• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.899-925
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• 2013

The purpose of this study was to examine how constructive-response questions in regular test was in aligned with the nature and goals of 2007 Curriculum Amendment. For this purpose, data were collected and analysed by using the framework for mathematical task and the cognitive demand of tasks suggested by Smith & Stein(1998) and mathematical proficiency suggested by National Research Council(2001). In particular, it aimed to reveal the overall picture of the level of cognitive demand and the proportion of mathematical proficiency of constructed-response items created by secondary mathematics teachers. The findings from the analysis showed that 70 percent of the constructed-response items were at low-level and the rest at high-level in terms of cognitive demand. Also, the constructed-response assessment focused on conputing (89%), understanding(45%), applying(30%) and least reasoning(17%). Most of the constructed-response items included computing and were algorithmic.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.163-178
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• 2012

The efforts to represent the numbers based on the decimal system give us fundamental understanding to construct and teach the concept network on the related knowledge of elementary and secondary school mathematics. In the process to represent natural numbers, integers, rational numbers, real numbers as decimal system, we will classify the extended decimal system. Moreover we will obtain the view to classify real numbers. In this paper, we will study the didactical significance of mathematical knowledge, which arise from process to represent real numbers as decimal system, starting from decimal system representation of natural numbers, and provide the theoretical base about the classification of real numbers. This study help math teachers to understand school mathematics in critical inside-measurement and provide the theore tical background of related knowledge. Furthermore, this study provide a clue to construct coherent curriculum and internal connections of related mathematical knowledge.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.527-546
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• 2021

The purpose of this study is to reveal what mathematics teachers focus on and how they assess students' thinking during lessons enacted. For this purpose, we googled and searched internet sites to collect formative assessment materials for the year 2014 to 2019. The formative assessment tasks data were analyzed according to the levels cognitive demand levels and tasks suggested in textbooks in terms of degrees to which how they are related. The data analysis suggested as follows: a) most of the formative assessment tasks were at the low-level, in particular, PNC level tasks that require applying particular procedures without connections to concepts and meaning underlying the procedures, b) the assessment tasks appeared to be very similar to the tasks suggested in the secondary mathematics textbooks, and c) it seemed that 3 types of formative assessment, observation notes, self-assessment, and peer-assessment were dominantly utilized during mathematics lessons and these different types of formative assessment were employed apparently to find out whether students participated actively in class and in group activity, not how they go through understanding or thinking processes.

• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.131-145
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• 2005

This study intends to analyze didactically on triangle-determining conditions and triangle-congruence conditions. The result of this study revealed the followings: Firstly, many pre-service mathematics teachers and secondary school students have insufficient understanding or misunderstanding on triangle-determining conditions and triangle-congruence conditions. Secondly, the term segment instead of edge may show well the concern of triangle-determining conditions. Thirdly, when students learn the method of finding six elements of triangle using the law of sines and cosines in high school, they should be given the opportunity to reflect the relation and the difference between triangle-determining situation and the situation of finding six elements of triangle. Fourthly, accepting some conditions like SSA-obtuse as a triangle-determining condition or not is not just a logical problem. It depends on the specific contexts investigating triangle-determining conditions. Fifthly, textbooks and classroom teaching need to guide students to discover triangle-deter-mining conditions in the process of inquiry from SSS, SSA, SAS, SAA, ASS, ASA, AAS, AAA to SSS, SAS, ASA, SAA. Sixthly, it is necessary to have students know the significance of 'correspondence' in congruence conditions. Finally, there are some problems of using the term 'correspondent' in describing triangle-congruence conditions.

• The Mathematical Education
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• v.63 no.1
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• pp.105-122
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• 2024

This study analyzed the research trends of 101 articles published in prominent international mathematics education journals over 24 years from 2000, when NCTM's recommendation emphasizing argumentation was released, until September 2023. We first examined the overall trend of argumentation research and then analyzed representative research topics. We found that students were the focus of the studies. However, several studies focused on teachers. More studies were examined in secondary school than in elementary school, and many were conducted in argumentation in classroom contexts. We also found that argumentation research is becoming increasingly popular in international journals. The representative research topics included 'teaching practice,' 'argumentation structure,' 'proof,' 'student understanding,' and 'student reasoning.' Based on our findings, we could categorize three perspectives on argumentation: formal, contextual, and purposeful. This paper concludes with implications on the meaning and role of argumentation in Korean mathematics education.

• The Mathematical Education
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• v.27 no.1
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• pp.15-23
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• 1988

