic function, evaluative function, adaptive teaching function, error identification and correction function, collaboration function, and instructional management function. Conclusion The conclusion of this study is that teachers want the AI mathematics learning system to be developed in the direction of overcoming the limitations of offline public education. The requirements for AI systems are different depending on the school level. At a time when remote classes are generalized, AI systems need to include manipulation activities using AR/VR. Teachers thought that using AI should be based on huge cloud-based big data and have an open source so that the platform can be continuously improved like Google.

Connecting Mathematics to Humanity and Character Education

( Park Mangoo ) 한국수학교육학회 2017 수학교육 학술지 Vol.2017 No.2

One of the main purposes of teaching and learning mathematics is for students to enhance reasoning and problem solving abilities. Mathematics is fundamental basis for every thinking. However, most students learn and even teachers teach "just" mathematics in mathematics classes, which leads students to having negative attitudes towards mathematics. Students need to have broad perspectives when they learn mathematics by having opportunities to connect mathematics to humanity and character education. In this session, the researcher will talk why we need to broaden our perspectives towards mathematics connecting mathematics to humanity and character education.

Children's Representations of Numbers

Park, ManGoo 한국수학교육학회 2002 수학교육연구 Vol.6 No.1

The purpose of this paper was to examine early numerical representations between American and Korean children. Fifty-five first graders (35 Korean and 20 American) participated in the study. According to the findings of the current study, the author concluded that the Korean children had a stronger conception of base ten representations of numbers than that of the American children. The Korean children used various strategic reasoning such as decomposition and recomposition on the basis of base 10 structure to solve addition and subtraction problems effectively. However, the author cannot conclude that language differences would be the largest factor that would make Korean children salient in the representations of base ten structures.

수학교육에서 인공지능의 활용 동향

박만구 ( Park Mangoo ) 서울교육대학교 초등교육연구원 2020 한국초등교육 Vol.31 No.특별호

본 연구는 수학교육에서 인공지능을 활용 선도 국가들의 간략한 사례와 국내 적용의 구체적인 내용을 알아보고 인공지능이 수학교육에 주는 시사점을 제시하는 것을 목적으로 한다. 본 연구를 위해 Google의 검색을 통하여 “Artificial Intelligence”, "AI”“인공지능”으로 검색하여 수학교육과 관련이 있는 2000년 이후 발행한 관련 논문 및 웹사이트 자료들을 분석하였다. 분석 결과 대표적인 사례로 미국은 K-12학년 학생들을 위한 MATHia 프로그램, 중국은 Squirrel AI Learning Program, 뉴질랜드에서는 인공지능 수학교사 Amy, 그리고 스페인은 ARTIE라는 로봇을 활용하고 있다. 이외의 교육 선진국에서는 나름대로 인공지능을 수학교육에 활용하고 있음을 알았다. 그러나 대부분은 수학교육 ㅇ을 위환 인공지능 프로그램을 계속적으로 개발을 하고 있는 단계이다. 국내 수학교육에서 인공지능 적용 사례로 위두커뮤니케이션즈는 학습자의 학습 빅데이터를 스스로 분석하여 추천 알고리즘을 고도화하는 머신러닝 기반의 추천 모듈 고도화를 하고, 학습자의 학업성취도 향상을 위해 러닝로그 분석기반 맞춤형 학습 코스와 콘텐츠 추천이 가능한 학습 서비스를 제공하는 개발하고 있다. 그 외에 웅진 AI 수학, Quanda 프로그램 등을 간략히 살펴보았다. 본 연구 결과 시사점으로, 수학교육을 위해 공교육 지원을 위한 맞춤형 학습을 지원하기 위한 인공지능 기반 종합 플랫폼을 구축할 필요가 있고, 인공지능 기술을 활용하여 인간 교사를 효과적으로 지원할 수 있는 방안에 대한 연구가 필요함을 제안하였다. 그리고 인공지능을 활용한 교육을 위하여 양질의 수학 콘텐츠를 지속적으로 개발하고 기술이 고도화되면서 민감한 개인정보를 포함하여 빅데이터를 다루는 일이 더 많아지기 때문에 인공지능을 활용한 수학교육에서 윤리적인 문제를 교육할 필요가 있음을 제안하였다. 인공지능은 궁극적으로 학습자의 자발적인 수학 학습을 돕기 위하여 사용할 필요가 있고 교사의 교육 등에도 적절하게 활용하는 방안에 대한 연구도 필요하다. The purpose of this study is to investigate the examples of leading countries using artificial intelligence in mathematics education and the specific applications of artificial intelligence in Korea, and to present its implications for mathematics education. For this study, the researcher searched "Artificial Intelligence," "AI" and artificial intelligence" to analyze related papers and website data related to mathematics education. The U.S. uses the MATHia program for K-6 to K-12 students, China uses the Squirrel AI Learning Program, New Zealand uses artificial intelligence mathematics teacher Amy, and Spain uses a robot called ARTIE. Other advanced countries in education were using artificial intelligence in their own way for math education. In Korea, Wedu Communications is developing a machine learning-based recommendation module that analyzes learners' learning big data on its own to advance recommended algorithms, and providing customized learning courses based on running log analysis and learning services that can recommend content to improve learners' academic performance. As a suggestion of this study, it was suggested that it is necessary to establish an artificial intelligence-based comprehensive platform to support customized learning to support public education for mathematics education, and that research on how to effectively support human teachers by utilizing artificial intelligence technology is needed. It also suggested the need to educate students on ethical issues in mathematics education using artificial intelligence as the technology has been advanced and the technology has become more involved in dealing with big data, including sensitive personal information. It is necessary that artificial intelligence should be used ultimately to help learners learn mathematics voluntarily, and research on how to properly utilize it in teachers' education, and so forth.

