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THE LAKATOSIAN METHODOLOGY IN TEACHING THE SURFACE AREA OF A CONE AND A STUDENT’S CONCEPTUAL TRANSITION 拉卡托斯方法在圆锥表面积教学中的应用与学生概念转换
Infinity Journal Pub Date : 2022-01-17 DOI: 10.22460/infinity.v11i1.p103-114
U. Ogbonnaya, Chrysoula Dimitriou-Hadjichristou
{"title":"THE LAKATOSIAN METHODOLOGY IN TEACHING THE SURFACE AREA OF A CONE AND A STUDENT’S CONCEPTUAL TRANSITION","authors":"U. Ogbonnaya, Chrysoula Dimitriou-Hadjichristou","doi":"10.22460/infinity.v11i1.p103-114","DOIUrl":"https://doi.org/10.22460/infinity.v11i1.p103-114","url":null,"abstract":"Although many scholars support the Lakatosian method of mathematics education for enhancing students learning, the use of the method to foster students’ transition from alternative to scientific conceptions in mathematics does not seem to have been a focus of any research. This study explored if the Lakatosian heuristic method of teaching could foster a students’ transition from alternative to scientific conceptions of the surface area of a cone. The study used a qualitative, exploratory single case study design to undertake an in-depth study of a student in the 11th grade at a secondary school in Cyprus. Data was collected through lesson observation and analyzed using deductive content analysis.  The study found that beginning from informal conjectures and proofs to more formal proofs the student was able to transit from alternative conception to the scientific conception of the surface area of a cone. The finding suggests that the Lakatosian method of mathematics can foster students’ conceptual understanding of some mathematical concepts.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117326161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ALTERNATIVE LEARNING DURING A PANDEMIC: USE OF THE WEBSITE AS A MATHEMATICS LEARNING MEDIA FOR STUDENT MOTIVATION 流感大流行期间的另类学习:利用网站作为数学学习媒体来激励学生
Infinity Journal Pub Date : 2022-01-12 DOI: 10.22460/infinity.v11i1.p17-32
Suripah Suripah, W. Susanti
{"title":"ALTERNATIVE LEARNING DURING A PANDEMIC: USE OF THE WEBSITE AS A MATHEMATICS LEARNING MEDIA FOR STUDENT MOTIVATION","authors":"Suripah Suripah, W. Susanti","doi":"10.22460/infinity.v11i1.p17-32","DOIUrl":"https://doi.org/10.22460/infinity.v11i1.p17-32","url":null,"abstract":"In March 2020, direct learning activities were transferred online due to the Covid-19 pandemic. There are many alternative technology-based learning media used for online learning systems. However, the use of this media has not been able to increase students' motivation to learn mathematics. One of the media that can be used as an alternative learning media during this pandemic is a website. The purpose of this study was to find out how to use the website as a learning media in the midst of this pandemic, and to determine student learning motivation. This research is a descriptive study with a quantitative approach, the subjects in this study were 25 students of grade 8 and 9 Junior High School. The results of this study were that many students agreed with the use of websites as alternative learning media during this pandemic and students' high motivation to learn mathematics when using the website with an average percentage of 66,3%. From this research, it can be concluded that the website can be an alternative media for learning mathematics in the midst of this pandemic because the website has various advantages that can also increase student learning motivation.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"467 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120877055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
CLUSTERS OF PREVALENT PATTERNS OF GEOMETRIC THINKING LEVELS AMONG MATHEMATICS STUDENTS 数学学生几何思维水平的流行模式群
Infinity Journal Pub Date : 2022-01-12 DOI: 10.22460/infinity.v11i1.p77-86
J. Ordiz, Ghanine Rhea Mecate
{"title":"CLUSTERS OF PREVALENT PATTERNS OF GEOMETRIC THINKING LEVELS AMONG MATHEMATICS STUDENTS","authors":"J. Ordiz, Ghanine Rhea Mecate","doi":"10.22460/infinity.v11i1.p77-86","DOIUrl":"https://doi.org/10.22460/infinity.v11i1.p77-86","url":null,"abstract":"Geometric thinking skills are the perceived abilities of an individual to think and reason in geometric contexts. These skills acquired by students in geometry remain poor and unsettling because of the misconceptions that hinder the students in learning the components of geometry. The study described the common unplaceable patterns in geometric thinking of 153 mathematics education students in a state university in Eastern Visayas, Philippines. Frequency Analysis was employed in the study to determine the number of occurrences of the patterns stressing the cause for students placed under level 0 or unplaceable. Van Hiele Achievement Test was used to gather the students’ performance in geometry at all levels, namely: visualization, analysis, informal deduction, deduction, and rigor. The findings attested that only 13.1% of the students managed the third level of the Van Hiele Levels while 43.1% of them were unplaceable. Common patterns were drawn and describe to understand the consequences in geometric thinking ability at level 0. These observable patterns were grouped into core-remedial, topical-corrective, and close-corrective groups. The clusters will enable educational institutions to address the individual gaps in geometry.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117345639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
