Effects of reflective journal writing to mathematics selfefficacy in reciprocal peer tutoring
최계현 Kye Hyen Choi , 황우형 Woo Hyung Whang
53(1) 124, 2014
최계현 Kye Hyen Choi , 황우형 Woo Hyung Whang
DOI: JANT Vol.53(No.1) 124, 2014
This study examines the effects of reflective journal writing on the mathematics selfefficacy in reciprocal peer tutoring. Participants were 38 high school students in Gyeonggi province who attended at a summer intensive mathematics course for 4 weeks. This study used a mixed method. SPSS 21.0 program was used to analyze the quantitative data, and the interviews, observational journals and reflective journals of 6 students were used to analyze qualitative data. According to the results, all the subcategories of mathematics selfefficacy,  mathematics problemefficacy, mathematics successefficacy, mathematics learningefficacy, and mathematics subjectefficacy  improved except mathematics occupationefficacy. In case of mathematics successefficacy and mathematics problemefficacy, students revealed the greatest improvement. In conclusion, reflective journal writing in reciprocal peer tutoring could be suggested as a treatment program to improve students` mathematics selfefficacy.

On the students` thinking of the properties of derivatives
최영주 Young Ju Choi , 홍진곤 Jin Kon Hong
53(1) 2540, 2014
최영주 Young Ju Choi , 홍진곤 Jin Kon Hong
DOI: JANT Vol.53(No.1) 2540, 2014
Mathematical concept exists in the structural form, not in the independent form. The purpose of this study is to consider the network which students actually have for the mathematical concept structure related to the properties of derivatives. First, we analyzed the properties of derivatives in ``Mathematics II`` and showed the mathematical concept structure of the relations among derivatives, functions, and primitive functions as a network. Also, we investigated the understanding of high school students for the mathematical concept structure between derivatives and functions, and the structure between functions and second order derivatives when the functional formula is not given, and only the graph is given. The results showed that students mainly focus on the relation of ``functionderivatives``, the thinking process for direction of derivative and the thinking style for algebra. On this basis, we suggest the educational implication that is necessary for students to build the network properly.

An investigation in learnability of counterexamples in secondary school mathematics textbooks
오혜미 Hye Mi Oh , 권오남 Oh Nam Kwon
53(1) 4155, 2014
오혜미 Hye Mi Oh , 권오남 Oh Nam Kwon
DOI: JANT Vol.53(No.1) 4155, 2014
In recent years, there has been increasing interest in the pedagogical importance of counterexamples that contradict statements about mathematics education research and the curriculum revision process for high school mathematics courses. Using a literature research method, this study analyzed views about counterexamples according to a method of approach to statements and the classification of counterexamples and their criteria. The study also described the learnability of the content of counterexamples presented in Korean secondary school mathematics textbooks. The results showed that generating many counterexamples enables learners to understand mathematical concepts exactly, construct links between mathematical contents, and have flexible thoughts about mathematical objects. Considering the learnability of counterexamples, the contents of counterexamples in school mathematics textbooks are needed for mathematics teachers and students to generate numerous counterexamples and verify the justification of generating counterexamples in various manners.

An analysis of the connections of mathematical thinking for multiplicative structures by second, fourth, and sixth graders
김유경 Yu Kyung Kim , 방정숙 Jeong Suk Pang
53(1) 5773, 2014
김유경 Yu Kyung Kim , 방정숙 Jeong Suk Pang
DOI: JANT Vol.53(No.1) 5773, 2014
This study investigated the connections of mathematical thinking of students at the second, fourth, and sixth grades with regard to multiplication, fraction, and proportion, all of which have multiplicative structures. A paperandpencil test and subsequent interviews were conducted. The results showed that mathematical thinking including vertical thinking and relational thinking was commonly involved in multiplication, fraction, and proportion. On one hand, the insufficient understanding of preceding concepts had negative impact on learning subsequent concepts. On the other hand, learning the succeeding concepts helped students solve the problems related to the preceding concepts. By analyzing the connections between the preceding concepts and the succeeding concepts, this study provides instructional implications of teaching multiplication, fraction, and proportion.

