• Research in Mathematical Education
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• v.26 no.4
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• pp.291-310
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• 2023

In this paper, we propose a theoretical framework for Chinese high school mathematics teachers use new textbooks based on the work of Remillard (1999) and Chau (2014). Based on this framework, a multiple case approach was used to investigate how two high school mathematics teachers from Shanghai use new textbooks. The results suggest that in the curriculum mapping arena, both the novice teacher and the expert teacher often planned to appropriate the unit content, and sometimes planned to add supplemental content. When organizing the unit content, novice teacher always planned to follow the new textbook in sequence, while expert teacher often would follow the new textbook in sequence, but sometimes planned to rearrange the unit content. In the design arena, both the novice teacher and the expert teacher tended to appropriate the introduced tasks and definitions. The novice teacher often planned to appropriate the example problems and exercise problems, while the expert teacher often intended to flexibly use the example problems and exercise problems. In the construction arena, the novice teacher seldom adjusted the planned tasks; in contrast, the expert teacher adjusted the planned tasks more frequently. In the reflection arena, the novice teacher often thought she should improve the mathematics tasks, while the expert teacher almost always thought he needed to improve the mathematics tasks. The framework shown in this paper provides a tool to investigate how mathematics teachers use textbooks.

• East Asian mathematical journal
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• v.40 no.2
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• pp.149-166
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• 2024

This study is to establish the domains and the standards of instructional evaluation on the teacher knowledge dealing with the knowledge of 'teaching and learning methods and assessment'. Especially, in this study, the instruction assessment standards are developed focused on the five types of mathematics competencies such as problem solving, communication, reasoning, connection, information and handling, which were emphasized in the mathematical curriculum revised in 2022. By the result, ten domains such as an instruction involving instruction goal and content, problem-solving competency, data treatment competency, learners' achievement level and attitude, communication competency, reasoning competency, connection competency, the assessment method and procedure based on the competency, the assessment tool development based on the competency, assessment result based on the competency were new established. According to those domains, the total 20 instructional evaluation standards were developed. This study is limited to consider the domain of 'teaching and learning methods and assessment' among the domains of teacher knowledge, while dealing with the elements of mathematics competencies in the standards. However, instructional evaluation standards reflecting these competencies should be developed in the other diverse domains of teacher knowledge.

• Communications of Mathematical Education
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• v.31 no.4
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• pp.457-485
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• 2017

The Self-reported Evaluation tool developed in this study allows the learners to check and evaluate their own learning by determining the details that are self-assessed. Also this tool allows learners to receive feedback on their self - evaluation results. In this study pre - post test was performed to investigate the effect of self - assessment on the learners' tendency of studying math. The result showed that Self-reported evaluation improved self - confidence, self - strategy on learning mathematics, and meta-cognitive ability. Also by conducting a qualitative analysis of the Self-reported evaluation, students practiced the cognitive activities such as summarizing the contents they have learned that day. They also tried to understand and improve the learning habit, attitude, and learning state. Teachers were also able to communicate with students by providing individual questions and feedback through student's individual Self-reported Evaluation.

• The Mathematical Education
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• v.60 no.2
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• pp.159-172
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• 2021

The purpose of this study is to compare and analyze the effects of physical manipulative and exploratory geometry software on the spatial sense for 5^th grade elementary school students in learning nets. For this purpose, ton experimental group used Geofix, an operational learning tool, and the experimental group used Cabri 3D, an exploratory geometry software to learn the nets of solids. The comparison group was learned by worksheet only without any manipulative or software. Spatial sense tests were conducted before and after to determine the level, and eye tracking were used to analyze the strategies of students in solving nets problems. As a result, it was confirmed that the using Geofix group was the most effective for the spatial sense, and Cabri 3D could also be a good tool for learning the nets of solids. In addition, after learning the nets of solids, the analytical strategy, which was the most effective strategy for students' solving strategies, increased. In the process of solving spatial tasks such as the spatial sense tasks, eye tracking technology become a very useful tool for exploring students' strategies, so it is expected that objective and useful data will be collected through more active use in the future.

• The Mathematical Education
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• v.57 no.3
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• pp.231-246
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• 2018

In this paper, we applied Sfard's reification theory to analyze the secondary students' level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget's theory as a criterion of content judgement in order to grasp students' conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the $9^{th}$ and $10^{th}$ graders. The main results are as follows. First, approximately 45% of $9^{th}$ graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of $10^{th}$ graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of $9^{th}$ graders, and there was no change in $10^{th}$ graders.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.12
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• pp.1110-1116
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• 2013

A 3D-ray tracing tool is a software considering reflection, penetration, and diffraction of the signals to provide accuracy. To provide communication resources effectively, communication standards adopt Heterogeneous Networks (HetNets) that includes small cells. A 3D performance evaluation methodology becomes more and more important since the coverage of the small cell networks is narrower than that of the macro cell networks. It is difficult to directly apply conventional 2D mathematical models due to the complexity of small cell network; since they have many considerations such as topography, placement of buildings and 3D beamforming techniques. In this paper, we introduce an effective performance evaluation methodology for small cell networks using 3D-ray tracing tool. From simulation results, we conclude that new performance evaluation methodologies by using 3D-ray tracing tool is more suitable than conventional methodology for small cell networks.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.273-289
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• 2001

