• Communications of Mathematical Education
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• v.27 no.4
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• pp.357-367
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• 2013

It is important to make students do research for oneself. But the practice of inquiry activity is not easy in the mathematics education field. Intellectual curiosities of students are unpredictable. It is important to meet intellectual curiosities of students. We could get a sequence in the process solving a problem. This sequence was expressed in a form of the recurrence relation $a_n=a_{n-1}+a_{n-3}$ ($n{\geq}4$), $a_1=a_2=a_3=1$. We tried to look for the general terms of this sequence. This sequence is similar to Fibonacci sequence, but the process finding the general terms is never similar to Fibonacci sequence. We can get two general terms expressed in different form after our a great deal of effort. We hope that this study will give the spot of education energy.

• Journal of Science Education
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• v.41 no.2
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• pp.248-266
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• 2017

The purpose of this study is to present various examples of collaborative learning based on the Instruction of Internet in the 6th grade elementary school mathematics class. So we introduce the design method of classroom environment for classroom Internet and give example of various teaching methods. This study was conducted for nine months from March to November, 2016, one sixth grade of elementary school in D area. During this period, we conducted Instruction of Internet-based collaborative learning to classify typical teaching cases. We classified into 5 type collaborative learning. First, collaborative learning in the classroom. Second, remote collaborative learning between classroom and classroom. Third, Live participation classes. Forth, project collaborative learning. Fifth, using virtual reality in collaborative learning. In addition, we could identify that there is a difference compared to the conventional learning. It became possible to conduct collaborative learning with other students simultaneously or have opening class with both parents and teachers by using Youtube. These examples can be presented as a case to depart from traditional mathematics class in one classroom. In this regard, we will be able to provide several implications about teaching methods utilizing smart device and Internet in future classroom.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.1-29
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• 2013

The main goal of the research is to develop instructional consulting manual to help math teachers improve classroom teaching. Improving the quality of teaching in schools is stressed as a central focus of meaningful classroom instruction and high quality education. In this research, teaching consulting was defined as an activity that covers reflection process oriented towards formative assessment and continuing professional development. Within this context, subject-specific teaching consulting and teaching professionalism with focus on PCK was reviewed. Further, the questionnaire survey was conducted to investigate the current situation of teaching consulting and teachers' needs for consulting. And also, specific examples of subject-specific consulting based on our previous consulting experiences in math classes were shown. Alternative ways to improve subject teaching were derived through the conferences where consultants and consultees analyze video-taped lessons conducted by the consultees. By those results, a manual for invigorating teaching consulting was developed. The contents of the manual consists of setting conditions of teaching consulting and its implementation in the classroom teaching. The first part of the manual contains steps to establish teaching consulting system, the qualification and role of the consultant, system evaluation, etc. The second part of the manual presents the pre-preparation, prescription and implementation and follow-up management steps. Each part of the manual provides consultants with specific guidelines for each step. Finally, recommendations for making policy related to ways to invigorate teaching consulting was suggested. It is expected that specific examples and cases of subject-specific teaching consulting presented in this research will be used to narrow the gap between theory and practice of teaching consulting, and to help math, science and English teachers develop teaching professionalism.

• Education of Primary School Mathematics
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• v.21 no.1
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• pp.55-73
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• 2018

The purpose of this study is to investigate the effects of cognitive activity on cognitive activities that students imagine and cope with continuously changing quantitative changes in functional tasks represented by linguistic expressions, table of value, and geometric patterns, We identified covariational reasoning levels and investigated the characteristics of students' reasoning process according to the levels of covariational reasoning in the elementary quantitative problem situations. Participants were seven 4th grade elementary students using the questionnaires. The selected students were given study materials. We observed the students' activity sheets and conducted in-depth interviews. As a result of the study, the students' covariational reasoning level for two quantities that are continuously covaried was found to be five, and different reasoning process was shown in quantitative problem situations according to students' covariational reasoning levels. In particular, students with low covariational level had difficulty in grasping the two variables and solved the problem mainly by using the table of value, while the students with the level of chunky and smooth continuous covariation were different from those who considered the flow of time variables. Based on the results of the study, we suggested that various problems related with continuous covariation should be provided and the meanings of the tasks should be analyzed by the teachers.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.85-108
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• 2009

The purposes of the study were to develop instructional materials based on Freudenthal's guided reinvention principle for teaching proofs and to investigate how the teaching method based on guided reinvention principle affects on 8th grade students' ability to write proofs and learning attitude toward proofs. Teaching based on guided reinvention principle placed emphasis on providing students opportunities to make a mathematical statement and prove the statement by themselves throughout various activities such as exploring, conjecturing, and testing the conjectures. The study found that students who studied proving with instructional materials developed by guided reinvention principle showed statistically higher mean scores on the posttest than students who studied by a traditional teaching method depending onteacher's explanation. Especially, on the posttest item which requested to prove a whole statement without presenting a picture corresponding to the statement, a big difference among students' responses was found. Many more students in the traditional group did not provide any response on the item. According to the results of the questionnaire regarding students' learning attitudes, the group who studied proving by guided reinvention principle indicated relatively more positive attitudes toward learning proofs than the counterparts.

