• Title/Summary/Keyword: the middle school mathematics

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Developing the mathematics model textbook based on storytelling with real-life context - Focusing on the coordinate geometry contents - (실생활 연계형 스토리텔링 수학 교과서 개발 -도형의 방정식 단원을 중심으로-)

  • Kim, Yujung;Kim, Ji Sun;Park, Sang Eui;Park, Kyoo-Hong;Lee, Jaesung
    • Communications of Mathematical Education
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    • v.27 no.3
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    • pp.179-203
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    • 2013
  • The purpose of this study was to discuss the example that developed geometry model textbook based on storytelling using real-life context. To achieve this purpose, we first elaborated the meaning of the textbook based on storytelling with real-life context, and then we discussed the outline of the story and the summary of each lesson. This study defined the storytelling textbook with real-life context as the textbook consisting of activities that explored and organized mathematical concepts by using real-life situations as materials of stories. The geometry textbook we developed employed two real-life materials, a map and a set square: we used a map for the coordinate geometry and a set square for the equation of a line. To attract students' interest, we introduced confrontation between a teacher and two students and a villain. We implemented experimentation with the textbook based on storytelling in order to verify its validity. The participants were 25 students that were enrolled in a high school in Seoul. Among them, 17 participants were surveyed. Students' answers from the survey questionnaire suggested that the geometry textbook we developed based on storytelling helped them learn mathematics and that the instruments such as a map and a set square helped them understand mathematical concepts. However, their opinion implied that the story of the textbook needed to be improved so that the story reflected more realistic contexts that were familiar with students.

An Analysis of Students' Communication in Lessons for the Geometric Similarity Using AlgeoMath (알지오매스를 활용한 도형의 닮음 수업에서 학생들의 의사소통 분석)

  • Kim, Yeonha;Shin, Bomi
    • Journal of the Korean School Mathematics Society
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    • v.26 no.2
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    • pp.111-135
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    • 2023
  • This study conducted a student-centered inquiry lesson on the similarity of figures using AlgeoMath, with student learning aspects analyzed from a communication perspective. This approach aimed to inform pedagogical implications related to teaching geometric similarity. Through utilizing AlgeoMath, students were able to visually confirm that their chosen figures were similar, experiencing key mathematical concepts such as the ratio of similarity to the area of similar figures, and congruency and similarity conditions of triangles. In the lessons applying this concept, we categorized the features of similarity learning displayed by students, as seen in the communication aspects of their exploratory activities, into 'Understanding similarity ratios', 'Grasping conditions of similarity in triangles', and 'Comparing concepts of congruency and similarity'. Through exploratory activities based on AlgeoMath, students discussed the meaning and mathematical relationships of key concepts related to similarity, such as the ratio of similarity to the area of figures, and the meaning and conditions of congruence and similarity in triangles. By improving misconceptions about the similarity of figures, they were able to develop deeper mathematical understanding. This study revealed that in teaching and learning the geometric similarity using AlgeoMath, obtaining meaningful pedagogical outcome was not solely due to the features of the AlgeoMath environment, but also largely depended on the teacher's guidance and intervention that stimulated students' thinking.

Analysis on the Thinking Characteristics of the Mathematically Gifted Students in Modified Prize-Sharing Problem Solving Process (변형된 상금 분배 문제의 해결과정에 나타나는 초등학교 수학영재들의 사고 특성 분석)

  • Kim, Woo-Hyun;Song, Sang-Hun
    • School Mathematics
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    • v.11 no.2
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    • pp.317-333
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    • 2009
  • The purpose of this study was to examine the thinking characteristics of mathematically gifted elementary school students in the process of modified prize-sharing problem solving and each student's thinking changes in the middle of discussion. To determine the relevance of the research task, 19 sixth graders enrolled in a local joint gifted class received instruction, and then 49 students took lessons. Out of them, 19 students attended a gifted education institution affiliated to local educational authorities, and 15 were in their fourth to sixth grades at a beginner's class in a science gifted education center affiliated to a university. 15 were in their fifth and sixth grades at an enrichment class in the same center. Two or three students who seemed to be highly attentive and express themselves clearly were selected from each group. Their behavioral and teaming characteristics were checked, and then an intensive observational case study was conducted with the help of an assistant researcher by videotaping their classes and having an interview. As a result of analyzing their thinking in the course of solving the modified prize-sharing problem, there were common denominators and differences among the student groups investigated, and each student was very distinctive in terms of problem-solving process and thinking level as well.

