• Title/Summary/Keyword: 수학화 과정

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Performance Assessment for Mathematically Gifted (수학영재교육에서의 관찰평가와 창의력평가)

  • Shin, Hui-Young;Ko, Eun-Sung;Lee, Kyung-Hwa
    • School Mathematics
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    • v.9 no.2
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    • pp.241-257
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    • 2007
  • The study aims to figure out how to improve existing examination tools to distinguish mathematically gifted children and to clarify procedures and criteria for selecting candidates. Toward this end, it examined correlations between grades of gifted children selected through evaluation by pen-and-pencil tests and their creative problem-solving capability and performance assessment, and analyzed learning activities of the gifted children. According to the analysis, results of pen-and-pencil tests turned out to have low correlations with their creative problem-solving capability and performance assessment, but it was found that their creative problem-solving capability has high correlations with results of performance assessment. The analysis also found that there were some students who participated in a program for gifted children with high marks but had difficulties in adapting themselves to it. It found that there were children who joined the program with low marks but emerged as successive performers later on. In this regard, the existing examination tools to tell the gifted students apart need to be used to the fullest extent, and other diversified tools to evaluate mathematical capabilities that include mathematical creativity need to be further studied and developed. Qualitative studies on affective development of the gifted students and their creative problem-solving processes need to be conducted.

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A Design of Teaching Unit to Foster Secondary pre-service Teachers' Mathematising Ability : Exploring the relationship between partition models and generalized fobonacci sequences (예비중등교사의 수학화 학습을 위한 교수단원의 설계: 분할모델과 일반화된 피보나치 수열 사이의 관계 탐구)

  • Kim, Jin-Hwan;Park, Kyo-Sik
    • Journal of Educational Research in Mathematics
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    • v.18 no.3
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    • pp.373-389
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    • 2008
  • In this paper, we designed a teaching unit for the learning mathematization of secondary pre-service teachers through exploring the relationship between partition models and generalized fibonacci sequences. We first suggested some problems which guide pre-service teachers to make phainomenon for organizing nooumenon. Pre-service teachers should find patterns from partitions for various partition models by solving the problems and also form formulas front the patterns. A series of these processes organize nooumenon. Futhermore they should relate the formulas to generalized fibonacci sequences. Finding these relationships is a new mathematical material. Based on developing these mathematical materials, pre-service teachers can be experienced mathematising as real practices.

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Analyzing Tasks in the Geometry Area of 7th Grade of Korean and US Textbooks from the Perspective of Mathematical Modeling (수학적 모델링 관점에 따른 한국과 미국의 중학교 1학년 교과서 기하 영역에 제시된 과제 분석)

  • Jung, Hye-Yun;Jung, Jin-Ho;Lee, Kyeong-Hwa
    • Journal of the Korean School Mathematics Society
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    • v.23 no.2
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    • pp.179-201
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    • 2020
  • The purpose of this study is to analyze tasks reflected in Korean and US textbooks according to the mathematical modeling perspectives, and then to compare the diversity of learning opportunities given to students from both countries. For this, we analyzed mathematical modeling tasks of textbooks based on three aspects: mathematical modeling process, data, and expression. Results are as follows. First, with respect to modeling process, Korean textbook provides a high percentage of the task at all stages of modeling than US textbook. Second, with respect to data, both countries' textbooks have the highest percentage of matching task. Korean textbooks have a large gap in data characteristics by textbook. Third, with respect to expression, both countries' textbooks have the highest percentage of text and picture. Korean textbooks have a large gap in the type of expression than US textbooks, and some textbooks have no other expression except for text and picture. Fourth, tasks were analyzed by integrating the three features. The three features were not combined in various ways. It is necessary to diversify the integration of the three features.