• Journal of Gifted/Talented Education
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• v.26 no.3
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• pp.515-539
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• 2016

The purpose of this study is to develop the integrated curriculum for gifted elementary students based on ICM (Integrated Curriculum Model) and to apply it for analysis of the relationship between creativity and creative problem solving skills. An integrated curriculum for gifted students attending a university-affiliated institute was developed and applied to twenty mathematically gifted 5th and 6th grade students. TTCT language test and CAT test for students' products from activities were conducted. In addition, tape-recorded group discussions and activities during instruction, and interview with students and teacher, activity sheets were analyzed. As results, their language abilities shown TTCT test have been improved. Furthermore, the correlation between the test results of automata and language creativity, the average of two projects and language creativity, and future problem solving and the average of TTCT showed significant correlations. Results showed the gifted students' understanding of high level concepts and cooperation among groups were needed in order to improve creative problem solving. It suggested a further study research the integrated curriculum applying creativity and giftedness to real-life problem situations for gifted students to make them grow into essential competent persons in the future.

• Journal of vocational education research
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• v.29 no.3
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• pp.41-60
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• 2010

The purpose of this study was to investigate the relationships between teachers' characteristics and schools' peculiarities and to analyze relevant variables which influence the organization and implementation of the curriculum in specialized industry high schools. Subject were 414 teachers in specialized industry high school. The main result of this study are as follows. First, according to teachers' sex distinction, position, teaching experience, career of industry-related companies, subtle stress difference were found in establishment of education programs, relevance of educational activity, propriety of equipment. Second, in case of schools' subject of establishment, dormitory, specialized types, number of class, type of the sex of recruitment, subtle difference were found in connectivity of graders and subjects, relevance of the organization of education activity, substantial curriculum, push ahead with specialized high school. Third, measures to support development of specialized curriculum arrange sub-items in order of frequency. The way we understand things on vocational education must be settled without delay.

• The Mathematical Education
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• v.61 no.2
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• pp.323-338
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• 2022

The purpose of this study are to analyze how well middle and high school students understand the concept definition of quadrangle and to explore the phenomenon about their concept image. A test tool was developed and 60 8th graders, 63 9^th graders and 65 10^th graders were tested, and some students who needed in-depth analysis were interviewed. The results are as follows. First, it cannot be said that understanding level of the concept definition of the quadrangle naturally improves as the grade level goes up. Particularly, it was found that the understanding of the definition of the rhombus is the lowest in all three grades compared to other quadrangle. Second, although female students understood the definition of square better than male students, the understanding level of the definition of trapezoid, parallelogram, rhombus, and rectangle did not differ by gender. Third, it was found that the students who did not understand the concept definition of the quadrangle were more and more influenced by the concept image as the grade level went up. Fourth, it showed that a tendency to be less influenced by the concept definition and more influenced by textbooks and teachers as the grades go up when students form a concept image.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.131-155
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• 2015

The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.2
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• pp.85-110
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• 2005

The purpose of this study is to examine the characteristics of visual representation used in problem solving process and examine the representation types the students used to successfully solve the problem and focus on systematizing the visual representation method using the condition students suggest in the problems. To achieve the goal of this study, following questions have been raised. (1) what characteristic does the representation the elementary school students used in the process of solving a math problem possess? (2) what types of representation did students use in order to successfully solve elementary math problem? 240 4th graders attending J Elementary School located in Seoul participated in this study. Qualitative methodology was used for data analysis, and the analysis suggested representation method the students use in problem solving process and then suggested the representation that can successfully solve five different problems. The results of the study as follow. First, the students are not familiar with representing with various methods in the problem solving process. Students tend to solve the problem using equations rather than drawing a diagram when they can not find a word that gives a hint to draw a diagram. The method students used to restate the problem was mostly rewriting the problem, and they could not utilize a table that is essential in solving the problem. Thus, various errors were found. Students did not simplify the complicated problem to find the pattern to solve the problem. Second, the image and strategy created as the problem was read and the affected greatly in solving the problem. The first image created as the problem was read made students to draw different diagram and make them choose different strategies. The study showed the importance of first image by most of the students who do not pass the trial and error step and use the strategy they chose first. Third, the students who successfully solved the problems do not solely depend on the equation but put them in the form which information are decoded. They do not write difficult equation that they can not solve, but put them into a simplified equation that know to solve the problem. On fraction problems, they draw a diagram to solve the problem without calculation, Fourth, the students who. successfully solved the problem drew clear diagram that can be understood with intuition. By representing visually, unnecessary information were omitted and used simple image were drawn using symbol or lines, and to clarify the relationship between the information, numeric explanation was added. In addition, they restricted use of complicated motion line and dividing line, proper noun in the word problems were not changed into abbreviation or symbols to clearly restate the problem. Adding additional information was useful source in solving the problem.