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Relationships between milk consumption and academic performance, learning motivation and strategy, and personality in Korean adolescents

  • Kim, Sun Hyo;Kim, Woo Kyoung;Kang, Myung-Hee
    • Nutrition Research and Practice
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    • v.10 no.2
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    • pp.198-205
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    • 2016
  • BACKGROUND/OBJECTIVES: A healthy diet has been reported to be associated with physical development, cognition and academic performance, and personality during adolescence. This study was performed to investigate the relationships among milk consumption and academic performance, learning motivation and strategies, and personality among Korean adolescents. SUBJECTS/METHODS: The study was divided into two parts. The first part was a survey on the relationship between milk consumption and academic performance, in which intakes of milk and milk products and academic scores were examined in percentiles among 630 middle and high school students residing in small and medium-sized cities in 2009. The second part was a survey on the relationships between milk consumption and learning motivation and strategy as well as personality, in which milk consumption habits were collected and Learning Motivation and Strategy Test (L-MOST) for adolescents and Total Personality Inventory for Adolescents (TPI-A) were conducted in 262 high school students in 2011. RESULTS: In the 2009 survey, milk and milk product intakes of subjects were divided into a low intake group (LM: ${\leq}60.2g/day$), medium intake group (MM: 60.3-150.9 g/day), and high intake group (HM: ${\geq}151.0g/day$). Academic performance of each group was expressed as a percentile, and performance in Korean, social science, and mathematics was significantly higher in the HM group (P < 0.05). In the 2011 survey, the group with a higher frequency of everyday milk consumption showed significantly higher "learning strategy total," "testing technique," and "resources management technique" scores (P < 0.05) in all subjects. However, when subjects were divided by gender, milk intake frequency, learning strategy total, class participation technique, and testing technique showed significantly positive correlations (P < 0.05) in boys, whereas no correlation was observed in girls. Correlations between milk intake frequency and each item of the personality test were only detected in boys, and milk intake frequency showed positive correlations with "total agreeability", "organization", "responsibility", "conscientiousness", and "intellectual curiosity" (P < 0.05). CONCLUSION: Intakes of milk and milk products were correlated with academic performance (Korean, social science, and mathematics) in Korean adolescents. In male high school students, particularly, higher milk intake frequency was positively correlated with learning motivation and strategy as well as some items of the personality inventory.

The Use of Traditional Algorithmic Versus Instruction with Multiple Representations: Impact on Pre-Algebra Students' Achievement with Fractions, Decimals, and Percent (전통적 알고리즘 교수법과 다양한 표상을 활용한 교수법의 비교: 분수, 소수, 퍼센트 내용을 중심으로)

  • Han, Sunyoung;Flores, Raymond;Inan, Fethi A.;Koontz, Esther
    • School Mathematics
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    • v.18 no.2
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    • pp.257-275
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    • 2016
  • The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

Case Study on Meaningful use of Parameter - One Classroom of Third Grade in Middle School - (매개변수개념의 의미충실한 사용에 관한 사례연구 -중학교 3학년 한 교실을 대상으로-)

  • Jee, Young Myong;Yoo, Yun Joo
    • School Mathematics
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    • v.16 no.2
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    • pp.355-386
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    • 2014
  • Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

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Summative Evaluation of 1993, 1994 Discussion Contest of Scientific Investigation (제 1, 2회 학생 과학 공동탐구 토론대회의 종합적 평가)

