수학문제에 대한 예비교사의 인식분석

박만구 ( Park Mangoo ) 한국수학교육학회 2022 초등수학교육 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.

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.

초등수학 수업의 동기 유발 방법 분석

박만구 ( Park Mangoo ) 한국수학교육학회 2017 초등수학교육 Vol.20 No.1

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.

수학교육에서 인공지능 활용 가능성

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

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.

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

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.

학생성장을 위한 초등수학 수행평가모델의 개발 및 적용1)

고상숙,박만구 ( Mangoo Park ),강경은 ( Kyung Eun Kang ),김혜영 ( Hye Young Kim ) 한국수학교육학회 2015 수학교육논문집 Vol.29 No.4

The purpose of this study was to develop and verify the feedback-enhanced performance assessment model through a variety of assessment strategies focused on the development of students. In order to achieve the purpose of this study, we analyzed the achievements of the sixth grade curriculum standards and set the central achievement standards in core competencies. We then established an evaluation plan to take advantage of a variety of methods and develop an assessment tool for process-based evaluation during lessons. We applied this assessment model to 6th grade students while teaching and learning mathematics in the classroom. The result of applying the performance evaluation model showed the improvement of students`` reflective thinking ability. Also, some students who was not achieved at the level of ``N`` could develop to the level of ``N + 1``. A long term research using various assessment strategies should be continued for effective help of students`` mathematical development.

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

박유나 ( Yuna Park ),박만구 ( Mangoo Park ) 한국수학교육학회 2015 초등수학교육 Vol.18 No.2

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.

동료 멘토링 수학 수업에서 학생의 수학적 인성 및 수학 학업성취도 분석

배경준 ( Bae Kyung Joon ),박만구 ( Park Mangoo ) 한국수학교육학회 2016 초등수학교육 Vol.19 No.4

This study was to investigate the effects of peer mentoring on students` mathematical characters and mathematics achievements in mathematics class. The participants were twenty four 6th grade elementary students at the S school in Sungbuk-Gu, Seoul, Korea. They were divided into 4 groups according to the combination of groups. The researchers analyzed the experimental group and the control group with covariances on the sub-factors of the mathematical characters such as respect, caring, sharing, and openness. However, there were no statistically significant changes. However, with the help of the two analyses on the mathematical logs and the worksheets which had been carried out in advance by the quantitative and qualitative research methods, the researchers investigated how the peer mentoring-applied instructions would change the mathematical characters for each sub-factor in detail. In conclusion, the peer mentoring-applied instructions makes a positive contribution to the students` mathematical character and mathematical academic achievements. We suggest that peer mentoring in mathematics lessons should be adopted in various mathematical ability levels of students.

수학 학습 평가틀 비교 분석 -NAEP 2015, TIMSS 2015, PISA 2015를 중심으로-

한채린 ( Chaereen Han ),박만구 ( Mangoo Park ) 한국수학교육학회 2015 수학교육 Vol.54 No.3

The purpose of this study was to provide insights on making Korean mathematics framework by analytical comparison of three major assessments such as the NAEP 2015, the TIMSS 2015 and the PISA 2015. This study focused on the key differences and common themes of mathematics frameworks among three major assessments. In order to achieve this purpose, mathematical frameworks of the NAEP 2015, the TIMSS 2015, and the PISA 2015 were analyzed and compared. The criteria of the comparison were content domain and cognitive domain. The comparing criteria of content domain were based on NCTM content standards and cognitive domain were used the three understanding levels of Jan de Lange`s pyramid model. Based on these comparisons, researchers discussed that Korea mathematical framework was needed to have a set of content categories that reflect the range of underlying mathematical phenomena and a set of cognitive levels which contain the range of underlying fundamental mathematical capabilities including consideration of contexts.

합리적 의사결정을 강조한 수학영재교육프로그램이 초등수학영재의 수학적 신념에 미치는 영향: 게임이론을 중심으로

김영현(Kim, Younghyun),박만구(Park, Mangoo) 한국과학영재교육학회 2019 과학영재교육 Vol.11 No.2

이 연구의 목적은 합리적 의사결정을 강조한 수학영재교육프로그램을 개발하고 적용하여 그 특징과 수학적 신념 변화를 알아보는데 있다. 본 연구에서는 수학적 사고활동이 합리적인 의사결정을 내리는데 좋은 훈련이 될 수 있다는 점을 바탕으로 프로그램을 구성하였으며, 그 소재로 게임이론을 택하였다. 프로그램 개발을 위한 사전연구를 실시하고 개발 유형 및 준거를 설정하였으며, 이를 바탕으로 합리적 의사결정을 강조한 수학영재교육프로그램을 개발하였다. 개발한 프로그램은 초등수학영재에게 적용하고 수학적 신념의 사전-사후 결과를 비교하고 연구대상의 반응을 분석하여 그 영향을 검증하였으며, 적용결과를 바탕으로 프로그램의 특징을 도출하였다. 연구 결과 본 프로그램은 초등수학영재의 수학적 신념에 긍정적인 영향을 주었으며, 풍부한 의사결정의 경험 제공과 함께 수학의 가치와 중요성에 대해 제고할 수 있는 계기를 마련하였다. 합리적 의사결정을 강조한 영재교육프로그램의 소재와 난이도를 조정하여 다양한 대상에서의 적용 가능성 연구를 제안하였다. The purpose of the study is to develop and apply a mathematically gifted education program that emphasizes rational decision-making to examine its characteristics and changes in students mathematical beliefs. Based on the fact that mathematical thinking activities can be make a good role to make rational decisions, researchers have organized programs and selected game theory as its theoretical background. With preliminary surveys for program development and setting development types and compliance, and researchers developed a mathematically gifted education program emphasizing rational decision-making. The developed programs were applied to mathematically talented elementary school students for comparing students mathematical beliefs by examining results after each step, analyzing the responses of the students, verifying the impacts, and deriving program characteristics. As a result of the study, the program provided positive influences on the mathematical beliefs of mathematically talented elementary school students and improve the value and importance of mathematics along with providing rich decision-making experiences. Researchers suggest that applications to various subjects by adjusting the program that emphasizes rational decision-making.