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Journey to the cosmos: Navigating stellar evolution with differential equations 宇宙之旅用微分方程导航恒星演化
Pub Date : 2023-12-31 DOI: 10.35316/alifmatika.2023.v5i2.282-297
Anshuman Jha, S. K. Sahani, Aditya Jha, K. Sahani
Differential equations are a fundamental and versatile mathematical tool that finds widespread application across diverse academic disciplines, from physics and biology to economics and engineering. The primary objectives of this report are to demonstrate the application of differential equations in stellar evolution, construct a mathematical model to demonstrate nuclear reactions in a star, and illustrate energy transport within a star. Triangulation was used to prepare this report, with literature studies being the primary method. This study includes several documents and field data analyzed using qualitative research. Through research and observations, two hypothetical case studies illustrate the indispensable application of differential equations in modeling energy transport and nuclear reactions within stars through which the value of luminosity was calculated in a particular star due to both radiative energy transport and convective energy transport while in another star, the helium abundance in the core was estimated to approach a value of 1.195*1077. These differential equations are not only limited to the growth of a lead but also have broader applications that are essential for understanding the chemical composition of the universe and its prolonged evolution. The report also underscores the enduring importance of differential equations in advancing our understanding of the cosmos and their vital role in space exploration and technological innovations.
微分方程是一种基础性的多功能数学工具,广泛应用于从物理学、生物学到经济学和工程学等不同学科。本报告的主要目的是展示微分方程在恒星演化中的应用,构建一个数学模型来展示恒星中的核反应,并说明恒星内部的能量传输。编写本报告时采用了三角测量法,其中文献研究是主要方法。本研究包括采用定性研究方法分析的若干文献和实地数据。通过研究和观察,两个假定案例研究说明了微分方程在恒星内部能量传输和核反应建模中不可或缺的应用,通过这两个案例研究,计算出了某颗恒星由于辐射能量传输和对流能量传输而产生的光度值,而在另一颗恒星中,内核中的氦丰度估计值接近 1.195*1077。这些微分方程不仅局限于铅的增长,还具有更广泛的应用,对于了解宇宙的化学成分及其长期演化至关重要。报告还强调了微分方程在推动我们了解宇宙方面的持久重要性及其在太空探索和技术创新中的重要作用。
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引用次数: 0
Mathematical Olympiad issues to identify students' reasoning ability using Polya's model 利用波利亚模型确定学生推理能力的数学奥林匹克问题
Pub Date : 2023-12-31 DOI: 10.35316/alifmatika.2023.v5i2.264-281
Mohammad Tohir, Muhasshanah Muhasshanah, Riyan Hidayat, Erik Valentino, Tommy Tanu Wijaya
This research aims to describe the level of mathematical reasoning ability of students in solving mathematical Olympiad problems based on problem-solving of the Polya model. This study employed descriptive analysis with a qualitative approach. Data were collected by using observation, documentation, and interviews. The study subjects were 27 junior high school students participating in the National Science Competition in Indonesia. Meanwhile, the Miles and Huberman analysis model was used as the data analysis. The results of this study indicated that: (1) the level of students’ mathematical reasoning-ability based on the problem-solving of Polya models in the category of "sufficiently competent" (high-group students), in the category of "less competent" (medium-group students), and in the category of "incompetent" (low-group students); (2) the most complex and rarely performed stages by students in Polya’s model were at the "devising a plan" and "looking back" stages; and (3) the Polya's model used in solving mathematical Olympiad test items was more suitable for those considered as routine-questions, and it was not suitable for non-routine questions. This study also showed that, on average, the students had difficulty finding initial ideas to start working on the test items.
