The 4th Grade Elementary Students` Cognitive Load of Mathematics Textbooks based on Storytelling  Focused on one Theme in `Number and Operations` 
이세형 Se Hyung Lee , 유윤재 Yoon Jae Yoo
56(1) 117, 2017
이세형 Se Hyung Lee , 유윤재 Yoon Jae Yoo
DOI: JANT Vol.56(No.1) 117, 2017
The purpose of this study is to analyze the differences between the cognitive load of mathematics textbooks based on storytelling and traditional mathematics textbooks that are presented to students. In order to verify this, we have selected two 4th grade classes in elementary school that were identified as a homogeneous group through prior testing, and thus were separated into experimental group and comparative group. Then, without the teacher`s lessons, the experimental group learned from mathematics textbooks based on storytelling and the comparative group learned from traditional mathematics textbooks. Afterwards, the two groups` cognitive load was measured through a questionnaire, and the following results were obtained: In the `mental effort` and `self evaluation` categories, the students that learned from the mathematics textbook based on storytelling showed higher scores than the students that learned from the traditional mathematics textbook. also there was statistically significant difference in some items. However, no statistically significant difference was found in the remaining categories `task difficulty`, `self evaluation`, and `material design`.

Preservice Secondary Mathematics Teachers` Statistical Literacy in Understanding of Sample
탁병주 Tak Byungjoo , 구나영 Ku Nayoung , 강현영 Kang Hyunyoung , 이경화 Lee Kyeonghwa
56(1) 1939, 2017
탁병주 Tak Byungjoo , 구나영 Ku Nayoung , 강현영 Kang Hyunyoung , 이경화 Lee Kyeonghwa
DOI: JANT Vol.56(No.1) 1939, 2017
Taking samples of data and using samples to make inferences about unknown populations are at the core of statistical investigations. So, an understanding of the nature of sample as statistical thinking is involved in the area of statistical literacy, since the process of a statistical investigation can turn out to be totally useless if we don`t appreciate the part sampling plays. However, the conception of sampling is a scheme of interrelated ideas entailing many statistical notions such as repeatability, representativeness, randomness, variability, and distribution. This complexity makes many people, teachers as well as students, reason about statistical inference relying on their incorrect intuitions without understanding sample comprehensively. Some research investigated how the concept of a sample is understood by not only students but also teachers or preservice teachers, but we want to identify preservice secondary mathematics teachers` understanding of sample as the statistical literacy by a qualitative analysis. We designed four items which asked preservice teachers to write their understanding for sampling tasks including representativeness and variability. Then, we categorized the similar responses and compared these categories with Watson`s statistical literacy hierarchy. As a result, many preservice teachers turned out to be lie in the low level of statistical literacy as they ignore contexts and critical thinking, expecially about sampling variability rather than sample representativeness. Moreover, the experience of taking statistics courses in university did not seem to make a contribution to development of their statistical literacy. These findings should be considered when design preservice teacher education program to promote statistics education.

Development and Validation of a Testing Tool for Mathematical Creativity and Character
황우형 Whang Woohyung , 김동중 Kim Dongjoong , 김원 Kim Won , 이다희 Lee Dahee , 최상호 Choi Sangho
56(1) 4162, 2017
황우형 Whang Woohyung , 김동중 Kim Dongjoong , 김원 Kim Won , 이다희 Lee Dahee , 최상호 Choi Sangho
DOI: JANT Vol.56(No.1) 4162, 2017
The purpose of this study is to propose the possibility of integrating creativity and character education and its need in mathematics education by developing and validating a testing tool assessing students` perceptions of mathematical creativity and character. For this purpose, we developed sixty questions in total to extract factors of mathematical creativity and character based on a literature review. Then, questionnaire data were collected for 1258 middle school students. After the collected data were randomly divided into two (n1=615, n2=643), the first group of data was used for exploratory factor analysis and the second one was employed for confirmatory factor analysis. As a result, 45 problems showing nine factors were extracted. The cognitive components of creativity includes divergent thinking, convergent thinking, imagination/visualization, and reasoning, whereas its affective components are interest, motivation, and openness. The character components contain participation, communication, responsibility, and promise. In addition, it is concluded that the developed testing tool, in which character in the model of this study impacts creativity meaningfully, has a measurement consistency which is not affected by gender and grade differences. These results have implications for a guide to curriculum development promoting creativity and character at school by showing objective and practical foundations of helping how to integrate creativity and character education.

