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Examining students' cognitive processes in solving algebraic numeracy problems: A Phenomenology study 检视学生解决代数计算问题的认知过程:一项现象学研究
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.13266
Monika Agnes Henny Kinanti, I. Sujadi, D. Indriati, K. S. Kuncoro
Problem-solving can be understood as a cognitive process in which students know facts, processes, concepts, and procedures and then apply the knowledge to solve problems in real situations. Indonesia’s national average achievement of numeracy skills in 2021, the cognitive process of competence reasoning is higher than the competencies of knowing and applying. This study aims to analyze students' cognitive processes in solving numeration problems related to the algebraic domain. The algebraic domain in this study is limited to competencies in making generalizations from patterns in number sequences and object configuration sequences. This research was conducted qualitatively with a phenomenological design using three high-category and three low-category students to achieve data saturation. The supporting instruments are students' answers and interview results related to the algebraic domain. This study concluded that students' cognitive processes in solving numeracy problems associated with the algebraic domain in the high and low categories have different descriptions. This difference in intelligence has an impact when solving math problems. This research can help enrich the understanding of students' cognitive processes and contribute to the development of better mathematics learning strategies and curricula.
问题解决可以理解为一个认知过程,在这个过程中,学生了解事实、过程、概念和程序,然后将这些知识应用到实际情况中解决问题。印度尼西亚2021年全国计算技能平均成绩表明,能力推理的认知过程高于了解和应用的能力。本研究旨在分析学生在解决代数领域的计算问题时的认知过程。本研究的代数领域仅限于从数字序列和对象构型序列的模式中进行概括的能力。本研究采用现象学设计,采用三名高类别和三名低类别学生进行定性研究,以达到数据饱和。辅助工具是学生的回答和与代数领域相关的访谈结果。本研究的结论是,学生在解决与代数领域相关的算术问题的认知过程中,在高类别和低类别有不同的描述。这种智力上的差异会对解决数学问题产生影响。本研究有助于丰富对学生认知过程的理解,有助于制定更好的数学学习策略和课程。
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引用次数: 0
Level of visual geometry skill towards learning style Kolb in junior high school 初中生视觉几何技能水平对学习风格Kolb的影响
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.15121
A. Anwar, T. Turmudi, D. Juandi, Saiman Saiman, M. Zaki
This study aims to conduct an in-depth analysis of the visual thinking level of junior high school students with the learning style of assimilators, converges, accommodators, and divergers in solving geometry problems. The type of research used is qualitative research with a grounded theory and case study design. The subjects studied were junior high school students consisting of 6 of 56 students. Data were collected through a learning style inventory (LSI) test given to 56 students to group participants based on the learning style of the Kolb model, then a geometry problem-solving test and interviews were given to 6 students, namely two assimilator students, one converges, one accommodator, and two diverger students. The analysis is based on data from written test results and interviews. Then, time triangulation is carried out to obtain valid research data. The analysis was conducted based on data from written test results and interview results paired with video recordings. Then, triangulation of time is carried out to obtain valid research data. The results of the analysis showed that assimilator students and converger students were able to achieve at the global visual level, namely being able to carry out visual thinking activities well in solving problems, illustrate the problem correctly in geometric drawings/objects, represent problems in mathematical symbols precisely and can express relationships between images well. While accommodator and diverger students can only reach the local visual level, they have yet to be able to show every visual thinking activity well in solving geometry problems, illustrating problems in geometry drawings that could be more precise, and solving rudimentary geometry problems.