INTEGRATING SUNDANESE ETHNOMATHEMATICS INTO MATHEMATICS CURRICULUM AND TEACHING: A SYSTEMATIC REVIEW FROM 2013 TO 2020 将巽他民族数学融入数学课程与教学:2013 - 2020年系统回顾
Infinity Journal Pub Date : 2022-01-12 DOI: 10.22460/infinity.v11i1.p33-54
D. A. M. Lidinillah, R. Rahman, W. Wahyudin, S. Aryanto
{"title":"INTEGRATING SUNDANESE ETHNOMATHEMATICS INTO MATHEMATICS CURRICULUM AND TEACHING: A SYSTEMATIC REVIEW FROM 2013 TO 2020","authors":"D. A. M. Lidinillah, R. Rahman, W. Wahyudin, S. Aryanto","doi":"10.22460/infinity.v11i1.p33-54","DOIUrl":"https://doi.org/10.22460/infinity.v11i1.p33-54","url":null,"abstract":"As a country with the most ethnic, cultural, and linguistic backgrounds globally, Indonesia has great potential for the development of ethnomathematics studies. Among those ethnic groups, Sundanese ethnic group and culture is the second-largest after the Javanese ethnic group and culture, making it interesting to study because it has rich cultural elements that can be integrated into the mathematics curriculum in schools. This article explores the development of research on ethnomathematics based on Sundanese culture, including those which are based on the study's scope, the integration of Sundanese ethnomathematics into the school curriculum, and mathematics learning. Based on the investigation, there has been no systematic literature review on Sundanese ethnomatematics. The research was conducted using the Systematic Literature Review method with the PRISMA protocol. The results showed that there were various kinds of research on Sundanese ethnomathematics. There were various kinds of study on Sundanese ethnomathematics integration into mathematics curriculum and teaching using five model categories. The results also showed that RME, CTL and PBL were the most widely used teaching approaches for learning Sundanese ethnomathematics. However, most of Sundanese ethnomathematics teaching uses a special approach  that varies, developing teaching material, teaching media and using the context of traditional games.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115584091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
HIGH SCHOOL STUDENTS’ ERROR IN SOLVING WORD PROBLEM OF TRIGONOMETRY BASED ON NEWMAN ERROR HIERARCHICAL MODEL 基于纽曼误差层次模型的高中生解题误差分析
Infinity Journal Pub Date : 2022-01-12 DOI: 10.22460/infinity.v11i1.p87-102
Thalitha Ariesti Widhia Wardhani, D. P. A. D. Argaswari
{"title":"HIGH SCHOOL STUDENTS’ ERROR IN SOLVING WORD PROBLEM OF TRIGONOMETRY BASED ON NEWMAN ERROR HIERARCHICAL MODEL","authors":"Thalitha Ariesti Widhia Wardhani, D. P. A. D. Argaswari","doi":"10.22460/infinity.v11i1.p87-102","DOIUrl":"https://doi.org/10.22460/infinity.v11i1.p87-102","url":null,"abstract":"This study aims to identify students’ errors in solving word problems of trigonometry according to the Newman Error Hierarchical Model. This study uses qualitative descriptive data gathered based on fact, and data analysis presented descriptively. The population is students of X IPA 2 at SMAN 1 Cikarang Utara, West Java, Indonesia, and to understand more about the error that happened, the researcher took six students of SMAN 1 Cikarang Utara as a sample. The sample is chosen by purposive sampling. Instrument tests, interviews, and documentation are the data collected. This study used the Newman Error Hierarchical Model to analyze high school students’ errors in solving word problems of trigonometry. The results show that students made errors in comprehension, transformation, process skill, and encoding stage. The errors were caused by their lack of understanding some words and terms in the word problem, lack of ability in transforming the word problem to the mathematical model and strategy, lack of processing the algebra and calculation, lack of motivation, and carelessness.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125999229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
COLLABORATIVE LEARNING THROUGH LESSON STUDY IN PMRI TRAINING FOR PRIMARY SCHOOL PRE-SERVICE TEACHER: THE SIMULATION OF POLYGON MATTER 在小学职前教师pmri训练中,透过课程学习的合作学习:多边形物质的模拟
