• Research in Mathematical Education
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• v.22 no.4
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• pp.283-304
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• 2019

This paper investigates what informal knowledge and strategies fifth-grade students brought to a classroom and how much they had potential to solve fraction division story problems. The findings show that most of the participants were engaged to understand the meaning of fraction division prior to their formal instruction at school. In order to solve the story problems, the informal knowledge related to fractions as well as division was actively utilized in student's strategies and justification. Students also used various informal strategies from mental calculation, direct modeling, to relational thinking. Formal instructions about fraction division at schools can be facilitated for sense-making of this complex fraction division conception by unpacking informal knowledge and thinking they might bring to the classrooms.

• East Asian mathematical journal
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• v.27 no.2
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• pp.181-202
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• 2011

The study was planned to analyze the figure concepts teachers have according to the years of experiences based on the two aspects, the subject matter knowledge and the pedagogical content knowledge. Further, it aims to have the results utilized in teacher education and training, and ultimately to help elementary school students to establish the accurate figure concepts. We administered the test to the random sample of 77 elementary school teachers of the grade 3 to grade 6, from nine schools of the Daegu, Ulsan and Gyeongsangbuk-do districts, and we analyzed the results. Correlational analysis between the years of experience and the knowledge showed that the content understanding and knowledge decreases as the years of experience increases, while the experiential knowledge related to the understanding of the students and the pedagogical methods increases as the years of experience increases.

• 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.

• The Mathematical Education
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• v.42 no.1
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• pp.57-67
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• 2003

In this paper we analyze educational aspects of a mathematical problem. As a result of the analysis, we extract five meaningful mathematical knowledge and ideas. Corresponding with these we suggest some chains of mathematical problems that are expected to activate student's self-oriented mathematical investigation.

• 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 Engineering Education Research
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• v.24 no.3
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• pp.50-57
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• 2021

Although the mathematics education process in AI education is a very important issue, little cases are reported in developing effective methods on AI and mathematics education at the university level. The universities cover all fields of mathematics in their curriculums, but they lack in connecting and applying the math knowledge to AI in an efficient manner. Students are hardly interested in taking many math courses and it gets worse for the students in humanities, social sciences and arts. But university education is very slow in adapting to rapidly changing new technologies in the real world. AI is a technology that is changing the paradigm of the century, so every one should be familiar with this technology but it requires fundamental math knowledge. It is not fair for the students to study all math subjects and ride on the AI train. We recognize that three key elements, SW knowledge, mathematical knowledge, and domain knowledge, are required in applying AI technology to the real world problems. This study proposes a modular approach of studying mathematics knowledge while connecting the math to different domain problems using AI techniques. We also show a modular curriculum that is developed for using math for AI-driven autonomous driving.

• Journal of Gifted/Talented Education
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• v.25 no.4
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• pp.581-605
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• 2015

The purpose of this study is to build an instruction method focused on the mathematical process and apply it to 12, 5-year-olds from Kindergarten located in Seoul with a view to explore the changes in their mathematical thinking. In addition, surveys with parents and teachers, as well as those conducted in the field of early childhood education, were conducted to analyze the current situation. The effects focused on the five mathematical processes, namely problem solving, reasoning and proof, connecting, representing and communication was found to help the interactions between teacher-child and child-child stimulate the mathematical thinking of the children and induce changes. The mathematical process-focused instruction aimed to advance mathematical thinking internalized mathematical knowledge, presented an integrated problematic situation, and empathized the mathematical process, which enabled the children to solve the problem by working together with peers. As such, the mathematical thinking of the children was integrated and developed within the process of a positive change in the mathematical attitude in which mathematical knowledge is internalized through mathematical process.

• School Mathematics
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• v.15 no.4
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• pp.995-1013
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• 2013

The purpose of this paper was to investigate mathematics teachers' mathematical content knowledge about quadratic curves. Three components of mathematical knowledge are needed for teaching: (i) knowing school mathematics, (ii) knowing process of school mathematics, (iii) making connections between school mathematics and advanced mathematics. 24 mathematics teachers were asked to perform 10 questions based on mathematics curriculum. The results showed that mathematics teachers had some difficulties in conic section definitions and eccentricity definitions of ellipse and hyperbola. And they also got difficulty in Dandellin sphere proof of the equivalence of conic section definitions and quadratic curve definitions. Especially, no one answered correctly to the question about the definition of eccentricity. The ratio of correct answer for the question about constructing tangent lines of quadratic curves is less than that for the question about the applications of the properties of tangent lines. These findings suggests that it is needed that to provide plenty of opportunities to learn mathematical content knowledge in teacher education programs.

• The Mathematical Education
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• v.60 no.3
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• pp.281-295
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• 2021

This study examines the breadth and depth of knowledge of the teacher employment test for secondary mathematics. For the breadth of knowledge, we attempted to figure out the range of knowledge in terms of the content areas using the standards from the Korea Society Educational Studies in Mathematics[KSESM](2008). For the depth of knowledge, we chose Anderson & Krathwohl(2001) framework to analyze levels of each item in the test. The results from the analysis of 180 items in the teacher employment test between 2014 and 2021 show that while items in mathematics education have considerable variation in terms of range and levels of knowledge, those in some subjects of mathematics can be found only certain level of knowledge. i.e., merely certain topics or levels of knowledge have been heavily evaluated. Thus, considering the breadth and depth of knowledge teachers should have, the current exam needs to be improved in terms of teacher knowledge. It does not mean that every topic and every level of knowledge should be evaluated. However, it is a meaningful opportunity to think about what kinds of knowledge teachers should have in relation to K-12 mathematics curriculum and how we can evaluate the knowledge. More collaborative effort is inevitable for the improvement of teacher knowledge and teacher employment test.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.127-150
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• 2021

Recently, in the field of mathematics education, mathematical noticing has been considered as an important element of teacher expertise. The meaning of mathematical noticing is the ability of teachers to notice and interpret significant events among various events that occur in mathematics class. This study attempts to analyze the differences of pre-service secondary teachers' mathematical noticing and confirm the factors that cause the differences between them. To accomplish this, the items on class critiques were established to identify pre-service secondary school teachers' mathematical noticing, and each of 18 pre-service secondary mathematics teachers were required to write a class critique by watching a video in which their micro-teaching was recorded. It was that the teachers' mathematical noticing can be identified by analyzing their critiques in three dimensions such as actor, topic, and stance. As a result, there were differences in mathematical noticing between pre-service secondary mathematical teachers in terms of topic and stance dimensions. The result suggests that teachers' mathematicl noticing can be differentiated by subject matter knowledge, pedagogical content knowledge, curricular knowledge, beliefs, experiences, goals, and practical knowledge.