• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.153-171
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• 2013

The purpose of this study is to investigate characteristics of students' problem solving processes based on their mathematical thinking styles and thus to provide implications for teachers regarding how to employ multiple representations. In order to analyze these characteristics, 202 university freshmen were recruited for a paper-and-pencil survey. The participants were divided into four groups on a mathematical-thinking-style basis. There were two students in each group with a total of eight students being interviewed. Results show that mathematical thinking styles are related to defining a mathematical concept, problem solving in relation to representation, and translating between mathematical representations. These results imply methods of utilizing multiple representations in learning and teaching mathematics by embodying Dienes' perceptual variability principle.

• KIISE Transactions on Computing Practices
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• v.23 no.4
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• pp.226-231
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• 2017

Word representation, an important area in natural language processing(NLP) used machine learning, is a method that represents a word not by text but by distinguishable symbol. Existing word embedding employed a large number of corpora to ensure that words are positioned nearby within text. However corpus-based word embedding needs several corpora because of the frequency of word occurrence and increased number of words. In this paper word embedding is done using dictionary definitions and semantic relationship information(hypernyms and antonyms). Words are trained using the feature mirror model(FMM), a modified Skip-Gram(Word2Vec). Sense similar words have similar vector. Furthermore, it was possible to distinguish vectors of antonym words.

• The Journal of Korean Association of Computer Education
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• v.11 no.6
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• pp.53-64
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• 2008

The 'Informatics' curriculum for middle school revised in 2007 will be applied since 2010 in school. However, it is difficult to utilize directly school setting because educational contents presented in the curriculum are very comprehensive. Therefore, we need to present specific standards and examples to guide teaching and learning and assessment activities in school setting and right comprehension about new revised curriculum. In this study, we developed the achievement and assessment standards for the 'Representation and Management of Information' unit of Informatics curriculum for middle school revised in 2007. And then, we presented sample questions base on achievement and assessment standards we developed. The levels of the achievement unit were set in the small unit level through the understanding and the analysis of the new curriculum. We described the achievement standards from student's viewpoint and the assessment standards divide into three level(high/middle/low).

• Journal of Educational Research in Mathematics
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• v.27 no.2
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• pp.171-189
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• 2017

By designing and applying the lesson helping to discover the power laws, we tried to investigate the characteristics on the class. To do this, we designed a discovery lesson on the power laws and applied to 54 8th grade students. As results, we could observe the overproduction of monotonous laws, tendency to vary the type of development and increase error to students without prior learning experience, and various errors. All participants failed to express the generalization of $a^m{\div}a^n$ and some participants expressed an incomplete generalization using variables partially for the base or power. We could also observe an error of limited generality or a representation error which did not use the equal sign or variables. In the survey of students, there were two contradictory positions to appeal to the enjoyment of the creation and to talk about the difficulty of creation. Based on such results, we discussed the pedagogical implications relating to the discovery of power laws.

• Korean Journal of Child Studies
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• v.34 no.6
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• pp.139-158
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• 2013

Karmiloff-Smith was first to propose the 'Representational Redescription model'. It describes a process through which children elaborate their knowledge from the unconscious and implicit levels to the conscious and explicit levels. The model also assumes that children in perfectly explicit levels are able to express their own representation of knowledge verbally. This study was conducted to investigate Karmiloff-Smith's Representational Redescription(RR) model(1990, 1992, 1999) within the drawing domain. Additionally, how verbalization training influences children's development of representational redescription in drawing were also examined. First, 331 children (4- to 6-year-olds and an older comparison group of 7- to 9-year-olds) were asked to create six drawings of both familiar and novel topics. From these drawings, children were measured for procedural rigidity and developmental differences. Thereafter 80 5-year-olds children who were not able to manipulate their drawings with flexibility were selected. They were divided into an experimental group and two control groups. A group of verbalization training was given a session using 5 tasks. Compared to the control groups, children who practiced verbalization in the training group showed more advanced levels of representation than their previous levels in the pretest. The results were interpreted as meaning that verbalization is likely to facilitate children's reorganization of implicit knowledge within the drawing domain and to transfer this toward explicit forms. Further research needs to pay more attention to the educational applications of learning processes based on representational redescription.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.12
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• pp.3836-3854
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• 2022

The student group division is benefit for universities to do the student management based on the group profile. With the widespread use of student smart cards on campus, especially where students living in campus residence halls, students' daily activities on campus are recorded with information such as smart card swiping time and location. Therefore, it is feasible to depict the students with the daily activity data and accordingly group students based on objective measuring from their campus behavior with some regular student attributions collected in the management system. However, it is challenge in feature representation due to diverse forms of the student data. To effectively and comprehensively represent students' behaviors for further student group division, we proposed to adopt activity data from student smart cards and student attributes as input data with taking account of activity and attribution relationship types from different perspective. Specially, we propose a novel student group division method based on a multi-view student attribute heterogeneous information network (MSA-HIN). The network nodes in our proposed MSA-HIN represent students with their multi-dimensional attribute information. Meanwhile, the edges are constructed to characterize student different relationships, such as co-major, co-occurrence, and co-borrowing books. Based on the MSA-HIN, embedded representations of students are learned and a deep graph cluster algorithm is applied to divide students into groups. Comparative experiments have been done on a real-life campus dataset collected from a university. The experimental results demonstrate that our method can effectively reveal the variability of student attributes and relationships and accordingly achieves the best clustering results for group division.

