• Title/Summary/Keyword: Conceptual understanding

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Students' Cognitive Style and Mathematical Word Problem Solving

  • Almolhodaei, Hassan
    • Research in Mathematical Education
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    • v.6 no.2
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    • pp.171-182
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    • 2002
  • Students approach mathematical problem solving in fundamentally different ways, particularly problems requiring conceptual understanding and complicated strategies such as mathematical word problems. The main objective of this study is to compare students' performance with different cognitive styles (Field-dependent vs. Field-independent) on mathematics problem solving, particularly, in word problems. A sample of 180 school girls (13-years-old) were tested on the Witkin's cognitive style (Group Embedded Figures Test) and two mathematics exams. Results obtained support the hypothesis that students with field-independent cognitive style achieved much better results than Field-dependent ones in word problems. The implications of these results on teaching and setting problems emphasizes that word problems and cognitive predictor variables (Field-dependent/Field- independent) could be challenging and rather distinctive factors on the part of school learners.

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Notes on "Perpetual Question" of Problem Solving: How Can Learners Best Be Taught Problem-Solving Skills?

  • Oleksiy, Yevdokimov;Peter, Taylor
    • Research in Mathematical Education
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    • v.12 no.3
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    • pp.179-191
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    • 2008
  • Although problem solving was a major focus of mathematics education research in many countries throughout the 1990s, not enough is known about how people best acquire problem-solving skills. This paper is an attempt to advance further development of problem-solving skills of talented school students through combination of some methods accessible from curriculum knowledge and more special techniques that are beyond curriculum. Analysis of various problems is provided in detail. Educational aspects of challenging problems in mathematical contests up to IMO level are, also, taken into account and discussed in the paper.

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Analogies and metaphors in school mathematics (학교수학에서의 유추와 은유)

  • 이승우;우정호
    • Journal of Educational Research in Mathematics
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    • v.12 no.4
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    • pp.523-542
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    • 2002
  • The matter of understanding mathematical concepts in learning mathematics is one of the most important issues in mathematics education. There have been so many studies about it but the more practical study has been asked. When we Think using intuitional models such as examples, figures of speech, situations and activities, it is supposed that the major elements of cognitive mechanism are prototypes, analogies, metaphors and metonymies. In this paper, we tried to examine Rosch's prototype theory, the studies about analogies in congnitive psychology, Lakoff and Johnson's metaphor theory from the viewpoint of teaching mathematics, and then tried to analyze examples, analogies, analogical transfers, metaphorical expressions, metonymies in middle school mathematics text books used in Korea now.

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How middle-school mathematics textbooks of Korea and the US support to develop students' statistical reasoning (한국과 미국 중학교 교과서의 통계 영역 수학과제가 제시하는 통계적 추론에 대한 학습기회 탐색)

  • Lee, Sunjung;Kim, Gooyeon
    • The Mathematical Education
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    • v.58 no.1
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    • pp.139-160
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    • 2019
  • This study attempts to examine statistical tasks in the middle-school mathematics textbooks of Korea and Connected Mathematics 3 [CMP] of the US in terms of an opportunity-to-learn for statistical reasoning. We utilized an analytical framework consisting of types of context, statistical reasoning level, cognitive demand of the tasks, and types of student response. The findings from the task analysis suggested that Korean textbooks focused on finding answers by applying previously learned algorithms or formulas and thus provided students with very limited opportunities to experience statistical reasoning. Also, the results proposed that the mathematical tasks in statistics unit of CMP3 offer more essential and complex tasks that promote students' conceptual understanding of various statistical ideas and statistical reasoning in a meaningful way.

Conceptual understanding of ubiquitous superconductivity

  • Hwang, Jungseek
    • Progress in Superconductivity and Cryogenics
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    • v.22 no.4
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    • pp.6-9
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    • 2020
  • Since the discovery of superconductivity, the unique and mysterious phenomenon has been observed in various metallic material systems. Now days, the superconductivity becomes ubiquitous because almost every metallic material system shows the superconductivity when it is cooled down enough. This ubiquity of the superconductivity is associated with the fermionic nature and itinerancy of electrons in metallic materials. Because fermions are governed by the Pauli's exclusion principle the total energy of fermions is much larger than that of bosons. Therefore, fermionic itinerant electrons are fundamentally instable. Itinerant electrons are able to find "a way" to lead them to their lowest possible energy state through an available bosonization (or pairing) process and Bose-Einstein condensation. Therefore, the lowest possible energy state of itinerant electrons will be a superconducting state, which is "their ultimate destination". This may explain the reason why the superconductivity is ubiquitous.