  • Kim, Eun-Sook;Yoon, Hye-Gyoung
    • Journal of The Korean Association For Science Education
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    • v.16 no.4
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    • pp.376-388
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    • 1996
  • The first and the second "Discussion Contest of Scientific Investigation" was evaluated in this study. This contest was a part of 'Korean Youth Science Festival' held in 1993 and 1994. The evaluation was based on the data collected from the middle school students of final teams, their teachers, a large number of middle school students and college students who were audience of the final competition. Questionnaires, interviews, reports of final teams, and video tape of final competition were used to collect data. The study focussed on three research questions. The first was about the preparation and the research process of students of final teams. The second was about the format and the proceeding of the Contest. The third was whether participating the Contest was useful experience for the students and the teachers of the final teams. The first area, the preparation and the research process of students, were investigated in three aspects. One was the level of cooperation, participation, support and the role of teachers. The second was the information search and experiment, and the third was the report writing. The students of the final teams from both years, had positive opinion about the cooperation, students' active involvement, and support from family and school. Students considered their teachers to be a guide or a counsellor, showing their level of active participation. On the other hand, the interview of 1993 participants showed that there were times that teachers took strong leading role. Therefore one can conclude that students took active roles most of the time while the room for improvement still exists. To search the information they need during the period of the preparation, student visited various places such as libraries, bookstores, universities, and research institutes. Their search was not limited to reading the books, although the books were primary source of information. Students also learned how to organize the information they found and considered leaning of organizing skill useful and fun. Variety of experiments was an important part of preparation and students had positive opinion about it. Understanding related theory was considered most difficult and important, while designing and building proper equipments was considered difficult but not important. This reflects the students' school experience where the equipments were all set in advance and students were asked to confirm the theories presented in the previous class hours. About the reports recording the research process, students recognize the importance and the necessity of the report but had difficulty in writing it. Their reports showed tendency to list everything they did without clear connection to the problem to be solved. Most of the reports did not record the references and some of them confused report writing with story telling. Therefore most of them need training in writing the reports. It is also desirable to describe the process of student learning when theory or mathematics that are beyond the level of middle school curriculum were used because it is part of their investigation. The second area of evaluation was about the format and the proceeding of the Contest, the problems given to students, and the process of student discussion. The format of the Contests, which consisted of four parts, presentation, refutation, debate and review, received good evaluation from students because it made students think more and gave more difficult time but was meaningful and helped to remember longer time according to students. On the other hand, students said the time given to each part of the contest was too short. The problems given to students were short and open ended to stimulate students' imagination and to offer various possible routes to the solution. This type of problem was very unfamiliar and gave a lot of difficulty to students. Student had positive opinion about the research process they experienced but did not recognize the fact that such a process was possible because of the oneness of the task. The level of the problems was rated as too difficult by teachers and college students but as appropriate by the middle school students in audience and participating students. This suggests that it is possible for student to convert the problems to be challengeable and intellectually satisfactory appropriate for their level of understanding even when the problems were difficult for middle school students. During the process of student discussion, a few problems were observed. Some problems were related to the technics of the discussion, such as inappropriate behavior for the role he/she was taking, mismatching answers to the questions. Some problems were related to thinking. For example, students thinking was off balanced toward deductive reasoning, and reasoning based on experimental data was weak. The last area of evaluation was the effect of the Contest. It was measured through the change of the attitude toward science and science classes, and willingness to attend the next Contest. According to the result of the questionnaire, no meaningful change in attitude was observed. However, through the interview several students were observed to have significant positive change in attitude while no student with negative change was observed. Most of the students participated in Contest said they would participate again or recommend their friend to participate. Most of the teachers agreed that the Contest should continue and they would recommend their colleagues or students to participate. As described above, the "Discussion Contest of Scientific Investigation", which was developed and tried as a new science contest, had positive response from participating students and teachers, and the audience. Two among the list of results especially demonstrated that the goal of the Contest, "active and cooperative science learning experience", was reached. One is the fact that students recognized the experience of cooperation, discussion, information search, variety of experiments to be fun and valuable. The other is the fact that the students recognized the format of the contest consisting of presentation, refutation, discussion and review, required more thinking and was challenging, but was more meaningful. Despite a few problems such as, unfamiliarity with the technics of discussion, weakness in inductive and/or experiment based reasoning, and difficulty in report writing, The Contest demonstrated the possibility of new science learning environment and science contest by offering the chance to challenge open tasks by utilizing student science knowledge and ability to inquire and to discuss rationally and critically with other students.

