• The Mathematical Education
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• v.42 no.1
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• pp.41-56
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• 2003

As the information society appears, the increasing power and access of personal computers along with wide spread use of the information technology has not only changed the landscape for communication but it has opened up new and exciting opportunities for education. One of the ways that information technology could help improve education is to be used in interactive communication to share the knowledge and experience of all the teachers as well as students. In this paper, the use and application of information communication technology[ICT] into mathematics classroom are described and showed several examples. furthermore, the web site design and developed for this study was introduced of the purpose of sharing the ideas about the knowledge and usage of the history of mathematics and examples of mathematical connections. The study suggests that enabling mathematics in incorporating of ICT by teachers and students requires more effort to be made in training teachers on the use and application of ICT into mathematics classroom.

• Research in Mathematical Education
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• v.22 no.2
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• pp.83-97
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• 2019

Science, Technology, Engineering, and Mathematics (STEM) education has been at the forefront of K-12 curricula in the technology-rich 21st century, with emphasis on how these fields reinforce each other in preparing students for a dynamic future. However, there is a need for greater attention to STEM education research in the mathematics education community, in particular to pedagogical approaches that facilitate integrating the mathematics component of STEM education. Toward this end, the authors report the outcomes of a Project-based Learning (PBL) unit in which upper elementary students integrated STEM elements by researching, crafting, testing, and evaluating kites they created by applying scientific knowledge of aerodynamics and mathematical knowledge of polygons, surface area, graphs, and data analysis. This unit, which the authors developed, implemented, and assessed, demonstrates how STEM subjects and in particular mathematics can be effectively integrated in upper elementary school classrooms through PBL.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.239-266
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• 2004

This article presents new perspectives for analysing and diagnosing students' mathematical errors on the basis of Pascaul-Leone's neo-Piagetian theory. Although Pascaul-Leone's theory is a cognitive developmental theory, its psychological mechanism gives us new insights on mathematical errors. We analyze mathematical errors in the domain of proof problem solving comparing Pascaul-Leone's psychological mechanism with mathematical errors and diagnose misleading factors using Schoenfeld's levels of analysis and structure and fuzzy cognitive map(FCM). FCM can present with cause and effect among preconceptions or misconceptions that students have about prerequisite proof knowledge and problem solving. Conclusions could be summarized as follows: 1) Students' mathematical errors on proof problem solving and LC learning structures have the same nature. 2) Structures in items of students' mathematical errors and misleading factor structures in cognitive tasks affect mental processes with the same activation mechanism. 3) LC learning structures were activated preferentially in knowledge structures by F operator. With the same activation mechanism, the process students' mathematical errors were activated firstly among conceptions could be explained.

• The Mathematical Education
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• v.41 no.3
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• pp.273-289
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• 2002

It tends to be emphasized that mathematics is the important discipline to develop students' mathematical reasoning abilities such as deduction, induction, analogy, and visual reasoning. This study is aimed for investigating the present state about mathematical reasoning in secondary school. We survey teachers' opinions and analyze the results. The results are analyzed by frequency analysis including percentile, t-test, and MANOVA. Results are the following: 1. Teachers recognized mathematics as knowledge constructed by deduction, induction, analogy and visual reasoning, and evaluated their reasoning abilities high. 2. Teachers indicated the importances of reasoning in curriculum, the necessities and the representations, but there are significant difference in practices comparing to the former importances. 3. To evaluate mathematical reasoning, teachers stated that they needed items and rubric for assessment of reasoning. And at present, they are lacked. 4. The hindrances in teaching mathematical reasoning are the lack of method for appliance to mathematics instruction, the unpreparedness of proposals for evaluation method, and the lack of whole teachers' recognition for the importance of mathematical reasoning

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.409-434
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• 2013

The mathematical ability is an essential element for achieving professional competencies and for enhancing application ability in a vocational world and exploring its experiences. In this aspect, for vocational high school students, it is an important and urgent issue to develop remedial learning programs for developing mathematical basic and application ability. In particular, the program is developed based on the individual achievement level, focused on a mathematical basic ability to be applied efficiently in a vocational world. Because of this reason, in this study, the program is comprised of two phases; one is diagnosis test and the other is remedial teaching and learning materials. Then, diagnosis test includes three test; I) level testing evaluation for selecting the subject of remedial learning, ii) pre-test for deciding on which area and level of the materials when students begin to study, and iii) post-test for confirming the learning status is satisfied and the possibility of next step(level) or the other area of the materials. To accomplish this, this study tried to devise an efficient remedial learning system. Based on the system, this study developed remedial learning programs on the four areas of number and quantity, change and relation, uncertain thing, and figure and shape in the middle school level. In particular, this program is comprised of two types of knowledge. One is K-knowledge which is an essential knowledge to achieve a basic mathematical ability. The other is C-knowledge which is the advanced knowledge required to apply efficiently in a vocational world. This paper deals with the content mentioned above, but examples of the materials is shown focused on the area of change and relation.

