• The Mathematical Education
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• v.56 no.3
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• pp.281-300
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• 2017

This study analyzed the difficulties of middle school students in computer simulation of the law of large numbers through eye movement analysis. Some students did not attend to the simulation results and could not make meaningful inferences. It is observed that students keep the existing concept even though they observe the simulation results which are inconsistent with the misconceptions they have. Since probabilistic intuition influence student's thinking very strongly, it is necessary to design a task that allows students to clearly recognize the difference between their erroneous intuitions and simulation results. In addition, we could confirm through eye movements analysis that students could not make meaningful observations and inferences if too much reasoning was needed even though the simulation included a rich context. It is necessary to use visual representations such as graphs to provide immediate feedback to students, to encourage students to attend to the results in a certain intentional way to discover the underlying mathematical structure rather than simply presenting experimental data. Some students focused their attention on the visually salient feature of the experimental results and have made incorrect conclusion. The simulation should be designed so that the patterns of the experimental results that the student must discover are not visually distorted and allow the students to perform a sufficient number of simulations. Based on the results of this study, we suggested that cumulative relative frequency graph showing multiple results at the same time, and the term 'generally tends to get closer' should be used in learning of the law of large numbers. In addition, it was confirmed that eye-tracking method is a useful tool for analyzing interaction in technology-based probabilistic learning.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.507-522
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• 2009

In general, we do fold paper and unfold, it remain paper traces. We can be obtained by using rectangular paper, a mathematical fact and the program had a combination. Depending on the direction of the rectangle, folding paper in the form of variety shows valley and ridge signs of the appearance of this paper. By using (0,1)-code and (0,1)-matrix, we study four kinds of research. Therefore, traces of this view upside down rectangle folding paper how to fold inductive reasoning ability of the code and explore the relationship of traces. Finally, the mathematical content and program development can practice in the field.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.231-254
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• 2019

As the teacher-centered education is transformed into learning-centered education, the active knowledge construction of learner becomes important. Along with this change, project-based learning is receiving attention. However, there are many problems to apply the results of research to pre-service teachers because most of the previous studies have focused on elementary middle high school students. Therefore, this study examined the changes in perceptions of pre-service mathematics teachers while project-based learning progressed for one year. Pre-service mathematics teachers had less experience with project-based learning than group discussions, group activities. Also their perceptions was classified as five factors: 'Instructional effects', 'Application and participant of project-based learning', 'Achievement', 'Diffusion of project-based learning', 'Student motivation'. Pre-service mathematics teachers responded positive changes in perception that project-based learning could be motivated to students but they responded negative changes in perception that project-based learning could be distributed to school. They responded positive changes in perception that teachers can show their achievements by project-based learning but they responded negative change in perception that teachers would be fun to apply project-based learning. Also, they responded positive changes in perception that teachers and students were easy to apply or utilize project-based learning.

• Educational Technology International
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• v.20 no.2
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• pp.195-221
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• 2019

This study explored middle and high school students' learning experiences using e-textbooks in online learning courses. Data were collected from in-depth interviews. The interviewees for this study were 19 students who enrolled voluntarily in an online mathematics and science inquiry program, actively participated in the online learning. The students generally have high academic achievement and motivation for learning in science and mathematics. Data were analyzed based on a grounded theory approach. As a result, the characteristics of the online learning environment using e-textbooks were conceptualized via three different categories including temporal, spatial, and technical. Such characteristics of the learning environment were able to provoke self-directed learning, extended learning, interactive learning, in-depth learning, improved ICT literacy, and formation of positive emotions and learning habits. Most of the learners showed positive feedback towards the use of e-textbooks, while some mentioned the technical limitations compared to conventional paper-based learning. This study suggested that e-textbooks are likely to induce positive experiences for learners in the context of online learning, so it is necessary to design contents that utilize various functions and advantages of electronic teaching materials in order to use e-textbooks effectively.

