거북 행동을 통한 함수 그래프 구성

조한혁 ( Han Hyuk Cho ),송민호 ( Min Ho Song ) 한국수학교육학회 2008 수학교육논문집 Vol.22 No.2

교육공학 관련 교직과목과 교과교육 과목의 연계를 위한 도구

조한혁 ( Han Hyuk Cho ),송민호 ( Min Ho Song ) 한국수학교육학회 2010 수학교육논문집 Vol.24 No.4

사범대학 교칙과목인 교육방법 및 교육공학 과목과 수학교육 교과교육 과목인 수학교육과 교육공학(또는 컴퓨터와 수학교육)을 연계시켜 강의하는 방안을 제안한다. 현실적으로 예비교사들이 임용고사와 관련된 교직과목의 내용을 필수적으로 들어야 하기에, 우리는 교육공학 관련 교직과목의 내용을 중심으로 수학교육과 교육공학을 실습으로 접목시키는 연계방안을 실시하였다. 우리는 이러한 연계 교육과 실습을 위해 먼저 웹 2.0 기반 교육공학 이론과 수학사 기반 수학실험을 위한 마이크로월드 수학실험실을 설계하였다. 또한 인터넷에 구축된 수학실험실을 기반으로 교육공학 관련 교직과목 이론과 수학교육공학 관련 교과교육 내용의 실습을 진행하며 두 과목의 연계를 시도하였다. To get an undergraduate degree from mathematics education department, a student not only take a general educational technology course from education department, but also take an educational technology in mathematics education course from mathematics education department. We believe that these two courses can be integrated for preparing better mathematics teachers. For this purpose, we design an educational technology tool called JavaMAL microworld, and study strategy to integrate two courses harmoniously. This kind of approach is good for internationalization of researches on mathematics education by Korean researchers since most SSCI journal prefer an integrated approach in the educational technology related papers. In short, integrating general educational technology course and educational technology in mathematics education course is not only good to student but to professors. But just integrating two courses is not enough. Students must understand the needs and the usefulness of educational technology tool in the learning and teaching of mathematics, and must have such experience from their mathematics courses.

교육용 컴퓨터 언어 MAL과 FRACTALS 표현

조한혁(Han-Hyuk Cho) 대한수학교육학회 1992 수학교육학연구 Vol.2 No.1

수학사와 수학실험을 통한 다면체 탐구

조한혁 ( Han Hyuk Cho ),송민호 ( Min Ho Song ),최재연 ( Jae Yeun Choi ) 한국수학교육학회 2009 수학교육논문집 Vol.23 No.2

사이버 수학멘토링 시스템 설계에 대한 연구

조한혁 ( Han Hyuk Cho ),송민호 ( Min Ho Song ),진만영 ( Man Young Jin ) 한국수학교육학회 2009 수학교육논문집 Vol.23 No.2

큰 수의 법칙 시뮬레이션에서 중학생의 안구 운동 분석

최인용,조한혁,Choi, In Yong,Cho, Han Hyuk 한국수학교육학회 2017 수학교육 Vol.56 No.3

This study analyzed the difficulties of middle school students in computer simulation of the law of large numbers through eye movement analysis. Some students did not attend to the simulation results and could not make meaningful inferences. It is observed that students keep the existing concept even though they observe the simulation results which are inconsistent with the misconceptions they have. Since probabilistic intuition influence student's thinking very strongly, it is necessary to design a task that allows students to clearly recognize the difference between their erroneous intuitions and simulation results. In addition, we could confirm through eye movements analysis that students could not make meaningful observations and inferences if too much reasoning was needed even though the simulation included a rich context. It is necessary to use visual representations such as graphs to provide immediate feedback to students, to encourage students to attend to the results in a certain intentional way to discover the underlying mathematical structure rather than simply presenting experimental data. Some students focused their attention on the visually salient feature of the experimental results and have made incorrect conclusion. The simulation should be designed so that the patterns of the experimental results that the student must discover are not visually distorted and allow the students to perform a sufficient number of simulations. Based on the results of this study, we suggested that cumulative relative frequency graph showing multiple results at the same time, and the term 'generally tends to get closer' should be used in learning of the law of large numbers. In addition, it was confirmed that eye-tracking method is a useful tool for analyzing interaction in technology-based probabilistic learning.

