The Mathematical Education

Issue: Vol.59 No.1

An analysis of the curriculum on inequalities as regions: Using curriculum articulation and mathematical connections 이송희 Lee Song Hee , 임웅 Lim Woong 59(1) 1-15, 2020 An analysis of the curriculum on inequalities as regions: Using curriculum articulation and mathematical connections 이송희 Lee Song Hee , 임웅 Lim Woong DOI: JANT Vol.59(No.1) 1-15, 2020 In this paper, we analyzed curriculum materials on inequalities as regions. Constructs such as mathematical connections and curriculum articulation were used as a framework. As for articulation, our findings indicate the topic of inequalities as regions addresses meaningful subordinate mathematical thinking and skills that serve prerequisite to calculus. Regarding connections, mathematical concepts involving inequalities extend to multivariate calculus. One implication is, as an unintended consequence of curricular decision of 2015 Revised National Curriculum to teach the topic only in mathematical economics, students who plan to study STEM subjects in college but opt out of mathematics economics in high school may miss the key concept and naturally struggle to understand calculus especially the theory of multivariate function of calculus.
Interaction patterns between teachers-students and teacher's discourse structures in mathematization processes 최상호 Choi Sang-ho 59(1) 17-29, 2020 Interaction patterns between teachers-students and teacher's discourse structures in mathematization processes 최상호 Choi Sang-ho DOI: JANT Vol.59(No.1) 17-29, 2020 The purpose of this study is to analyze the teacher's discourse structure of teachers according to the interaction pattern between teacher and student in the process of mathematization. To achieve this goal, we observed a semester class (44 lessons) of an experienced teacher who had practiced teaching methods for promoting student engagement for more than 20 years. Among them, one lesson case would be match the teacher’s intention and the student’s response and the other one lesson case would be to mismatch between the teacher’s intention and the student’s response was analyzed. In other words, in the process of mathematization based on students' engagement, the intention of the teacher and the reaction of the student was determined according to the cases where students did not make an error and when they made an error. A methodology used to develop a theory based on data collected through classroom observations(grounded theory). Because the purpose of the study is to identify the teacher's discourse structure to help students’ mathematization, observe the teacher's discourse and collect data based on student engagement. Based on the teacher's discourse, conceptualize it as a discourse structure for students to mathematization. As a result, teacher's discourse structure had contributed to the intention of the teacher and the reaction of the student in the process of mathematization. Based on these results, we can help the development of classroom discourse for mathematization by specifying the role of the teacher to help students experience the mathematization process in the future.
Meta analysis on the improvement of academic performance by the teaching method for underachievers of learning mathematics 김홍겸 Kim Hong-kyeom 59(1) 31-45, 2020 Meta analysis on the improvement of academic performance by the teaching method for underachievers of learning mathematics 김홍겸 Kim Hong-kyeom DOI: JANT Vol.59(No.1) 31-45, 2020 Despite the trend of the times and the government's efforts to implement policies, a number of students, having difficulties in learning math, are still growing. Reflecting this, many studies related to underachiever of learning mathematics were conducted in the field of mathematics education. Most of these studies, however, were intended to find the cause of underachievers of learning mathematics or experimental studies that applied the specific teaching procedures to the underachievers of learning mathematics and found their effectiveness in terms of academic achievement, compared it beforehand. Thus, in this study, 49 studies, from including theses and published journal papers from 2001, were meta-analyzed to find out how effective the teaching treatment for underachievers of learning mathematics has improved academic performance. As a result of this analysis, we found that teaching treatment generally have moderate effect sizes for children with having difficulties in learning mathematics. It was also possible to analyze the effect of various interventions and to obtain some suggestions on which circumstances the greatest effect could be achieved. Teaching treatments for underachiever of learning mathematics could have greater effectiveness in elementary school level, institution certified testing tool was used, targeted for each individual, taught by peer student, lasted for at least 8 weeks, and using teaching aids and ICT tools.