• The Mathematical Education
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• v.61 no.1
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• pp.63-82
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• 2022

The aim of this study was to analyze the changing process in a middle school teacher's discourse capability through reflection to lessons, thereby providing the implications for activities to improve the quality of lessons. To that end, this study explored the characteristics of change in the teacher's discourse capability of promoting students' participation while the teacher repeated instruction implementation and meeting for reflecting the implementation. Through the reflection, the teacher noticed his own matters about dealing with the students' responses and presentations. By attempting to address the matters in the instructions and reflecting the attempt, the teacher was able to accelerate the students' participation in the lesson discourse through enhancing productivity and openness of the discourse. The result of this study demonstrated that lesson reflection beneficially influenced development of teaching profession related to discourse capability.

• The Mathematical Education
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• v.61 no.3
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• pp.441-456
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• 2022

The purpose of the current study is to report a part of our larger project whose focus is to understand a relationship between students' units coordination and K-12 school mathematics. In particular, in this paper we report how students who exhibit distinct levels of units coordinations used their knowledge of proportion to solve quadratic function problems of the form y = ax². To this end, three 7th grade students all of whom assimiliated whole number problem situations with three levels of units but showed different levels for fraction problems were chosen. We carried out clinical interviews not only to understand their ability to coordinate units but to understand their problem solving process of proportion and the quadratic function problems. The analysis suggest that their abilities to coordinate units influenced their ways to solving proportion problems, and in turn influenced their ways to solve the specific form of quadratic functions. We have finalized our study by discussing how students' ability to construct and coordinate units, their proportion knowledge, and their knowledge associated with expressing the specific type of quadractic functions could be related.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.1-17
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• 2004

According to the 7-th curriculum, irrational number should be introduced using repeating decimals in 8-th grade mathematics. To do so, the relation between rational numbers and repeating decimals such that a number is rational number if and only if it can be represented by a repeating decimal, should be examined closely Since this relation lacks clarity in some text books, irrational numbers have only slight relation with repeating decimals in those books. Furthermore, some text books introduce irrational numbers showing that $\sqrt{2}$ is not rational number, which is out of 7-th curriculum. On the other hand, if we use numeral 0 as a repetend, many results related to repeating decimals can be represented concisely. In particular, the treatments of order relation with repeating decimals in 8-th grade text books must be reconsidered.

• Journal of the Korean School Mathematics Society
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• v.19 no.2
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• pp.153-176
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• 2016

The purpose of this study is to suggest ways to promote student engagement by analyzing how a teacher's student engagement strategies and questioning strategies affect class participation and problem solving in a peer mentoring teaching method. As for the purpose, after recording 7th grader's classroom using a peer mentoring and transcribing classroom discourse, we analyzed student engagement strategies for class participation and questioning strategies for helping mathematical concepts and problem solving, and compared mathematics achievements in mid-term and final exams. As results, in learning environments based on comfortable atmosphere, diverse student engagement strategies and appropriate questioning strategies with effectiveness of peer mentoring encouraged students to participate in class by motivating them, helped them to develop mathematical concepts and deepen understanding of problem solving through effective social interactions, and improved student achievement in mathematics. The results can practically help to develop class design considering both student engagement strategy and questioning strategy by specifically presenting a teaching method for promoting student engagement and teacher's contributions to it.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.257-271
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• 2009

Stochastical independence is separated into two. One can be intuitively judged and the other is not. Independence is a concept based on assumption. However, It is defined as multiplication rule and it has produced extension of concept. Analysis on this issue is needed, assuming the cause is on the intersection sign which is used for both simultaneous events and compatible events. This study presented the extension process of independence concept in detail and constructed twofold interpretation of simultaneous events and compatible events which use the same sign $P(A\cap{B})$ with Pierce Semiotics.

• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.4
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• pp.111-118
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• 2013

Today, universities in Korea give a great effort to complement basic college scholastic ability of freshman. Maybe it could be unnecessary effort from university. However, we cannot just leave students who have poor academic performance about 10 to 30% in a university. Universities have to prepare to solve this problem. Thus government and universities investigate a lot of efforts but there is no guarantee. As a result, e-learning could be the best solution to complement poor academic performance of freshman and it also could be the best way to reduce financial burden of university. So, many universities introduce e-learning system and they also support professors to make e-learning content. We need to promote content usage and to improve overall operations. In this paper, we discuss poor academic performance problems under the current middle and high school education systems and review approaches to solve these problems. From this analysis, we propose the design of an effective e-learning system and a method of operation to complement students who achieve poor academic performance.