The Mathematical Education

Issue: Vol.56 No.2

A textbook analysis of irrational numbers unit: focus on the view of process and object 오국환 Kukhwan Oh , 박정숙 Jung Sook Park , 권오남 Oh Nam Kwon 56(2) 131-145, 2017 A textbook analysis of irrational numbers unit: focus on the view of process and object 오국환 Kukhwan Oh , 박정숙 Jung Sook Park , 권오남 Oh Nam Kwon DOI: JANT Vol.56(No.2) 131-145, 2017 The representation of irrational numbers has a key role in the learning of irrational numbers. However, transparent and finite representation of irrational numbers does not exist in school mathematics context. Therefore, many students have difficulties in understanding irrational numbers as an `Object`. For this reason, this research explored how mathematics textbooks affected to students` understanding of irrational numbers in the view of process and object. Specifically we analyzed eight textbooks based on current curriculum and used framework based on previous research. In order to supplement the result derived from textbook analysis, we conducted questionnaires on 42 middle school students. The questions in the questionnaires were related to the representation and calculation of irrational numbers. As a result of this study, we found that mathematics textbooks develop contents in order of process-object, and using `non repeating decimal`, `numbers cannot be represented as a quotient`, `numbers with the radical sign`, `number line` representation for irrational numbers. Students usually used a representation of non-repeating decimal, although, they used a representation of numbers with the radical sign when they operate irrational numbers. Consequently, we found that mathematics textbooks affect students to understand irrational numbers as a non-repeating irrational numbers, but mathematics textbooks have a limitation to conduce understanding of irrational numbers as an object.
Singapore`s Higher Social Gender Equality and Girls` Higher Mathematics Achievement in TIMSS 2011 유양석 Yoo Yang Seok 56(2) 147-160, 2017 Singapore`s Higher Social Gender Equality and Girls` Higher Mathematics Achievement in TIMSS 2011 유양석 Yoo Yang Seok DOI: JANT Vol.56(No.2) 147-160, 2017 The purpose of this study was to examine (1) if sociocultural factors that are known to influence gender gap in mathematics achievement are gender equitable for Singaporean eighth grade students, (2) if there is a higher level of gender equitability in students` attitudes towards mathematics and (3) how sociocultural factors influence mathematics achievement for Singaporean eighth grade students. This study is based on 5,923 Singaporean eighth grade students who participated in TIMSS 2011 assessment. The study found that there were no statistically significant gender differences in `parental involvement in education` and `teacher efficacy.` There were no statistically significant gender differences in students` attitudes of `like learning mathematics,` and `value learning mathematics`. A significant gender difference was identified for the attitude of `confident with mathematics.` The boys displayed a higher level of confidence in mathematics than the girls consistent with other study findings for Asian students. The degree of effect from `parental involvement in education,` `teacher efficacy,` and `confident with mathematics` on mathematics achievement are found to be stronger for girls than boys. The finding implies that girls` mathematics achievement can benefit from having more positive encouragement and involvement of parents and teachers and strengthening confidence in mathematics.
The comparison on the learning effect of low-achievers in mathematics using Blended e-learning and Personalized system of instruction 송다겸 Song Dagyeom , 이봉주 Lee Bongju 56(2) 161-175, 2017 The comparison on the learning effect of low-achievers in mathematics using Blended e-learning and Personalized system of instruction 송다겸 Song Dagyeom , 이봉주 Lee Bongju DOI: JANT Vol.56(No.2) 161-175, 2017 The purpose of this study is to compare and analyze the impact on low-achievers in mathematics who studied mathematics using Blended e-learning and Personalized system of instruction after school. Blended e-learning is defined as the management of e-learning using the e-study run by the education office in local. Personalized system of instruction was proceeded as follows; (1) all students are given a syllabicated learning task and a study guide, (2) students study the material autonomously according to their own pace for a certain period of time, (3) the teacher strengthens the students` motivation through grading and feedback after students study a subject and solve the evaluation problem. The learning materials for Personalized system of instruction are re-edited the offline education contents provided by the blended e-learning to the level of students. The 118 7th grade students from the D middle school participated in this study. The results were verified by achievement tests before and after the study, as well as survey regarding their attitude toward mathematics. The results are as follows. First, Blended e-learning has more positive impacts than Personalized system of instruction in mathematics achievement. Second, there was no difference in mathematics achievement according to their self-directed learning between Blended e-learning and Personalized system of instruction. Third, both types utilizing Blended e-learning and Personalized system of instruction have positive effect on attitude toward mathematics, and there is not their difference between two methods of teaching and learning mathematics.
