• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.223-237
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• 2008

In this paper, We focus on grasping De Morgan's perspectives on mathematics education systematically. His perspectives can be summarized as followings. First, historico-genesis of mathematics must be considered in the teaching and learning of mathematics. Second, mathematical conception of students must be formulated progressively. Third, it is important to use errors which come out continually in the process of passing from inductive stage to deductive stage. Fourth, personal knowledge of students is important in the teaching and learning of mathematics. These De Morgan's four perspectives are the way of approach for experiencing moral certainty first of all to get to mathematical certainty. Moral certainty which he presented is a combination of rationality and humanity to fill up gaps between Platonism and general public education.

• Journal of Fisheries and Marine Sciences Education
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• v.16 no.1
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• pp.21-34
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• 2004

The purpose of this study was to analyze the current implementation states of the differentiated curriculum at the middle school and to propose ways to improve it. For that purpose this study conducted a survey and had the interviews with the middle school mathematics teachers. The items of survey and interviews consisted of the two main parts: current states and needs about the special supplementary courses and enriched supplementary courses. The results showed that there were discrepancies between the current states and the needs of the differentiated curriculum. This means the efforts to improve the current states are needed. The strategies for improving the implementation of the differentiated curriculum are as follows: 1. The use of various standards including the subject-achievement level and students' or parents' opinions is needed in selecting the students of special supplementary course. 2. More relevant special supplementary materials need to be developed and utilized. 3. The ability grouping is recommended for the differentiated instruction. 4. The deliberation of developing the enriched and supplementary texts is requested. 5. The study for differentiated evaluation of students is demanded.

• Education of Primary School Mathematics
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• v.2 no.1
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• pp.65-73
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• 1998

The purpose of this study is to investigate significant differences of structural knowledges among the groups(high, middle, low) when the 6th grade subjects structured the concepts of the plane figures, triangle and quadrangle, by concept maps, and to analyse the features of concept maps according to hierarchy. For this purpose, the following two research contents were investigated： 1. Investigating significant differences of structural knowledge in the concepts of the plane figures using concept maps among the groups(high, middle, low). 2. Analysing the features of concept maps according to hierarchy. The structural knowledges represented on the concept maps of triangle and quadrangle which were drawn by the subjects were analysed by propositions, hierarchies, and cross-links. Subject-self Reports about how to make the concept maps were used to analyse the features of concept maps according to hierarchy. The conclusions drawn from the results were as fellows： First, there were significant differences among the groups in proposition links. Second, there wasn't my significant difference among the groups in hierarchy. Third, there were significant differences among the groups in cross-links, and Fourth, the results of analysing the concept maps by hierarchy showed that there were differences among the individuals in constructing the knowledges.

• The Mathematical Education
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• v.54 no.1
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• pp.13-30
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• 2015

The mathematical object is conceptual. Thus we can not prove the property of mathematical object in experimental viewpoint but in conceptual viewpoint. We performed the experiment for 28 middle school students to investigate whether they understand this. As a result, the majority of student didn't cognize the limit of experimental method. We had also individual interviews with four students. As results, one student was exactly cognizing the limit of experimental method, but he couldn't prove logically. The others didn't cognize the limit of experimental method. They thought that the proposition was already true regardless of the error. And one of them even thought that to be equal approximately was the same of to be equal exactly. Also, one student has confused between the experimental viewpoint and the conceptual viewpoint. This implies that it is necessary to help students understand the limit of experimental method.