Infinity Journal Pub Date : 2022-01-12 DOI: 10.22460/infinity.v11i1.p1-16
A. Fauziah, R. Putri, Z. Zulkardi
{"title":"COLLABORATIVE LEARNING THROUGH LESSON STUDY IN PMRI TRAINING FOR PRIMARY SCHOOL PRE-SERVICE TEACHER: THE SIMULATION OF POLYGON MATTER","authors":"A. Fauziah, R. Putri, Z. Zulkardi","doi":"10.22460/infinity.v11i1.p1-16","DOIUrl":"https://doi.org/10.22460/infinity.v11i1.p1-16","url":null,"abstract":"Collaborative learning through lesson study has become one of the promising methods for improving the quality of education and improving teachers' quality, likewise with the PMRI approach. The combination of the two in the training for primary school pre-service teachers, specifically in the second simulation session, was observed and reported. This article aims to describe the collaboration process in the second session of the simulations about polygon learning at PMRI training for primary school pre-service teachers. A design research method of the development type was used in this study, only at the preliminary and development or prototyping phase. The research subjects are students of Primary School Pre-service Teachers of Sriwijaya University that consisted of eight students for the small group and 32 students for the field test. Data was collected through documentation, observation, and field notes. The result showed that there were good collaboration occurs between researcher-lecturer, lecturer-student, and between students at the plan-do-see-redesign stage of the lesson study.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129404432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PROSPECTIVE TEACHERS REPRESENTATIONS IN PROBLEM SOLVING OF SPECIAL ANGLE TRIGONOMETRY FUNCTIONS BASED ON THE LEVEL OF ABILITY 准教师在特殊角度三角函数解题中的表现基于能力水平
Infinity Journal Pub Date : 2022-01-12 DOI: 10.22460/infinity.v11i1.p55-76
Y. Setiawan
{"title":"PROSPECTIVE TEACHERS REPRESENTATIONS IN PROBLEM SOLVING OF SPECIAL ANGLE TRIGONOMETRY FUNCTIONS BASED ON THE LEVEL OF ABILITY","authors":"Y. Setiawan","doi":"10.22460/infinity.v11i1.p55-76","DOIUrl":"https://doi.org/10.22460/infinity.v11i1.p55-76","url":null,"abstract":"One of the materials used as the basis for solving trigonometric function problems is special angle trigonometry. Prospective teachers' representation in problem-solving of trigonometric functions with special angles is thought to be influenced by prospective teachers' abilities. Therefore, this study aims to analyze the representations used by prospective teachers in problem-solving of special angle trigonometric function based on ability categories. This research is qualitative descriptive. The research subjects are prospective teachers of the mathematics education study program at a university in Malang. The data collected in this study are in the form of work results and observation. The research instrument consisted of the problem of the trigonometric function value of the special angle and the interview guide developed by the researcher. The analysis of prospective teacher work results was carried out by classifying the ability categories into low, medium, and high abilities. The work results of each of these categories are classified based on verbal, numeric, image, and algebraic representations. The analysis of the interview transcripts was carried out by coding the words or sentences which aims to determine prospective teachers' understanding of using representations. The results showed that prospective teachers with low ability use a lot of verbal representation, while prospective teachers with medium and high abilities use a lot of image representation in problem-solving of special angle trigonometric function. The implication of the results of this study is to teach special angle trigonometric function material based on appropriate representations.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117272308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
INVESTIGATION OF STUDENTS' BEHAVIOR IN MATHEMATICAL PROBLEM SOLVING 学生数学解题行为的调查
Infinity Journal Pub Date : 2021-07-28 DOI: 10.22460/infinity.v10i2.p235-258
Y. Harisman, M. S. Noto, W. Hidayat
