• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.461-477
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• 2009

In this study, an operational analysis in the context of linear equations is presented. For the analysis, several second-order models concerning students' whole number knowledge and fraction knowledge based on teaching experiment methodology were employed, in addition to our first-order analysis. This ontogenetic analysis begins with students' Explicitly Nested number Sequence (ENS) and proceeds on through various forms of linear equations. This study shows that even in the same representational forms of linear equations, the mathematical knowledge necessary for solving those equations might be different based on the type of coefficients and constants the equation consists of. Therefore, the pedagogical implications are that teachers should be able to differentiate between different types of linear equation problems and propose them appropriately to students by matching the required mathematical knowledge to the students' potential constructs.

• The Mathematical Education
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• v.39 no.2
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• pp.179-186
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• 2000

Although computer technology has a great potential for improving mathematics learning practice, it rarely used in mathematics classroom. The purpose of this study is to suggest the future direction for research in mathematics computer technology. First, there has to be a research on mathematics curriculum that take computer technology into account. Second, research on teaching sequence for certain content area is needed. Because computer technology would change the order of teaching sequence. Third, how students would learn with computer technology? how do they acquire knowledge and make sense of it? Fourth, how could we assess the learning with computer technology? Most of all, because teachers play a key role to succeed in educational reform, they have to be familiar with computer technology and software to introduce it into mathematics learning and to use it properly.

• Research in Mathematical Education
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• v.26 no.3
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• pp.127-146
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• 2023

Statistical thinking has a broad definition but focuses on the context of regression modelling in the present study. To foster students' statistical thinking within the context, teaching should no longer be seen as transfer of knowledge from teacher to students but as a process of engaging with learning activities in which they develop ownership of knowledge. This study aims at collaborative learning contexts; students were divided into small groups in order to increase opportunities for peer collaboration. Each group of students was asked to do a regression project after class. Through doing the project, they learnt to organize and connect previously accrued piecemeal statistical knowledge in an integrated manner. They could also clarify misunderstandings and solve problems through verbal exchanges among themselves. They gave a clear and lucid account of the model they had built and showed collaborative interactions when presenting their projects in front of class. A survey was conducted to solicit their feedback on how peer collaboration would facilitate learning of statistics. Almost all students found their interaction with their peers productive; they focused on the development of statistical thinking with concerted effort.

• The Mathematical Education
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• v.60 no.3
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• pp.387-407
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• 2021

The present study was conducted on the assumptions that both progressivist and constructivist education emphasized the subjective knowledge of learners and confronted similar problems when the derived educational principles from the two perspectives were adopted and applied to mathematics research and practice. We argue that progressivism and constructivism should have clarified the meaning, purpose, and direction of 'emphasizing subjective knowledge' in application to the particular educational field. For the issue, we reflected Dewey's theory on the application of past progressivism, and aligned with it, we took a critical view of the educational applications of current constructivism. As a result, first, the meaning of emphasizing subjective knowledge is that each of the students constructs a unique mathematical reality based on his or her experience of situations and cognitive structures, and emphasizes our understanding of this subjective knowledge as researchers/observers. Second, the purpose of emphasizing subjective knowledge is not to emphasize subjective knowledge itself. Rather, it concerns the meaningful learning of objective knowledge: internalization of objective knowledge and objectification of subjective knowledge. Third, the application of the emphasis on subjective knowledge does not specify certain teaching/learning methods as appropriate, but orients us toward a genuine learner-centered reform from below. The introspections, we wish, will provide new momentum for discussion to establish constructivism as a coherent theory in mathematics classrooms.

