• Research in Mathematical Education
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• v.19 no.1
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• pp.1-17
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• 2015

In this study, we examined the prompted reflections of four middle school mathematics teachers after their lessons. We used Cohen and Ball's instructional triangle (1999) to investigate teachers' reflections. With this framework, we addressed questions of what characteristics in reflections the participant teachers have and how the reflections differ over time. Findings indicated that the teachers showed differences in the instances of assessing and changes over time in the ways they gained more insights about students' understanding.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.675-690
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• 2015

This study explore the features of mathematical tasks as an effective means to foster pre-service primary teachers' mathematical knowledge for teaching and develop mathematical task for pre-service primary teachers. As a result, prospective teachers have while solving a mathematical task, converting a given situation to a mathematical problem, and solve problems through connections with existing knowledge, and experience seeing the existing mathematical concepts from a new perspective. Finally, we discussed the conditions for a suitable mathematical task in teacher education.

• The Mathematical Education
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• v.45 no.2 s.113
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• pp.217-230
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• 2006

The purpose of this study is to inquire the building process of Pedagogical Content Knowledge of prospective mathematics teachers about the function concepts. For this purpose, We performed the following steps; First, we performed the survey relaying to the prospective mathematics teachers' teaching experiences, capabilities of their error evaluation of the students, and viewpoints about the function concepts. Second, we performed the survey on the subject-matter knowledge about the function concepts and the key items of designing teaching plans about the function concepts. And then, we interviewed the participants to check the results of the surveys and to supplement the necessary contents. The collected data was relatively correlative and analyzed in the process. As a result, we found the followings; First, subject-matter knowledge of prospective mathematics teachers about the function concepts is different depending on the grades. Second, prospective mathematics teachers are building more extended function concepts through the major subjects. Third, the major subjects are important to build the Pedagogical Content Knowledge of function concepts. Fourth, teaching experience plays an important role in transforming subject-matter knowledge of function concepts to Pedagogical Content Knowledge of it. Fifth, building the Pedagogical Content Knowledge means transferring the teacher's viewpoint from himself/herself to the learner.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.1-17
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• 2005

The purpose of this paper was to investigate the mathematical knowledge and perspective of elementary school teachers in the development and evaluation of students' mathematical tests, analyse test questions, and suggest several principles for the several issues of making and evaluating test-questions. The researcher surveyed 268 elementary school teachers who attended a teachers training program at the A university during January, 2005. The data were analysed by the patterns. The patterns were ambiguity or uncorrectly-described test questionnaires, wrong interpretation of students' responses by the teachers, teacher's deficiency of student' levels and perspectives of mathematics, problematic questionnaires against test-making method, and so forth. Teachers are encourages to cross check to avoid the above problems, to have a strong mathematical knowledge, and to see students' mathematical answers in a flexible manners.

• 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.

• Research in Mathematical Education
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• v.17 no.4
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• pp.221-241
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• 2013

The data for the present paper was a part of a large research project conducted to assess preservice teachers' knowledge related to fractions and place value at a southwestern public university in 2007. The study utilized convenience sampling, consisting of 150 elementary preservice teachers who were enrolled in a mathematics methods course before their student teaching. The results demonstrated preservice teachers' knowledge of teaching comparison, addition, subtraction, and multiplication of fractions was insufficient even though these should be basic knowledge. Teacher preparation programs should emphasize profound knowledge for teaching fractions using representations.

• 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.

• The Mathematical Education
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• v.47 no.2
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• pp.169-180
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• 2008

The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

• The Mathematical Education
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• v.40 no.2
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• pp.161-177
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• 2001

This study is to investigate what students want to learn and what mathematics teachers should teach in their classrooms. 1314 students and 527 mathematics teachers were randomly selected to administer the questionnaire. The result shows that their is a considerable mismatch between students'learning desires and teachers'teaching practices in classrooms. What students want to learn is creative knowledge; however, what they learn in the classroom is ‘imitative’ knowledge. This study suggests that the overall educational goal of mathematics education in Korea should emphasize (1) learning to communicate mathematically, (2) loaming to reason mathematically, (3) becoming confident in pupils'own ability, (4) learning to$.$value mathematics, and (5) becoming mathematical problem solvers.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.109-120
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• 2004

This study investigated three pre-service teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of pre- service teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.