Using Concrete-representational-abstract Integrated Sequence to Teach Geometry to Students who Struggle

  • Flores, Margaret
    • Research in Mathematical Education
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    • v.25 no.3
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    • pp.227-244
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    • 2022
  • The concrete-representational-abstract integrated (CRA-I) sequence is an explicit approach for teaching students who struggle in mathematics. This approach is beneficial because it assists students in the development of conceptual understanding. This article describes how the approach is used in general as well as its use with a specific geometry concept, area of a rectangle. The author will describe why one might choose CRA-I and the steps needed for implementation. Finally, the CRA-I steps will be shown with a lesson series related to teaching the concept of area. The article will describe lesson activities, methods, materials, and procedures.

Public Diplomacy and Social Capital: Bridging Theory and Activities

  • Naddeo, Rachel;Matsunaga, Lucas
    • Journal of Public Diplomacy
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    • v.2 no.1
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    • pp.116-135
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    • 2022
  • Public diplomacy activities can benefit from social capital theory, when its social dynamics is elucidated in the investment of complex social networks and in the establishment and management of relationships with foreign publics. Social capital theory explains that actors can produce purposive actions to mobilize resources in social structures, which thus explains the dynamics of social interactions. In response to the lack of conceptual frameworks for understanding public diplomacy activities within social capital theory, we conducted a narrative literature review that intends to identify the means through which international actors, such as governments, engage with foreign publics through the dynamics of social networks and the resources embedded in them. In addition, we explored the multidimensional characteristics of social capital to enhance the comprehension of the manner in which actors access, share, and maintain resources in target communities, institutions, or organizations through public diplomacy activities. In summary, we highlight the importance of new theoretical explorations on the application of social capital theory to public diplomacy and the need for a research agenda in the field.

The Understanding on the Teacher and Student's Noticing in Mathematics Education (수학 교과에서의 교사와 학생 상호 주목하기(Noticing)에 관한 이해)

  • Kim, Seul Bi;Hwang, Hye Jeang
    • East Asian mathematical journal
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    • v.38 no.4
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    • pp.397-414
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    • 2022
  • This study tried to explore and understand the meaning, and the properties of noticing. The result of this study were first, the difference in mathematical noticing is distinguished in either the object which is paid attention is different or the object is same but differently interpreted or react. The cause of each difference could be described as mathematical objects such as conceptual objects and perceptual features. Second, teachers' teaching strategies, which narrow the gap in attention and play a key role in the formation of mathematical meaning, appeared in various places. This teaching strategy was implemented to distract students' attention. This study confirmed that the mathematical attention of teachers and students in math classes will differ depending on the object to which they pay attention, and that difference will be narrowed through teacher's discourse practice and teaching strategies through communication strategies.

Effect of Transport Capacity Formula on Spatial Distribution of Soil Erosion

  • Nguyen, Van Linh;Yeon, Minho;Cho, Seongkeun;Lee, Giha
    • Proceedings of the Korea Water Resources Association Conference
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    • 2021.06a
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    • pp.150-150
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    • 2021
  • Soil erosion due to climate change is one of the global environmental issues. Especially, Korea is vulnerable to soil erosion as the frequency of extreme rainfall events and rainfall intensity are increasing. Soil erosion causes various problems such as reduced farmlands, deterioration of water quality in rivers, etc. To these severe problems, understanding the process of soil erosion is the first process. Then, it is necessary to quantify and analyze soil ersoion using an erosion model. Soil erosion models are divided into empirical, conceptual, and physics-based models according to the structures and characteristics of models. This study used GSSHA (Gridded Surface Subsurface Hydrologic Analysis), the physics-based erosion model, running on WMS (Watershed Modeling System) to analyze soil erosion vulnerability of the CheonCheon watershed. In addition, we compared the six sediment transport capacity formulas provided in the model and evaluated the equations fir on this study site. Therefore, this result can be as a primary tool for soil conservation management.

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An Introduction to Causal Mediation Analysis With a Comparison of 2 R Packages

  • Sangmin Byeon;Woojoo Lee
    • Journal of Preventive Medicine and Public Health
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    • v.56 no.4
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    • pp.303-311
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    • 2023
  • Traditional mediation analysis, which relies on linear regression models, has faced criticism due to its limited suitability for cases involving different types of variables and complex covariates, such as interactions. This can result in unclear definitions of direct and indirect effects. As an alternative, causal mediation analysis using the counterfactual framework has been introduced to provide clearer definitions of direct and indirect effects while allowing for more flexible modeling methods. However, the conceptual understanding of this approach based on the counterfactual framework remains challenging for applied researchers. To address this issue, the present article was written to highlight and illustrate the definitions of causal estimands, including controlled direct effect, natural direct effect, and natural indirect effect, based on the key concept of nested counterfactuals. Furthermore, we recommend using 2 R packages, 'medflex' and 'mediation', to perform causal mediation analysis and provide public health examples. The article also offers caveats and guidelines for accurate interpretation of the results.