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On the analysis and correction of error for the simultaneous inequality with two unknown quantities (미지수가 2개인 연립일차부등식의 문제해결과정에서 발생하는 오류 분석 및 지도방안 연구)

  • Jun, Young-Bae;Roh, Eun-Hwan;Kim, Dae-Eui;Jung, Chan-Sik;Kim, Chang-Su;Kang, Jeong-Gi;Jung, Sang-Tae
    • Communications of Mathematical Education
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    • v.24 no.3
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    • pp.543-562
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    • 2010
  • The purpose of this thesis is to analyze the error happening in the process of solving the simultaneous inequality with two unknown qualities and to propose the correct teaching method. We first introduce a problem about the simultaneous inequality with two unknown qualities. And we will see the solution which a student offers. Finally we propose the correct teaching method by analyzing the error happening in the process of solving the simultaneous inequality with two unknown qualities. The cause of the error are a wrong conception which started with the process of solving the simultaneous equality with two unknown qualities and an insufficient curriculum in connection with the simultaneous inequality with two unknown qualities. Especially we can find out the problem that the students don't look the interrelation between two valuables when they solve the simultaneous inequality with two unknown qualities. Therefore we insist that we must teach students looking the interrelation between two valuables when they solve the simultaneous inequality with two unknown qualities.

Investigation of the Components for Assessing the Ability of Engineering Design (공학설계능력의 평가 요소 구명)

  • Kim Tae-Hoon;Lee So-Yee;Rho Tae-Cheon
    • Journal of Engineering Education Research
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    • v.8 no.3
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    • pp.49-56
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    • 2005
  • The purposes of this study are to select assessment components for the engineering design ability and to verify the validity of the selected assessment components. From the results of the study, the following conclusions were made. $\cdot$ Social Ability : 'Communication' and 'Teamwork' $\cdot$ Procedure Ability : 'Acknowledging and Defining Problems', 'Planning and Maintaining', 'Collecting Information', 'Deriving Ideas' and 'Evaluating Ideas' $\cdot$ Experience : 'Engineering Experience' and 'Science Experience' $\cdot$ Knowledge : 'Engineering Knowledge', 'Science Knowledge' and 'Mathematics Knowledge', 'Visualization Ability': 'Sketching' and 'Drawing' $\cdot$ Reasoning : 'Converging Reasoning' 'Inductive Reasoning' and 'Intuitive Reasoning'

Analysis of abduction and thinking strategies by type of mathematical problem posing (수학 문제 만들기 유형에 따른 가추 유형과 가추에 동원된 사고 전략 분석)

  • Lee, Myoung Hwa;Kim, Sun Hee
    • The Mathematical Education
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    • v.59 no.1
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    • pp.81-99
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    • 2020
  • This study examined the types of abduction and the thinking strategies by the mathematics problems posed by students. Four students who were 2nd graders in middle school participated in problem posing on four tasks that were given, and the problems that they posed were classified into equivalence problem, isomorphic problem, and similar problem. The type of abduction appeared were different depending on the type of problems that students posed. In case of equivalence problem, the given condition of the problems was recognized as object for posing problems and it was the manipulative abduction. In isomorphic problem and similar problem, manipulative abduction, theoretical abduction, and creative abduction were all manifested, and creative abduction was manifested more in similar problem than in isomorphic problem. Thinking strategies employed at abduction were examined in order to find out what rules were presumed by students across problem posing activity. Seven types of thinking strategies were identified as having been used on rule inference by manipulative selective abduction. Three types of knowledge were used on rule inference by theoretical selective abduction. Three types of thinking strategies were used on rule inference by creative abduction.