本研究旨在深入分析同化型、收敛型、包容型和发散型学习风格的初中生在解决几何问题时的视觉思维水平。所使用的研究类型是定性研究,具有扎实的理论和案例研究设计。研究对象为初中生,56名学生中有6名。通过对56名学生进行学习风格量表(LSI)测试来收集数据,并对6名学生进行几何问题解决测试和访谈,即同化型学生2名、收敛型学生1名、包容型学生1名和发散型学生2名。该分析基于笔试成绩和面试数据。然后进行时间三角剖分,获得有效的研究数据。该分析是根据笔试成绩和面试结果以及录像数据进行的。然后对时间进行三角剖分,获得有效的研究数据。分析结果表明,同化型学生和融合型学生在整体视觉层面上都能达到,即在解决问题时能很好地进行视觉思维活动,在几何图形/物体中能正确地说明问题,在数学符号中能准确地表示问题,能很好地表达图像之间的关系。而迁就型和发散型学生只能达到局部的视觉水平,在解决几何问题、用更精确的几何图形说明问题、解决基本的几何问题等方面,还不能很好地表现出每一种视觉思维活动。
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引用次数: 0
Project-based learning assisted augmented reality in increasing students’ mathematical understanding of concepts 基于项目的学习有助于增强现实提高学生对概念的数学理解
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.12703
Axl Ferrari Fatahillah, A. Faradillah
The gap in this study uses Augmented Reality media when the learning system takes place. This research aims to determine the effectiveness of the Project-Based Learning (PjBL)—model in increasing mathematical understanding of concepts assisted by Augmented Reality. The method used in this study uses a quantitative methodology with a quasi-experimental research design with a nonequivalent control group design approach. The random cluster sampling technique was used for sampling in this study. The class used was ten science four class as the control class and ten science five class as the experimental class. Validity and reliability test were carried out with the help of Winstep 3.73 software and data analysis techniques using SPSS 24.0 for Windows software. The total question of the instrument is five, which contains indicators of mathematical understanding concepts. The results of this study are that the experimental class using the Augmented Reality-assisted Project Based Learning (PjBL) model is better than the control class using conventional models. The implications of this research are to assist teachers in improving students’ ability to mathematical understanding concepts and improve innovative learning methods in the classroom with the PjBL models and augmented reality.
本研究的差距是在学习系统发生时使用增强现实媒体。本研究旨在确定基于项目的学习(PjBL)模型在增强现实辅助下提高概念数学理解的有效性。本研究中使用的方法采用准实验研究设计的定量方法,采用非等效对照组设计方法。本研究采用随机整群抽样技术进行抽样。班级采用十个科学四班作为对照班,十个科学五班作为实验班。采用Winstep 3.73软件进行效度和信度检验,采用SPSS 24.0软件进行数据分析。该工具的总问题为五个,其中包含数学理解概念的指标。本研究的结果是,使用增强现实辅助项目学习(PjBL)模型的实验班优于使用传统模型的对照班。本研究旨在透过PjBL模型与扩增实境技术,协助教师提升学生对数学概念的理解能力,并改善课堂上的创新学习方法。
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引用次数: 0
How do students solve reversible thinking problems in mathematics? 学生如何解决数学中的可逆思维问题?
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.17821
Aneu Pebrianti, S. Prabawanto, E. Nurlaelah
Reversible thinking is a cognitive activity in finding a solution to a problem by arranging the direction of logical thinking from the end to the starting point. Reversible thinking requires a student to think logically in two ways. Therefore, reversible thinking influences students' success in solving problems. This study aims to identify students' thinking processes in solving problems that require reversible thinking ability. This research was conducted on junior high school students in Bandung, West Java, Indonesia, using test instruments, interviews, and documentation studies. The tests given consisted of two types of problems, including tests on forward-thinking problems and tests on reversible thinking problems. The research subjects were students with high average mathematics scores in their class. The study found that students could answer the tests on forward-thinking problem-solving very well but could not work on similar questions with the backward-thinking process. Based on the interview results, one of the causes for the need for more backward-thinking ability is the limited learning resources or context when students first learn the concept.