Analysis on Connection of Curriculum and Textbooks in Elementary School Mathematics : Focused on 5~6 Grades (초등학교 수학과 교육과정과 교과서의 연계 분석 - 2009 개정 교육과정 초등학교 5~6학년군을 중심으로 -)

  • Chang, Hyewon;Kang, Teaseok;Lim, Miin
    • Journal of Educational Research in Mathematics
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    • v.26 no.1
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    • pp.121-141
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    • 2016
  • In Korea where there is the national curriculum and teachers depend highly on textbooks, the school mathematics is based on curriculum and textbooks. Especially considering responsibility that textbooks should reflect the curriculum properly, it is necessary to analyze the connection of mathematics curriculum and textbooks in order to review and improve the quality of our mathematics education. This research analyzes the connection of curriculum and textbooks for 5~6 grades and aims to have some implications for revision of the textbooks when application of elementary mathematics textbooks based on the 2009 revised national curriculum is completed to all grades. Following the preceding research for 1~2 and 3~4 grades, this research sets 5~6 grades as a subject of analysis and has four contents of analysis; analysis of textbooks based on restructured achievement criteria, analysis of connections between unit objectives of textbooks and the reconstructed achievement criteria, analysis of textbooks related to mathematical terms and symbols, and analysis of textbooks related to mathematical process. The result of analysis has some implications to develop textbooks based on the 2015 revised national curriculum.

Note on a Method for Mathematical Creativity Assessment by Differentiating the Student's Solutions of the Posed Problems (문제해결 방법의 차등화를 통한 수학적 창의성 평가에 대한 소고)

  • Kim, Pan Soo;Kim, Nan Young
    • Journal of Elementary Mathematics Education in Korea
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    • v.17 no.3
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    • pp.503-522
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    • 2013
  • In the 2009 new curriculum reform, where creativity is the key point, assessment methods for mathematical creativity is recommended. However, lessons for creativity are not carried out well in mathematics classes. One of the reasons for this is the lack of assessment methods for student's creativity and specific instructions on how teachers should evaluate their students using a written test. Therefore, in this paper, we propose a simple way to evaluate student's creativity by differentiating the student's solutions of the posed problems. For validation of the proposed method, we identified the properties of excellent problem solutions cited by both the students group and teachers group. A chi-square test was then carried out to compare any differences in frequency that each of the groups chose as an excellent solution as a result of the student's problem solving

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초등수학 기하문제해결에서의 시각화 과정 분석

  • Yun, Yea-Joo;Kim, Sung-Joon
    • East Asian mathematical journal
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    • v.26 no.4
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    • pp.553-579
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    • 2010
  • Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

테크놀로지를 활용한 교수학적 환경에서 대수적 연산 오류 지도에 관한 연구

  • Park, Yong-Beom;Tak, Dong-Ho
    • Communications of Mathematical Education
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    • v.18 no.1 s.18
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    • pp.223-237
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    • 2004
  • 본 연구는 중학교 1학년을 대상으로 일차방정식의 풀이 과정에서 나타나는 오류를 분석하고 그래핑 계산기를 활용하여 오류의 교정 과정을 제시하였다. 오류의 유형을 개념적 이해 미흡 오류, 등식의 성질에 대한 오류, 이항에 대한 오류, 계산 착오로 인한 오류, 기호화에 의한 오류로 분류하였으며, 이 중에서 등식의 성질에 대한 오류와 개념적 이해 미흡으로 인한 오류를 많이 범하고 있었다. 학생들이 TI-92를 활용하여 일차방정식의 해를 구할 때, Home Mode에서 Solve 기능을 이용하여 단순히 결과만을 보는 것 보다 Symbolic Math Guide를 이용하여 풀이 과정을 선택하여 대수적 알고리즘을 형성하면서 해를 구하는 것을 선호하였다. 그리고 학생들의 정의적 및 기능적 측면을 고려해야 할 필요성을 느끼게 되었다.

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Analyzing the Performance Expectations of the 2022 Revised Mathematics and Science Curriculum from a Data Visualization Competency Perspective (데이터 시각화 역량 관점에서 2022 개정 수학/과학 교육과정의 성취기준 분석)