Development and Implementation of the Program for the Free Learning Semester Focused on Career Exploration 강태경 Kang Tae Kyung , 이서빈 Lee Seo Bin , 고상숙 Choi-koh Sang Sook 56(2) 177-191, 2017 Development and Implementation of the Program for the Free Learning Semester Focused on Career Exploration 강태경 Kang Tae Kyung , 이서빈 Lee Seo Bin , 고상숙 Choi-koh Sang Sook DOI: JANT Vol.56(No.2) 177-191, 2017 This study was to investigate the effect of the statistics education program for the test-free semester. Two tests of questionnaires were used after revising some items for the subjects and statistical contents covered according to the purpose of the study during the 2nd semester, 2016. one was for finding students` attitude toward statistics and the other for understanding my career exploration. The statistics education program was developed for 5 lesson units and was applied to two classes with 53 students of one middle school in Gyeonggi-province. The results showed that students` understanding on career exploration was improved especially, in self understanding, perceiving career world related to statistics, and economical & educational understanding in statistical career. Also, the three areas such as interest, value, and effort among five areas about students` statistical attitude which was measured by the attitude test revised from the previous study, were improved with statistical significance. Moreover, we analyzed the degree of students` satisfaction over the program. Most of students were satisfied with the program saying that “I could not believe it is over now. The time has gone so fast.” or “My mentor(a pre-service teacher) helped me a lot.” Therefore, the program for the test-free semester should include the contents for exploring future-career and relating to real life.
A Critical Review on the Use of Cuisenaire Rods in Learning of Fraction 이지영 Lee Jiyoung 56(2) 193-212, 2017 A Critical Review on the Use of Cuisenaire Rods in Learning of Fraction 이지영 Lee Jiyoung DOI: JANT Vol.56(No.2) 193-212, 2017 This study focuses on cuisenaire rods that can be used when teaching fractions to elementary school students. First of all, this study critically examines the use of cuisenaire rods in learning of fraction proposed by various researches. Then, based on this review, this study explores in detail the use of cuisenaire rods in teachers` manuals developed from the revised curriculum by 2009 and in lessons related to fraction. The results of this study show that there are subtle differences in how to use cuisenaire rods in learning fractions and these subtle differences have a significant impact on students` understanding of the fractions. Therefore, the teachers should be able to accurately grasp the differences and utilize appropriate methods for teaching purpose. The followings are some of the implications for teachers or textbook developers when using cuisenaire rods in fraction learning: First, we should use cuisenaire rods in ways that can fully exploit the interpretations of the fraction as a part-whole and the fraction as a ratio. Second, we should focus on quantitative reasoning with unit to determine what each cuisenaire rod refers to. Third, it is necessary to take a more careful and sensitive approach to the use of cuisenaire rods. Teachers and textbook developers should constantly explore ways to make good use of mathematical manipulatives to help students understand conceptually in fractional learning. Furthermore, when teaching various mathematical topics using different manipulatives, I expect that there will be sufficient discussions and specific studies on how to use each of these manipulatives.
Elementary school teachers` perceptions and demands on the 2015 Revised Mathematics Curriculum 권점례 Kwon Jeom Rae 56(2) 213-234, 2017 Elementary school teachers` perceptions and demands on the 2015 Revised Mathematics Curriculum 권점례 Kwon Jeom Rae DOI: JANT Vol.56(No.2) 213-234, 2017 The purpose of this study is to examine the perceptions and needs of the 2015 revised curriculum for elementary school teachers and to draw implications for the application of the 2015 revised mathematics curriculum. For this, the major changes in the 2015 revised mathematics curriculum were examined. Major changes in the 2015 revised mathematics curriculum are as follows: 1) Introduce and emphasize mathematical competencies, 2) Restructure the content system, 3) Reduce mathematics contents to teach, 4) Emphasize the learner`s affective domain, 5) Emphasize the use of technology, 6) Improve teaching and learning methods and evaluation methods. Also, a survey was conducted for elementary school teachers to analyze the perceptions and demands of the 2015 Revised Mathematics Curriculum. The contents of the survey are consisted of contents of the teachers` awareness of the main changes of the 2015 Revised Curriculum and their demands to implement the 2015 Revised Curriculum in schools. Finally, conclusions and suggestions were drawn based on the survey results. The conclusions and suggestions are as follows: 1) there is a lack of teachers` awareness of the 2015 Revised Curriculum, 2) Support for mathematics curriculum competencies is needed, 3) A variety of teaching and learning materials are needed for emphasizing the learner`s affective domain, using the technology, and improving teaching and learning methods and evaluation methods.