• Research in Mathematical Education
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• v.19 no.4
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• pp.247-265
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• 2015

Mathematics textbook plays a significant role in shaping students' learning of mathematics. Logic, rigor and abstraction as typical features of the formalization of mathematics, dominate mathematics textbooks around the world, which is regarded as one of the important origins of students' learning difficulties in mathematics. An innovative series of Chinese mathematic textbooks is presented in this paper. Supported by the supplementary materials excerpts from the textbooks, it gives a comprehensive theoretical analysis of the principles of design and implementation of this series of mathematics textbooks. The effectiveness of this series of textbooks is demonstrated by student achievement and secondary research data. It shows that series of Chinese mathematic textbooks has largely decreased students' learning difficulties in mathematics and enhance classroom teaching efficiency. It suggests that prioritizing the essence of mathematics and reducing abstraction is an important notion for mathematics textbook design and implementation.

• Education of Primary School Mathematics
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• v.20 no.3
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• pp.237-252
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• 2017

The era of the Fourth Industrial Revolution has also influenced the direction of mathematics education. In particular, the convergence capability that recognizes how mathematics can be applied and utilized in various fields is an important point. The purpose of this study is to examine the point of convergence and to develop a fusion program that can be used in the mathematics classroom. Specifically, we analyze the tiles used in ancient Islamic architecture from a mathematical point of view and develop mathematics and multifamily convergence programs based on them. Through the mathematical analysis of the geometric tiling made 500 years earlier than Penrose, I hope that understanding of design, the use of mathematics and the possibility of convergence of other disciplines through mathematics will be widened.

• The Mathematical Education
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• v.56 no.4
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• pp.365-385
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• 2017

This study aims to explore mathematics teachers' pedagogical design capacity. For this purpose, we googled and collected 327 lesson plans for middle-school mathematics and investigated how mathematics teachers plan and design their mathematics lessons through the format and structures, objectives and mathematical tasks, anticipation for students' thinking, and assessment and technology use. The findings from the data analysis suggest as follows: a) all the lesson plans are structured in a very similar way; b) the lesson plans seem to be based on the textbooks exclusively, that is, the mathematical tasks and flow is strictly followed and kept in the lesson plans in the way the textbooks suggested; c) the lesson plans do not include any evidence of what teachers anticipate for students' thinking and would do to resolve the students' issues; and d) the lesson plans do not contain any specific plans to assess students' thinking processes and reasoning qualitatively, and not intend to use technology in order to promote effective teaching and meaningful understanding.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.109-119
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• 2002

Some sufficient conditions on the existence and uniqueness of certain symmetric balanced incomplete block design are introduced. Also, a construction algorithm for the design and some examples are presented. The algorithm is developed based on the construction of subspaces of the three-dimensional vector space over a field.

• International Journal of Contents
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• v.17 no.2
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• pp.9-19
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• 2021

The purpose of this survey-based study was to investigate high school students' perceptions of mathematics teachers' implementation of Universal Design for Learning (UDL)-based practices and technology in their mathematics classes in 2017. A total of 303 high school students in South Korea participated in this online survey on teachers' use of technology for instructional practices, the frequency of technology tool use, and the meeting of UDL guidelines in mathematics instruction. According to frequency analysis, high school students generally perceived their teachers' mathematics teaching as somewhat positive in providing multiple means of representation, action and expression, and engagement. However, mathematics teachers' implementation of technology tools in their mathematics classes was generally limited. This study indicated significant and positive relationships between variables regarding the use of technology tools and teachers' efforts to follow the UDL guidelines. Applying the Chi-squared test, we further examined how each survey result differed according to high school students' academic achievements and grade levels.

• Journal of Korea Multimedia Society
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• v.20 no.6
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• pp.935-949
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• 2017

The purpose of this study was to analyze the characteristics of virtual manipulatives apps that can be used to teach students struggling to learn mathematics. To achieve this goal, ten general characteristics of 23 virtual manipulatives apps were evaluated. The instructional, interface, and interactive design features of apps were also evaluated on five-point scale ratings of 18 items. In addition, SPSS frequency analysis and the correlation between each feature was analyzed. Frequently presented instructional contents among 23 virtual manipulatives apps were geometry, arithmetic operation, number concept and measurement. The frequently presented level of instructional contents was lower grade elementary school and kindergarten age. The frequently presented instructional type was the simulation. Regarding the design features, instructional design was rated as the highest (mean = 3.7); interactive design (mean = 3.6) and interface design (mean = 3.3) were also rated higher than neural. In addition, as the learning strategy was appropriately presented, it was evaluated that there was less screen linkage and content error.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.159-177
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• 2020

Education researchers have been continuously interested in the teacher's ability to design lessons and conducted various studies in order to improve the teacher's professionalism in determining the quality of school instruction. So, this study explored the change of instructional design through the lesson reflection of pre-service mathematics teachers who participated in practicum settings. As a result, in the lesson plan prepared by pre-service mathematics teachers, the motivation to induce learning in the introduction stage, to present the learning contents in the development stage, and to reconstruct the formative evaluation of the closing stage was the highest rate. And the categories of the reconstructed contents appeared intensively in terms of curriculum contents and teaching and learning methods. This result can be attributed to the lack of experience in designing and performing lessons by pre-service mathematics teachers, so it suggests that the opportunity to design and conduct classes that take into account the practical aspects of education should be provided in the preparation process for pre-service mathematics teachers.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.313-325
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• 2009

The purpose of this paper is to design a cyber mathematics mentoring system which is helpful for interactive mathematics mentoring among mentors and learners. We review theories about various technological tools that are related to students' interest, participation and motivation in the course of on-line and off-line activities, and we also research the effectiveness of such tools. Also we consider educational implications of the cyber mathematics mentoring system for pre-service teachers, in-service teachers, learners and mentors.

• Research in Mathematical Education
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• v.6 no.2
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• pp.159-170
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• 2002

The undergraduate curriculum in differential equations has undergone important changes in favor of the visual and numerical aspects of the course primarily because of recent technological advances. Yet, research findings that have analyzed students' thinking and understanding in a reformed setting are still lacking. This paper discusses an ongoing developmental research effort to adapt the instructional design perspective of Realistic Mathematics Education (RME) to the teaching and learning of differential equations at Ewha Womans University. The RME theory based on the design heuristic using context problems and modeling was developed for primary school mathematics. However, the analysis of this study indicates that a RME design for a differential equations course can be successfully adapted to the university level.

• Steel and Composite Structures
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• v.27 no.3
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• pp.297-310
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• 2018

A simple and efficient numerical optimization approach for the lightweight optimal design of composite laminated beams is presented in this paper. The proposed procedure is a combination between the finite element method (FEM) and a global optimization algorithm developed recently, namely Jaya. In the present procedure, the advantages of FEM and Jaya are exploited, where FEM is used to analyze the behavior of beam, and Jaya is modified and applied to solve formed optimization problems. In the optimization problems, the objective aims to minimize the overall weight of beam; and fiber volume fractions, thicknesses and fiber orientation angles of layers are selected as design variables. The constraints include the restriction on the first fundamental frequency and the boundaries of design variables. Several numerical examples with different design scenarios are executed. The influence of the design variable types and the boundary conditions of beam on the optimal results is investigated. Moreover, the performance of Jaya is compared with that of the well-known methods, viz. differential evolution (DE), genetic algorithm (GA), and particle swarm optimization (PSO). The obtained results reveal that the proposed approach is efficient and provides better solutions than those acquired by the compared methods.