• East Asian mathematical journal
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• v.39 no.2
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• pp.141-166
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• 2023

The purpose of this study is to confirm the MKT(Mathematical Knowledge for Teaching) of the in-service mathematics teachers on the statistics(Representative value, Degree of scattering) through the comparative analysis between the sub-elements of the MKT. In addition, it is to examine the factors that cause the difference of the subjects' MKT. To accomplish this, by the subject of 12 secondary in-service mathematics teachers, in this study the test items of the MKT on the statistics were developed and data were collected and analyzed. As a result of the analysis of the MKT test sheet, the CCK(Common Content Knowledge) and SCK(Specialized Content Knowledge) of the mathematics teacher was confirmed as a high score, whereas the and KCS(Knowledge of Content and Students) and KCT(Knowldge of Curriculum and teaching) were confirmed as low scores. In addition, through these results, it was shown that the difference in MKT's elements the middle school and high school teachers obtain occurred slightly.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.365-380
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• 1998

Structualist view distinguishes structure(reality) from phenomenon(appearance). Phenomenon is the outside aspect of structure and structure is the inside aspect of phenomenon. From the structualist view, the knowledge could e divided into two parts, the appearance of knowledge(the outside aspect of knowledge)and the structure of knowledge(the inside aspect of knowledge). Structualist view advices teachers to understand knowledge more totally from the inside-outside viewpoint, and not to teach mere the one aspect of knowledge, especially the outside aspect of knowledge, that is, the written expressions in textbook, but to teach the inside and outside aspects fo knowledge totally. In the history of mathematics education, the attempts to teach the structure of knowledge were flourishing in the period of discipline-centered curriculum. 'New Math movement' represents the attempts. The advocators of New Math, however, did not succeed sufficiently to understand the inside-outside view which the term the structure of knowledge represents, and failed to make mathematics teachers to understand the view well. Their attention was put on to introduce the modern mathematics to school math rather than to understand the educational and epistemological perspective which the term the structure of knowledge represents. To teach the structure of knowledge, mathematics teacher should be able to understand mathematical knowledge more totally from the inside-outside viewpoint. Especially, s/he should not regard the outside aspect of mathematical knowledge written in textbook as the totality of knowledge, but inquire into the inside aspect of mathematical knowledge from the outside aspect of mathematical knowledge.

• Research in Mathematical Education
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• v.8 no.2
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• pp.81-93
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• 2004

This study investigated three preservice 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 preservice 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.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.527-540
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• 2007

It takes much of times and efforts for mathematical knowledge to be regarded as truth. Mathematical knowledge has been added, and modified, and even proved to be false. Mathematical knowledge consists of mathematical languages, statements, reasonings, questions, metamathematical views. These elements have been changed constantly by investigations and refutations of mathematicians, by modification of proofs considering the refutations, by introduction of new concepts, by additions of questions about new concepts, by efforts to get answers to new questions, by attempts to apply previous studies to the present, constantly. This study introduces the change of mathematical knowledge instituted by filcher, and presents examples of the change.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.163-180
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• 2002

The purpose of this paper is to reconsider the meaning of mathematical literacy based on the investigation of the nature of mathematical knowledge communicated in university level mathematics classes. The analysis of classroom discourse has revealed three different kinds of mathematical knowledge circulated in mathematics class, which include 'factual mathematics', 'mathematical fantasy', and 'mathematical savior faire.' The fact that a mathematics teacher delivers diverse categories of mathematics knowledge suggests that the mathematical literacy is not confined to the development of technical competence. More specifically, the kinds of mathematical knowledge identified above tell that mathematical literacy developed through learning mathematics reflects the cultural norms and values of doing mathematics. This means that mathematical literacy is not merely involve with technical competence but rather with cultural competence. In this regard, this paper highlights the meaning of mathematical literacy as a cultural identity, which has been underestimated in the theory and practice of mathematics education dominated by technocracy of the twentieth century In particular, the notion of mathematical savior faire implies that teaching and teaming mathematics ultimately deals with a system of cultural meaning. Hence, through learning mathematics, a learner gets transformed as a whole person according to the cultural norms and values. In this regard, it is concluded that mathematical literacy can be considered as a necessary condition to become a competent member of mathematics community sharing cultural norms of doing mathematics as well as a repertoire of mathematical skills.

