• The Mathematical Education
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• v.41 no.2
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• pp.173-187
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• 2002

The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

• Research in Mathematical Education
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• v.6 no.1
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• pp.39-51
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• 2002

This study described an elementary teacher's practical knowledge of selecting and using mathematical tasks for promoting students' understanding and discourse. The informant of this ethnographic inquiry was a third grade teacher and has 10 years of teaching experience. According to the analysis of multiple data sources, this study showed that based on his beliefs about the development of understanding of mathematics and discourse, he continually employed two different types of tasks: open-ended tasks and tasks from students' mistakes and comments during discourse. Teachers' practical knowledge of teaching mathematics and the classroom norms for students' understanding and discourse are suggested to be given attention for further research on this area.

• Journal of the Korean School Mathematics Society
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• v.19 no.3
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• pp.261-275
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• 2016

Many students have dualistic beliefs about mathematics and its learning- for example, there is always just one right answer in mathematics and their role in the classroom is receiving and absorbing knowledge from teacher and textbook. This article investigated some epistemic implications and limitations of common mathematics teaching practices, which often present mathematical facts(or procedures) and treat students' errors in a certain and absolute way. Langer and Piper's (1987) experiment and Oliveira et al.'s (2012) study suggested that presenting knowledge in conditional language which allows uncertainty can foster students' productive epistemological beliefs. Changing the focus and patterns of classroom communication about students' errors could help students to overcome their dualistic beliefs. This discussion will contribute to analyze the implicit epistemic messages conveyed by mathematics instructions and to investigate teaching strategies for stimulating students' epistemic development in mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.103-121
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• 2010

The University of Education trains the teachers who are experts in the education and expects them to achieve the purpose of the education in the field. The goal of this study is to apprehend the characteristics of the belief and the faith of the elementary teacher and of the university student who are preliminary elementary teachers, about the mathematics and the mathematical teaching and learning and also to figure out what differences those belief and faith shows as the year goes by. In order to find the characteristics of the belief and faith, we have set up three research-problems and have found the answers of that by analyzing the replies of several multiple choice questions and essay questions we have invested for. We also have collected several information through the interviews and inspection. As a result, we have analyzed and charted the outcome of the statistical analysis of the answers about each questions and have discussed the remarkable features of those results which showed significant changes in the belief of elementary teachers about the mathematics and mathematical teaching & learning after taking the courses of "Life & Mathematics".

• Research in Mathematical Education
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• v.13 no.2
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• pp.109-122
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• 2009

This study investigates the change in two theoretical constructs, attitudes toward mathematics and mathematics self-efficacy, among college students involved in a learning community model. The case of this study was a developmental mathematics class offered at a historically black college located in the southeastern United States. Subjects included 31 students enrolled in an introductory mathematics course, some of whom participated in a learning community (treatment group). The participants completed mathematics attitudes and mathematics efficacy instruments twice: at the beginning of the semester and again at the end. Data was analyzed using descriptive statistics and a non-parametric statistic. The results showed that students' attitudes toward mathematics and mathematics self-efficacy are strongly correlated; the mathematical problem-solving efficacy changed significantly over time and it is significantly higher in the treatment group than in the control group; and the treatment group produced better outcomes. These findings indicate that a learning community model can increase students' mathematics self-efficacy beliefs. It is recommended that mathematics self-efficacy and attitudes toward mathematics be measured over an extended period of time when a learning community is implemented.

• The Mathematical Education
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• v.47 no.3
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• pp.291-310
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• 2008

This article is based on an international collaborative study that aimed to investigate mathematical preparation of prospective elementary teachers in several selected education systems in East Asia. This article reports the Korean portion of the study. A survey instrument was developed to explore not only prospective teachers' knowledge of elementary mathematics curriculum and their beliefs in their preparation and mathematics instruction but also their subject matter knowledge and pedagogical content knowledge on the topic of fraction division. A total of 291 seniors in 3 universities participated in the survey. The results reveal these prospective teachers' strengths and weaknesses with regard to their knowledge of fraction division, and suggest that content-specific pedagogical knowledge needs to be emphasized in the teacher preparation program.

• Research in Mathematical Education
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• v.18 no.1
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• pp.55-74
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• 2014

This study examined the potential teaching strategies of prospective elementary teachers and their perceptions of the procedural/conceptual nature of examples. Fifty-four prospective teachers participated in this study, engaging in two-phase tasks. Analysis of data indicated that: (a) Overall, the participants' perceptions were geared toward putting emphasis on conceptual understanding rather than procedural understanding; but (b) Generally, procedure-oriented strategies were more frequently incorporated in participants' potential teaching plans. This implied that participants' preconceived ideas regarding math examples were not always reliable indicators of their potential teaching strategies. Implications and suggestions for mathematics teacher preparation are discussed.

• Research in Mathematical Education
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• v.3 no.2
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• pp.89-98
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• 1999

The purpose of this review of literature is to investigate what kinds of research have been done on social construction of mathematics understanding among elementary students in small groups. Only empirical studies were reviewed, and then grouping was done in terms of the purpose of the study. This grouping identified three categories: 1) Social and mathematical norms in mathematics classroom, 2) Teaching productive communication behaviors for active learning in small group, and 3) Participation roles and communication behaviors in different group structure. To enhance social construction of mathematics understanding in small group settings two suggestions are made: the importance of the selection of collaborative tasks or problems and teachers' beliefs about mathematics and the teaching an learning of mathematics.

• Korean Journal of Childcare and Education
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• v.9 no.5
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• pp.131-156
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• 2013

The purpose of this study was to examine the importance of parental beliefs, parental attitudes and parental behaviors of parents with preschool children and the relationship of the variables in an attempt to help preschoolers to gain multiple-intelligence experiences in an integrated manner in consideration of their interests, needs, strengths and weaknesses. A survey was conducted on the selected parents who had preschool children, and a multiple regression analysis was carried out to look for connections among the variables. The findings of the study were as follows: First, the preschool girls were ahead of the preschool boys in linguistic intelligence, musical intelligence and spatial intelligence, and the latter surpassed the former in logical-mathematical intelligence. Second, whether there would be any differences among the preschoolers in multiple intelligences according to age was analyzed, and those who were at the Western age of five were ahead of the four-year-olds in logical-mathematical intelligence, bodily-kinesthetic intelligence and naturalist intelligence. Third, the parental attitude of the parents was identified as the most influential variable for the multiple intelligences of the preschoolers, followed by parental behavior. Parental beliefs just had a very small impact on their multiple intelligences. The findings of the study imply that parents should be helped to improve their parental attitude and parental behavior to boost the multiple intelligences of their preschool children.

• Research in Mathematical Education
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• v.12 no.2
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• pp.85-108
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• 2008

In this study, we created, implemented, and evaluated the impact of proportional reasoning authentic investigative activities on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher training programs conducted in Israeli teacher colleges. The model was developed following pilot studies investigating the change in mathematical and pedagogical knowledge of pre- and in-service mathematics teachers, due to experience in authentic proportional reasoning activities. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience and are exposed to authentic proportional reasoning activities with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers' mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.