• The Mathematical Education
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• v.43 no.2
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• pp.199-210
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• 2004

This study investigates 55 preservice secondary mathematics teachers' situational understanding of functional relationship. Functional thinking is fundamental and useful because it develops students' quantitative thinking about the world and analytical thinking about complex situations through examination of the relations between interdependent factors. Functional thinking is indispensable for understanding natural phenomena, for investigation by science, and for the technological inventions in engineering and navigation. Therefore, it goes without saying that teachers should be able to represent and communicate about various functional situations in the course of teaching and learning functional relationships to develop students' functional thinking. The result of this study illustrates that many preservice teachers were not able to appropriately represent and communicate about various functional situations. Additionally, it shows that most preservice teachers have limited understanding of the value of teaching function.

• Research in Mathematical Education
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• v.26 no.1
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• pp.1-17
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• 2023

Over the last three decades, there has been an increasingly strong emphasis on group-centered approaches to mathematics teaching. One primary responsibility for teachers who use group-centered instruction is to "check in", or intervene, with groups to monitor group learning and provide mathematical support when necessary. While prior research has contributed valuable insight for successful teacher interventions in mathematics group work, there is a need for more fine-grained analyses of interactions between teachers and students. In this study, we co-conducted research with an exemplary middle grade teacher (Ms. Green) to learn about fine-grained details of her intervention practices, hoping to generate knowledge about successful teacher interventions that can be expanded, replicated, and/or contradicted in other contexts. Analyzing Ms. Green's practices as an exemplary case, we found that she used exceptionally short interventions (35 seconds on average), provided space for student dialogue, and applied four distinct strategies to support groups to make mathematical progress: (1) observing/listening before speaking; (2) using a combination of social and analytic scaffolds; (3) redirecting students to task instructions; (4) abruptly walking away. These findings imply that successful interventions may be characterized by brevity, shared dialogue between the teacher and students, and distinct (and sometimes unnatural) teaching moves.

• The Mathematical Education
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• v.63 no.2
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• pp.295-318
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• 2024

This narrative review explores the transformative potential of immersive virtual reality (IVR) in enhancing high school students' mathematics competence, viewed through the lens of the technological, pedagogical, and content knowledge (TPACK) framework. This review comprehensively illustrates how IVR technologies have not only fostered a deeper understanding and engagement with mathematical concepts but have also enhanced the practical application of these skills. Through the careful examination of seminal papers, this study carefully explores the integration of IVR in high school mathematics education. It highlights significant contributions of IVR in improving students' computational proficiency, problem-solving skills, and spatial visualization abilities. These enhancements are crucial for developing a robust mathematical understanding and aptitude, positioning students for success in an increasingly technology-driven educational landscape. This review emphasizes the pivotal role of teachers in facilitating IVR-based learning experiences. It points to the necessity for comprehensive teacher training and professional development to fully harness the educational potential of IVR technologies. Equipping educators with the right tools and knowledge is essential for maximizing the effectiveness of this innovative teaching approach. The findings also indicate that while IVR holds promising prospects for enriching mathematics education, more research is needed to elaborate on instructional integration approaches that effectively overcome existing barriers. This includes technological limitations, access issues, and the need for curriculum adjustments to accommodate new teaching methods. In conclusion, this review calls for continued exploration into the effective use of IVR in educational settings, aiming to inform future practices and contribute to the evolving landscape of educational technology. The potential of IVR to transform educational experiences offers a compelling avenue for research and application in the field of mathematics education.

• The Mathematical Education
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• v.52 no.2
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• pp.163-174
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• 2013

This study conducted a survey to examine the knowledge formation and utilization of computer among beginning teachers of secondary school mathematics. We found that beginning teachers who had more experiences of taking computer utilization classes at teacher education institutes showed more interest in computer and saw the necessity and effectiveness of computer usage for teaching students. Teachers chose GSP the most among computer utilization knowledge learned in pre-service teachers program, and GSP is used the most in mathematics classes. However, they answered that computer is not so much available in class due to lack of hours and the relevant resources. Lastly, beginning teachers answered that the computer knowledge learned in in-service teacher program was more useful than that in pre-service. Thus, the professional development in utilizing computer should be improved through diversifying teacher training contents for beginning teachers as well as for pre-service teachers in teacher education institutes.