本研究旨在描述学生在解决基于波利亚模型的数学奥林匹克问题时的数学推理能力水平。本研究采用定性描述分析法。通过观察、记录和访谈收集数据。研究对象是参加印度尼西亚全国科学竞赛的 27 名初中生。同时,采用迈尔斯和休伯曼分析模型进行数据分析。研究结果表明(1) 学生基于 Polya 模型解决问题的数学推理能力水平分为 "足够胜任 "类(高分组学生)、"不太胜任 "类(中分组学生)和 "不胜任 "类(低分组学生);(2) 在波利亚模型中,学生最复杂、最少完成的阶段是 "制定计划 "和 "回顾 "阶段; (3) 在解决数学奥林匹克测试题目时使用的波利亚模型更适合于那些被认为是常规性的题目,而不适合于非常规性的题目。这项研究还表明,平均而言,学生很难找到开始解题的初步思路。
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引用次数: 0
Computational thinking ability becomes a predictor of mathematical critical thinking ability 计算思维能力成为数学批判性思维能力的预测指标
Pub Date : 2023-12-31 DOI: 10.35316/alifmatika.2023.v5i2.247-263
Sekar Rani Candraningtyas, H. Khusna
This research aims to determine the relationship between computational thinking ability and mathematical critical thinking ability of seventh-grade students at SMPN 49 Jakarta. Computational thinking ability is skills or processes in solving problems effectively, while mathematical critical thinking ability is a process of analyzing problems to make an accurate decision. This research used correlation research with research subjects consisting of 14 female students and 16 male students. The instrument in this study is a test in the form of a description, which is measured using indicators. This study used decomposition, pattern recognition, abstraction, and algorithm thinking as indicators of computational thinking ability. This study uses elementary clarification, essential support, inference, advanced clarification, strategy, and tactics as indicators of mathematical critical thinking. The outcome of this research showed a positive correlation between computational thinking ability and students’ mathematical critical thinking ability. The relationship analysis shows a simultaneous and significant relationship between computational thinking and essential mathematical thinking abilities. The correlation test results using Pearson Product Moment obtained a result of 0.897 with a coefficient of determination of 80.5%. The magnitude of the correlation indicates that the two abilities have a solid relationship. If computational thinking ability is high, then mathematical critical thinking ability is also high, and if computational thinking ability is low, then mathematical critical thinking ability is also low.
本研究旨在确定雅加达第四十九中学七年级学生的计算思维能力与数学批判性思维能力之间的关系。计算思维能力是有效解决问题的技能或过程,而数学批判性思维能力是分析问题以做出准确决策的过程。本研究采用相关研究法,研究对象包括 14 名女生和 16 名男生。本研究的工具是描述形式的测试,使用指标进行测量。本研究将分解、模式识别、抽象和算法思维作为计算思维能力的指标。本研究将初级澄清、基本支持、推理、高级澄清、策略和战术作为数学批判性思维的指标。研究结果表明,计算思维能力与学生的数学批判性思维能力呈正相关。关系分析表明,计算思维能力与基本数学思维能力之间同时存在显著关系。利用皮尔逊乘积矩进行的相关检验结果为 0.897,决定系数为 80.5%。相关性的大小表明,这两种能力之间有着稳固的关系。如果计算思维能力高,则数学批判性思维能力也高,如果计算思维能力低,则数学批判性思维能力也低。
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引用次数: 0
Students' analysis literacy and numeracy in linear algebra: A comparison across personality types 学生在线性代数中的分析素养和计算能力:不同人格类型的比较
Pub Date : 2023-12-31 DOI: 10.35316/alifmatika.2023.v5i2.311-327
Wulandari Wulandari, Aklimawati Aklimawati, Erna Isfayani, Cut Morina Zubainur, E. Elizar, Yeni Listiana
The imperative drives this research endeavour for educators to comprehend the diverse personality types exhibited by students. It is crucial as each personality type encompasses unique strengths and weaknesses that influence cognitive processes, decision-making, literacy, and numeracy skills. The primary objective of this study is to assess the literacy and numeracy skills of students categorized into sanguine, melancholic, choleric, and phlegmatic personality types within the context of Linear Algebra courses. Employing a descriptive research design with a qualitative approach, the subjects of this investigation comprised 47 students enrolled in the Education Mathematics Major at Malikussaleh University: the research employed personality type tests, literacy and numeracy tests, and interviews as the assessment instruments. The data analysis techniques followed the framework proposed by Miles and Huberman that involved stages such as data collection (including students' personality and literacy numeracy test results), data reduction (highlighting key elements), data presentation (displaying test and interview data), and concluding. The findings revealed that (1) 8 individuals (17.02%) exhibited a choleric personality type, eight individuals (17.02%) demonstrated a melancholic personality type, 16 individuals (34.05%) displayed a phlegmatic personality type, and 15 individuals (31.91%) manifested a sanguine personality type; (2) students' literacy and numeracy skills averaged 78.6%, falling into the high category; (3) The phlegmatic personality type exhibited the lowest literacy and numeracy ability, while the sanguine personality type demonstrated the highest literacy and numeracy ability. Consequently, this underscores the importance of students leveraging their strengths and addressing the weaknesses associated with their respective personality types to refine their literacy and numeracy skills.
