• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.99-120
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• 2001

The purpose of this thesis is to find the guiding direction of mathematical communication in lower grade students of elementary school and to present a new direction about the effect of using concrete material in communication. It is expected that mathematical communication increases when concrete material is used for the students of the lower grades, who are in concrete operational period. Therefore, this study ai s to investigate what characteristics there are in mathematical communication of second grade students and what effect concrete materials have on mathematical communication and learning. The analysis of the teaching record shows that the second grade students use alternative terms in the process of communication since they are not familiar with mathematical symbols or terms, which is a characteristic of communication in a mathematics class in which concrete material is used. In the process of teaming the students apply their living experiences to their teaming. Since a small number of students lead class, the interaction between students is also led by them. The direction of communication in a small group is not centered around solution of a problem, and most students show a more interest in finding answers than in the process of learning. The effect that concrete material has on communication plays an important role in promoting students' speaking activity; it allows students to identify and correct their errors more easily. It also makes students' activities more predictable, and it increases a small group activities through the medium of concrete material. However, it was also noticed that students' listening activities are not appropriately developed since they do not pay attention to a teacher who uses concrete material. The effects that concrete material has on mathematics class can be summarized as follows. Concrete material promotes students' participation in class by triggering their interest of learning of mathematics and helps them to understand the course of learning. It also helps the teaming and formation of concepts for children of low academic performance. And it makes a phased learning possible according to students' ability to use concrete material and to solve a problem. Based upon the results above mentioned, the use of concrete material is absolutely needed in mathematics classes of lower grade elementary school students since it increases communication and gives much influence on mathematics learning. Therefore, teachers need to develop teaching or learning method which can help increase communication, considering the characteristics of students' communication.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.353-370
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• 2016

This study examined elementary mathematics teacher's guidebook to determine the inclusion level of 11 critical features of evidence based instruction. And the inclusion level of the features in teacher's guidebook were interpreted as 'Low', 'Middle' and 'High'. The results are as followings. First, The overall inclusion level of the features in teacher's guidebook is 'Middle' The inclusion level of the features in teacher's guidebook for 1st, 2nd, 3rd and 4th were 'Middle' but for 5th and 6th were 'Low'. Second, the inclusion level of the features 'Clarity of Objective', 'Single Concepts and Skill Taught', 'Use of Manipulatives and Representation', 'Explicit Instruction', 'Provision of Examples for new concepts and skill', 'Adequate Independent Practice Opportunities' and 'Progress Monitoring' were 'Middle' The inclusion level of the features 'Review of Prerequisite Mathematical Skills', 'Error correction and Corrective Feedback' and 'Instruction of Strategies' were 'Low'. And discussed the results.

• Journal of Music and Human Behavior
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• v.3 no.1
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• pp.63-76
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• 2006

Melody is defined as adding spatial dimension to the rhythm which is temporal concept. Being able to understand melodic pattern and to reproduce the pattern also requires cognitive skills. Since 1980, there has been much research on the relationship between academic skills and music cognitive skills, and how to transfer the skills learned in music work to the academic learning. The study purported to examine various research outcomes dealing with the correlational and causal relationships between musical and academic skills. The two dominating theories explaining the connection between two skills ares are "neural theory" and "near transfer theory." The theories focus mainly on the transference of spatial and temporal reasoning which are reinforced in the musical learning. The study reviewed the existing meta-analysis studies, which provided evidence for positive correlation between academic and musical skills, and significance of musical learning in academic skills. The study further examined specific skills area that musical learning is correlated, such as mathematics and reading. The research stated that among many mathematical concepts, proportional topics have the strongest correlation with musical skills. Also with reading, temporal processing also has strong relationship with auditory skills and motor skills, and further affect language and literacy ability. The study suggest that skills learned in the musical work can be transferred to other areas of learning and structured music activities may be every efficient for children for facilitating academic concepts.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.443-465
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• 2016

The study aims to compare our newest mathematics curriculum with Singapore's and analyse the differences of them. Because the levels of our mathematics education have been evaluated to be difficult to our students, we try to find that the evaluation is appropriate and there are other characteristics we have to notice carefully, and provide some implications for our mathematics curriculum. We mainly compared both mathematics curriculums focussed on the national documents of mathematics curriculum, and textbooks in the level of middle school. The results are following. Firstly, Singapore has three tracks based on students' abilities and there are three kinds of textbooks on the tracks. This is a different from our teaching on students level. Secondly, the introductions of our mathematics curriculum contents are not faster than Singapore's, but they have more concrete ranges of contents than us. Thirdly, the focus of Singapore's mathematics education lies on problem solving, and we can find some good examples of contents of textbook focussed on problem solving. Some mathematical concepts are introduced simply without any process of students discoveries or investigations, and the focus lies on the problem solving using the concepts. Fourthly, Singapore's mathematics textbooks are more emphasis on the internal connections than ours.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.19-44
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• 2014

