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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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The Mathematical Education
Journal Basic Information
Journal DOI :
Korea Society of Mathematical Education
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Volume & Issues
Volume 55, Issue 3 - Aug 2016
Volume 55, Issue 2 - May 2016
Volume 55, Issue 1 - Feb 2016
Selecting the target year
Analysis of weights depending on scoring domains of the mathematical creativity test
Kim, Sungyeun ;
The Mathematical Education, volume 55, issue 2, 2016, Pages 147~169
DOI : 10.7468/mathedu.2016.55.2.147
This study analyzes the mathematical creativity test as an illustrative example with scoring domains of fluency, flexibility and originality in order to make suggestions for obtaining maximum reliability based on a composite score depending on combinations of each scoring domain weights. This is done by performing a multivariate generalizability analysis on the test scores, which were allowed to access publicly, of 30 mathematically gifted elementary school students, and therefore error variances, generalizability coefficients, and effective weights have been calculated. The main results were as follows. First, the optimal weights should adjust to .5, .4, and .1 based on the maximum generalizability coefficient even though the original weights in the mathematical creativity test were equal for each scoring domain with fluency, flexibility and originality. Second, the mathematical creativity test using the three scoring domains of fluency, flexibility, and originality showed higher reliability than using one scoring domain such as fluency. These results are limited to the mathematical creativity test used in this study. However, the methodology applied in this study can help determine the optimal weights depending on each scoring domain when the tests constructed in various researchers or educational fields are composed of multiple scoring domains.
A Study of Criteria for Self-Assessment of Lesson Planning and Teaching Performance
Kim, Sohyung ; Kim, Yongseok ; Han, Sunyoung ;
The Mathematical Education, volume 55, issue 2, 2016, Pages 171~192
DOI : 10.7468/mathedu.2016.55.2.171
As teachers' competency is evaluated based on their teaching performance. pre-service teachers need to have an opportunity to reflect on themselves by systematically analyzing and evaluating their own lesson planning and teaching performance through self-assessment. In this study, we aimed to examine what evaluation criteria for lesson planning and teaching performance pre-service mathematics teachers consider in the process of self-assessment. This study used a mixed-methods research design. To draw the self-evaluation criteria for lesson planning and teaching performance, pre-service self-reported assessments were analyzed using qualitative analyses. In addition, descriptive statistics were used to investigate the pre-service teachers' distribution across the criteria and check the ratio of pre-service mathematics teachers for each element. As a result, it was disclosed that pre-service mathematics teachers considered eight elements in self evaluating their own lesson planning and teaching performance. In addition, we found that pre-service mathematics teachers tended to consider Pedagogical Content Knowledge (PCK) more than Subject-Matter Knowledge (SMK). Moreover, the results of this study provide educational implications for the curriculum in the pre-service teacher's education program.
A Study on Analysis of Likelihood Principle and its Educational Implications
Park, Sun Yong ; Yoon, Hyoung Seok ;
The Mathematical Education, volume 55, issue 2, 2016, Pages 193~208
DOI : 10.7468/mathedu.2016.55.2.193
This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.
The Development and Application of Posing Open-Ended Problems Program with Renzulli's Enrichment Triad Model for Mathematics-Gifted Elementary Students
Lee, Ja Hye ; Kim, Min Kyeong ;
The Mathematical Education, volume 55, issue 2, 2016, Pages 209~232
DOI : 10.7468/mathedu.2016.55.2.209
This study analyzed the process of steps in a program introducing Renzulli's enrichment triad model and various levels of posing open-ended problems of those who participated in the program for mathematics-gifted elementary students. As results, participants showed their abilities of problem posing related to real life in a program introducing Renzulli's enrichment triad model. From eighteen mathematical responses, gifted students were generally outstanding in terms of producing problems that demonstrated high quality completion, communication, and solvability. Amongst these responses from fifteen open-ended problems, all of which showed that the level of students' ability to devise questions was varied in terms of the problems' openness (varied possible outcomes), complexity, and relevance. Meanwhile, some of them didn't show their ability of composing problem with concepts, principle and rules in complex level. In addition, there are high or very high correlations among factors of mathematical problems themselves as well as open-ended problems themselves, and between mathematical problems and open-ended problems. In particular, factors of mathematical problems such as completion, communication, and solvability showed very high correlation with relevance of the problems' openness perspectives.
An Educational Consideration on the Condition that Four Points lie on a Circle
Kang, Jeonggi ;
The Mathematical Education, volume 55, issue 2, 2016, Pages 233~249
DOI : 10.7468/mathedu.2016.55.2.233
In this study, we extracted the background meaning of the condition that four points lie on a circle, analyzed textbooks critically and proposed the orientation to improve the content in the textbook. As results, the condition has a realistic background meaning which is 'mathematical modeling of finding a fair location'. The condition has a mathematical background meanings which are 'a first complex situation distinguished from two points and three points', 'the condition described in the perspective of side and angle in order to overcome the disadvantages of the perpendicular bisectors context' and 'being possible to transfer more than five points'. However it is difficult to understand the reason why the condition is on four points in the current textbook. In addition, it is difficult to recognize the connectivity of a circumcenter of triangle. To overcome these problems, we proposed five orientations to improve the content in the textbook.