• The Mathematical Education
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• v.62 no.4
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• pp.531-549
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• 2023

Despite the significance of mathematics teacher guidebooks as a support for teacher learning, there are few studies that address how elementary mathematics teacher guidebooks support teacher learning. The purpose of this study was to analyze the educative features of elementary mathematics teacher guidebooks for grades 3 and 4. For this, six units from each of ten kinds of teacher guidebooks were analyzed in terms of seven dimensions of Teacher Learning Opportunities in Korean Mathematics Curriculum Materials (TLO-KMath). The results of this study showed that mathematics content knowledge for teaching was richly provided and well organized. Teacher guidebooks provided teacher knowledge to anticipate and understand student errors and misconceptions, but were not enough. Sample dialogues between a teacher and students were offered in the teacher guidebooks, making it easier for teachers to identify the overall lesson flow and key points of classroom discourse. Formative assessment was emphasized in the teacher guidebooks, including lesson-specific student responses and their concomitant feedback examples per main activity. Supplementary activities and worksheets were provided, but it lacked rationales for differentiated instruction in mathematics. Teacher knowledge of manipulative materials and technology use in mathematics was provided only in specific units and was generally insufficient. Teacher knowledge in building a mathematical community was mainly provided in terms of mathematical competency, mathematical classroom culture, and motivation. This paper finally presented implications for improving teacher guidebooks to actively support teacher learning.

• School Mathematics
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• v.10 no.3
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• pp.423-441
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• 2008

The purpose of this study was to examine the Pedagogical Content Knowledge(PCK) of teachers and their educational practice in the category of plane figure, to make a comparative analysis of their PCK and educational practice, and to discuss the relationship between their PCK and the characteristics of their instruction. Instruction of four selected elementary school teachers was analyzed to find out their educational practice. In conclusion, the characteristics of the PCK and actual instruction of the teachers could be listed as below: First, as a result of comparing their PCK and educational practice on plane figure by applying selected analysis criteria, there was a close correlation between their PCK and actual instruction. Second, the teachers had various levels of PCK on different areas. Especially, there was a large disparity in mathematical content knowledge and knowledge of teaching methods. Third, the teachers who had plenty of PCK were more excellent in textbook reconstructing, and those who fell behind in terms of PCK were more reliant on textbooks as if the textbooks had been the Bible.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.137-156
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• 2008

This article discusses the purpose of mathematics education based on the epistemology of Michael Polanyi. According to Polanyi, studying is seeking after the truth and pursuing the reality. He opposes to separate humanity and knowledge on account that no knowledge possibly exists without its owners. He assumes tacit knowledge hidden under explicit knowledge. Tacit knowing is explained with the relation between focal awareness and subsidiary awareness. In the epistemology of Polanyi, teaching and learning of mathematics should aim for change of students' minds in whole pursuing the intellectual beauty, which can be brought about by the operation of their minds in whole. In other words, mathematics education should intend the cultivation of mind. This can be accomplished when students learn mathematical knowledge as his personal knowledge and obtain tacit mathematical knowledge.

• The Mathematical Education
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• v.49 no.2
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• pp.175-198
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• 2010

To understand natural or social phenomena, we need various information, knowledge, and thought skills. In this context, mathematics and sciences provide us with excellent tools for that purpose. This explains the reasons why there is always significant emphasis on mathematics and sciences in school education; some of the general goals in school education today are to illustrate physical phenomena with mathematical tools based on scientific consideration, to encourage students understand the mathematical concepts implied in the phenomena, and provide them with ability to apply what they learned to the real world problems. For the mentioned goals, we extract six fundamental principles for the integrated mathematics and science education (IMSE) from literature review and suggest a instructional design model. This model forms a fundamental of a case study we performed to which the IMSE was applied and tested to collect insights for design and practice. The case study was done for 10 students (2 female students, 8 male ones) at a coeducational high school in Seoul, the first semester 2009. Educational tools including graphic calculator(Voyage200) and motion detector (CBR) were utilized in the class. The analysis result for the class show that the students have successfully developed various mathematical concepts including the rate of change, the instantaneous rate of change, and derivatives based on the physical concepts like velocity, accelerate, etc. In the class, they described the physical phenomena with mathematical expressions and understood the motion of objects based on the idea of derivatives. From this result, we conclude that the IMSE builds integrated knowledge for the students in a positive way.

• The Mathematical Education
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• v.60 no.2
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• pp.229-247
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• 2021

Students' mathematical thinking is represented via various forms of outcomes, such as written response and verbal expression, and teachers could infer and respond to their mathematical thinking by using them. This study analyzed 39 elementary teachers' competency to notice students' problem-solving strategies containing mathematical errors in fraction addition and subtraction with uncommon denominators problems. Participants were provided three types of students' problem-solving strategies with regard to fraction addition and subtraction problems and asked to identify and interpret students' mathematical understanding and errors represented in their artifacts. Moreover, participants were asked to design additional questions and problems to correct students' mathematical errors. The findings revealed that first, teachers' noticing competency was the highest on identifying, followed by interpreting and responding. Second, responding could be categorized according to the teachers' intentions and the types of problem, and it tended to focus on certain types of responding. For example, in giving questions responding type, checking the hypothesized error took the largest proportion, followed by checking the student's prior knowledge. Moreover, in posing problems responding type, posing problems related to student's prior knowledge with simple computation took the largest proportion. Based on these findings, we suggested implications for the teacher noticing research on students' artifacts.