• The Mathematical Education
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• v.48 no.4
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• pp.399-417
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• 2009

The purpose of this study was to explore the adaptability of U.S. multiple-choice items to measure Mathematical Knowledge for Teaching (MKT) in Korea. For this purpose, the authors selected the number and operations form B which was developed by Learning Mathematics for Teaching (LMT) project at the University of Michigan and then adapted items in terms of general cultural context, school cultural context, mathematical substances, and language in Korea. The survey was administrated to 77 Korean in-service teachers who had more than three years of teaching experiences. Based on the survey, the authors compared the data to that of U.S. teachers who had participated California's Mathematics Professional Development Institute. As a result, the survey measures less knowledge Korean teachers than more knowledgable Korean teachers and there are strong correlations of relative item difficulties between Korean teachers and U.S. teachers for both Content Knowledge (CK) items and Knowledge of Content and Students (KCS) items. This study implies the future direction for developing items to measure teacher knowledge as well as designing effective teacher education programs.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.349-368
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• 2023

The purpose of this study is to explore ways for students to connect conceptual and procedural knowledge in mathematical modeling lessons. Accordingly, we selected the greatest common divisor among the learning contents in which elementary school students have difficulties connecting conceptual and procedural knowledge. A mathematical modeling lesson was designed and implemented to solve problems related to the greatest common divisor while connecting conceptual and procedural knowledge. As a result of the analysis, it was found that the mathematical modeling lesson had positive effects on students solving problems by connecting conceptual and procedural knowledge. In addition, through actual class application, a teaching and learning plan was derived to meaningfully connect conceptual and procedural knowledge in mathematical modeling lessons.

• Research in Mathematical Education
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• v.14 no.4
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• pp.323-332
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• 2010

It is the development of a mathematics teachers' teaching knowledge that manifests a mathematics teacher's professional knowledge growth. It is becoming a direct and effective approach of conversion of mathematical knowledge into the knowledge of mathematics teaching. Through the investigation, the study revealed that the knowledge conversion process of mathematics teachers in middle school is restricted by three aspects including eight factors. From this point, the authors have structured the path and model on influencing factors of middle school Mathematics Teaching Knowledge Conversion (MPCK), and discuss the mechanism of the transformation process.

• The Mathematical Education
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• v.43 no.1
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• pp.70-85
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• 2004

Comparing to the other subject, hierarchy among mathematical contents is strong from the perspective of knowledge order as grades go up. That is, the knowledge that students already have learned, are learning and will learn are closed related from grade to grade. We expect students to be proactive and creative in studying mathematics, which is the goal of 21th century, analyzing their. knowledge structure based on the hierarchy of knowledge through assessment. Especially, using computer system we provide students with substantial feedback for the assessment as well as objective validity is increased along with speedy and exact process in a bid to help students' mathematical understanding grow. This paper seeks to analyze the assessment data by applying knowledge spaces to computer system and develops efficient methods based on the analyzed results, to diagram each student's knowledge structure.

• School Mathematics
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• v.15 no.1
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• pp.201-219
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• 2013

The purpose of this study was to analyse the belief about mathematics teaching of elementary preservice teachers and mathematics teachers. This study involved 100 respondents from the preservice teachers and 114 respondents from the mathematics teachers. The instruments used in this study consist 15 items of mathematical knowledges and 19 items of mathematical activities. The finding showed that preservice teachers emphasized the conceptual knowledge, whereas mathematics teachers emphasized the procedural knowledge in the mathematical knowledges. And preservice teachers emphasized the knowledge representation, knowledge generation, knowledge deliberation, knowledge communication, whereas mathematics teachers emphasized the use of knowledge(syntax) in the mathematical activities. Finally, even though two groups showed the significant difference in some items, preservice teachers and mathematics teachers emphasized the various mathematical knowledges and mathematical activities.