머신러닝 추천모듈이 적용된 맞춤형 학습 플랫폼 효과성 탐색: 학습시간, 자기주도적 학습능력, 수학에 대한 태도, 수학학업성취도를 중심으로

박만구 ( Park Mangoo ),임현정 ( Lim Hyunjung ),김지영 ( Kim Jiyoung ),이규하 ( Lee Kyuha ),김미경 ( Kim Mikyung ) 한국수학교육학회 2020 수학교육 Vol.59 No.4

본 연구의 목적은 학습 빅데이터 분석을 통해 추천 알고리즘을 스스로 고도화하는 머신러닝 추천모듈이 적용된 개인 맞춤형 학습 플랫폼이 학생들의 학습시간, 자기주도적 학습능력, 수학에 대한 태도, 수학학업성취도에 미치는 영향과 이들 사이의 구조적 관계를 검증하는 것이다. 연구 결과 개인 맞춤형 학습은 학생들의 학습시간, 자기주도적 학습능력, 수학에 대한 태도, 수학학업성취도에 대해 긍정적인 영향을 미치고 있었다. 또한, 맞춤형 학습과 수학에 대한 태도와 수학학업성취도의 관계에서 학습시간과 자기주도적 학습능력의 매개효과가 유의하였다. The purpose of this study is to verify the effects of personalized learning platforms applied with machine learning recommendation modules that upgrade recommended algorithms by themselves through learning big data analysis on students' learning time, self-directed learning ability, mathematics achievement, and attitudes toward mathematics, and the correlation between them. According to the study, customized learning affected learning time, self-directed learning ability and mathematics attitude, while learning time affected self-directed learning ability. Self-directed learning ability has had a significant impact on the attitude of mathematics and mathematical achievements. As a result of the mediated effectiveness test, the indirect impact of customized learning on mathematics attitude and mathematics performance was significant through the medium of learning time and self-directed learning ability.

