• Journal of Science Education
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• v.46 no.1
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• pp.121-149
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• 2022

Descriptive assessment is a meaningful assessment method in relation to problem solving ability, reasoning ability, and communication ability as emphasized in mathematics curriculum. In Korea, as performance assessment has been emphasized since the 7th mathematics curriculum, descriptive assessment is being conducted as a method of performance assessment in schools. However, descriptive assessment has not been introduced in the university scholastic ability test for various reasons. Considering that descriptive assessment is emphasized in the mathematics classroom and has sufficient educational value, a serious discussion on the implementation of descriptive assessment in the university scholastic ability test will be necessary. In this study, we analyzed the descriptive assessment of Russia's unified state examination (USE) in the mathematics, which corresponds to Korea's university scholastic ability test. Through a literature review, we investigated how mathematics examination problems were structured in the USE and which mathematical abilities were required for the examination. In particular, the outer structure of the problems was analyzed focusing on the mathematics problems of the USE 2021, and the scoring method of the descriptive problems was also analyzed. The results of this study are expected to provide a variety of information on the possibility of introducing descriptive assessment in the Korean university scholastic ability tests.

• Journal of Educational Research in Mathematics
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• v.23 no.3
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• pp.335-351
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• 2013

This research assumes that abduction is so important as much as all the creative plausible reasoning to be based upon. We expect it to be deeply appreciated and be taught positively in school mathematics. We are noticing that every problem solving process must contain some steps of abduction and thus, we believe that those who are afraid of abduction cannot solve any newly faced problem. Upon these thoughts, we are looking into the middle school mathematics textbooks to see that how strongly various abductions are emphasized to solve problems in it. We modified types of abduction those were suggested by Eco(1983) or by Bettina Pedemonte, David Reid (2011) and investigated those books to see if, we may regard, various types of abduction be intended to be used to solve their problems. As a result of it, we found that more than 92% of the problems were not supposed to use creative abduction necessarily to solve it. And we interpret this as most authors of the textbooks have emphasis more on the capturing and understanding of basic knowledge of school mathematics rather than the creative reasoning through them. And we believe this need innovation, otherwise strong debates are necessary among the professionals of it.

• School Mathematics
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• v.15 no.3
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• pp.603-617
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• 2013

The major purpose of this article is to examine what kind of gap exists between mathematically gifted students' probability knowledge and the reality actually applying that knowledge and then analyze the cause of the gap. To attain the goal, 23 elementary mathematically gifted students at the highest level from G region were provided with problem situations internalizing a probability and expectation, and the problems are in series in which conditions change one by one. The study task is in a gaming situation where there can be the most reasonable answer mathematically, but the choice may differ by how much they consider a certain condition. To collect data, the students' individual worksheets are collected, and all the class procedures are recorded with a camcorder, and the researcher writes a class observation report. The biggest reason why the students do not make a decision solely based on their own mathematical knowledge is because of 'impracticality', one of the properties of probability, that in reality, all things are not realized according to the mathematical calculation and are impossible to be anticipated and also their own psychological disposition to 'avoid loss' about their entry fee paid. In order to provide desirable probability education, we should not be limited to having learners master probability knowledge included in the textbook by solving the problems based on algorithmic knowledge but provide them with plenty of experience to apply probabilistic inference with which they should make their own choice in diverse situations having context.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.143-161
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• 2009

This study was designed to gain insights into students' visualization process in geometric problem solving. The visualization model for analysing visual process for geometric problem solving was developed on the base of Duval's study. The subjects of this research are two Grade 9 students and six Grade 10 students. They were given 2D-geometric problems. Their written solutions were analyzed problem is research depicted characteristics of process of visualization of individually. The findings on the students' geometric problem solving process are as follows: In geometric problem solving, visualization provided a significant insight by improving the students' figural apprehension. In particular, the discoursive apprehension and the operative apprehension contributed to recognize relation between the constituent of figures and grasp structure of figure.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.169-182
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• 2008

This study has been searching for reasoning process solving the problem effectively in activities related to meaningful classification of pieces and geometric properties with tangram. In activities using some pieces of tangram, we systematically came up with every solution in classifying properties of pieces and combining selected pieces. It is very difficult for regular students to do this tangram. In order to solve this problem effectively, we need to show that there are activities using the idea acquired in reasoning process. Through this process, we do not simply use tangram to understand he concept and play for interest but to use it more meaningfully. And the best solution an not be found by a process of trial and error but must be given by experience to look or it systematically and methods to reason it logically.

• Archives of design research
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• v.12 no.2
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• pp.89-95
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• 1999

Carlo H. Sequin, a computer scientist, became to know a sculpture of subtle space construction which was created by Brent Collins, a sculptor, and introduced it as 'Visual Mathematics' in a journal. Sequin who was able to deduce a basic logic of the construction, has developed a software which can be used for virtual modeling merely by substituting simple numerical values using a computer and supplied it to Collins. The present author who was exposed to their collaboration works through series of their papers published in the journal, Leonardo, introduces the Collins' sculptures and the author's modeling procedures of animation works both of which show many common things in visual characteristics and modeling expansion method. The author investigates the mathematical characteristics which is used as a basic motive of modeling and then supplied as a principal visual characteristics of a material. 'Modeling Development by Principle Expansion,' in which the expansion is developed on the base of space twist as for Collins whereas the space section as for the present author, is introduced in this study. With the same stream of the mutual reaction in 'arts, sciences and technology' which has been stressed with the development of sciences and technology, this modeling technology is suggested as a research theme which has a possiblity of various applications.