An Analysis of Errors in Describing Solving Process for High School Geometry and Vectors
황재우 Hwang Jaewoo , 부덕훈 Boo Deok Hoon
56(1) 6380, 2017
황재우 Hwang Jaewoo , 부덕훈 Boo Deok Hoon
DOI: JANT Vol.56(No.1) 6380, 2017
By analysing the examination papers from third grade high school students, we classified the errors occurred in the problem solving process of high school `Geometry and Vectors` into several types. There are five main types ― (A)Insufficient Content Knowledge, (B)Wrong Method, (C)Logical Invalidity, (D)Unskilled Expression and (E)Interference.. Type A and B lead to an incorrect answer, and type C and D cannot be distinguished by multiplechoice or closed answer questions. Some of these types are classified into subtypes ― (B1)Incompletion, (B2)Omitted Condition, (B3)Incorrect Calculation, (C1)Nonreasoning, (C2)Insufficient Reasoning, (C3)Illogical Process, (D1)Arbitrary Symbol, (D2)Using a Character Without Explanation, (D3) Visual Dependence, (D4)Symbol Incorrectly Used, (D5)Ambiguous Expression. Based on the these types of errors, answers of each problem was analysed in detail, and proper ways to correct or prevent these errors were suggested case by case. When problems that were used in the periodical test were given again in descriptive forms, 67% of the students tried to answer, and 14% described flawlessly, despite that the percentage of correct answers were higher than 40% when given in multiplechoice form. 34% of the students who tried to answer have failed to have logical validity. 37% of the students who tried to answer didn`t have enough skill to express. In lessons on curves of secondary degree, teachers should be aware of several issues. Students are easily confused between `focus` and `vertex`, and between `components of a vector` and `coordinates of a point`. Students often use an undefined expression when mentioning a parallel translation. When using a character, students have to make sure to define it precisely, to prevent the students from making errors and to make them express in correct ways.

An Analysis of Variable Concept in the Elementary Mathematics Textbooks and Workbooks
방정숙 Jeongsuk Pang , 조선미 Sunmi Cho , 김정원 Jeongwon Kim
56(1) 81100, 2017
방정숙 Jeongsuk Pang , 조선미 Sunmi Cho , 김정원 Jeongwon Kim
DOI: JANT Vol.56(No.1) 81100, 2017
The concept of variable is a big idea to develop algebraic thinking. Variable has multiple meanings such as the unknown, a tool for generalization, and the relationship between varying quantities. In this study we analyzed in what ways the meanings of variable were presented in the current elementary mathematics textbooks and workbooks. The results showed that the most frequent meaning of variable was `the unknown`, `a tool for generalization`, and `the relationship between varying quantities` in order. A close look at the results revealed that the same symbol was often used in representing different values of variable as the unknown. In taking variable as a tool for generalization, questions to provoke generalization were sometimes included not in the textbooks but in the teachers` manuals. The main focus in dealing with variable as the relationship between varying quantities was on finding out the dependent values compared to the independent ones. Building on these results, this study is expected to suggest implications for how to deal with variable concept in elementary mathematics instructional materials.

A Study on Reconstruction of Trigonometry Based on Ascent from the Abstract to the Concrete
강미광 Mee Kwang Kang , 한인기 Inki Han
56(1) 101118, 2017
강미광 Mee Kwang Kang , 한인기 Inki Han
DOI: JANT Vol.56(No.1) 101118, 2017

A Study on the Development of Professional Learning Community in Mathematics Based on the Collaboration with University and Its Affiliated Elementary School
김남균 Kim Nam Gyun
56(1) 119130, 2017
김남균 Kim Nam Gyun
DOI: JANT Vol.56(No.1) 119130, 2017
The purpose of this study is to explain the long term growth and development of elementary teachers` Professional Learning Communities(PLC) about mathematics implemented on an institutional basis. Especially, it is meaningful to analyze and present the development process and characteristics of PLC, which was started by the basis on the collaboration of a National University of Education and its affiliated elementary school. In this study, PLC activities during three years were analyzed according to the capacities and dimensions of a professional learning community. The developmental capacity of the PLC analyzed in this study can be summarized as follows. In the first year, development of organizational competence in terms of capacity, resources, structure, and system of exchanges was the main factor in personal competence, and the development of individual competence began to share collective learning and practice. In the second year, personal exchanges were active in all the topics of activities, and personal level competence was activated such that more activities of critical knowledge formation were performed on an individual level. On the basis of the development of the individual level formed in the second, individual competence and organizational capacity developed. Factors that have influenced the development of capacities of PLC include: disclosure of activities outside the community, participation in outsiders, provision of procedures to share equal participation and leadership, voluntary and critical participation of teachers, improvement of mathematics teaching methods, sharing themes and visions.