当务之急是促使教育工作者努力了解学生表现出的不同人格类型。这一点至关重要,因为每种人格类型都有其独特的优点和缺点,这些优点和缺点会影响认知过程、决策、读写和计算能力。本研究的主要目的是在线性代数课程的背景下,评估被分为血型、忧郁型、胆汁质和痰质人格类型的学生的读写和计算能力。本研究采用描述性研究设计和定性研究方法,调查对象包括马里库萨雷大学教育数学专业的 47 名学生:研究采用人格类型测试、读写能力和计算能力测试以及访谈作为评估工具。数据分析技术遵循迈尔斯和休伯曼提出的框架,包括数据收集(包括学生的人格和读写算测试结果)、数据缩减(突出关键要素)、数据展示(展示测试和访谈数据)和总结等阶段。研究结果显示:(1) 8 人(17.02%)表现为胆汁质人格类型,8 人(17.02%)表现为忧郁质人格类型,16 人(34.05%)表现为痰质人格类型,15 人(31.91%)表现为阴郁质人格类型。(2)学生的识字和计算能力平均为 78.6%,属于较高类型;(3)痰型人格的学生识字和计算能力最低,而阴型人格的学生识字和计算能力最高。因此,这强调了学生利用自身的优势和解决与各自人格类型相关的弱点来提高识字和计算能力的重要性。
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引用次数: 0
Development of numeracy skills: Analysis of students in junior high schools in Ambon City based on teacher's perspective 发展计算技能:基于教师视角的安汶市初中学生分析
Pub Date : 2023-12-31 DOI: 10.35316/alifmatika.2023.v5i2.298-310
Jurnal Pendidikan, dan Pembelajaran Matematika, R. H. Y. Silitonga
Numeration is important as it is a fundamental skill, but based on the evaluation of the Programme for International Student Assessment, showed that the student's numeration ability is still low. This study aims to analyze the various problems that occur in the development of numeration skills of high school students. The research was carried out at the Catholic High School in Ambon, with the subject of the research being teachers of mathematics and non-mathematics. This research is qualitative research using methods of narrative inquiry. Data collection techniques include questionnaires, interviews, and recording and documentation. The results of this research indicate that there are a number of issues with developing numeracy skills, one of which is the lack of implementation of classic game-based learning strategies. School facilities are inadequate to encourage increased student numeracy. The implementation of training for teachers to improve teacher numeracy is still rare, so it affects the lack of innovation of teachers in teaching by applying games as well as traditional games to improve numeracy.
计算是一项重要的基本技能,但根据国际学生评估项目的评估结果显示,学生的计算能力仍然较低。本研究旨在分析高中生在发展计算能力过程中出现的各种问题。研究在安汶天主教高中进行,研究对象是数学教师和非数学教师。本研究采用叙事探究的方法进行定性研究。数据收集技术包括问卷调查、访谈、记录和文献。研究结果表明,在培养计算能力方面存在一些问题,其中之一就是缺乏经典的游戏式学习策略。学校设施不足以鼓励提高学生的计算能力。为提高教师计算能力而开展的教师培训仍然很少,因此影响了教师在应用游戏以及传统游戏提高计算能力的教学中缺乏创新。
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引用次数: 0
Developing smart fractions as a learning media assisted by ispring suite 9 and geogebra for escalating students’ computational thinking skills 利用 ispring suite 9 和 geogebra 开发智能分数作为学习媒体,提高学生的计算思维能力
Pub Date : 2023-12-15 DOI: 10.35316/alifmatika.2023.v5i2.188-206
Rafiantika Megahnia Prihandini, D. Dafik, Dahri Novan Uji Iskandar
In the era of the Industrial Revolution 4.0, learning mathematics puts more demands on students’ computational thinking skills. This research responds to this challenge by developing learning media assisted by iSpring Suite 9 and GeoGebra Software, known as the Smart Fractions. This development method employed Borg and Gall’s ten-stage method. These stages included preliminary research, product planning and development, preliminary product design, product validation, preliminary product revision, user trial, product revision, effectiveness tests, final product and mass production, and product dissemination and implementation. The research data corroborated the validity, effectiveness, and practicality of the Smart Fractions interactive learning media. Media experts, material and learning experts, and students as users have acknowledged these properties. A validity test demonstrated a value of V_a = 3.53, which implied a decent extent of validity. The practicality test through questionnaire and observation generated a practicality score of 86.67%, another decent product property. The product's effectiveness was tested by assessing students’ learning outcomes, which indicated an N-Gain score of 0.8. This inferred a noteworthy increase in computational thinking skills after implementing learning media. A t-test (2-tailed) also confirmed a significant difference in students' computational thinking skills before and after using learning media, as indicated by p = 0.000. The findings have concluded that Smart Fractions is a highly appropriate learning medium to improve students' computational thinking skills and help them visually understand fractions. The recommendation is to encourage students to use the learning media with the aid of manuals and tutorials on using the media. Teachers are also advised to combine the media with appropriate models, methods, strategies, and approaches.
