• East Asian mathematical journal
• /
• v.36 no.4
• /
• pp.493-513
• /
• 2020

The reason for this study is that the learning content of geometric construction in school mathematics is very insufficient. Geometric construction not only enables in-depth understanding of shapes, but also improves deductive proof skills. In school mathematics education, geometric construction is a very important learning factor, and educational significance is very high in that it can develop reasoning skills essential to the future society. Nevertheless, the reduction of geometric construction learning content in Korean curriculum and mathematics textbooks is against the times. Therefore, the purpose of this study is to analyze the transition of geometric construction learning contents in middle school mathematics curriculum and mathematics textbooks. In order to achieve the purpose of this study, the following studies were conducted. First, we analyze the characteristics of geometric construction according to changes in curriculum and textbooks. Second, we develop a framework for analyzing geometric construction tasks. Third, we explore geometric construction tasks according to the developed framework. Through this, it is expected to provide significant implications for the geometric areas of the new middle school curriculum that will be developed in the future.

• Journal of the Korean School Mathematics Society
• /
• v.11 no.1
• /
• pp.55-68
• /
• 2008

In this paper, we investigated difficulties that middle school students face in the teaming process of proof, and then inquired how does learning of proof using GSP ease students' difficulties. Throughout the inspection, we identified that students have difficulties in understanding process of premise and conclusion, use of notation, process of reasoning. And we identified, throughout learning process of proof using GSP, students can be feedbacked for their guess or reasoning, generalize the special case to general properties and have attitude checking ideas needed in proof by themselves.

• Journal of Educational Research in Mathematics
• /
• v.19 no.2
• /
• pp.233-256
• /
• 2009

The notions of conditional probability and independence are fundamental to all aspects of probabilistic reasoning. Several previous studies identified some misconceptions in students' thinking in conditional probability. However, they have not analyzed enough the nature of conditional probability. The purpose of this study was to analyze conditional probability and students' knowledge on conditional probability. First, we analyzed the conditional probability from mathematical, historico-genetic, psychological, epistemological points of view, and identified the essential aspects of the conditional probability. Second, we investigated the high school students' and undergraduate students' thinking m conditional probability and independence. The results showed that the students have some misconceptions and difficulties to solve some tasks with regard to conditional probability. Based on these analysis, the characteristics of reasoning about conditional probability are investigated and some suggestions are elicited.

• Journal of the Korean School Mathematics Society
• /
• v.16 no.4
• /
• pp.927-941
• /
• 2013

In this paper, we investigate and analysis high school students' generalization of cosine rule using analogy, and we study teaching and learning methods improving students' analogical thinking ability to improve mathematical thinking process. When students can reproduce what they have learned through inductive reasoning process or analogical thinking process and when they can justify their own mathematical knowledge through logical inference or deductive reasoning process, they can truly internalize what they learn and have an ability to use it in various situations.

• Journal of the Korean School Mathematics Society
• /
• v.17 no.2
• /
• pp.291-319
• /
• 2014

The purpose of this study is to investigate students' thinking and understanding through working on Worked-out Examples on numbers and operations, specifically, radical and real numbers and operations in the middle grades. For this purpose, we developed a set of Worked-out Examples; middle school students independently worked on them. Then two students were interviewed. These data were analyzed by using the framework of mathematical proficiency. The data analysis suggested that the students seemed to go through the processes involving a combination of understanding and computation, computation and reasoning, and understanding, computation and reasoning. Also, it appeared that most of the students have difficult solving problems involving with radical and real numbers in related to strategic competence.

• Journal of Elementary Mathematics Education in Korea
• /
• v.20 no.4
• /
• pp.521-539
• /
• 2016

The structures of partitive and quotitive division of fractions are dealt with differently, and this led to using partitive division context for helping develop invert-multiply algorithm and quotitive division for common denominator algorithm. This approach is unlikely to provide children with an opportunity to develop an understanding of common structure involved in solving different types of division. In this study, I propose two approaches, measurement approach and isomorphism approach, to develop a unifying understanding of fraction division. From each of two approaches of solving quotitive division based on proportional reasoning, I discuss an idea of constructing a measure space, unit of which is a quantity of divisor, and another idea of constructing an isomorphic relationship between the measure spaces of dividend and divisor. These ideas support invert-multiply algorithm for quotitive as well as partitive division and bring proportional reasoning into the context of fraction division. I also discuss some curriculum issues regarding fraction division and proportion in order to promote the proposed unifying understanding of partitive and quotitive division of fractions.

• Journal of Educational Research in Mathematics
• /
• v.21 no.3
• /
• pp.239-259
• /
• 2011

This study investigated the elementary school students' ability on the algebraic reasoning as generalized arithmetic. It analyzed the written responses from 648 second graders, 688 fourth graders, and 751 sixth graders using tests probing their understanding of the properties of whole number operations. The result of this study showed that many students did not recognize the properties of operations in the problem situations, and had difficulties in applying such properties to solve the problems. Even lower graders were quite successful in using the commutative law both in addition and subtraction. However they had difficulties in using the associative and the distributive law. These difficulties remained even for upper graders. As for the associative and the distributive law, students had more difficulties in solving the problems dealing with specific numbers than those of arbitrary numbers. Given these results, this paper includes issues and implications on how to foster early algebraic reasoning ability in the elementary school.

• Journal of Educational Research in Mathematics
• /
• v.17 no.4
• /
• pp.359-380
• /
• 2007

This study was conducted with two 6-graders to identify how were their proportional reasoning abilities, whether they evolved proportional thinking in a various context, and what had influence on their proportional thinking. The findings, as previous researches noted, suggested that the proportional expression obtaining by instrumental understanding could not provide rich opportunities for students to improve understanding about ratio and proportion and proportional reasoning abilities, while being useful for determining the answers. The students were able to solve proportional problems with incorporating their knowledge of divisor, multiples, and fraction into proportional situations, but not the lack of number sense. The students easily solved proportional problems experienced in math and other subjects but they did not notice proposition in problems with unfamiliar contexts.

• School Mathematics
• /
• v.18 no.3
• /
• pp.457-478
• /
• 2016

The purpose of this study is to investigate middle school students' understanding and development of function graphs. We collected the data from the teaching experiment with two middle school students who had not yet received instruction on linear function in school. The students participated in a 15-day teaching experiment(Steffe, & Thompson, 2000). Each teaching episode lasted one or two hours. The students initially focused on numerical values rather than the overall relationship between the variables in functional situations. This study described meaning, role of and students' responses for the given tasks, which revealed the students' understanding and development of function graphs. Especially we analyzed students' responses based on their methods to solve the tasks, reasoning that derived from those methods, and their solutions. The results indicate that their continuous reasoning played a significant role in their understanding of function graphs.

• Research in Mathematical Education
• /
• v.18 no.4
• /
• pp.289-305
• /
• 2014

The current mathematical education calls for a learning environment from the constructionism perspective that actively creates mathematical objects. This research first analyzes JavaMAL's expression 'move' that enables students to express the agent's behavior constructively before they learn vector as a formal concept. Since expression 'move' is based on a coordinate, it naturally corresponds with the expression of vectors used in school mathematics and lets students take an embodied approach to the concept of vector. Furthermore, as a design tool, expression 'move' can be used in various activities that include vector structure. This research studies the educational significance entailed in JavaMAL's expression 'move'.