This study aims to develop strategies for improving the affective characteristics of Korean students based on results from international achievement tests. In pursuing the goal, different research methods are employed including a) analysis of the theories and literature regarding the affective domains included in PISA and TIMSS studies; b) analysis of the current situation and needs of Korean students with respect to the affective factors based on PISA and TIMSS results; c) case studies of best practices in relation to students' affective domains in Korea and abroad; and d) development of strategies for improving and supporting Korean students' affective characteristics. In this paper, first of all, relevant theories on affective characteristics in literature are introduced. In other words, the concepts of three affective domains in question - interest, self-efficacy, and value - are reviewed, and their definitions for the present study are made. Also, teaching strategies and support plans for improving students' affective factors are extracted from previous studies. Furthermore, this paper reviews recent trends in research on how the affective domains are related to mathematics education and how one can teach them effectively. The teaching guidelines for each affective domain are developed according to the instruction principles extracted through literature review in general for all subjects. Based on the results of the findings mentioned above, this paper establishes and suggests the guidelines on how to teach mathematics reflecting the affective characteristic.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.459-483
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• 2010

This study aims to develop materials related to math education for the aged and to identify the effects of application as part of active measures to the aging society with its growing elderly population which is one of the greatest changes in our society. In this purpose, the necessity and objectives for development of materials of 'Silver Math' as education for the aged are explained. Developing and disseminating materials with a role as a program for intelligent needs and physical and spiritual health of the aged presents standards for development of more systemic and meaningful educational materials at this point of time when the importance of education of the aged increases to help the old enjoy qualitatively successful lives in later years in the perspective of lifelong education. Also it aims to present standards of contents and requirements in learning that are adequate and meaningful to old learners at the actual learning sites where education takes place only in terms of making good use of spare time while at the same time suggesting plans of teaching and learning as well as conditions for learning environment. Next, the effectiveness of 'Silver Math' are explored by applying developed materials to the aged. materials of 'Silver Math' for the aged with contents that are appropriate to the definitive and cognitive level of the aged are presented. The developed materials for mathematical activities are divided into 'computation of basic numbers' for those wishing to learn calculation and concepts of numbers, 'active math' that corresponds to definitive factors of old learners, facilitates leisure time through mathematical activities, and Improves communication abilities through cooperative learning among learners, and 'math with thinking power' to solve simple calculation problems by applying to various actual situations.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.95-103
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• 2008

The 7th national mathematics curriculum was revised in 2007. According to the revision curriculum, new texts and guides are developed and will come into effect for elementary and secondary school in 2009. Some contents are shifted and also newly added at the revision curriculum. This paper analyzed the gap between the revision and the 7th national mathematics curriculum based on the shifts in contents, and investigated on the difficulties that some graders probably will undergo owing to shifting the contents between grades. As a result, several important problems were found in some graders between the revision and the 7th national mathematics curriculum. In particular, some graders could not have a chance to learn some mathematical concepts without another lesson plans. For some graders, special lesson plans and supplementations are required. The brief summary of these supplementations as follows: ⅰ) For entering students in 2005, the supplementations about equations and direct proportion and inverse proportion should be needed at the 6th grade in 2010 or at the 7th grade in 2011. ⅱ) For entering students in 2006, the supplementations about estimations and correspondence should be needed at the 4th grade in 2009 or at the 5th grade in 2010. And the supplementations about the relation of fractions and decimals and the ratio should be needed at the 5th grade in 2010. ⅲ) For entering students in 2007, the supplementations about the addition and subtraction of time using second unit and the addition and subtraction of weight should be needed at the 3th grade in 2009 or at the 4th grade in 2010.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.271-293
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• 2007

Mathematics workbook is developed according to the amendment of the 7th national curriculum of mathematics. This study polled 300 national mathematics teachers in the elementary school, middle school, and high school to find out what they think in conjunction with the introduction of mathematics workbook such as needs for mathematics workbook, teachers' recognition about the system of mathematics textbook and workbook which are proper for lesson of achievement level and organization of mathematics workbook before using the mathematics workbook in school. As a results, mathematics teachers want the introduction of workbook because it helps students' self-regulated learning of mathematics and it is material very valuable for teachers to give lessons of achievement level. Also, we suggest the organization and contents of mathematics workbook on the base of our survey. Mathematics workbook has a lot of exercises assessing into the upper, intermediate, lower level in the contents, concepts of mathematics learning. It has the items developed with various problem solving methods and emphasis on performance tests, an essay-type examination and a periodical assessment. It has the problem posing items and the corner that helps students revise their mathematical errors and proposes useful, interesting mathematical activities and the commentary of a correct answer to questions at the tail of the book.

• School Mathematics
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• v.15 no.4
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• pp.975-994
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• 2013

In this paper, we analyzed the utilization trend of technology in the secondary mathematics textbooks based on the 6th, 7th and 2007 revised mathematics curriculums in Korea. We analyzed 30, 60 and 90 mathematics books based on the 6th, 7th and 2007 revised mathematics curriculums respectively. The analysis focused on three aspects of using technology, i.e., contents areas in which technology used, technological tools and programs used, and methods of using technology in teaching and learning mathematics. The results shows that the frequency of using technology in mathematics books has been increased as mathematics curriculum has been revised. In the mathematics books based on th 6th curriculum, only 25 scenes were found, but in 7th and 2007 revised curriculum 248 and 355 scenes were found. In the 6th curriculum, calculators and graphing calculators were used mainly, but in the 7th and 2007 revised curriculum many kinds of technological tools and softwares were used including CAS, dynamic geometry software, spreadsheets, programming language, and the Internet. Especially the internet was used frequently in the 7th curriculum. And the methods of using technology has been diversified as time passed. In the 6th curriculum, the technology mainly used for introducing technology and simple calculation, but in the 7th and 2007 revised curriculum the technologies and software were also used for understanding mathematical laws, principles and concepts and students-centered exploring the mathematical properties.