원뿔곡선의 수학사와 수학교육

진만영,김동원,송민호,조한혁,Jin, Man Young,Kim, Dong Won,Song, Min Ho,Cho, Han Hyuk 한국수학사학회 2012 Journal for history of mathematics Vol.25 No.4

고등학교 교육과정에서 학생들은 원뿔곡선 조작 환경을 제공 받지 못하고 초점과 준선을 이용하여 대수적 정의를 받아들이며, 원뿔곡선을 동적인 의미 없이 정적인 대수적 문제로 국한해서 생각하는 경향이 있다. 대수적인 표현뿐만 아니라 동적인 기하학적 표현을 보완하기 위해 원뿔곡선을 원뿔 절단으로 정의한 역사적 근거를 해시계에서 찾고 원뿔 절단으로는 설명할 수 없는 초점과 준선 개념의 역사도 살펴본다. 그리고 원뿔곡선을 연속적으로 그리기 위해 사용된 도구들에 대해서 알아보고, 학생들의 활동을 위한 공학적 도구로 컴퓨터 환경을 살펴본다. The conic sections are defined as algebraic expressions using the focus and the directrix in the high school curriculum. However it is difficult that students understand the conic sections without environment which they can manipulate the conic sections. To make up for this weak point, we have found the evidence for generating method of a conic section through a sundial and investigated the history of terms 'focus', 'directrix' and the tool of drawing them continuously.

공간 시각화 과제에 체화된 거북 스킴 적용에 관한 연구

이지윤 ( Ji Yoon Lee ),조한혁 ( Han Hyuk Cho ),송민호 ( Min Ho Song ) 한국수학교육학회 2013 수학교육 Vol.52 No.2

The theory of embodied cognition assumes that behaviors, senses and cognitions are closely connected, and there is a growing interest in investigating the significance of embodied cognition in the field of mathematics education, This study aims to applicate the embodied turtle metaphor and expressions when students visualize three-dimensional objects. We used MRT(Verdenberg & Kuse, 1978) & SVT for this research and both tests turned out that turtle schemes are useful to the students in a low level group. In addition, students found turtle schemes more useful in SVT which requires constructing three-dimensional objects, than in MRT which requires just rotating the image of three-dimensional objects in their mind. These results suggest that providing students who are less capable of spatial visualizing with the embodied schemes like turtle metaphor and expressions can be an alternative to improve their spatial visualization ability.

수학교과와 정보교과를 융합하는 코딩수학 교육과정 및 교육방법 연구

강하람 ( Kang¸ Ha Ram ),임채령 ( Lim¸ Chae Lyeong ),조한혁 ( Cho¸ Han Hyuk ) 한국수학교육학회 2021 수학교육 Vol.60 No.4

