• School Mathematics
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• v.4 no.4
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• pp.565-580
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• 2002

연구자들은 학생들에게 문제해결 전략을 지도하는 것이 학생들의 문제해결력을 신장시켜 준다는 보고하고 있다. 이와 같은 연구결과를 배경으로 수학 교과서를 통하여 문제해결 전략을 지도하려는 시도들이 미국을 비롯하여 한국에서도 있어 왔다. 본 논문은 문제해결 전략을 교과서에 제시할 수 있는 가능한 세 가지 모델들을 논의하고, 미국과 한국의 수학교과서에서 문제해결 전략을 제시하는 방법을 분석하였다. 한 가지 모델은 문제해결 전략에 한 단원을 할애하는 것이다. 두 번째 모델은 각 수학내용을 지도하는 단원에 문제해결 전략의 지도를 위한 하위단원을 할당하는 것이다. 마지막, 세 번째 모델은 문제해결 전략 지도를 위한 특정 단원이나 하위 단원을 설정하는 것이 아니라 가능한 많은 쪽에 전략을 제시하는 것이다. 위에 언급한 세 가지 가능한 모델을 바탕으로 미국과 한국의 초등학교 수학교과서에서 문제해결 전략을 제시하는 양상을 비교하였다. 이 비교를 위하여 각 학년별로 제시되는 모든 전략들을 교과서와 교사용 지도서를 토대로 추출하였다. 각 교과서에서 전략을 제시한 양식을 비교한 결과 다음과 같은 결론을 얻게 되었다. 한국의 수학교과서는 전형적으로 첫 번째 모델의 양식으로 문제해결전략을 제시하고 있었다. 각 단원마다 별개의 문제해결 전략이 제시되었다. 또한, 학년별 지도 전략을 살펴보면 학년별로 연계성이 있게 전략이 제시 되었다기 보다는 학년별로 다른 다양한 전자의 지도에 중점을 둔 듯하다. 미국의 수학교과서는 두 번째 모델과 세 번째 모델의 중간적인 양식으로 문제해결 전략을 제시하고 있다. 즉, 각 단원마다 문제해결 전략 지도를 위한 하위 단원을 지정하였으며 필요한 경우에는 본 단원의 주 학습요소와 관련된 문제해결 전략은 단원 중에도 제시되고 있었다. 따라서, 차기 수학교과서 개정시기에는 세 번째 모델을 그 모형으로 삼아 문제해결 전략들을 제시하는 방안을 강구해야 할 것으로 기대된다.

• School Mathematics
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• v.19 no.3
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• pp.617-638
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• 2017

In order to make a connection in teaching similar concepts between mathematics and science in teaching similar concepts, this paper analyzed the contents related to capacity, volume, weight, and mass in the mathematics and science textbooks aligned with the national elementary curriculum. We first explored when to present such topics in both textbooks, and then analyzed in what ways the topics were addressed in terms of quantitative comparison, vocabulary, units of measurement, measurement, tools for measurement, estimation, and connections to real life. The results of this study showed that there were some aspects emphasized in common both in mathematics and science textbooks. The analysis of this study also demonstrated subtle but considerable differences according to the characteristics of two subject matters. Based on these results, this paper provides implications for elementary school teachers to consider in teaching capacity, volume, weight, and mass through mathematics and science lessons.

• The Mathematical Education
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• v.58 no.3
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• pp.367-381
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• 2019

This investigation engaged elementary and middle school pre-service teachers in a task of modeling and explaining the magnitude of $0.14m^2$ and examined their responses. The study analyzed both successful and unsuccessful responses in order to reflect on the patterns of misconceptions relative to pre-service teachers' prior knowledge. The findings suggest a need to promote opportunities for pre-service teachers to make connections between different domains through meaningful tasks, to reason abstractly and quantitatively, to use proper language, and to refine conceptual understanding. While mathematics teacher educators (MTEs) could use such mathematical tasks to identify the mathematical content needs of pre-service teachers, MTEs generally use instructional time to connect content and pedagogy. More importantly, an early and consistent exposure to a combined experience of mathematics and pedagogy that connects and deepens key concepts in the program's curriculum is critical in defining the important content knowledge for K-8 mathematics teachers.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.281-300
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• 2015

The purpose of this research is to analyze cognitive demands, answer types, and storytelling types on the basis of mathematical tasks in five different mathematics textbooks based on 2009 revised curriculum in order to suggest directions for the development and use of storytelling mathematics textbooks in school. Results show that first, PNC (Procedures without Connections) task was the largest category in cognitive demands of all mathematical tasks, Low-Level task was larger than others in cognitive demands of mathematical content tasks, and High-Level task was larger than others in cognitive demands of mathematical activity tasks. Second, a short-answer type was the largest category in answer types of all mathematical tasks, the majority of mathematical content tasks were a short-answer type, and the majority of mathematical activity tasks were both short-answer and explanation-answer types. Finally, storytelling connected to real-life was the largest category in storytelling types, and the number of mathematical activity tasks was less than that of mathematical content tasks. However, in the tasks reflected on storytelling, the percentage of mathematical activity tasks was higher than that of mathematical content tasks. Based on the results, while developing storytelling mathematics textbooks and using storytelling textbooks in school, it suggests to consider the need for balance and diversity in cognitive demands, answer types, and storytelling types according to mathematical tasks.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.295-322
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• 2021