可逆性思维是一种通过安排逻辑思维从终点到起点的方向来寻找问题解决方案的认知活动。可逆思维要求学生以两种方式进行逻辑思考。因此,可逆思维影响学生成功解决问题。本研究旨在找出学生在解决需要可逆思维能力的问题时的思维过程。本研究以印尼西爪哇省万隆市初中生为研究对象,采用测试仪器、访谈及文献研究等方法。给出的测试包括两种类型的问题,包括前瞻性思维问题的测试和可逆思维问题的测试。研究对象是班里数学平均成绩较高的学生。研究发现,学生可以很好地回答前瞻性思维问题的测试,但不能用逆向思维解决类似的问题。从访谈结果来看,学生需要更多的后向思维能力的原因之一是学生第一次学习概念时的学习资源或语境有限。
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引用次数: 0
Ethnomathematics approach integrated flipped classroom model: Culturally contextualized meaningful learning and flexibility 民族数学方法整合翻转课堂模式:文化情境化的有意义学习与灵活性
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.7871
R. Ramadhani, Edi Syahputra, Elmanani Simamora
The student-centered learning model has yet to adapt to the environment around students, including cultural contexts and traditions, and is less applicable and less effective for improving students' mathematical abilities. The meaningfulness obtained from mathematics learning based on activity has yet to provide optimal results, and there are still contradictions between learning theories and the application results. Therefore, this study aims to provide recommendations for developing new models and theories to optimize flexible and meaningful learning implementation using qualitative research methods with an integrative literature review approach. The results show that student-centered learning needs attention to personal factors and behaviors. Furthermore, learning with a cultural approach through an ethnomathematics context and flexibility in learning are also needed. The implication of this research is to recommend developing a model that integrates the flipped classroom model and the ethnomathematics approach. Meanwhile, a new theory was also proposed due to the development of the Cognitive-Social-Cultural Constructivist Theory of Learning (CSCCTL). Further studies on developing theories from the ethno-flipped classroom model should be conducted.
以学生为中心的学习模式还没有适应学生周围的环境,包括文化背景和传统,对提高学生的数学能力不太适用,也不太有效。基于活动的数学学习所获得的意义还没有达到最优的效果,学习理论与应用结果之间还存在着矛盾。因此,本研究旨在以整合文献的方法,运用质性研究方法,为优化灵活而有意义的学习提供新的模型和理论建议。结果表明,以学生为中心的学习需要关注个人因素和行为。此外,还需要通过民族数学背景和学习灵活性的文化方法进行学习。本研究的意义在于建议开发一种将翻转课堂模式与民族数学方法相结合的模式。同时,由于认知-社会-文化建构主义学习理论(CSCCTL)的发展,一种新的理论也被提出。对民族翻转课堂模式的理论发展进行进一步的研究。
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引用次数: 0
Research trends on flipped classrooms of mathematics creative thinking, critical thinking, and problem-solving skills 数学创造性思维、批判性思维和解决问题能力的翻转课堂研究趋势
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.15150
Muhammad Fayakuun, A. Agoestanto
Some studies discussed learning outcomes, challenges, and the effect of media learning on flipped classrooms of mathematics creative thinking (MCeT), critical thinking (MCiT), and problem-solving (MPS) skills. None of the studies reviewed the research information. This study aimed to examine trend research by year and the diversity of research methods, quantitative research designs, research subjects, mathematics topics, research variables, data collection tools, test designs, data analysis methods, and learning media in articles published in Scopus,  Education Resources Information Centre (ERIC), and Garba Rujukan Digital (Garuda) databases of mathematics educational journals from January 2018 to April 2023. The method of this study was the content analysis method. Twenty-two articles were evaluated in this study. The results showed that the research trend by year was increasing. The most type of research methods, quantitative research design, research subjects, mathematics topic, research variables, data collecting tools, kind of test design, data analysis techniques, and learning media were quasi-experimental design, eighth-grade junior high school students, three-dimensional shape, problem-solving, test sheet, pretest-posttest, t-test, and video, respectively. This study gave insights to other researchers for future decision-making on flipped classrooms of MCeT, MCiT, and MPS skills.
