• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.315-334
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• 2005

The purpose of this study is to find out the implications on when and how the correlation concept can be taught. we investigate the development time and method of the concept in a statistical perspective those initially have discussed in psychology by Piaget. We first reviewed the 1958 research by Inhelder and Piaget. It was the first one which researched the development of the correlation and has become the foundation of psychological perspective. According to them, the correlation concept needs proportional and probability concept ahead of its development and argued on the coefficient of correlation based on formal and logical position. However, from a statistical perspective, the correlation concept is a part of the distribution concept. So, the level of the correlation concept grows from the comparison of conditional distributions to the conditional probability distribution where the proportional concept and probability concept are applied. As reviewed through the literature, we found that 11-12 years old students in early formal operation stage reasoned about correlation through the comparison of conditional distributions. In our study, we argue that we need to consider the possibility of beginning didactic mediation for correlation concept earlier and the method approaching it in a distribution perspective.

• Education of Primary School Mathematics
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• v.26 no.3
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• pp.181-197
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• 2023

The importance of reasoning processes based on fractional concepts and number senses, rather than a formalized procedural method using common denominators, has been noted in a number of studies in relation to compare the magnitudes of unlike fractions. In this study, a unlike fraction magnitudes comparison test was conducted on fourth-grade elementary school students who did not learn equivalent fractions and common denominators to analyze the reasoning perspectives of the correct and wrong answers for each of the eight problem types. As a result of the analysis, even students before learning equivalent fractions and reduction to common denominators were able to compare the unlike fractions through reasoning based on fractional sense. The perspective chosen by the most students for the comparison of the magnitudes of unlike fractions is the 'part-whole perspective', which shows that reasoning when comparing the magnitudes of fractions depends heavily on the concept of fractions itself. In addition, it was found that students who lack a conceptual understanding of fractions led to difficulties in having quantitative sense of fraction, making it difficult to compare and infer the magnitudes of unlike fractions. Based on the results of the study, some didactical implications were derived for reasoning guidance based on the concept of fractions and the sense of numbers without reduction to common denominators when comparing the magnitudes of unlike fraction.

• School Mathematics
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• v.13 no.3
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• pp.363-384
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• 2011

This study is based on the recognition that the school mathematics education should reinforce the heuristic and constructional aspects related with discoveries of mathematical rules and understanding of mathematical concepts from real world situations as well as the deductive and formal aspects emphasizing on mathematical contents precisely. The 11th grade students of one class from a city high school with average were chosen. They were given time to learn various functions of Excel in regular classes of "Information Society and Computer" subject. They don't have difficulty using cells, mathematical functions and statistical functions in spreadsheet. Experiment was performed for six weeks and there were two hours of classes in a week. Considering the results of this research, teaching materials using spreadsheets play an important role in helping students to experience probabilistic and statistical reasoning and construct mathematical thinking. This implies that teaching materials using spreadsheet provide students with an opportunity to interact with probabilistic and statistical situations by adopting engineering which can encourage students to observe and experience various aspects of real world in authentic situations.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.565-584
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• 2012

This study investigates how the GSP helps gifted and talented students understand geometric principles and concepts during the inquiry process in the generalization of the internal triangle, and how the students logically proceeded to visualize the content during the process of generalization. Four mathematically gifted students were chosen for the study. They investigated the pattern between the area of the original triangle and the area of the internal triangle with the ratio of each sides on m:n respectively. Digital audio, video and written data were collected and analyzed. From the analysis the researcher found four results. First, the visualization used the GSP helps the students to understand the geometric principles and concepts intuitively. Second, the GSP helps the students to develop their inductive reasoning skills by proving the various cases. Third, the lessons used GSP increases interest in apathetic students and improves their mathematical communication and self-efficiency.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.13-30
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• 2006

The purpose of this study is to investigate the meaning and roles of rhymes in oriental mathematics. To do this, we consider the rhymes in traditional chinese, korean, indian, arabian mathematical books and the mathematical knowledge which they implicate. And we discuss the reasons for which they were often used and the roles which they played. In addition, we suggest how to use them in teaching mathematics.