• The Mathematical Education
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• v.61 no.3
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• pp.499-519
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• 2022

Ratio and rate are key topics in the area of 'Patterns', but there are various perspectives on them. This study compared and analyzed the perspectives of Korean and Singaporean mathematics textbooks on ratio and rate, and explored how teaching and learning methods develop according to each perspective in terms of quantitative reasoning. To this end, we reorganized the analysis criteria based on some studies, and analyzed the textbooks of the two countries in relation to context, relationship, and representation. The results of the study are as follows. Regarding the context, there were differences in the situations, types of units and use of units of the problems presented in textbooks. In terms of relationship, there were differences in the types of two quantities and relationship of quantities. Lastly, there were differences in the representation of ratio and rate. Through these results, we found that elementary mathematics textbooks in Korea and Singapore take different perspectives on ratio and rate. In particular, the perspective taken by Korean textbooks on ratio and rate had unique points different from that of other previous studies. Considering this Korean perspective, we suggested some implications that could help improve textbooks related to ratio and rate and teach them meaningfully.

• Journal of The Korean Association For Science Education
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• v.26 no.4
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• pp.510-517
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• 2006

This study investigated the influences of situational interest, attention, and cognitive effort on drawing as a method to assist students to connect and integrate multiple external representations provided in learning chemical concepts. Seventh graders (N=178) at two coed middle schools were taught about the "Boyle's Law" and the "Charles's Law" for two class hours through drawing. They observed macroscopic phenomena through demonstrations. After these observations, they drew their mental model from the external verbal representation, and then compared their drawings with external visual representation. The tests assessing situational interest, attention, cognitive effort, and conceptual understanding were administered as post-tests. Correlation and path analyses supported a causal model which situational interest had a positive direct effect on attention to the drawing. Attention led to conceptual understanding directly as well as through cognitive effort. These results suggest that situational interest may be induced by drawing first of all, and attention and cognitive effort may be direct causes of conceptual understanding in drawing. Educational implications are discussed.

• Journal of The Korean Association For Science Education
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• v.34 no.4
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• pp.335-347
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• 2014

Size/scale is a central idea in the science curriculum, providing explanations for various phenomena. However, few studies have been conducted to explore student understanding of this concept and to suggest instructional approaches in scientific contexts. In contrast, there have been more studies in mathematics, regarding the use of number lines to relate the nature of numbers to operation and representation of magnitude. In order to better understand variations in student conceptions of size/scale in scientific contexts and explain learning difficulties including alternative conceptions, this study suggests an approach that links mathematics with the analysis of student conceptions of size/scale, i.e. the analysis of mathematical structure and reasoning for a number line. In addition, data ranging from high school to college students facilitate the interpretation of conceptual complexity in terms of mathematical development of a number line. In this sense, findings from this study better explain the following by mathematical reasoning: (1) varied student conceptions, (2) key aspects of each conception, and (3) potential cognitive dimensions interpreting the size/scale concepts. Results of this study help us to understand the troublesomeness of learning size/scale and provide a direction for developing curriculum and instruction for better understanding.

• Journal of Korean Elementary Science Education
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• v.41 no.2
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• pp.418-431
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• 2022

In this study, we analyzed the form, presentation, and interactivity of external representations presented in the matter units of elementary school science digital textbooks developed under the 2015 Revised National Curriculum. The analytic framework of the previous study was modified and supplemented. The matter units in the 3rd-6th grade science digital textbooks were analyzed by dividing them into "body texts" and "inquiries" area. The results revealed that visual-verbal and visual-nonverbal representations were presented the most. Conversely, audial-nonverbal representations were presented at a high frequency only in the body texts, and audial-verbal representations were presented at a low frequency in both the body texts and the inquiries. Regarding the presentation, when verbal and visual-nonverbal representations appeared together, visual-verbal and visual-nonverbal representations were primarily presented together. In some cases where visual-verbal, audial-verbal, and visual-nonverbal representations were presented together, information on visual-verbal and audial-verbal representations was presented redundantly. Audial-nonverbal representations unrelated to contents were presented along with other external representations, and the frequency was particularly high in the body texts. Regarding the contiguity, no visual-verbal and visual-nonverbal representations were presented on different pages, and no audial-verbal representations were presented asynchronously with visual-nonverbal representations. Regarding the interactivity, explanatory feedback and low-level manipulations were mainly presented. Based on the results, implications to improve digital textbooks are discussed from the perspective of multiple representation-based learning.