一些研究讨论了学习成果、挑战以及媒体学习对翻转课堂数学创造性思维(MCeT)、批判性思维(MCiT)和解决问题(MPS)技能的影响。没有一项研究回顾了研究信息。本研究旨在考察2018年1月至2023年4月期间,在Scopus、教育资源信息中心(ERIC)和Garba Rujukan Digital (Garuda)数据库中发表的数学教育期刊文章的研究趋势,以及研究方法、定量研究设计、研究对象、数学主题、研究变量、数据收集工具、测试设计、数据分析方法和学习媒体的多样性。本研究采用内容分析法。本研究共评估了22篇文章。研究结果表明,该领域的研究有逐年增加的趋势。研究方法类型最多、定量研究设计类型最多、研究对象最多、数学主题最多、研究变量最多、数据收集工具最多、测试设计类型最多、数据分析技术最多、学习媒介最多的分别是准实验设计、初中生最多、三维造型最多、问题解决最多、测试单最多、前测后测最多、t检验最多、视频最多。这项研究为其他研究人员未来对MCeT、MCiT和MPS技能的翻转课堂决策提供了见解。
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引用次数: 0
Development of a logarithmic module equipped with a jigsaw cooperative model 配备拼图协作模型的对数模块的开发
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.17520
Jitu Halomoan Lumbantoruan, Evi Deliviana
The teacher's task is to compile lesson plans, books, or modules assess and evaluate. However, the fact is that the low learning outcomes are due to the difficulty level of the book. The results of the 2022 study show that students' scores are below 75, which is 74.80. Urgency, there is a difference between teacher assignments, expectations, and learning outcomes. The research aims to design practical and effective modules. The research method used is Research and Development (RD): Determination, Design, Development, Implementation, and Evaluation. The subject is high school, and the subject is 32 students. They are collecting data with assessment instruments from material experts, teachers, and students. Modules are measured by practicality through instruments, and tests measure effectiveness. Analysis technique with validation. Average values and interpretations. As a result, the logarithmic module is practical, effective, and can increase value. The validation of material experts and math teachers assessed 92.35% and 91.45% in the very good category. Student assessment of the module is 95.81%, a very good category. Post-test learning outcomes use the 90.28 module, and those that do not use the 68.40 module.
教师的任务是编写教案、书籍或模块进行评估和评价。然而,事实是,低学习效果是由于书的难度水平。2022年的研究结果显示,学生的分数低于75分,为74.80分。紧迫性,教师布置的任务、期望和学习成果之间存在差异。本研究旨在设计实用有效的模块。使用的研究方法是研究与开发(RD):确定、设计、开发、实施和评估。对象是一所高中,对象是32名学生。他们用评估工具从材料专家、教师和学生那里收集数据。模块通过仪器测量实用性,通过测试测量有效性。具有验证的分析技术。平均值和解释。因此,该对数模块实用、有效,具有增值作用。材料专家和数学教师的验证率分别为92.35%和91.45%。学生对该模块的评价为95.81%,属于很好的一类。测试后学习结果使用90.28模块,未使用68.40模块。
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引用次数: 0
Examining the effectiveness of a GeoGebra-assisted open-ended approach on students’ mathematical creative thinking ability 考察geogebra辅助开放式方法对学生数学创造性思维能力的影响
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.16483
Andini Dwi Rachmawati, D. Juandi, D. Darhim
Researchers use open-ended as a learning method to help students improve their math skills. Each open investigation of mathematical knowledge produces mixed results for components of mathematical ability, each school level, and the content taught. There are more and more studies on open-ended questions nowadays. This study tested the effectiveness of the open-ended approach assisted by GeoGebra on students' mathematical creative thinking abilities. The use of meta-analysis techniques is to analyze the effect (effect size) of a preliminary study. The instruments used were coding protocol sheets and coding sheets/Comprehensive Meta-Analysis (CMA) programs to analyze data. The resulting findings are that there are differences in the research method with the most significant effect size in the quasi-experimental research method, the research year with the most significant effect size in the 2012-2022 research year, indexing journals with the most significant effect size on web indexing scientific journals; the type of publication that has the most critical influence on the kind of thesis publication. Furthermore, the GeoGebra-assisted open-ended approach to creative thinking ability has no significant effect when viewed from the research characteristics of the sample size and level of education.