  • Dong-Young Lee;Ae-Lyeong Park;Ju-Hee Jeong;Ju-Hyun Hwang;Youn-Kyeong Nam
    • Journal of the Korean Society of Earth Science Education
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    • v.17 no.2
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    • pp.123-136
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    • 2024
  • This study examines the performance expectations (PEs) and clarification statements of each PE in the 2022 revised national science and mathematics education standards from a data visualization competency perspective. First, the authors intensively reviewed data visualization literature to define key competencies and developed a framework comprising four main categories: collection and pre-processing skills, technical skills, thinking skills, and interaction skills. Based on the framework, the authors extracted a total of 191 mathematics and 230 science PEs from the 2022 revised science and mathematics education standards (Ministry of Education Ordinance No. 2022-33, Volumes 8 and 9) as the main data set. The analysis process consisted of three steps: first, the authors organized the data (421 PEs) by the four categories of the framework and four grade levels (3-4th, 5-6th, 7-9th, and 10th grade); second, the numbers of PEs in each grade level were standardized by the accomplishing period (1-3 years) of each PE depending on the grade level; lastly, the data set was represented by heatmaps to visualize the relationship between the four categories of visualization competency and four grade levels, and the differences between the competency categories and grade levels were quantitatively analyzed using the Mann-Whitney U test and independent sample Kruskal-Wallis tests. The analysis results revealed that in mathematics, there was no significant difference between the number of PEs by grade. However, on average, the number of PEs categorized in 'thinking skills' was significantly lower than those in the technical skills (p = .002) and interaction skills categories (p = .001). In science, it was observed that as grade level increased, PEs also increased (pairwise comparison: Grades 5-6 vs. 7-9, p = .001; Grades 5-6 vs. Grade 10, p = .029; Grades 3-4 vs. 7-9, p = .022). Particularly, the frequency of PEs in 'thinking skills' was significantly lower than in the other skills (pairwise comparison: technical skills p = .024; collection and pre-processing skills p = .012; interaction skills p = .010). Based on the results, two implications for revising national science and mathematics standards and teacher education were suggested.

Visualization of Linear Algebra concepts with Sage and GeoGebra (Sage와 GeoGebra를 이용한 선형대수학 개념의 Visual-Dynamic 자료 개발과 활용)

  • Lee, Sang-Gu;Jang, Ji-Eun;Kim, Kyung-Won
    • Communications of Mathematical Education
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    • v.27 no.1
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    • pp.1-17
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    • 2013
  • This work started with recent students' conception on Linear Algebra. We were trying to help their understanding of Linear Algebra concepts by adding visualization tools. To accomplish this, we have developed most of needed tools for teaching of Linear Algebra class. Visualizing concepts of Linear Algebra is not only an aid for understanding but also arouses students' interest on the subject for a better comprehension, which further helps the students to play with them for self-discovery. Therefore, visualizing data should be prepared thoroughly rather than just merely understanding on static pictures as a special circumstance when we would study visual object. By doing this, we carefully selected GeoGebra which is suitable for dynamic visualizing and Sage for algebraic computations. We discovered that this combination is proper for visualizing to be embodied and gave a variety of visualizing data for undergraduate mathematics classes. We utilized GeoGebra and Sage for dynamic visualizing and tools used for algebraic calculation as creating a new kind of visual object for university math classes. We visualized important concepts of Linear Algebra as much as we can according to the order of the textbook. We offered static visual data for understanding and studied visual object and further prepared a circumstance that could create new knowledge. We found that our experience on visualizations in Linear Algebra using Sage and GeoGebra to our class can be effectively adopted to other university math classes. It is expected that this contribution has a positive effect for school math education as well as the other lectures in university.

A Study on Improving the Quality of the Assessment Items by Analyzing the Types of Their Modification (평가 문항의 질 향상을 위한 문항 수정 유형 분석)

  • Ko, Jung-Hwa
    • School Mathematics
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    • v.12 no.2
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    • pp.113-136
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    • 2010
  • According to the self-assessment tool identifying teacher's competence in assessment, many teachers have difficulty in making assessment tools. This study analyzes the types of modification with data of NAEA(National Assessment of Educational Achievement) items from 2006 to 2008. NAEA goes through complicated formalities from begin to make draft items to completing them. This study shows the types of item modification and its specific examples. NAEA analyzes the degrees of studuents' achievement according to the educational objectives of the National Curriculum. This study provides specific comments on making mathematics assessment items to the teachers who embody national curriculem. Therefore this study will contribute to improve mathematics teacher's professional competence in the area of assessment tool development.

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