• Journal of Educational Research in Mathematics
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• v.16 no.3
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• pp.251-272
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• 2006

The purpose of the present study is to explore the process of teacher change as elementary school teachers participated in a community focused on improving mathematics teaching. To do so, a professional community lot improving instructional practice consisted of a group of voluntary elementary school teachers. The professional community provides participating teachers with great opportunities to share their understanding of practical knowledge related to mathematics teaching and learning and change mathematical beliefs as well as to learn pedagogical content knowledge. This study approached to teacher professionality in terms of mathematical beliefs and teaching practice. The change of teaching practice was measured coherently both with a questionnaire and with a mathematics teaching standard developed for this study. The findings of this study point out that techers' beliefs about how students learn mathematics have chantged. This study also indicated that after participating in the professional community focused on improving mathematics teaching, teachers' mathematical teaching is changed toward the more students' oriented way. Especially, it is observed that the meaningful change in participating teachers' teaching practice took place with respect to the role of teachers, students' interaction, mathematical tasks, and problem solving. Finally, this study implies that teachers can have an opportunity to change their beliefs and deepen their professionality about elementary mathematics teaching and learning through participating in the community of practice, through which participating teachers can share their practical knowledge and their understandings about teaching and learning of elementary mathematics.

• Research in Mathematical Education
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• v.20 no.1
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• pp.21-29
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• 2016

Metacognition means "thinking about one's own thinking". There are generally two aspects of metacognition: i) Reflection - thinking about what we know; and ii) Self-regulation - managing how we go about learning. Developing metacognitive abilities is not simply about becoming reflective learners, but about acquiring specific learning strategies as well. There are several strategies that may be used by teachers to develop metacognitive skills amongst learners. As part of a Professional Development project secondary school mathematics teachers have been developing their knowledge and skills to teach for metacognition. In this paper we analyze two lessons presented by groups of teachers in the project and tease out similarities and differences between the lessons that afford or hinder the development of metacognitive skills of learners.

• Research in Mathematical Education
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• v.7 no.3
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• pp.125-137
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• 2003

At a time when mathematics is becoming more important in our everyday lives and more relevant in applications in industry and the emerging technologies, there are signs of a decrease in numbers of students and their interest in the subject. Teachers must be encouraged to take a new approach to generating enthusiasm amongst students by showing them that mathematics is an integral part of the future. To achieve this, opportunities for renewal of teachers' knowledge and updating of skills should be made available. In this paper, emphasis is placed on mathematics in the real world and how it can be used to develop the more general skills such as self-teaching and communication which are an essential part of preparation for entry into higher education or the workplace.

• Research in Mathematical Education
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• v.19 no.2
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• pp.89-100
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• 2015

The study investigated pre-service teachers' knowledge and computational skills by using Triangular Arithmagon. Participants included 90 pre-service teachers from two schools in the United States and Taiwan. The Triangular Arithmagons Test (TAT) was used to measure pre-service teachers' performance in whole number, fractions, and decimals operations (i.e., addition, subtraction, multiplication, and division), each of which included level-1 (basic) and level-2 (advanced) tests. MANOVA analysis was performed to compare the performance between teachers from the United States and Taiwan. Results indicated that overall, pre-service teachers in Taiwan outperformed those in the United States, especially on the advanced-level tests. Pre-service teachers in the United States were found to have poor ability of solving complex operation problems. Different curriculum plans and teaching methods may lead to the performance gap between the two countries.

• Education of Primary School Mathematics
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• v.8 no.2 s.16
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• pp.97-113
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• 2004

The purpose of this study is to develop instructional methods for the formalized algorithm through informal knowledge in teaching division of fractions. The following results have been drawn from this study: First, before students learn formal knowledge about division of fractions, they knowledge or strategies to solve problems such as direct modeling strategies, languages to reason mathematically, and using operational expressions. Second, students could solve problems using informal knowledge which is based on partitioning. But they could not solve problems as the numbers involved in problems became complex. In the beginning, they could not reinvent invert-and-multiply rule only by concrete models. However, with the researcher's guidance, they can understand the meaning of a reciprocal number by using concrete models. Moreover, they had an ability to apply the pattern of solving problems when dividend is 1 into division problems of fractions when dividend is fraction. Third, instructional activities were developed by using the results of the teaching experiment performed in the second research step. They consist of student's worksheets and teachers' guides. In conclusion, formalizing students' informal knowledge can make students understand formal knowledge meaningfully and it has a potential that promote mathematical thinking. The teaching-learning activities developed in this study can be an example to help teachers formalize students' informal knowledge.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.39-52
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• 2012

