The Mathematical Education

Issue: Vol.50 No.4

Model Lessons of mathematical practice focus on creativity and character education curriculum 권오남 Oh Nam Kwon , 박지현 Jee Hyun Park , 박정숙 Jeung Sook Park 50(4) 403-428, 2011 Model Lessons of mathematical practice focus on creativity and character education curriculum 권오남 Oh Nam Kwon , 박지현 Jee Hyun Park , 박정숙 Jeung Sook Park DOI: JANT Vol.50(No.4) 403-428, 2011 The direction of recent education literature points to the importance of creativity and creative practices, which also plays an important role in character education and has been recognized as being invaluable for the educational goals of the 21st century. As such, the goal of mathematics educators and researchers has also been on emphasizing the importance of building character and promoting creative practices. In this research, we study the pedagogical measures that can be easily implemented in classrooms to foster creative mathematical thinking and practices in students. In particular, the mathematical topic of interest is three-dimensional geometry, and especially polygons, and processes in which mathematical knowledge and creative practices play out in classrooms. For example, we explore how these creative lessons can be organized as the target internalization lessons, concepts definition lessons, regularity and relationship lessons, question posing lessons, and narrative story lessons. All of these lessons share three commonalities: 1) they require specific planning and execution challenges in order to achieve creative tasks, 2) they take advantage of open-ended problems, and 3) they are activity-oriented. Through this study, we hope to further our understanding on successful creative mathematical educational practices in the field of mathematics education, and help establish model lessons and materials for teachers and educators to use towards such goals.
The Transition from Everyday Definitions to Mathematical Definitions -Gifted Middle School Students` Conceptions of Point and Line definitions- 이지현 Ji Hyun Lee 50(4) 429-440, 2011 The Transition from Everyday Definitions to Mathematical Definitions -Gifted Middle School Students` Conceptions of Point and Line definitions- 이지현 Ji Hyun Lee DOI: JANT Vol.50(No.4) 429-440, 2011 This paper analysed gifted middle students` conception of the definitions of point and line and the uses of definitions in proving. The findings of this paper suggest that the concept of mathematical definitions is very unnatural to students, therefore teachers and textbooks need to explain explicitly the characteristics of mathematical definitions which are different from dictionary definitions using common sense. Also introducing undefined terms in middle school geometry would give students a critical chance to deal with the transition from dictionary definitions to mathematical definitions.
A Study on the Teaching Design of the Isoperimetric Problem on a Plane for Mathematically gifted students in the Elementary School -focused on the geometric methods- 최근배 Keun Bae Choi 50(4) 441-466, 2011 A Study on the Teaching Design of the Isoperimetric Problem on a Plane for Mathematically gifted students in the Elementary School -focused on the geometric methods- 최근배 Keun Bae Choi DOI: JANT Vol.50(No.4) 441-466, 2011 In this article, we study on the teaching design, focused on the geometric methods, of 2-D isoperimetric problem for the elementary mathematically gifted students. For our teaching design, we discussed the ideals of Zenodorus`s polygon proof, Steiner`s four-hinge proof, Steiner`s mean boundary proof, Steiner`s snowball-packing proof, Edler`s finite existence proof and Lawlor`s dissection proof, and then the ideals achieved were modified with the theoretical backgrounds-the theory of Freudenthal`s mathematisation, the method of analysis-synthesis. We expect that this article would contribute to the elementary mathematically gifted students to acquire and to improve spatial sense.
Effects of Project Based Material on Problem solving Ability and Attitude of Mathematically Gifted in Science High School -Focusing on Probability and Statistics- 이종학 Jong Hak Lee 50(4) 467-487, 2011 Effects of Project Based Material on Problem solving Ability and Attitude of Mathematically Gifted in Science High School -Focusing on Probability and Statistics- 이종학 Jong Hak Lee DOI: JANT Vol.50(No.4) 467-487, 2011 The purpose of this study is to analyze of gifted students` improvement on mathematical attitude and problem-solving ability through project-based materials in science high school. For this study, research questions are established as follows. 1. Does the project-based materials-used instruction have a positive effect on improving problem-solving ability? 2. Does the project-based materials-used instruction have a positive effect on improving mathematical attitude? To solve these research questions, this study employed a survey and interview type investigation for gifted students` mathematical attitude and problem-solving ability. A subject of classes were randomly selected among the 11th grader in Dscience high school and designated one class as the experimental group and the other class as the control group. Twelve hours of the project-based materials-used instruction and the traditional textbook-oriented instruction had been carried out in each class. Findings on this study are as follows: First, the project-based material-used instruction is shown to be more effective in enhancing problem-solving ability than the traditional textbook-oriented instruction. Second, the project-based material-used instruction is shown to be more effective in improving mathematical attitude than the traditional textbook-oriented instruction.
A summary-concept based analysis on the representative values and the measures of spread with the 9th grade Korean mathematics textbook 이영하 Young Ha Lee , 이은희 Eun Hee Lee 50(4) 489-505, 2011 A summary-concept based analysis on the representative values and the measures of spread with the 9th grade Korean mathematics textbook 이영하 Young Ha Lee , 이은희 Eun Hee Lee DOI: JANT Vol.50(No.4) 489-505, 2011 This study is an analysis on the focus of textbooks regarding the statistical chapters of "measures of representative(central tendency) and of the spread". Applying the summary-concept criteria of Juhyeon Nam(2007), 4 kinds of aspect of the chapter; (1)definition and its teleological validity of the measures of representative, (2) definition and practical value of the measures of spread (3) distributional form on the measures of representative and of spread (4) location and scale preservation or invariance of the measures of representative and of spread were observed. On the measures of representative, some definitions were insufficient to check the teleological validity of the measure. Most definitions of the measure of spread were based on the practical view points but no preparation for the future statistical inferences were found even by implication. Some books mention about the measures of representative and of spread for distributions, but we could not find any comments on the correspondence between the sample mean and the expectation of a distribution or population mean. However it is stimulant that some books check the validity of corresponding measures with the location and scale preservation or invariant property, that were not found in the previous curriculum.
Trends in Research on Mathematics Curriculum: An Analysis of Research Topics 권나영 Na Young Kwon , 김래영 Rae Young Kim , 김구연 Goo Yeon Kim 50(4) 507-520, 2011 Trends in Research on Mathematics Curriculum: An Analysis of Research Topics 권나영 Na Young Kwon , 김래영 Rae Young Kim , 김구연 Goo Yeon Kim DOI: JANT Vol.50(No.4) 507-520, 2011 Teaching and learning in schools can be influenced by the ways in which curriculum is understood in terms of its characteristics and range. Viewing curriculum as encompassing all activities pertaining to teaching and learning allows us to examine various aspects of education through curriculum studies. In this respect, this study explores the trends in research on K-12 mathematics curriculum by examining prior studies` research topics categorized into five themes in curriculum studies. In addition, implications for future research are discussed based on the findings of this study.