A study on learning action formation levels in the process of mathematics problem solving
한인기 In Ki Han , 강나경 Na Kyung Kang
53(1) 7592, 2014
한인기 In Ki Han , 강나경 Na Kyung Kang
DOI: JANT Vol.53(No.1) 7592, 2014
In this paper, we summarize briefly some of the most salient features of Repkina & Zaika`s theory of learning action formation levels. We concretize Repkina & Zaika`s theory by comparing various points of view of Uoo, Polya, Krutetskii, and Davydov et al. In this study we are able to diagnose students` learning action formation levels in the process of mathematics problem solving. In addition we use interview method to collect various information about students` levels. As a result we suggest data related with each level of learning action formation, and characteristics of students who belong to each level of learning action formation.

Study on recognition of the dependent generality in algebraic proofs and its transition to numerical cases
강정기 Jeong Gi Kang , 장혜원 Hye Won Chang
53(1) 93110, 2014
강정기 Jeong Gi Kang , 장혜원 Hye Won Chang
DOI: JANT Vol.53(No.1) 93110, 2014
Algebra deals with so general properties about number system that it is called as ``generalized arithmetic``. Observing students` activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

Ahn JiJae`s 《Xiang Ming Suan Fa》
이경언 Kyung Eon Lee
53(1) 111129, 2014
이경언 Kyung Eon Lee
DOI: JANT Vol.53(No.1) 111129, 2014
《Xiang Ming Suan Fa》written by Ahn JiJae, a scholar of Yuan Dynasty, is a very important mathematics text in development of mathematics in Joseon Dynasty. Also, 《Xiang Ming Suan Fa》in possession of Keimeung university was designated as a Korean National Treasure on February 25, 2011. In this paper, we analyzed the structure and contents of 《Xiang Ming Suan Fa》. Also, we studied the influences of 《Xiang Ming Suan Fa》on Joseon Dynasty`s mathematics according to the comparing with mathematics books such as 《Mook Sa Jib San Bub》and 《San Hak Yib Moon》.

A comparison of elementary and middle school mathematics teachers" beliefs and practices in constructedresponse assessment
김래영 Rae Young Kim , 이민희 Min Hee Lee , 김민경 Min Kyeong Kim , 노선숙 Sun Sook Noh
53(1) 131146, 2014
김래영 Rae Young Kim , 이민희 Min Hee Lee , 김민경 Min Kyeong Kim , 노선숙 Sun Sook Noh
DOI: JANT Vol.53(No.1) 131146, 2014
This study examines whether there is discrepancy between elementary and middle school mathematics teachers` beliefs and practices in constructedresponse assessment and how their beliefs and practices are interrelated. Analyzing the responses of 212 elementary teachers and 189 middle school mathematics teachers to the questionnaire, we found that there is lack of consistency among elementary and middle school teachers` beliefs, practices, and expected benefits regarding constructedresponse assessment. In addition, there was a weak correlation between each group of teachers` beliefs and expected benefits about constructedresponse assessment. The results from this study imply that such inconsistency in elementary and middle school teachers` beliefs and practices regarding assessments may determine the effects of constructedresponse assessment.

Preservice elementary school teachers` metaphors on mathematics textbooks
김진호 Jin Ho Kim , 김상미 Sang Mee Kim
53(1) 147162, 2014
김진호 Jin Ho Kim , 김상미 Sang Mee Kim
DOI: JANT Vol.53(No.1) 147162, 2014
The purpose of this study was to investigate the nature of preservice elementary teachers` metaphors on mathematics textbooks. Their metaphors describe individual and collective patterns of thinking and action on mathematics teaching and learning. To analyze their metaphors, qualitative analysis method based on Lakoff and Johnson`s theory of metaphor (1980) was adopted. Metaphors on mathematics textbooks were elicited from 161 preservice elementary school teachers through writing prompts. The writing prompt responses revealed three types and thirteen categories: As TypeⅠ, there were ① ``Principles``, ② ``Summary``, ③ ``Manual``, ④``Encyclopedia``, ⑤ ``Code``, ⑥ ``Guidelines``, and ⑦ ``Example``. As TypeⅡ, there were ⑨ ``Assistant``, ⑩ ``Friend``, ⑪ ``Scale``, and ⑫ ``Ongoing``. As TypeⅢ, there was ⑬ ``Trap``. Among these categories, ``Guidelines``, ``Assistant``, and ``Ongoing`` were the most frequently revealed. These results indicate that the relations of mathematics curriculum, textbooks, and classrooms are not a unilateral way but should communicate with each other.