• Journal of The Korean Association For Science Education
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• v.18 no.4
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• pp.589-600
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• 1998

The present study tested the hypothesis that adolescent's prefrontal lobe growth plateau and spurt exists and that this plateau and spurt influence students' ability to reason scientifically and to learn theoretical science concepts. In theory, maturation of the prefrontal lobes during early adolescence allows for improvements in students' abilities to inhibit task-irrelevant information and coordinate task-relevant information, which along with both physical and social experience, influences scientific reasoning ability and the ability to reject scientific misconceptions and accept scientific conceptions. Two hundred six students ages 13 to 16 years enrolled in four Korean secondary schools were administered tests of prefrontal lobe functions, scientific reasoning, and theoretical concepts derived from kinetic-molecular theory. A series of 14 lessons designed to teach the concepts were then taught. The concepts test was then re-administered following instruction. As predicted among the 14-year-olds, performance on the measures of prefrontal lobe functions, scientific reasoning, and conceptual change remained similar or regressed. Performance then improved considerably among the 15 and 16-year-olds. Because so few of the present students were able to undergo this apparently necessary conceptual change, the value of introducing theoretical concepts to early adolescent is questioned.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.281-302
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• 2015

In the current study, answer sheets from 8007 students in 236 Korean schools were selected and analyzed to examine errors that emerge in the process of solving descriptive questions of the National Educational Achievement Assessment in mathematics. Questions used in the analysis were response assessment covering middle school mathematics topics: "mathematical symbols and equations" and "functions." The behavioral domain of the questions was that of "problem solving and computation," which requires establishing an equation for a word problem and allows the calculation of an answer that meets a certain condition. The analysis results revealed various errors in each stage of each question, from understanding to solving; the study attempts to conjecture causes for these errors and draw pedagogical implications.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.377-394
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• 2019

The purpose of this study is to scrutinize the characteristics of a teacher's discursive competence on the basis of mathematical competencies. For this purpose, we observed all semester-long classes of a middle school teacher, who changed her own teaching methods for the last 20 years, collected video clips on them, and analyzed classroom discourse. Data analysis shows that in problem solving competency, she helped students focus on mathematically important components for problem understanding, and in reasoning competency, there was a discursive competence which articulated thinking processes for understanding the needs of mathematical justification. And in creativity and confluence competency, there was a discursive competence which developed class discussions by sharing peers' problem solving methods and encouraging students to apply alternative problem solving methods, whereas in communication competency, there was a discursive competency which explored mathematical relationships through the need for multiple mathematical representations and discussions about their differences. These results can provide concrete directions to developing curricula for future teacher education by suggesting ideas about how to combine practices with PCK needed for mathematics teaching.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Journal of The Korean Association For Science Education
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• v.36 no.4
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• pp.539-550
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• 2016

The purpose of the study is to conceptualize SSI-PCK by identifying major components and sub-components to promote science teachers' confidence and knowledge on teaching SSIs. To achieve this, I conducted extensive literature reviews on teachers' perceptions on SSI, case studies of teachers addressing SSIs, SSI instructional strategies, etc. as well as PCK. Results indicate that SSI-PCK include six major components: 1) Orientation for Teaching SSI (OTS), 2) Knowledge of Instructional Strategies for Teaching SSI (KIS), 3) Knowledge of Curriculum (KC), 4) Knowledge of Students' SSI Learning (KSL), 5) Knowledge of Assessment in SSI Learning (KAS), and 6) Knowledge of Learning Contexts (KLC). OTS refers to teachers' instructional goals and intentions for teaching SSIs. Teachers often present a) activity-driven, b) knowledge and higher order thinking skills, c) application of science in everyday life, d) nature of science and technology, e) citizenship and f) activism orientations for teaching SSIs. KIS indicates teachers' instructional knowledge required for effectively designing and implementing SSI lessons. It includes a) SSI lesson design, b) utilizing progressive instructional strategies, and c) constructing collaborative classroom cultures. KC refers to teachers' knowledge on a) connection to science curriculum (horizontal/vertical) and b) connection to other subject matters. KSL refers to teachers' knowledge on a) learner experiences in SSI learning, b) difficulties in SSI learning, and c) SSI reasoning patterns. KAS indicates teachers' knowledge on a) dimensions of SSI learning to assess, and b) methods of assessing SSI learning. Finally, KLC refers to teachers' knowledge on the cultures of a) classrooms, b) schools, and c) community and society where they are located when teaching SSIs.