在工业革命 4.0 时代,数学学习对学生的计算思维能力提出了更高的要求。为应对这一挑战,本研究开发了由 iSpring Suite 9 和 GeoGebra 软件辅助的学习媒体,即智能分数。这种开发方法采用了 Borg 和 Gall 的十阶段法。这些阶段包括初步研究、产品规划和开发、产品初步设计、产品验证、产品初步修订、用户试用、产品修订、效果测试、最终产品和批量生产,以及产品推广和实施。研究数据证实了智能分数互动学习媒体的有效性、有效性和实用性。媒体专家、教材和学习专家以及作为用户的学生都认可了这些特性。效度测试表明,V_a=3.53,这意味着效度相当高。通过问卷调查和观察进行的实用性测试得出的实用性得分为 86.67%,这是另一个不错的产品特性。通过评估学生的学习成果检验了产品的有效性,结果显示 N-Gain 得分为 0.8。这推断出在使用学习媒体后,学生的计算思维能力有了显著提高。t检验(双尾)也证实,使用学习媒体前后,学生的计算思维能力有显著差异,P = 0.000。研究结果认为,"智能分数 "是一种非常适合提高学生计算思维能力和帮助他们直观理解分数的学习媒体。我们的建议是鼓励学生使用学习媒体,并提供使用手册和指导。还建议教师将媒体与适当的模型、方法、策略和途径相结合。
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引用次数: 0
Cohen's kappa curves, new geometrical forms of dual curves 科恩卡帕曲线,对偶曲线的新几何形式
Pub Date : 2023-12-15 DOI: 10.35316/alifmatika.2023.v5i2.226-246
Laith H. M. Al-ossmi, Imad Ibrahim Dawood
In this article, we introduce the concepts of taxicab and uniform products in the context of dual curves associated with Cohen's kappa, primarily defined by a set of inflection curvatures of an ellipse and a circle using parallel asymptotes. The novel curve under scrutiny, denominated as the "Like-Bulb Filament" (LBF) curve, is delineated as the locus of dual vertices originating from a couple of conic curvatures. The emergence of LBF transpires through the orchestrated arrangement of line segments emanating from a predetermined central focal point upon an elliptical form concomitant with a circular entity possessing a radius equivalent to the ellipse's minor axis. The LBF’s curve is intricately choreographed through the dynamic interplay of a constant unit circle and three asymptotic lines. Notably, two of these asymptotes achieve tangential intersections with the LBF curve, while the third gracefully traverses its central core. Additionally, we embark on a comprehensive algebraic examination complemented by a geometrically informed construction methodology. In these instances, a consistent conic curvature of the uint circle and an elliptical structure assume pivotal roles in the genesis of the LBF’s curve. Also, a geometric connection is speculated between these curve configurations and their relevance to engineering processes across fields. However, the document acknowledges the need for more intensive study on the presented traits. Hence, it emphasizes addressing the existing research gap in subsequent investigations.