초등수학 수업의 동기 유발 방법 분석

박만구 ( Park Mangoo ) 한국수학교육학회 2017 初等 數學敎育 Vol.20 No.1

본 연구의 목적은 초등 예비교사들의 관점에서 수학 수업을 관찰하면서 동기 유발의 측면을 중심으로 동기 유발의 내용 및 방법, 그리고 예비교사들의 동기 유발에 대하여 분석하는 것이다. 연구 참여자들은 서울 지역의 2학년 또는 3학년에 재학 중인 예비교사 62명이었다. 이 예비교사들이 1주 또는 2주간의 교육실습 중 수학수업의 동기 유발 부분을 집중적으로 관찰한 후, 자신들의 관점에서 수학 수업에서의 동기 유발에 대한 분석한 결과와 의견을 제시하도록 하였다. 연구 결과, 예비교사들은 동기 유발을 주로 학생들의 흥미를 진작하기 위한 것과 주위집중을 위한 것으로 생각하였다. 동기 유발의 시간은 평균 5분 50초이고, 제한된 자료만을 사용하여 동기를 유발하였다. 연구자는 동기 유발 내용 및 방법이 차시의 목표와 세밀하게 연계할 수 있는 방안에 대한 후속 연구를 제언하였다. This study was to analyze motivations in the mathematics lessons from the perspectives of preservice elementary school teachers. The participants were three groups of 62 preservice elementary teachers who were sophomore or junior students in Seoul city in Korea. Two groups of the students were enrolled at teaching and learning mathematics courses, whereas one group of students were at mathematics problem solving course. They were randomly assigned to elementary schools for their student teaching. They were required to observe mathematics lessons focusing on motivations during their participating at the two-week student teaching period. The preservice teachers were asked to observe and submit the reports of the observation in the mathematics lesson. The researcher suggested a guideline of observation and analyzed the reports according to the categories those were suggested in the guideline. The results of the analysis on the reports are summarized as follows. First, the preservice elementary school teachers considered the purpose of motivations as attracting students` interest. Second, the major ratio of motivations were attracting students` attention in the mathematics lessons. Third, the duration average time was 5 minutes 50 seconds and only limited materials for the motivations. At last, most mathematics lessons need to stimulate students` curiosity that fits to the objectives of the lessons. The researcher suggests that we need to develop various motivations in mathematics lessons with which teachers should subtlely connected to the objectives of the lessons.

수학문제에 대한 예비교사의 인식분석

박만구 ( Park Mangoo ) 한국수학교육학회 2022 初等 數學敎育 Vol.25 No.1

The purpose of this study is to analyze how pre-service teachers perceive mathematics problems by making good mathematics problems at the elementary school level and applying them to elementary school students. In this study, 86 pre-service teachers enrolled in the second and third grades of A University of Education presented good mathematics problems they thought of. In addition, these pre-service teachers predicted the solution strategies of elementary school students for the proposed mathematics problem and described the teacher's expertise while observing the problem-solving process of elementary school students. As a result of the study, pre-service teachers preferred mathematical problems needed for using mathematical concepts or algorithms, motivation, and open-ended problems as good mathematics problems, and thought that students' in-depth observation and analysis experiences could help improve teachers' problem-solving expertise. In order to enhance teachers' expertise in solving mathematics problems, the researcher proposed for pre-service teachers to observe students' mathematics problem-solving processes, to experience in developing high-quality mathematics problems, and also to distribute high-quality mathematics problems linked to textbook problems.

문제해결에서 생산적 실패의 경험이 초등학생의 수학적 문제해결력 및 수학적 성향에 미치는 영향

박유나 ( Yuna Park ),박만구 ( Mangoo Park ) 한국수학교육학회 2015 初等 數學敎育 Vol.18 No.2

본 연구의 목적은 수학 수업에서 생산적 실패를 한 경험이 초등학생들의 수학적 문제해결력과 수학적 성향에 미치는 영향을 알아보는 것이다. 이를 위해 선행 연구를 바탕으로 생산적 실패를 경험할 수 있도록 수업 과정을 고안하였다. 연구대상으로 서울 은평구 Y초등학교 4학년 2개 학급을 선정하여 실험반은 생산적 실패를 활용한 수업을 진행하였으며, 비교반은 전통적인 강의식 수업을 진행하였다. 사전·사후 검사로 수학 개념이해 검사, 다양한 수학적 문제해결력 검사, 수학적 성향 검사를 실시하여 각각 t-검정하였으며, 학생들의 토의과정 및 활동지, 면담 등을 활용하여 수학적 문제해결력과 성향을 질적으로 분석하였다. 그 결과 생산적 실패를 경험한 학생들의 문제해결력과 수학적 성향에 유의미하게 개선되는 효과를 보였다. 이는 학생들이 실패를 통해 수학 개념을 스스로 구성하면서 보다 명확한 이해를 하는 과정에서 긍정적인 효과를 가져 온 것으로 보인다. 심층적인 추후 연구로 수학교과서 개발 및 수업 방법 개선에서 이를 활용해야 함을 제안하였다. The purpose of this study was to investigate the effects of the experiences of productive failures on students` mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students` various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students`s activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students` enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students` mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.