{"title":"INVESTIGATION OF STUDENTS' BEHAVIOR IN MATHEMATICAL PROBLEM SOLVING","authors":"Y. Harisman, M. S. Noto, W. Hidayat","doi":"10.22460/infinity.v10i2.p235-258","DOIUrl":"https://doi.org/10.22460/infinity.v10i2.p235-258","url":null,"abstract":"This study is a qualitative research by using the descriptive method that aims to examine the behaviour of eighteen students in Bandung, Indonesia. Six issues related to geometry were given to eighteen of second-grade junior high school students with heterogeneous abilities. The problems given to the students contained all of the problem-solving strategies such as guessing and checking, make a picture, make a list, make a table, working backwards, looking patterns, and using a logical reason, solving simple problems and making questions. Data collection was conducted through mathematical problem-solving tests, recording students’ presentations, and interviewing among researchers and students after doing the problems. The result of recording was a video during the presentation process, and the interview would explore their understanding of the given problems to see the behaviour used by subjects of the research. The data in this research showed that many students’ behaviour identified; in the relevant literature, there are terms of the behaviour of problem-solving naive, routine, and sophisticated. However, the category \"naïve,\" \"routine,\" and \"sophisticated\" did not fully draw various behaviours observed, it was obtained additional category termed behavioural problem solver \"naïve,\" \"routine,\" \"semi-sophisticated\" and \"sophisticated\". It was due to the category of regular students can be divided into two, some students can be directed, and some of them cannot be directed to sophisticated behaviour. Thus, the routine category can be classified into two categories: routine and semi-sophisticated.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123108958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
PISA-LIKE PROBLEMS USING ISLAMIC ETHNOMATHEMATICS APPROACH 用伊斯兰民族数学方法求解类似pisa的问题
Infinity Journal Pub Date : 2021-06-15 DOI: 10.22460/INFINITY.V10I2.P203-216
M. W. Afgani, R. Paradesa
{"title":"PISA-LIKE PROBLEMS USING ISLAMIC ETHNOMATHEMATICS APPROACH","authors":"M. W. Afgani, R. Paradesa","doi":"10.22460/INFINITY.V10I2.P203-216","DOIUrl":"https://doi.org/10.22460/INFINITY.V10I2.P203-216","url":null,"abstract":"Received Nov 19, 2019 Revised Apr 8, 2021 Accepted Apr 11, 2021 The study aimed to produce PISA-like mathematics problems with the Islamic ethnomathematics approach that were valid and practical. A development study with formative evaluation was used as the method in this study with 32 9th-grade students as the subjects at one of the junior high schools in Palembang, South Sumatra province, Indonesia. There are five phases: selfevaluation, expert review, one-to-one, small group, and field test. Interviews, questionnaires, and tests were used in this study as the instruments to collect the data. The results showed that three experts from the expert review phase assess that 77.78% agree that six PISA-like mathematics problems meet the validity criteria. For the practicality criteria, three students from the one-toone step set about 77,78% agree, three students from the small group phase assessed about 61,11% strongly agree, and 26 students from the field test phase considered 61,33% agree. This result is supported by the average test result that was classified as a low category. This showed that the results obtained are not optimal because students still did not understand the problems and had difficulty solving them.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124994283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
IDENTIFICATION OF JUNIOR HIGH SCHOOL STUDENTS’ ERROR TYPES IN UNDERSTANDING CONCEPT ABOUT RELATION AND FUNCTION 初中生对关系和功能概念的错误类型识别
Infinity Journal Pub Date : 2021-06-11 DOI: 10.22460/INFINITY.V10I2.P175-190
A. Y. Fitrianna, R. Rosjanuardi
{"title":"IDENTIFICATION OF JUNIOR HIGH SCHOOL STUDENTS’ ERROR TYPES IN UNDERSTANDING CONCEPT ABOUT RELATION AND FUNCTION","authors":"A. Y. Fitrianna, R. Rosjanuardi","doi":"10.22460/INFINITY.V10I2.P175-190","DOIUrl":"https://doi.org/10.22460/INFINITY.V10I2.P175-190","url":null,"abstract":"This study aims to identify types of errors made by students and their conceptions related to the concept of relations and functions. This research is a descriptive study with a qualitative approach conducted in eight grades at one of Madrasah Tsanawiyah in Kabupaten Bandung Barat. The research subjects were taken from 26 students who answered incorrectly on a given test. The research instrument was in the form of a diagnostic test based on basic competencies and indicators in the Relations and Function material. In-depth interviews were conducted with students who made mistakes in answering. Based on the data analysis, the mistakes made were: 1) conceptual error type 1, 2) conceptual error type 2, 3) procedural error, 4) technical error, and 5) error in understanding the problem. One of the causes of students' mistakes is the dissimilar concept between students’ and scientific conceptions.","PeriodicalId":109878,"journal":{"name":"Infinity Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131871604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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