在这篇文章中,我们结合与科恩卡帕相关的对偶曲线,介绍了出租车和均匀积的概念,这些对偶曲线主要由椭圆和圆的一组拐点曲率利用平行渐近线定义。我们所研究的新曲线被称为 "Like-Bulb Filament"(LBF)曲线,它被划定为源自几个圆锥曲线的对偶顶点的位置。LBF 的出现是通过精心安排的线段,这些线段从一个预定的中心焦点发散到一个椭圆形上,并与一个半径相当于椭圆小轴的圆形实体相连接。通过一个恒定的单位圆和三条渐近线的动态相互作用,LBF 的曲线变得错综复杂。值得注意的是,其中两条渐近线与枸杞弧曲线相切,而第三条渐近线则优雅地穿过枸杞弧的中心核心。此外,我们还对这些渐近线进行了全面的代数研究,并辅以几何构造方法。在这些情况下,uint 圆的圆锥曲率和椭圆结构在枸杞曲线的形成过程中发挥了关键作用。此外,还推测了这些曲线构型之间的几何联系,以及它们与各领域工程过程的相关性。不过,该文件承认有必要对所提出的特征进行更深入的研究。因此,文件强调在后续研究中解决现有的研究空白。
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引用次数: 0
Development of soft skill-based interactive media on thematic learning 开发基于软技能的专题学习互动媒体
Pub Date : 2023-12-15 DOI: 10.35316/alifmatika.2023.v5i2.156-170
Urip Umayah, Gigih Winandika, Defry Azhari, Delly Nofiani
An interactive learning strategy was a method or technique the teacher used when presenting learning materials where the teacher became the main actor in creating an educative interactive situation. The objective of this study was to create interactive media for theme learning that focuses on the development of soft skills and to evaluate its quality and usefulness. This study used Borg and Gall's Research and Development (R&D) approach, with four parsimonious stages of development: analysis, design, development, and implementation. This research used observation and interview sheets as data collection methods. The assessment of the interactive media's validity, quality, and efficacy based on soft skills was conducted through instrument and product validation methods involving media specialists and reviews from instructors and students. The study showed that students and teachers rated interactive learning media based on soft skills in the high-quality category. In addition, soft skill-based learning media was considered effective in fulfilling the criteria for assessing teacher activity in learning media, namely in the very effective category. It was concluded that the soft skill-based interactive learning media developed in this study were valid, high quality, and effective, so they were suitable for use in Penggalang 4 public elementary schools. We recommend that schools implement interactive media based on soft skills so that students become active and critical learners. Future research can adapt our model to other educational levels or domains, such as employee business development.
互动学习策略是教师在展示学习材料时使用的一种方法或技巧,在这种方法或技巧中,教师成为创造教育互动情境的主要行为者。本研究的目的是为主题学习创建互动媒体,重点培养学生的软技能,并评估其质量和实用性。本研究采用了博格和加尔的研究与开发(R&D)方法,包括四个发展阶段:分析、设计、开发和实施。本研究采用观察和访谈表作为数据收集方法。通过有媒体专家参与的工具和产品验证方法,以及教师和学生的评论,对互动媒体基于软技能的有效性、质量和功效进行了评估。研究结果表明,学生和教师对基于软技能的互动学习媒体的评价属于高质量类别。此外,基于软技能的学习媒体在满足学习媒体中教师活动的评估标准方面被认为是有效的,即属于非常有效类。结论是,本研究中开发的基于软技能的互动学习媒体是有效的、高质量的和有效的,因此适合在 Penggalang 4 所公立小学使用。我们建议学校实施基于软技能的互动媒体,使学生成为积极主动的批判性学习者。未来的研究可以将我们的模式调整到其他教育层次或领域,如员工业务发展。
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引用次数: 0
Ethnomathematics explorations on the concept of two-dimensional shape in “Tadulako Bulili” folk story 关于 "塔都拉科-布利里 "民间故事中二维形状概念的民族数学探索
Pub Date : 2023-12-15 DOI: 10.35316/alifmatika.2023.v5i2.171-187
Indah Suciati, Windra Windra, Al-Afandi Al-Afandi, Hajerina Hajerina, Siti Hadija Alaydrus
To explore the folklore of Tadulako Bulili as a literacy medium in learning the two-dimensional shape, a qualitative descriptive study was carried out with an ethnographic approach. Methods of observation, interviews, documentation, and literature studies were used to collect research data, which were analyzed using the Miles & Huberman interactive model. The subjects of this study were traditional leaders, 3rd-grade elementary school teachers, lecturers, and several students who lived in Sigi Regency. The findings show that Tadulako Bulili's folklore can be thematic contextual learning in two-dimensional material that supports Ausubel, Bruner, and Gagne's learning theory. The results found four fundamental mathematical activities: counting, locating, designing, and explaining. In addition, various two-dimensional shapes were found in the illustrations of objects in the story. The exploration results also provided knowledge and information on the mention of two-dimensional shapes in the Kaili language and replicas of objects that were thought to be found in the story. Folklore could also introduce students to the local wisdom of Central Sulawesi, such as traditional houses, traditional weapons, hunting and farming tools, and the stories themselves.