A study on the understanding of mathematics preservice teachers for discrete probability distribution 이봉주 Lee Bongju , 윤용식 Yun Yong Sik , 임해미 Rim Haemee 59(1) 47-62, 2020 A study on the understanding of mathematics preservice teachers for discrete probability distribution 이봉주 Lee Bongju , 윤용식 Yun Yong Sik , 임해미 Rim Haemee DOI: JANT Vol.59(No.1) 47-62, 2020 Understanding the concept of probability distribution becomes more important. We considered probabilities defined in the sample space, the definition of discrete random variables, the probability of defined discrete probability distribution, and the relationship between them as knowledge of discrete probability distribution, and investigated the understanding degree of the mathematics preservice teachers. The results are as follows. Firstly, about 70% of preservice teachers who participated in this study expressed discrete probability distribution graphs in ordered pairs or continuous distribution. Secondly, with regard to the two factors for obtaining discrete probability distributions: probability for each element in the sample space and the concept of random variables that convert each element in the sample space into a real value, only 13% of the preservice teachers understood and addressed both factors. Thirdly, 39% of the preservice teachers correctly responded to whether different probability distributions can be defined for one sample space. Fourthly, when the probability of each fundamental event was determined to obtain the probability distribution of the discrete random variables defined in the undefined sample space, approximately 70% habitually calculated by the uniform probability. Finally, about 20% of preservice teachers understood the meaning and relationship of binomial distribution, discrete random variables, and sample space. In relation, clear definitions and full explanations of concept need to be provided from textbooks and a program to improve the understanding of preservice teachers need to be developed.
A comparative study of domestic and international research trends of mathematics education through topic modeling 신동조 Shin Dongjo 59(1) 63-80, 2020 A comparative study of domestic and international research trends of mathematics education through topic modeling 신동조 Shin Dongjo DOI: JANT Vol.59(No.1) 63-80, 2020 This study analyzed 3,114 articles published in KCI journals and 1,636 articles published in SSCI journals from 2000 to 2019 in order to compare domestic and international research trends of mathematics education using a topic modeling method. Results indicated that there were 16 similar research topics in domestic and international mathematics education journals: algebra/algebraic thinking, fraction, function/representation, statistics, geometry, problem-solving, model/modeling, proof, achievement effect/difference, affective factor, preservice teacher, teaching practice, textbook/curriculum, task analysis, assessment, and theory. Also, there were 7 distinct research topics in domestic and international mathematics education journals. Topics such as affective/cognitive domain and research trends, mathematics concept, class activity, number/operation, creativity/STEAM, proportional reasoning, and college/technology were identified from the domestic journals, whereas discourse/interaction, professional development, identity/equity, child thinking, semiotics/embodied cognition, intervention effect, and design/technology were the topics identified from the international journals. The topic related to preservice teacher was the most frequently addressed topic in both domestic and international research. The topic related to in-service teachers’ professional development was the second most popular topic in international research, whereas it was not identified in domestic research. Domestic research in mathematics education tended to pay attention to the topics concerned with the mathematical competency, but it focused more on problem-solving and creativity/STEAM than other mathematical competencies. Rather, international research highlighted the topic related to equity and social justice.
Analysis of abduction and thinking strategies by type of mathematical problem posing 이명화 Lee Myoung Hwa , 김선희 Kim Sun Hee 59(1) 81-99, 2020 Analysis of abduction and thinking strategies by type of mathematical problem posing 이명화 Lee Myoung Hwa , 김선희 Kim Sun Hee DOI: JANT Vol.59(No.1) 81-99, 2020 This study examined the types of abduction and the thinking strategies by the mathematics problems posed by students. Four students who were 2nd graders in middle school participated in problem posing on four tasks that were given, and the problems that they posed were classified into equivalence problem, isomorphic problem, and similar problem. The type of abduction appeared were different depending on the type of problems that students posed. In case of equivalence problem, the given condition of the problems was recognized as object for posing problems and it was the manipulative abduction. In isomorphic problem and similar problem, manipulative abduction, theoretical abduction, and creative abduction were all manifested, and creative abduction was manifested more in similar problem than in isomorphic problem. Thinking strategies employed at abduction were examined in order to find out what rules were presumed by students across problem posing activity. Seven types of thinking strategies were identified as having been used on rule inference by manipulative selective abduction. Three types of knowledge were used on rule inference by theoretical selective abduction. Three types of thinking strategies were used on rule inference by creative abduction.