We are at the onset of a major revolution in education, a revolution unparalleled since the invention of the printing press. The computer will be the instrument of this revolution. Computers and computer application are everywhere these days. Everyone can't avoid the influence of the computer in today's world. The computer is no longer a magical, unfamiliar tool that is used only by researchers or scholars or scientists. The computer helps us do our jobs and even routine tasks more effectively and efficiently. More importantly, it gives us power never before available to solve complex problems. Mathematics instruction in secondary schools is frequently perceived to be more a amendable to the use of computers than are other areas of the school curriculum. This is based on the perception of mathematics as a subject with clearly defined objectives and outcomes that can be reliably measured by devices readily at hand or easily constructed by teachers or researchers. Because of this reason, the first large-scale computerized curriculum projects were in mathematics, and the first educational computer games were mathematics games. And now, the entire mathematics curriculum appears to be the first of the traditional school curriculum areas to be undergoing substantial trasformation because of computers. Recently, many research-Institutes of our country are going to study on computers in orders to use it in mathematics education, but the study is still start ing-step. In order to keep abreast of this trend necessity, and to enhance mathematics teaching/learning which is instructed lecture-based teaching/learning at the present time, this study aims to develop/present practical method of computer-using. This is devided into three methods. 1. Programming teaching/learning method This part is presented the following five types which can teach/learn the mathematical concepts and principle through concise program. (Type 1) Complete a program. (Type 2) Know the given program's content and predict the output. (Type 3) Write a program of the given flow-chart and solve the problem. (Type 4) Make an inference from an error message, find errors and correct them. (Type 5) Investigate complex mathematical fact through program and annotate a program. 2. Problem-solving teaching/learning method solving This part is illustrated how a computer can be used as a tool to help students solve realistic mathematical problems while simultaneously reinforcing their understanding of problem-solving processes. Here, four different problems are presented. For each problem, a four-stage problem-solving model of polya is given: Problem statement, Problem analysis, Computer program, and Looking back/Looking ahead. 3. CAI program teaching/learning method This part is developed/presented courseware of sine theorem section (Mathematics I for high school) in order to avail individualized learning or interactive learning with teacher. (Appendix I, II)

• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.509-523
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• 2005

This study empirically examines motivations of entering college of education and academic problems that pre-service teachers encounter under the curricular activities. We analyze the phenomena of professional development under the four categories: motivation toward entering college of education, pedagogical content knowledge, subject matter knowledge and future vision. We conducted survey for the S university students first and interviewed 3 selected participants. Almost 50 students from college of education participated answering to the surveys. Using SPSS package, there was no significant difference between freshmen, sophomore and junior students in any category Male students responded more positively than female students in all the categories. To explore survey results deeply, we selected 3 students from sophomore and junior levels and 2 extra senior students to conduct interviews. The interpretation of the data described how their academic problems unfold partly because they seek another major and how their professional development take place carrying out practicum activities. Most of the interviewees felt that their academic lives were affected motivations of entering college of education and difficulties of studying subject matter knowledge. At the end, several suggestions are added for future research.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.717-746
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• 2014

The study aimed to explore how to improve mathematical thinking through metacognitive learning by stressing metacognitive abilities as a core strategy to increase mathematical creativity and problem-solving abilities. Theoretical exploration was followed by an analysis of correlations between metacognitive abilities and various ways of mathematical thinking. Various metacognitive teaching and learning methods used by many teachers at school were integrated for sharing. Also, the methods of learning application and assessment of metacognitive thinking were explored. The results are as follows: First, metacognitive abilities were positively related to 'reasoning, communication, creative problem solving and commitment' with direct and indirect effects on mathematical thinking. Second, various megacognitive ability-applied teaching and learning methods had positive impacts on definitive areas such as 'anxiety over Mathematics, self-efficacy, learning habit, interest, confidence and trust' as well as cognitive areas such as 'learning performance, reasoning, problem solving, metacognitive ability, communication and expression', which is a result applicable to top, middle and low-performance students at primary and secondary education facilities. Third, 'metacognitive activities, metaproblem-solving process, personal strength and weakness management project, metacognitive notes, observation tables and metacognitive checklists' for metacognitive learning were suggested as alternatives to performance assessment covering problem-solving and thinking processes. Various metacognitive learning methods helped to improve creative and systemic problem solving and increase mathematical thinking. They did not only imitate uniform problem-solving methods suggested by a teacher but also induced direct experiences of mathematical thinking as well as adjustment and control of the thinking process. The study will help teachers recognize the importance of metacognition, devise and apply teaching or learning models for their teaching environments, improving students' metacognitive ability as well as mathematical and creative thinking.

• Journal of the Korean School Mathematics Society
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• v.24 no.4
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• pp.369-390
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• 2021

It would be reasonable as a teacher to make efforts not only to reflect on the class on their own but also to improve the teacher' teaching e pertise by reflecting on the class with fellow teachers through lesson reflection sharing. This paper attempted to develop a lesson reflective framework that can provide standards and focus for lesson reflection and lesson sharing. First, based on the class evaluation criteria of previous studies, class reflection elements and a draft of lesson reflection were prepared. In a class conducted on 27 third graders at C High School where the co-researcher worked as a teacher, four peer teachers at the same high school were required to write personal opinions on the class based on the draft of lesson reflection. Based on this, lesson sharing was conducted, and modifications of the lesson reflection framework were developed by analyzing the case of class sharing. The implications of this paper indicate the need to clarify the perspective of viewing the lesson by sharing the intention of each question in advance. In addition to writing lesson reflections, it is necessary to share classes simultaneously.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.137-154
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• 2012

Approximation' is one of central conceptions in calculus. A basic conception for explaining 'approximation' is 'tangent', and 'tangent' is a 'line' with special condition. In this study, we will study pedagogically these mathematical knowledge on the ground of a viewpoint on the teaching of secondary geometry, and in connection with these we will suggest the teaching program and the chief end for the probable teaching. For this, we will examine point, line, circle, straight line, tangent line, approximation, and drive meaningfully mathematical knowledge for algebraic operation through the process translating from the above into analytic geometry. And we will construct the stream line of mathematical knowledge for approximation from a view of modern mathematics. This study help mathematics teachers to promote the pedagogical content knowledge, and to provide the basis for development of teaching model guiding the mathematical knowledge. Moreover, this study help students to recognize that mathematics is a systematic discipline and school mathematics are activities constructed under a fixed purpose.