• The Mathematical Education
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• v.51 no.2
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• pp.145-160
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• 2012

Prospective teachers need to have an opportunity to critically examine their initial perception with regard to effective mathematics instruction during the teacher education period. This study analyzed the perception in relation to good mathematics instruction by a total of 265 prospective teachers from four institutes for elementary teacher education using a survey. The results of this study showed that the pre-service teachers regarded learner, teaching and learning method, selection of content, and construction of curriculum as important for high-quality mathematics instruction. However, they revealed relatively low levels of agreement against the importance of instructional materials, classroom environment and atmosphere, and assessment. On the basis of teachers' perception on each element of effective mathematics instruction, this paper raises issues for discussion and includes some implications for teacher education.

• Journal of the Korean School Mathematics Society
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• v.25 no.3
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• pp.225-241
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• 2022

The purpose of this study is to analyze and present what aspects of the concept of function prospective mathematics secondary teachers emphasize when designing a class that introduces the concept of function using curriculum and textbooks. For this purpose, virtual instruction and reflections on virtual instruction were analyzed. The results are as follows. The prospective mathematics secondary teachers consider and introduce the concepts of function as correspondences and processes. Their conception of function was consistently observed during virtual instruction and reflections on virtual instruction. The prospective mathematics secondary teachers' conception of function was closely related to the form of expressing functions. These results provi e implications for prospective mathematics secondary teachers' education for introducing the concept of function based on the dependent relation between variables presented in the 2015 revision of the national mathematics curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.221-246
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• 2011

One of the main purposes in prospective elementary teacher education is to prepare for teaching each subject matter. For this purpose, it is necessary to explore how prospective teachers may analyze elementary mathematics instruction and they perceive their analytic foci. This study probed in what ways prospective teachers analyzed elementary mathematics instruction using two video cases. The results of this study showed that prospective teachers focused mainly on instructional strategies, specifically with regard to whether such strategies would be adequate both for mathematical content to be taught and for students' characteristics. They also focused on the effective use of instructional materials as well as the case teacher's adequate feedback. Prospective teachers claimed to have analytic foci not only on the degree of attainment of instructional purposes but also on students' responses and interest. Given this result, this paper includes several issues related to help prospective teachers prepare for better teaching.

• Research in Mathematical Education
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• v.9 no.1 s.21
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• pp.25-45
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• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.147-164
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• 2011

The national mathematics curriculum revised in 2007 emphasized students' mathematical communication and the curriculum is currently applied to all grades. In order to promote students' mathematical communication, the teacher needs to understand full implications and apply them to instruction. This study examined how teachers employed mathematical communication in their instruction and how they perceived it. The results showed that teachers had lack of understanding of student-centered instruction and mathematical communication. They also did not use various representation activities and discussion-based activities as expected. The number of students per classroom was reported by teachers as a main barrier to promote mathematical communication, but it did not make substantial differences in practice. Building on the results, this paper included implications for improving teachers' conception of mathematical communication.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.205-213
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• 2006

In this research, we interviewed primary school teachers and students with hypothetical situations questions and got a comprehensive picture of the status quo of what is happening in the new mathematics classrooms of Mainland China, that is, teachers' conceptions of mathematics and their teaching approaches influence the students' conceptions of mathematics to a large extent. For the teacher who emphasizes the precision and rigidity of mathematics, her students focus on the superficial characteristics of mathematics. On the contrary, for the teacher who believes that mathematics is an open process, related to real life and rich in content, her students are more interested in mathematics and have more diverse conceptions.

• Communications of Mathematical Education
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• v.26 no.3
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• pp.317-338
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• 2012

This paper compared and contrasted the views of effective mathematics instruction by 223 elementary school teachers and 151 middle school mathematics teachers using a questionnaire with 4 main domains (i.e., curriculum and content, teaching and learning, classroom environment and atmosphere, and assessment) and a total of 48 sub-elements. The analysis of results showed that elementary school teachers put their priority on the curriculum and content domain, while middle school counterparts did on the teaching and learning domain. The teachers commonly agreed with instruction which fosters students' self-directed learning ability, reconstructs the curriculum tailored to students' diverse levels, and establishes appropriate interaction between the teacher and students. However, elementary school teachers agreed more than middle school teachers with regard to the 23 elements related to effective mathematics instruction. In contrast, middle school teachers agreed more than their counterparts as for only 2 elements (instruction fostering mathematical representation and instruction eliciting students' learning motivation). This paper includes suggestions and implications related to Korean teachers' perception of effective mathematics instruction.

• Research in Mathematical Education
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• v.14 no.4
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• pp.361-380
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• 2010

Some 400 Secondary One (i.e. seventh-grade) students from 10 schools were provided with non-routine mathematical problems in their normal mathematics classes as exercises for one academic year. Their attitudes toward mathematics, their conceptions of mathematics and their problem-solving performance were measured both in the beginning and at the end of the year. Hierarchical regression analyses revealed that the introduction of an appropriate dose of non-routine problems would generate some effects on the students' conceptions of mathematics. A medium dose of non-routine problems (as reported by the teachers) would result in a change of the students' conception of mathematics to perceiving mathematics as less of "a subject of calculables." On the other hand, a high dose would lead students to perceive mathematics as more useful and more as a discipline involving thinking. However, with a low dose of non-routine problems, students found mathematics more "friendly" (free from fear). It is therefore proposed that the use of non-routine mathematical problems to an appropriate extent can induce changes in students' "lived space" of mathematics learning and broaden their conceptions of mathematics and mathematics learning.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.233-249
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• 2005

This study discusses on the historico-genetic instruction on fraction. The textbooks of the current curriculum include the variety of contexts of fraction to be intended to connect with the conception of ratio in the grade 6. However mary elementary students have understanding limited to whole-part relation only. This study propose a method on the basis of the process of measurement by an absolute unit. The idea is related to The genesis of fraction in Egypt.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.509-521
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• 2002

The purpose of this paper is as follows: $^{\circleda}$ to disclose the essence of symmetry $^{\circledb}$ to propose the desirable strategy of problem-solving as to symmetry $^{\circledc}$ to clarify the relationship between symmetry and group $^{\circledd}$ to propose a way of introduction of 'group' in school mathematics according to its fundamental characteristic, symmetry. This study shows that the nature of symmetry is 'invariance under a transformation' and symmetry is the main idea of 'group'. In mathematics textbooks and mathematics education literature, we find out that the logic of symmetry is widespread. We illustrate two paradigmatic problem related to symmetrical logic and exemplify a desirable instruction of Pascal's triangle. This study also suggests a possibility of developing students' unformal and unconscious conception of group with sym metry idea from elementary to secondary school mathematics.