• International Journal of Advanced Culture Technology
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• v.6 no.3
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• pp.1-11
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• 2018

The purpose of this study is to develop and analyze the meaning and contents of the "H-STEAM teaching & learning model" which combines Science, Technology, Engineering, Arts & Mathematics (STEAM) with the elements of Humanities. We developed this model based on the key competencies linked with career path for middle school students in Korea, with the recognition of two issues. First, the existing Korean STEAM education lacks the elements of humanities, thus failing to achieve an authentic convergence education. Second, it is necessary to develop a program that might correspond to the Free Semester Program that was first introduced in 2013, and implemented at full scale in 2016 for middle school students in Korea. The advantages of H-STEAM are as follows: First, H-STEAM enables students to flexibly think while traversing the physical world and the symbolic world in the process of dealing with the daily problems. Second, it combines advanced technology with human sensibility and imagination, and enables students to derive creative outcomes that stimulate their minds. Third, it makes students feel and realize a point of contact between the subject that students learn, and jobs of the real world.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.79-97
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• 2011

As the necessity of the special education for the gifted to develop their talents and national power is gradually recognized, many kinds of teaching-learning materials have been developed. However, the development tendency of the materials is not systematically studied because their database is not sufficiently constructed nor most of them are made public. In this research, we would like to provide the reference data to improve the quality of developed materials and reduce the deviation among the classified fields when we will develop the teaching-learning materials by collecting the already developed materials and analyse their development tendency by classifying them according to the contents.

• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 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.

• School Mathematics
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• v.5 no.4
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• pp.401-420
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• 2003

We have many problems in the teaching and learning of proof, especially in the demonstrative geometry of middle school mathematics introducing the proof for the first time. Above all, it is the serious problem that many students do not understand the meaning of proof. In this paper we intend to show that teaching the meaning of proof in terms of historic-genetic approach will be a method to improve the way of teaching proof. We investigate the development of proof which goes through three stages such as experimental, intuitional, and scientific stage as well as the development of geometry up to the completion of Euclid's Elements as Bran-ford set out, and analyze the teaching process for the purpose of looking for the way of improving the way of teaching proof through the historic-genetic approach. We conducted lessons about the angle-sum property of triangle in accordance with these three stages to the students of seventh grade. We show that the students will understand the meaning of proof meaningfully and properly through the historic-genetic approach.

• Journal of Fisheries and Marine Sciences Education
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• v.22 no.3
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• pp.316-329
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• 2010

The purpose of this study was to examine how middle school students perceived the operation of on-line and off-line math-gifted education. The research questions were as follows: 1. How do students recognize the current situation concerning the operation of on-line and off-line gifted education? 2. How do students recognize the effect and satisfaction level of on-line and off-line gifted education? 3. How do students recognize the improvement of on-line and off-line gifted education? The subjects in this study were 591 students who included 208 in on-line classes and 383 in off-line classes. The results were as follows: First, the students who were enrolled in the on-line and off-line classes regarded gifted people as ones who had a superb ability in a particular field and as ones who think creatively. Second, all the students in on-line and off-line classes found gifted education to be of use to developing their potentials, and they had the biggest preference for experiential field study as the most effective teaching method. Third, concerning their needs for the management of gifted classes, they asked for immediate Q&A services over the Internet.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.2
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• pp.727-746
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• 2018

The hash function RIPEMD-160 is a worldwide ISO/IEC standard and the hash function HAS-160 is the Korean hash standard and is widely used in Korea. On the basis of differential meet-in-the-middle attack and biclique technique, a preimage attack on 34-step RIPEMD-160 with message padding and a pseudo-preimage attack on 71-step HAS-160 without message padding are proposed. The former is the first preimage attack from the first step, the latter increases the best pseudo-preimage attack from the first step by 5 steps. Furthermore, we locate the linear spaces in another message words and exchange the bicliques construction process and the mask vector search process. A preimage attack on 35-step RIPEMD-160 and a preimage attack on 71-step HAS-160 are presented. Both of the attacks are from the intermediate step and satisfy the message padding. They improve the best preimage attacks from the intermediate step on step-reduced RIPEMD-160 and HAS-160 by 4 and 3 steps respectively. As far as we know, they are the best preimage and pseudo-preimage attacks on step-reduced RIPEMD-160 and HAS-160 respectively in terms of number of steps.