Given that the culture of the mathematics classroom has been perceived as an important topic in mathematics education research, this paper deals with the construct of sociomathematical norms which can be used as an analytical tool in understanding classroom mathematical culture. This paper first reviews the theoretical foundations of the construct such as symbolic interactionism and ethnomethodology, and describes the actual classroom contexts in which social and sociomathematical norms were originally identified. This paper then provides a critical analysis of the previous studies with regard to sociomathematical norms. Whereas such studies analyze how sociomathematical norms become constituted and stabilized in the specific classroom contexts, they tend to briefly document sociomathematical norms mainly as a precursor to the detailed analysis of classroom mathematical practice. This paper reveals that the trend stems from the following two facts. First, the construct of sociomathematical norms evolved out of a classroom teaching experiment in which Cobb and his colleagues attempted to account for students' conceptual loaming as it occurred in the social context of an inquiry mathematics classroom. Second, the researchers' main role was to design instructional devices and sequences of specific mathematical content and to support the classroom teacher to foster students' mathematical learning using those sequences Given the limitations in terms of the utility of sociomathematical norms, this paper suggests the possibility of positioning the sociomathematical norms construct as more centrally reflecting the quality of students' mathematical engagement in collective classroom processes and predicting their conceptual teaming opportunities. This notion reflects the fact that the construct of sociomathematical norms is intended to capture the essence of the mathematical microculture established in a classroom community rather than its general social structure. The notion also allows us to see a teacher as promoting sociomathematical norms to the extent that she or he attends to concordance between the social processes of the classroom, and the characteristically mathematical ways of engaging. In this way, the construct of sociomathematical norms include, but in no ways needs to be limited to, teacher's mediation of mathematics discussions.

• Journal of Gifted/Talented Education
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• v.18 no.3
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• pp.465-496
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• 2008

With leadership and speciality, creativity is cutting a fine figure among major values of human resource in 21C knowledge-based society. In the 7th school curriculum much emphasis is put on the importance of creativity by pursuing the image of human being based on creativity based on basic capabilities'. Also creativity is one of major factors of giftedness, and developing one's creativity is the core of the program for gifted education. Doing mathematics requires high order thinking and knowledgeable understandings. Thus mathematical creativity is used as a measure to test one's flexibility, and therefore it is the basic tool for creativity study. But theoretical study for mathematical creativity is not common. In this paper, we discuss mathematical creativity applied to 6 approaches suggested by Sternberg and Lubart in educational theory. That is, mystical approaches, pragmatical approaches, psycho-dynamic approaches, cognitive approaches, psychometric approaches and scio-personal approaches. This study expects to give useful tips for understanding mathematical creativity and understanding recent research results by reviewing various aspects of mathematical creativity.

• Journal of Music and Human Behavior
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• v.7 no.1
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• pp.1-15
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• 2010

The purpose of this study is to inquire into the theoretical background of music therapy interventions for the improvement of mathematical concepts among young children with special needs. The researcher provides a basis of theoretical background about musical activities as an effective tool for young children to understand and promote their mathematical concepts, and the necessity of practical application in the field of mathematics education is suggested. Music, as a multi-sensory modality, has an ability to hold and maintain one's attention, and can be used as a memory aid and a powerful and effective motivator and reinforcer for young children. Therefore, musical activities can be used to facilitate mathematical concepts in the field of education for young children. Possible musical activities for promoting mathematical development are suggested, and the necessity for developing various musical activities is discussed.

• The Mathematical Education
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• v.27 no.1
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• pp.15-23
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• 1988

We are at the onset of a major revolution in education, a revolution unparalleled since the invention of the printing press. The computer will be the instrument of this revolution. Computers and computer application are everywhere these days. Everyone can't avoid the influence of the computer in today's world. The computer is no longer a magical, unfamiliar tool that is used only by researchers or scholars or scientists. The computer helps us do our jobs and even routine tasks more effectively and efficiently. More importantly, it gives us power never before available to solve complex problems. Mathematics instruction in secondary schools is frequently perceived to be more a amendable to the use of computers than are other areas of the school curriculum. This is based on the perception of mathematics as a subject with clearly defined objectives and outcomes that can be reliably measured by devices readily at hand or easily constructed by teachers or researchers. Because of this reason, the first large-scale computerized curriculum projects were in mathematics, and the first educational computer games were mathematics games. And now, the entire mathematics curriculum appears to be the first of the traditional school curriculum areas to be undergoing substantial trasformation because of computers. Recently, many research-Institutes of our country are going to study on computers in orders to use it in mathematics education, but the study is still start ing-step. In order to keep abreast of this trend necessity, and to enhance mathematics teaching/learning which is instructed lecture-based teaching/learning at the present time, this study aims to develop/present practical method of computer-using. This is devided into three methods. 1. Programming teaching/learning method This part is presented the following five types which can teach/learn the mathematical concepts and principle through concise program. (Type 1) Complete a program. (Type 2) Know the given program's content and predict the output. (Type 3) Write a program of the given flow-chart and solve the problem. (Type 4) Make an inference from an error message, find errors and correct them. (Type 5) Investigate complex mathematical fact through program and annotate a program. 2. Problem-solving teaching/learning method solving This part is illustrated how a computer can be used as a tool to help students solve realistic mathematical problems while simultaneously reinforcing their understanding of problem-solving processes. Here, four different problems are presented. For each problem, a four-stage problem-solving model of polya is given: Problem statement, Problem analysis, Computer program, and Looking back/Looking ahead. 3. CAI program teaching/learning method This part is developed/presented courseware of sine theorem section (Mathematics I for high school) in order to avail individualized learning or interactive learning with teacher. (Appendix I, II)