A latent profile analysis of perceptions about Mathematics teachers in school lessons
고동현 Ko Dong Hyun , 정희선 Jung Hee Sun
57(2) 7592, 2018
고동현 Ko Dong Hyun , 정희선 Jung Hee Sun
DOI: JANT Vol.57(No.2) 7592, 2018
Based on Perceptions about Mathematics Teachers (PMT) perceived by high school students, measured by 2189 students from Seoul Educational Longitudinal Study 2014 (SELS 2014), latent profile analysis (LPA) identified five distinct types of student groups (positive, partial positive, middle, negative, extreme negative).
These student of positive, middle, and negative groups are positive, moderate and negative perceptions about math teachers. Partial positive group generally had a positive perception about mathematics teachers, extremely negative group was very negative about mathematics teachers. Both of these groups had peculiarly inconsistent trends and several anomalies.
The Multinomial logistic regression analyses also indicated that individual factors (gender, major, selfconcept, resilience, selfassessment, career maturity), school factors (friendship, relationship with school teachers) and parental factors (academicrelationship, emotionalrelationship) were significant predictors of PMT profile groups.
The Analysis of variance also indicated that mathematics class (attitude, satisfaction and atmosphere), Mathematics achievement were significant predictors of PMT profile groups.
The profiling of perceptions about mathematics teachers resulted in enhanced understanding of the complex range of processes students employed. During mathematics class, implementation of smooth interactions and communications between students and teachers added in the teaching and learning of mathematics.

A Study on Reorganization of ‘Pythagorean Theorem’ in School Mathematics
서보억 Suh Bo Euk
57(2) 93110, 2018
서보억 Suh Bo Euk
DOI: JANT Vol.57(No.2) 93110, 2018
One of the biggest changes in the 2015 revised mathematics curriculum is shifting to the second year of middle school in Pythagorean theorem. In this study, the following subjects were studied. First, Pythagoras theorem analyzed the expected problems caused by the shift to the second year middle school. Secondly, we have researched the reconstruction method to solve these problems.
The results of this study are as follows. First, there are many different ways to deal with Pythagorean theorem in many countries around the world. In most countries, it was dealt with in 7th grade, but Japan was dealing with 9th grade, and the United States was dealing with 7th, 8th and 9th grade.
Second, we derived meaningful implications for the curriculum of Korea from various cases of various countries. The first implication is that the Pythagorean theorem is a content element that can be learned anywhere in the 7th, 8th, and 9th grade. Second, there is one prerequisite before learning Pythagorean theorem, which is learning about the square root. Third, the square roots must be learned before learning Pythagorean theorem. Optimal positions are to be placed in the eighth grade 'rational and cyclic minority' unit.
Third, Pythagorean theorem itself is important, but its use is more important. The achievement criteria for the use of Pythagorean theorem should not be erased. In the 9th grade 'Numbers and Calculations' unit, after learning arithmetic calculations including square roots, we propose to reconstruct the square root and the utilization subfields of Pythagorean theorem.

Analysis of Mathematical Problem Based on Mathematical Problem Solving Competency
이선영 Lee Seon Yeong , 이지수 Lee Ji Soo , 한선영 Han Sunyoung
57(2) 111136, 2018
이선영 Lee Seon Yeong , 이지수 Lee Ji Soo , 한선영 Han Sunyoung
DOI: JANT Vol.57(No.2) 111136, 2018
This study suggests a framework for analyzing items based on the characteristics, and shows the relationship among the characteristics, difficulty, percentage of correct answers, academic achievement and the actual mathematical problem solving competency. Three mathematics educators’ classification of 30 items of Mathematics ‘Ga’ type, on 2017 College Scholastic Ability Test, and the responses given by 148 high school students on the survey examining mathematical problem solving competency were statistically analyzed. The results show that there are only few items satisfying the characteristics for mathematical problem solving competency, and students feel illdefined and nonroutine items difficult, but in actual percentage of correct answers, routineness alone has an effect. For the items satisfying the characteristics, lowachieving group has difficulty in understanding problem, and low and intermediateachieving group have difficulty in mathematical modelling. The findings can suggest criteria for mathematics teachers to use when developing mathematics questions evaluating problem solving competency.