• School Mathematics
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• v.18 no.2
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• pp.301-322
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• 2016

Even though measurement is an important strand of elementary mathematics education, there has been lack of research in this field. This study analyzed topics related to length and time in a series of mathematics textbooks aligned to 2007 or 2009 revised mathematics curriculum. The analysis was focused on three aspects: (a) overall instructional components of measurement, (b) instructional components specific to the topics of measurement, and (c) key competencies in mathematics. The results of this study showed that many topics dealing with length and time were represented with relation to real-life contexts or other subjects. The meanings of measurement terms and the necessity of calculation were well explained but other aspects still had room for improvement when it comes to the necessity of measurement units, appropriate choice of units, and use of students' common misconceptions. Another noticeable result was that problem solving, communication, and reasoning among key competencies in mathematics have been emphasized in the mathematics textbooks. Based on these results, this study provides textbook writers with implications on what to further consider in dealing with length and time.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.253-267
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• 2013

The newly revised mathematics curriculum of 2007 speaks of ultimate goal to develop ability to think and communicate mathematically, in order to develop ability to rationally deal with problems arising from the life around, which puts emphasize on mathematical communication. In this study, analysis on mathematical communication and analogical thinking process of group of students with similar level of academic achievement and that with different level, and thus analyzed if such communication has affected analogical thinking process in any way. This study contains following subjects: 1. Forms of mathematical communication took placed at the two groups based on achievement level were analyzed. 2. Analogical thinking process was observed through trapezoid's area obtaining activity and analyzed if communication within groups has affected such process anyhow. A framework to analyze analogical thinking process was developed with reference of problem solving procedure based on analogy, suggested by Rattermann(1997). 15 from 24 students of year 5 form of N elementary school at Gunpo Uiwang, Syeonggi-do, were selected and 3 groups (group A, B and C) of students sharing the same achievement level and 2 groups (group D and E) of different level were made. The students were led to obtain areas of parallelogram and trapezoid for twice, and communication process and analogical thinking process was observed, recorded and analyzed. The results of this study are as follow: 1. The more significant mathematical communication was observed at groups sharing medium and low level of achievement than other groups. 2. Despite of individual and group differences, there is overall improvement in students' analogical thinking: activities of obtaining areas of parallelogram and trapezoid showed that discussion within subgroups could induce analogical thinking thus expand students' analogical thinking stage.

• Journal of Korean Society of Transportation
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• v.24 no.7 s.93
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• pp.81-90
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• 2006

It is important to clarify the relationship between traffic accidents and various influencing factors in order to reduce the number of traffic accidents. This study developed a traffic accident frequency prediction model using by multi-linear regression and qualification theories which are commonly applied in the field of traffic safety to verify the influences of various factors into the traffic accident frequency The data were collected on the Korean National Highway 17 which shows the highest accident frequencies and fatality rates in Chonbuk province. In order to minimize the uncertainty of the data, the fuzzy theory and neural network theory were applied. The neural network theory can provide fair learning performance by modeling the human neural system mathematically. Tn conclusion, this study focused on the practicability of the fuzzy reasoning theory and the neural network theory for traffic safety analysis.

• Korean Journal of Cognitive Science
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• v.27 no.2
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• pp.159-219
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• 2016

Mathematical ability is important for academic achievement and technological renovations in the STEM disciplines. This study concentrated on the relationship between neural basis of mathematical cognition and its mechanisms. These cognitive functions include domain specific abilities such as numerical skills and visuospatial abilities, as well as domain general abilities which include language, long term memory, and working memory capacity. Individuals can perform higher cognitive functions such as abstract thinking and reasoning based on these basic cognitive functions. The next topic covered in this study is about individual differences in mathematical abilities. Neural efficiency theory was incorporated in this study to view mathematical talent. According to the theory, a person with mathematical talent uses his or her brain more efficiently than the effortful endeavour of the average human being. Mathematically gifted students show different brain activities when compared to average students. Interhemispheric and intrahemispheric connectivities are enhanced in those students, particularly in the right brain along fronto-parietal longitudinal fasciculus. The third topic deals with growth and development in mathematical capacity. As individuals mature, practice mathematical skills, and gain knowledge, such changes are reflected in cortical activation, which include changes in the activation level, redistribution, and reorganization in the supporting cortex. Among these, reorganization can be related to neural plasticity. Neural plasticity was observed in professional mathematicians and children with mathematical learning disabilities. Last topic is about mathematical creativity viewed from Neural Darwinism. When the brain is faced with a novel problem, it needs to collect all of the necessary concepts(knowledge) from long term memory, make multitudes of connections, and test which ones have the highest probability in helping solve the unusual problem. Having followed the above brain modifying steps, once the brain finally finds the correct response to the novel problem, the final response comes as a form of inspiration. For a novice, the first step of acquisition of knowledge structure is the most important. However, as expertise increases, the latter two stages of making connections and selection become more important.