• 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.

• School Mathematics
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• v.5 no.1
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• pp.115-133
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• 2003

Investigation of the students' mathematical misconceptions is very important for improvement in the school mathematics teach]ng and basis of curriculum. In this study, we categorize second-grade middle school students' misconceptions on the learning of linear function and make a comparative study of the error-remedial effect of students' collaborative learning vs explanatory leaching. We also investigate how to change and advance students' self-diagnosis and treatment of the milton ceptions through the collaborative learning about linear function. The result of the study shows that there are three main kinds of students' misconceptions in algebraic setting like this: (1) linear function misconception in relation with number concept, (2) misconception of the variables, (3) tenacity of specific perspective. Types of misconception in graphical setting are classified into misconception of graph Interpretation and prediction and that of variables as the objects of function. Two different remedies have a distinctive effect on treatment of the students' misconception under the each category. We also find that a misconception can develop into a correct conception as a result of interaction with other students.

• School Mathematics
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• v.5 no.4
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• pp.477-506
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• 2003

In this paper, we analyze nine-grade students' conceptions of parameters, their relation to unknowns and variables and the process of understanding of letters in problem solving of equations and functions. The roles of letters become different according to the letters-used contexts and the meaning of letters Is changed in the process of being used. But, students do not understand the meaning of letters correctly, especially that of parameter. As a result, students operate letters in algebraic expressions according to the syntax without understanding the distinction between the roles. Therefore, the parameter of learning should focus on the dynamic change of roles and the flexible thinking of using letters. We develop a self-regulation model based on the monitoring working question in teaching-learning situations. We expect that this model helps students understand concepts of letters that enable to construct meaning in a concrete context.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.21-58
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• 2015

The aim of this study is to look into the didactical background for teaching proportional reasoning in elementary school mathematics and offer suggestions to improve teaching proportional reasoning in the future. In order to attain these purposes, this study extracted and examined key ideas with respect to the didactical background on teaching proportional reasoning through a theoretical consideration regarding various studies on proportional reasoning. Based on such examination, this study compared and analyzed textbooks used in the United States, the United Kingdom, and South Korea. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: giving much weight on proportional reasoning, emphasizing multiplicative comparison and discerning between additive comparison and multiplicative comparison, underlining the ratio concept as an equivalent relation, balancing between comparisons tasks and missing value tasks inclusive of quantitative and qualitative, algebraic and geometrical aspects, emphasizing informal strategies of students before teaching cross-product method, and utilizing informal and pre-formal models actively.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.81-98
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• 2009

This study analyzed the types of quantitative reasoning and the characteristics of representation in order to figure out the characteristics of quantitative reasoning of the sixth graders. Three students who used quantitative reasoning in solving problems were interviewed in depth. Results showed that the three students used two types of quantitative reasoning, that is difference reasoning and multiplicative reasoning. They used qualitatively different quantitative reasoning, which had a great impact on their problem-solving strategy. Students used symbolic, linguistic and visual representations. Particularly, they used visual representations to represent quantities and relations between quantities included in the problem situation, and to deduce a new relation between quantities. This result implies that visual representation plays a prominent role in quantitative reasoning. This paper included several implications on quantitative reasoning and quantitative approach related to early algebra education.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.04a
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• pp.225-228
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• 2008

This paper presents out-of-plane shear strength models for composite wall with steel plates based on limit theorem in the framework of the plasticity theory. The formulas proposed by JEAG 4618 need to be reconsidered with a couple of limitations; ignoring the effect of bond stress generated by studs in the process of calculating arch action, illogically discriminating between concrete shear cracking strength and arch strength by algebraic relation in short shear span ratio(0-2.0). In most cases, reinforcement ratio is not sufficient to yield, as a result, arch strength is determined by accounting equilibrium including both bond strength and concrete compressive strength. We conducted experimental research assuming that SC wall is a continuous beam under the simplified loading patterns, changing main valuables involving the number of studs, stirrups. The results show good agreements with the formula and we quoted the test results of JEAG.

• Journal of Climate Change Research
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• v.4 no.2
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• pp.177-188
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• 2013

In this research, forest cover distribution change, forest volume and carbon stock in Yongin-city, Gyeonggi procince were estimated focused on the forest of Yongin-City using forest type map and HyTAG model in relation to climate change. Present forest volume of Yongin-city was estimated using the data from $5^{th}$ Forest Type Map and Korean National Forest Inventory (NFI). And for the future 100 years potential forest distribution by 10-year interval were estimated using HyTAG model. Forest volume was also calculated using algebraic differences form of the growth model. According to the $5^{th}$ Forest Type Map, present needleleaf forest occupied 37.8% and broadleaf forest 62.2% of forest area. And the forest cover distribution after 30 years would be changed to 0.13% of needleleaf forest and 99.97% of broadleaf forest. Finally, 60 years later, whole forest of Yongin-city would be covered by broad-leaf forest. Also the current forest carbon stocks was measured 1,773,862 tC(56.79 tC/ha) and future carbon stocks after 50 years was predicted to 4,432,351 tC(141.90 tC/ha) by HyTAG model. The carbon stocks after 100 years later was 6,884,063 tC (220.40 tC/ha). According to the HyTAG model prediction, Pinus koraiensis, Larix kaempferi, Pinus rigida, and Pinus densiflora are not suitable to the future climate of 10-year, 30-year, 30-year, and 50-year later respectively. All Quercus spp. was predicted to be suitable to the future climate.