Research in teachers' knowledge for teaching mathematics (KTM) has been gradually growing for the past several years. With various conceptualizations about what teachers need to teach mathematics, there have been studies to find out the relationship between teachers' KTM and their students' achievement. In this paper, I reviewed various conceptualizations of teacher's mathematical knowledge for teaching, and existing qualitative and quantitative studies about this relationship. Based on the review, I identified the challenges to studying this relationship mainly focusing on the existence of a phase-teaching practice-between teachers' KTM and students' learning. Considering the challenges that have been identified in the literature review, I proposed topics for future studies that would contribute to our understanding how the teachers' KTMare related to their students' achievement, and investigate further about whether and how teacher-student interaction in classroom is related to changes in teachers' KTM.

• School Mathematics
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• v.14 no.2
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• pp.233-253
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• 2012

The purpose of the study investigate mathematics content knowledge(MCK) of prospective teachers in differential area. 70 prospective teachers were asked to perform six questions based on Cho's MCK (2010, 2011). The results show that depending on whether they experience any teacher education program, the level of prospective teachers' mathematics content knowledge may vary. In particular, prospective teachers struggled with an unfamiliar problem situations. We also found that prospective mathematics teachers have some difficulty in solving problem about the use of mean value theorem and derivative.

• Education of Primary School Mathematics
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• v.6 no.1
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• pp.41-54
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• 2002

The purpose of this study is to find out what mathematical situation means, how to pose a meaningful situation and how situation-centered teaching could be done. The obtained informations will help learners to improve their math abilities. A survey was done to investigate teachers' perception on teaching-learning in mathematics by elementary teachers. The result showed that students had to find solutions of the textbook problems accurately in the math classes, calculated many problems for the class time and disliked mathematics. We define mathematical situation. It is artificially scene that emphasize the process of learners doing mathematizing from physical world to identical world. When teacher poses and expresses mathematical situation, learners know mathematical concepts through the process of mathematizing in the mathematical situation. Mathematical situation contains many concepts and happens in real life. Learners act with real things or models in the mathematical situation. Mathematical situation can be posed by 5 steps(learners' environment investigation step, mathematical knowledge investigation step, mathematical situation development step, adaption step and reflection step). Situation-centered teaching enhances mathematical connections, arises learners' interest and develops the ability of doing mathematics. Therefore teachers have to reform textbook based on connections of mathematics, other subject and real life, math curriculum, learners' level, learners' experience, learners' interest and so on.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.421-434
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• 2004

Cognitively Guided Instruction (CGI) is one of the most successful professional development programs for elementary mathematics teachers in US. This article introduces its theoretical background, research-based framework of addition and subtraction work, and how the program has been disseminated. Carpenter and Fennema started CGI aiming to develop a professional development program that focused on research knowledge of children"s thinking. Their goal was. to bring a significant change in teaching by helping teachers understand how children think mathematically. This 3-year NSF funded project grew to be 11-year long, and a number of publications have reported consistent successful learning and teaching by CGI students and teachers compared to counterparts throughout US. CGI′s success by focusing on improving teachers′ knowledge of children′s thinking offers possible opportunities for teacher educators to re-conceptualize teacher education in Korea.

• The Mathematical Education
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• v.45 no.2 s.113
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• pp.177-189
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• 2006

This study focuses on the analysis of prospective elementary teachers' representation of trapezoid area and teacher educator's reflecting in the context of a mathematics course. In this study, I use my own teaching and classroom of prospective elementary teachers as the site for investigation. 1 examine the ways in which my own pedagogical content knowledge as a teacher educator influence and influenced by my work with students. Data for the study is provided by audiotape of class proceeding. Episode describes the ways in which the mathematics was presented with respect to the development and use of representation, and centers around trapezoid area. The episode deals with my gaining a deeper understanding of different types of representations-symbolic, visual, and language. In conclusion, I present two major finding of this study. First, Each representation influences mutually. Prospective elementary teachers reasoned visual representation from symbolic and language. And converse is true. Second, Teacher educator should be prepared proper mathematical language through teaching and learning with his students.