为了探索塔都拉科-布利里民俗作为学习二维图形的识字媒介,我们采用民族志方法开展了一项定性描述研究。研究采用观察、访谈、文献记录和文献研究等方法收集研究数据,并使用迈尔斯和休伯曼互动模型对数据进行分析。研究对象包括传统领袖、小学三年级教师、讲师和几名生活在西吉县的学生。研究结果表明,Tadulako Bulili 的民间传说可以成为二维材料中的主题情境学习,支持奥苏贝尔、布鲁纳和加涅的学习理论。研究结果发现了四种基本的数学活动:计数、定位、设计和解释。此外,在故事中的物体插图中还发现了各种二维形状。探索结果还提供了有关凯里语中提到的二维形状的知识和信息,以及认为在故事中发现的物体的复制品。民间传说还可以向学生介绍中苏拉威西的地方智慧,如传统房屋、传统武器、狩猎和农耕工具以及故事本身。
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引用次数: 0
Analysis of the problem-based learning (PBL) models on geometry material in improving students' mathematics learning outcomes 基于问题的学习(PBL)模式在几何教材中提高学生数学学习成绩的分析
Pub Date : 2023-12-15 DOI: 10.35316/alifmatika.2023.v5i2.207-225
Fathul Bhary, M. Maswar, Moh. Atikurrahman, Ahmad Afandi
This study aimed to describe the increase in students' learning outcomes of geometry material at MTs Nuris Jember used a problem-based learning model. This type of research was classroom action research with a model design consisting of four steps: planning, acting, observing, and reflecting. Data collection techniques used tests and observations. The instruments used essay questions and checklists of student activities in class. Thirty students of class VII at MTs Nuris Jember served as the subjects, and samples were collected using purposive random sampling. In this study, descriptive and inferential statistics were employed in the data analysis for this investigation. It could be seen from the research results that the initial condition of the average test score was 61.33, meaning that 30% of students had passed the learning in the pre-cycle. In standard Cycle I, the average test score was 66.83, and 47% of students had reached standard learning. In Cycle II, the average score of students' tests was 71.67, and 83% of students had reached the standard learning. The significance test results of the average value showed a significant difference in average test results between students' mathematics learning outcomes in Cycle I and Cycle II, with a significance value of 0.000, which is less than 0.05. Based on the observation result of students' activity in the second Cycle, the average observation result for students' activities was 79,45% in the good category and got an alphabet score of B.
本研究旨在利用基于问题的学习模式,描述 Nuris Jember 初级中学学生几何教材学习成绩的提高情况。这种研究属于课堂行动研究,其模式设计包括四个步骤:计划、行动、观察和反思。数据收集技术使用测试和观察。研究工具包括作文题和学生课堂活动检查表。研究对象为 Nuris Jember MTs 七年级的 30 名学生,采用有目的的随机抽样方法收集样本。本研究采用了描述性和推论性统计方法进行数据分析。从研究结果中可以看出,初始条件下的平均测试分数为 61.33 分,这意味着 30% 的学生通过了前周期的学习。在标准周期 I 中,测试平均分为 66.83 分,47% 的学生学习成绩达标。在标准周期 II 中,学生测试的平均得分为 71.67 分,83% 的学生达到了标准学习水平。平均值的显著性检验结果显示,第一周期和第二周期学生数学学习成绩的平均测试结果差异显著,显著性值为 0.000,小于 0.05。根据对第二周期学生活动的观察结果,学生活动的平均观察结果为 79.45%,属于良好类,字母得分为 B。
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引用次数: 0
期刊
Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika
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