• Research in Mathematical Education
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• v.18 no.1
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• pp.31-40
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• 2014

Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.

• Journal of The Korean Association For Science Education
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• v.29 no.2
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• pp.156-167
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• 2009

This study investigated the effects of dynamic visual on students' field independence-dependence on connecting errors and conceptual understanding in learning chemistry concepts with multiple representations. Seventh graders (N=123) at a co-ed middle school were assigned to a static visual (SV) group learning with text and static visual, and a dynamic visual (DV) group learning with text and dynamic visual. The students then learned 'Boyle's Law' and 'Charles's Law' for two class periods. Results revealed that the percentages of the DV group were lower than those of the SV group on connecting errors. However, the percentages of the students' connecting errors were still high regardless of their field independence-dependence. There was a little different tendency in the percentages of connecting errors between the two groups by students' field independence-dependence according to the types of connecting errors. The scores of the DV group were significantly higher than those of the SV group in a test on conceptual understanding. However, there was no significant interaction between the instruction and the students' field independence-dependence. Educational implications of these findings are discussed.

• Journal of The Korean Association For Science Education
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• v.26 no.3
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• pp.367-375
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• 2006

This study investigated the effects of varying visuals in drawing and writing as methods to assist students in connecting and integrating multiple external representations provided in learning the particulate nature of matter. Seventh graders (N=233) at a coed middle school were assigned to control, static drawing (SO), dynamic drawing (DD), static writing (SW), and dynamic writing (DW) groups. The students were taught about "Boyle's Law" and "Charles's Law" for two class periods. Two-way ANCOVA results revealed that the scores of a conception test for the two drawing (SD, DD) groups and the two writing (SW, DW) groups were significantly higher than those for the control group. Within the writing groups, students of lower spatial visualization ability in the DW group scored significantly higher than those in the SW group. However, no significant differences were found in the scores of the conception test for the two drawing (SD, DD) groups regardless of students' visualization ability. Researchers also found that most students in both DD and DW groups had respectively positive perceptions of dynamic visuals in drawing or writing.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.173-192
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• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.

• The Journal of Information Technology
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• v.4 no.2
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• pp.69-81
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• 2001

In this paper, we examine work in the evolution of content-based retrieval systems that rely on an intelligent infrastructure. Here, we refer to intelligence as the capabilities of the systems to build and maintain situational or world models, utilize dynamic knowledge representations, exploit context and overage advanced reasoning and learning capabilities. We argue that these elements are essential to producing effective systems for retrieving visual information at semantic levels matching those of human perception and cognition. In this paper, we review relevant research on the understanding of human intelligence and construction of intelligent systems in the fields of cognitive psychology, artificial intelligence, semiotics. We also discuss how some of the principal ideas from these fields lead to new opportunities and capabilities for content-based retrieval systems. Finally, we discribe some of our efforts in these directions. In particular, we present MediaNet, a multimedia knowledge presentation framework that facilitate and enable intelligent content-based retrieval.

• The Mathematical Education
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• v.60 no.1
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• pp.1-19
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• 2021

This study investigates students' conceptions of fractions from a measurement approach while providing a technological environment designed to support students' understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students' constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field's understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.

• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.513-541
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• 2008

The purposes of the study were to investigate whether the use of the Geometer's Sketchpad(GSP) is more effective than the use of traditional tools such as ruler and protractor to enhance eighth- grade students' understanding of quadrilaterals and geometric reasoning ability and to examine how the use of the software affects on the development of students' understanding and reasoning ability. According to the results of the posttest, there was a significant difference in student achievement between students using GSP and students using ruler and protractor. Students using GSP significantly outperformed students using ruler and protractor on the posttest. Student interview data showed that the use of the GSP was more effective in developing students' geometric reasoning ability. Students using GSP achieved higher degrees of acquisition for van Hiele level 2 and 3 than students using ruler and protractor. Dynamic visual representations and hands-on experiences provided in GSP learning environment helped students approach quadrilateral concepts more conceptually and realize their pre-existing conceptual errors and re-conceptualize their mathematical ideas.