The cognitive load of middle school students according to problem types in collaborative learning for solving the function problems
김성경 Kim Seongkyeong , 김지연 Kim Ji Youn , 이선지 Lee Sun Ji , 이봉주 Lee Bongju
57(2) 137155, 2018
김성경 Kim Seongkyeong , 김지연 Kim Ji Youn , 이선지 Lee Sun Ji , 이봉주 Lee Bongju
DOI: JANT Vol.57(No.2) 137155, 2018
From the assumption that an individual’s working memory capacity is limited, the cognitive load theory is concerned with providing adequate instructional design so as to avoid overloading the learner’s working memory. Based on the cognitive load theory, this study aimed to provide implications for effective problembased collaborative teaching and learning design by analyzing the level of middle school students’ cognitive load which is perceived according to the problem types(short answer type, narrative type, project) in the process of collaborative problem solving in middle school function part. To do this, this study analyzed whether there is a relevant difference in the level of cognitive load for the problem type according to the math achievement level and gender in the process of cooperative problem solving. As a result, there was a relevant difference in the task burden and task difficulty perceived according to the types of problems in both first and second graders in middle schools students. and there was no significant difference in the cognitive effort. In addition, the efficacy of task performance differed between first and second graders. The significance of this study is as follows: in the process of collaborative problem solving learning, which is most frequently used in school classrooms, it examined students' cognitive load according to problem types in various aspects of grade, achievement level, and gender.

An analysis of the introduction and application of definite integral in < MathematicsⅡ > textbook developed under the 2015Revised Curriculum
박진희 Park Jin Hee , 박미선 Park Mi Sun , 권오남 Kwon Oh Nam
57(2) 157177, 2018
박진희 Park Jin Hee , 박미선 Park Mi Sun , 권오남 Kwon Oh Nam
DOI: JANT Vol.57(No.2) 157177, 2018
The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chaptersthe limit of a sequence followed by limit of a function, and differentiation and integration is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but “F(b)F(a)” for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

An Analysis of Measurement Equivalence in a Teaching Aptitude and Personality Test for Preservice Mathematics Teachers between a Graduate School of Education and a College of Education
김성연 Kim Sungyeun
57(2) 179196, 2018
김성연 Kim Sungyeun
DOI: JANT Vol.57(No.2) 179196, 2018
The purpose of this study was to investigate the measurement equivalence and to suggest application ways in teaching aptitude and personality test results for preservice mathematics teachers between a graduate school of education and a college of education. This study analyzed the scores of the teaching aptitude and personality test of 36 preservice mathematics teachers enrolled in a graduate school of education and 111 preservice mathematics teachers in a college of education by performing a multivariate generalizability analysis. The main results were as follows. First, graduate’s preservice mathematics teachers had a higher level of teaching aptitude and personality than that of college’s preservice mathematics teachers based on the total scores. In addition, graduate’s preservice mathematics teachers had higher levels of teaching aptitude and personality than those of college’s preservice mathematics teachers except for a creativity·application domain based on the subdomain scores. Second, cognitive domains were measured more precisely but affective domains were measured less precisely for graduate’s preservice mathematics teachers than for college’s preservice mathematics teachers. Third, regardless of school levels, Cronbach’s α values, which might be overestimated by applying the classical test theory, were higher than dependability coefficients. Fourth, this study showed a somewhat negative result in ensuring the measurement equivalence for a problem solving·exploration domain. However, regardless of school levels, this study indicated that the overall measurement was generally reliable on composite scores. Based on these results, it was confirmed that multivariate generalizability methodologies’ approach can be useful for exploring the measurement equivalence issues. Finally, this study suggests how to utilize the results of the test, how to apply a multivariate generalizability analysis for detecting the measurement equivalence, and how to develop future research based on limitations.