研究人员使用开放式学习方法来帮助学生提高数学技能。每一次对数学知识的公开调查都会对数学能力的组成部分、每个学校的水平和所教授的内容产生不同的结果。目前,开放式问题的研究越来越多。本研究测试了GeoGebra辅助的开放式方法对学生数学创造性思维能力的影响。荟萃分析技术的使用是分析初步研究的效果(效应大小)。使用的工具是编码协议表和编码表/综合元分析(CMA)程序来分析数据。结果发现:准实验研究方法中效应量最显著的研究方法、2012-2022研究年中效应量最显著的研究年份、网络索引科技期刊中效应量最显著的索引期刊存在差异;对论文发表类型影响最关键的出版类型。此外,从样本数量和受教育程度的研究特征来看,geogebra辅助开放式方法对创造性思维能力的影响不显著。
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引用次数: 0
Gender differences in written mathematical communication skills of junior high school students 初中生书面数学沟通能力的性别差异
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.14062
Muhamad Syahidul Qirom, J. Dahlan, T. Turmudi
Some research about identifying the differences between male and female students’ written communication skills has been done before. However, the previous research only focused on qualitative studies. Therefore, there is still a lack of empirical proof of the result. This study aims to test whether a significant difference exists between male and female students' written mathematical communication skills and identify their performance difficulties. The subjects were 14 male and 14 female students at the junior high school. The instrument was a test of mathematical communication skills on quadrilateral topics. The research method used was a mixed method with a sequential explanatory design. The data were analyzed using Mann-Whitney U to measure the difference between male and female students’ written mathematical communication skills, and document analysis was conducted to analyze their difficulties in performing written mathematical communication. The results showed that even though there is no significant difference between written mathematical communication skills between male and female students, there is a significant difference when viewed from each indicator.  In addition, the difficulties experienced by male and female students are difficulties expressing mathematical ideas using mathematical symbols, using facts and concepts to solve problems, and operating algebraic forms.
之前已经有一些关于男女学生书面沟通技巧差异的研究。然而,以往的研究主要集中在定性研究上。因此,该结果还缺乏实证证明。本研究旨在检验男女学生的书面数学沟通能力是否存在显著差异,并找出其表现困难。研究对象为14名男、14名女初中生。这个工具是对四边形题目的数学沟通技巧的测试。本研究采用序贯解释设计的混合方法。采用Mann-Whitney U对数据进行分析,衡量男女学生的书面数学沟通能力的差异,并采用文献分析法分析他们在进行书面数学沟通方面的困难。结果表明,尽管男女学生的书面数学沟通能力没有显著差异,但从各指标来看,男女学生的书面数学沟通能力存在显著差异。此外,男女学生遇到的困难是难以使用数学符号表达数学思想,难以使用事实和概念解决问题,难以操作代数形式。
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引用次数: 0
Learning obstacles analysis of lowest common multiple and greatest common factor in primary school 小学最低公倍数与最大公因数学习障碍分析
Pub Date : 2023-07-31 DOI: 10.29408/jel.v9i2.12359
Muhammad Rifqi Mahmud, T. Turmudi, W. Sopandi, S. Rohimah, I. M. Pratiwi
This research aims to find learning obstacles for students studying LCM and GCF as a reference in preparing teaching materials that can overcome these obstacles. This research involved 74 grade V students at three public schools in Bandung, Indonesia. The research method used in this study was case study research—data collection techniques using triangulation by providing tests, interviews, and documentation. Data analysis techniques use data collection, reduction, presentation, and conclusions. The results show three categories of learning obstacles: ontogenic, epistemological, and didactic. The ontogenic obstacle was found because the students understood multiples, factors, and arithmetic operations on natural numbers in solving LCM and GCF problems. Epistemological obstacles were discovered because of the limited context in which students understood the concepts of LCM and GCF, so they could not use them in contexts such as word problems. Didactical obstacles were found from learning that was given by the teacher procedurally using factoring methods, namely prime factorization or factor trees. Therefore, these obstacles must be anticipated by designing learning designs that can facilitate learning trajectories, focus on concepts, and make learning more meaningful.
本研究旨在发现学习LCM和GCF的学生的学习障碍,为编写能够克服这些障碍的教材提供参考。这项研究涉及印度尼西亚万隆三所公立学校的74名五年级学生。本研究使用的研究方法是案例研究研究数据收集技术,通过提供测试、访谈和文件。数据分析技术使用数据收集、简化、呈现和结论。结果显示学习障碍有三种类型:本体障碍、认识论障碍和教学障碍。在求解LCM和GCF问题时,学生理解了倍数、因子和自然数的算术运算,从而发现了本体障碍。由于学生理解LCM和GCF概念的语境有限,因此发现了认识论障碍,因此他们无法在诸如单词问题之类的语境中使用它们。在学习中发现了教学障碍,这些障碍是由老师程序性地使用因子分解方法,即质因数分解或因子树给出的。因此,必须通过设计学习设计来预测这些障碍,这些学习设计可以促进学习轨迹,关注概念,使学习更有意义。
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引用次数: 0
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Jurnal Elemen
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