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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
> Journal Vol & Issue
The Mathematical Education
Journal Basic Information
Journal DOI :
Korea Society of Mathematical Education
Editor in Chief :
Volume & Issues
Volume 51, Issue 4 - Nov 2012
Volume 51, Issue 3 - Aug 2012
Volume 51, Issue 2 - May 2012
Volume 51, Issue 1 - Feb 2012
Selecting the target year
Complex number on textbooks and Analysis on understanding state of students
Park, Seon-Ho ; Pyo, Sung-Soo ;
The Mathematical Education, volume 51, issue 1, 2012, Pages 1~19
DOI : 10.7468/mathedu.2012.51.1.001
In this study, contents of 'the 2007 revised curriculum handbook' and 16 kinds of mathematics textbooks were analyzed first. The purpose of this study is to examine the understanding state of students at general high schools by making questionnaires to survey the understanding state on contents of chapter of complex number based on above analysis. Results of research can be summarized as follows. First, the content of chapter of complex number in textbook was not logically organized. In the introduction of imaginary number unit, two kinds of marks were presented without any reason and it has led to two kinds of notation of negative square root. There was no explanation of difference between delimiter symbol and operator symbol at all. The concepts were presented as definition without logical explanations. Second, students who learned with textbook in which problems were pointed out above did not have concept of complex number for granted, and recognized it as expansion of operation of set of real numbers. It meant that they were confused of operation of complex numbers and did not form the image about number system itself of complex number. Implications from this study can be obtained as follows. First, as we came over to the 7th curriculum, the contents of chapter of complex number were too abbreviated to have the logical configuration of chapter in order to remove the burden for learning. Therefore, the quantitative expansion and logical configuration fit to the level for high school students corresponding to the formal operating stage are required for correct configuration of contents of chapter. Second, teachers realize the importance of chapter of complex number and reconstruct the contents of chapter to let students think conceptually and logically.
An Analysis of Students' Understanding of Operations with Whole Numbers and Fractions
Kim, Kyung-Mi ; Whang, Woo-Hyung ;
The Mathematical Education, volume 51, issue 1, 2012, Pages 21~45
DOI : 10.7468/mathedu.2012.51.1.021
The purpose of the study was to investigate how students understand each operations with whole numbers and fractions, and the relationship between their knowledge of operations with whole numbers and conceptual understanding of operations on fractions. Researchers categorized students' understanding of operations with whole numbers and fractions based on their semantic structure of these operations, and analyzed the relationship between students' understanding of operations with whole numbers and fractions. As the results, some students who understood multiplications with whole numbers as only situations of "equal groups" did not properly conceptualize multiplications of fractions as they interpreted wrongly multiplying two fractions as adding two fractions. On the other hand, some students who understood multiplications with whole numbers as situations of "multiplicative comparison" appropriately conceptualize multiplications of fractions. They naturally constructed knowledge of fractions as they build on their prior knowledge of whole numbers compared to other students. In the case of division, we found that some students who understood divisions with whole numbers as only situations of "sharing" had difficulty in constructing division knowledge of fractions from previous division knowledge of whole numbers.
A study of gifted students's mathematical process of thinking by connecting algebraic expression and design activities
Kwon, Oh-Nam ; Jung, Sun-A ;
The Mathematical Education, volume 51, issue 1, 2012, Pages 47~61
DOI : 10.7468/mathedu.2012.51.1.047
Students can infer mathematical principles in a very natural way by connecting mutual relations between mathematical fields. These process can be revealed by taking tasks that can derive mathematical connections. The task of this study is to make expression and design it and derive mathematical principles from the design. This study classifies the mathematical field of expression for design and analyzes mathematical thinking process by connecting mathematical fields. To complete this study, 40 gifted students from 5 to 8 grade were divided into two classes and given 4 hours of instruction. This study analyzes their personal worksheets and e-mail interview. The students make expressions using a functional formula, remainder and figure. While investing mathematical principles, they generalized design by mathematical guesses, generalized principles by inference and accurized concept and design rules. This study proposes the class that can give the chance to infer mathematical principles by connecting mathematical fields by designing.
On Social and Psychological Benefits of Cooperative Learning
Choi, Eun-Mi ;
The Mathematical Education, volume 51, issue 1, 2012, Pages 63~76
DOI : 10.7468/mathedu.2012.51.1.063
The purpose of this study is to investigate the effect of cooperative learning in mathematics in university level. We share reflections from 54 and 57 students in linear algebra courses which were conducted by cooperative learning. We examine how students increase self-confidence and reduce the anxiety in learning, and also develop the social skills in communication.
Students' conceptual development of eigenvalue and eigenvector based on the situation model
Shin, Kyung-Hee ;
The Mathematical Education, volume 51, issue 1, 2012, Pages 77~88
DOI : 10.7468/mathedu.2012.51.1.077
This qualitative research provides a situation model, which is designed for promoting learning of eigenvalue and eigenvector. This study also demonstrates the usefulness of the model through a small groups discussion. Particularly, participants of the discussion were asked to decide the numbers of milk cows in order to make constant amounts of cheese production. Through such discussions, subjects understood the notion of eigenvalue and eigenvector. This study has following implications. First of all, the present research finds significance of situation model. A situation model is useful to promote learning of mathematical notions. Subjects learn the notion of eigenvalue and eigenvector through the situation model without difficulty. In addition, this research demonstrates potentials of small groups discussion. Learners participate in discussion more actively under small group debates. Such active interaction is necessary for situation model. Moreover, this study emphasizes the role of teachers by showing that patience and encouragement of teachers promote students' feeling of achievement. The role of teachers are also important in conveying a meaning of eigenvalue and eigenvector. Therefore, this study concludes that experience of learning the notion of eigenvalue and eigenvector thorough situation model is important for teachers in future.