This study was conducted for one semester through one group pretest-posttest design with 49 first-year middle school students to explore the effects of mathematics-centered STEAM class experiences on students' mathematical modeling abilities. The main results of this study are as follows: First, the results of the pre and post-mathematical modeling ability tests showed that the average score of posttest was improved compared to the pretest, and that the experiences of mathematics-centered STEAM classes provided in this study had a positive effect on improving the mathematical modeling ability of first-year middle school students. Second, STEAM classes were more effective in solving mathematical modeling problems that require students' creative and divergent thinking. Third, the content analysis of student responses for each subquestion showed that STEAM classes were especially more helpful in activating students' mathematical model construction and validating steps.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.12
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• pp.16-22
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• 2020

The characteristics of the LCL filter for grid-connected inverters have been discussed in academia and industry. An online simulation tool was applied to compare and analyze the difference between the LCL filter and L filter. LCL filters were modeled and simulated using a range of professional simulation simulators, and the LCL filters were found to have good filtering effects for high-frequency harmonics. First, this paper summarizes the transfer functions of the LCL filter and provides the Bode plot diagram. The accuracy and validity of the filter attenuation characteristics were confirmed by a fast Fourier transform based on off-line simulation tools, such as PSIM and MATLAB, depending on the given parameters of the LCL filter. Finally, the Typhoon HIL402 real-time simulation was performed for hardware in the loop simulation to verify the actual filtering characteristics of the LCL filter.

• School Mathematics
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• v.15 no.2
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• pp.443-457
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• 2013

This study investigated the perceptions of beginning teachers about teacher knowledge. Reflections and improvement of their class knowledge have been perceived as the most important factors by beginning teachers. In terms of utilization of actual classes, teacher knowledge, mathematical concepts and correlations such as connection linked to class contents and hierarchy have been used the most. Among the needed teachers knowledge, knowledge of student understanding and mathematics content knowledge was the most essential knowledge that could be mainly formed through classroom experience and teacher training program. On the other hand, knowledge about technology and assessment was not necessary or useful factor for beginning teachers. To facilitate formation of beginning teachers' knowledge, teacher introductory program, mentoring program, interactive relationship with teacher education institutes, curriculum improvement for teacher education institute and the development and dissemination of various teachers training program would be required.

• Journal for History of Mathematics
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• v.26 no.1
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• pp.57-83
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• 2013

This study focuses on the use of mathematics notes in elementary school mathematics classes as a way of practicing mathematical communication, which was introduced as one of the main themes in the 2007 Mathematical Curriculum Revision. We investigate, through interviews with teachers and questionnaires, why and how mathematics notes are used and what are included in them, finding out various aspects of the use of mathematics notes such as the purposes, the necessities and the types. We draw some helpful suggestions for using mathematics notes in classes which has positive effects such as enhancing students' mathematical thinking and calculation ability. This study is to provide teachers with an appropriate information and basic materials on the use of mathematics notes.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.179-203
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• 2013

The purpose of this study was to discuss the example that developed geometry model textbook based on storytelling using real-life context. To achieve this purpose, we first elaborated the meaning of the textbook based on storytelling with real-life context, and then we discussed the outline of the story and the summary of each lesson. This study defined the storytelling textbook with real-life context as the textbook consisting of activities that explored and organized mathematical concepts by using real-life situations as materials of stories. The geometry textbook we developed employed two real-life materials, a map and a set square: we used a map for the coordinate geometry and a set square for the equation of a line. To attract students' interest, we introduced confrontation between a teacher and two students and a villain. We implemented experimentation with the textbook based on storytelling in order to verify its validity. The participants were 25 students that were enrolled in a high school in Seoul. Among them, 17 participants were surveyed. Students' answers from the survey questionnaire suggested that the geometry textbook we developed based on storytelling helped them learn mathematics and that the instruments such as a map and a set square helped them understand mathematical concepts. However, their opinion implied that the story of the textbook needed to be improved so that the story reflected more realistic contexts that were familiar with students.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.277-297
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• 2023

In mathematics, the concept of convolution is widely used. The convolution operation is required for understanding computer vision and deep learning in artificial intelligence. Therefore, it is vital for this concept to be explained in college mathematics education. In this paper, we present our new teaching and learning materials on convolution available for engineering mathematics. We provide the knowledge and applications on convolution with Python-based code, and introduce Convolutional Neural Network (CNN) used for image classification as an example. These materials can be utilized in class for the teaching of convolution and help students have a good understanding of the related knowledge in artificial intelligence.