본 연구는 초·중학교 수학교과와 정보교과를 융합하는 코딩수학 교육과정과 이를 위한 최소 코딩게임 기반 교육방법에 대한 연구이다. 지난 3년간 코딩수학 교육과정과 효과적인 교육방법을 초6학년과 중1학년 학생을 대상으로 연구하였다. 1차년도 연구결과, 공간좌표의 필요성에 따라 3차원 좌표의 수학적 개념을 포함하는 코딩환경으로 교육과정을 수정하였다. 2차년도 연구결과, 명령어의 위계성에 따라 건물 요소별 다른 수준의 명령어를 도입하여 자기주도적 학습이 가능하도록 개선하였다. 3차년도 연구 결과, 컴퓨팅 사고력 향상을 유도하는 최소 코딩게임 기반의 교수·학습 전략을 설계하고, 컴퓨팅 사고력 진단을 위한 평가 및 피드백을 개발하였다. 자기주도적 학습 및 컴퓨팅 사고력 증진을 유도하는 최소 코딩게임 기반 교육방법과 코딩수학 교육과정은 수학-정보교과의 융합교육 연구와 실천에 의미가 있다. This study is a study on the coding mathematics curriculum that converges elementary and middle school mathematics and information subjects and a minimum coding game-based education method for this. For the past 3 years, the coding mathematics curriculum and educational methods to effectively operate the curriculum were studied by applying them to 6th graders of elementary school and 1st graders of middle school. As a result of the first year of research, the coding mathematics curriculum was modified to a coding environment including the mathematical concept of a three-dimensional coordinate space, and the three-dimensional object was improved to be output as a real 3D print. As a result of the 2nd year study, it was improved so that even low-level students can build buildings by introducing different level commands for each component of the building so that self-directed learning is possible. As a result of the 3rd year study, a teaching-learning strategy based on a minimal coding game was designed to induce an increase in the level of computational thinking, and evaluation and feedback for diagnosing computational thinking were developed. Educational methods to promote self-directed learning and computing thinking ability, and researched coding mathematics curriculum are meaningful for the research and practice of the convergence education of school mathematics and informatics.

코딩수학 내용 및 환경 설계

김나리(Kim Na Ry),서용현(Seo Yong Hyun),조한혁(Cho Han Hyuk) 학습자중심교과교육학회 2018 학습자중심교과교육연구 Vol.18 No.4

4차 산업혁명 시대를 맞아 전세계적으로 컴퓨팅 사고력(Computational Thinking: CT)이 필수 학습역량으로 강조되고 있으며, 코딩과 수학이 융합된 코딩수학이 논의되고 있다. 본 연구에서는 Freudenthal ‘수학화’ 이론을 기반으로 제작된 MiC 교과서의 ‘패턴과 일반화’로 이루어진 대수교육과정을 CT의 대표적인 요소인 ‘추상화’와 ‘자동화’를 융합이 가능한 언플러그드 코딩수학의 대표적인 사례로 보고, 터틀 쌓기 나무 코딩 환경과 융합하여 학습자가 지식을 구성할 수 있는 플러그드 코딩수학으로 설계한다. 즉, 본 연구는 초기대수학습에 CT가 적절히 융합된 코딩수학의 한 사례를 제시하고 학교 현장에 대한 적용가능성을 높이는 데에 목적이 있다. 이를 프로젝트 학습에 기반하여 자기주도적 학습을 권고하는 자유학기제 수업에 적용한다. 자유학 기제 수업에 적용하기 위해서는 자발적 참여를 유도하는 것이 필수적인 바, 터틀 (Turtle) 쌓기나무 환경에 마인크래프트(MineCraft) 게임환경을 융합하여 제공하고 S중학교 자유학기제 수업에 적용한 결과를 분석한다. Computational Thinking (CT) is being emphasized as an essential learning capability around the world in the era of the Fourth Industrial Revolution, and coding mathmatics with fusion of coding and mathematics is being discussed. The algebraic curriculum consisting of Patterns and Generalization in MiC textbooks based on the Freudenthal mathematization can be intergrated with abstraction and automation which are the representative elements of CT. As representative example of unplugged coding mathematics, it is designed with plugged coding mathematics by merging it with Turtle Building Block environment. Because Turtle Building Block environment can make it possible for student to construct knowledge. So, the purpose of this study is to present an example of coding mathematics by integrating CT with early algebra and to increase applicability to the field of school. And we apply it to the free-semester class which is recommended for the Self - Directed Learning through Project Based Learning(PBL). It is necessary to induce voluntary participation from students in free-semester class so that this study integrated MineCraft s game environment into the Turtle Building Block environment. In this paper, we present and analyze the results applied to the free-semester class in S middle school.