Mathematical Comprehension Research Articles

Development of a rigorous mathematical thinking-based textbook in the house of worship context to enhance conceptual understanding

Background: This research develops a foundational mathematics textbook for PGMI students based on the Rigorous Mathematical Thinking (RMT) framework, contextualized within houses of worship to foster deeper understanding of mathematical concepts.Aim: The study aims to design and evaluate the feasibility and effectiveness of the textbook while gauging students’ responses and performance improvements.Method: Using a research and development (R&D) model, this study validated the textbook through expert reviews and tested its practicality and effectiveness in small-scale and broader applications. Data were obtained through a combination of observations, interviews, surveys, and tests measuring students' conceptual comprehension. Statistical evaluations, including descriptive analysis and t-tests, were employed.Results: The textbook received validation from subject matter, presentation, and language experts, who confirmed its content and structural accuracy. Trial phases categorized the textbook as highly practical, while broader field testing indicated that students using the textbook demonstrated significantly greater improvement in conceptual understanding compared to those without it.Conclusion: The RMT-based textbook aligns with its intended objectives and provides a contextually appropriate tool for improving mathematical comprehension. These findings highlight its potential as an effective resource for mathematics learning in PGMI contexts.

Analysis of mathematical concept comprehension ability in slow learners students

Mathematical comprehension is a fundamental skill that plays a crucial role in understanding and solving problems across various mathematical topics. This study aims to analyze the mathematical comprehension abilities of slow learners in the SPLDV (Two-Variable Linear Equation System) material. A descriptive qualitative approach was employed in this study. The subjects consisted of 20 slow learners in grade VIII of SMPIT in Sukabumi Regency. Data were collected through written tests and interviews, and analyzed using data reduction, data presentation, and conclusion drawing techniques. The results indicate that students with low comprehension skills have not fully mastered the SPLDV material and can only answer questions at levels 1, 2, and 3 but do not fully meet the indicators. Students with medium comprehension skills are able to answer questions at levels 1 and 2 according to the indicators. Meanwhile, students with high comprehension skills can answer questions at levels 1, 2, and 3 while meeting the indicators. The analysis of answers and interview data reveals that students in the low, medium, and high comprehension categories demonstrate distinct indicators of mathematical comprehension ability. In conclusion, slow learners exhibit varied levels of mathematical comprehension, highlighting the need for differentiated teaching strategies to address their specific needs and enhance their understanding of SPLDV concepts.

CONCEPT IMAGE AND CONCEPT DEFINITION SCHEMES AS TOOLS FOR ANALYZING STUDENTS’ COMPREHENSION OF LIMIT OF A FUNCTION

This paper aims to analyze one’s understanding of limit of a function based on Concept Image and Concept Definition schemes, which can be used as powerful tools in research that have mathematical comprehension as part of their object of study. For that, we developed and applied a set of tasks involving limits of functions to students who had already been in a Calculus course. Vinner’s study about concept image and concept definition was the theoretical framework of this paper. The results obtained let us observe the plurality of interpretations about limits and other adjacent concepts, which allowed us to trace, in this paper, a reflection upon the cognitive conflicts concerning the (lack of) understanding of these concepts.

Structural-mathematical thinking and its development in teaching Mathematics

Abstract The paper highlights the content and components of structural-mathematical thinking, substantiates its classification basis and establishes typological characteristics. In the conceptual-categorical section of the present study, structural-mathematical thinking is introduced as a form of theoretical thinking that embodies the specifics of mathematical comprehension of reality. The content as well as structural and functional characteristics of the phenomenon under study represent the content and components of the mathematical structure. Hence, the adherence to the deductive nature of Mathematics was ensured in the study, also emphasizing the phenomenological characteristic of structural-mathematical thinking regarded as the ability to reflect reality in accordance with the content components of the mathematical structure. Taking into account the theoretical advances, using the system approach and the modeling method, a model of developmental-conceptual teaching of Mathematics was elaborated. By considering the theoretical advancements and applying both a systemic approach and modeling method, a model for instructing Mathematics in a developmental-conceptual approach was elaborated, which represents a problem-based approach and develops students’ structural-mathematical thinking. The crux of teaching Mathematics through a developmental and conceptual approach lies in creating a framework that addresses the three-fold challenge of problem-solving ↔ competency-building ↔ problem-solving proficiency. Taking into account the addressed issue, the paper elicits the outcomes of a pilot study how structural-mathematical thinking is manifested by the would-be teachers of Mathematics. Furthermore, the efficacy of the authors’ approach to its enhancement is experimentally validated.

Effects of Geogebra use on the Academic Performance of Students in Mathematics in Public Secondary Schools in Rwanda

This study examines the impact of GeoGebra, a dynamic mathematics software, on the academic performance of students in mathematics at a public secondary school in Nyaruguru District, Rwanda. Specifically, it explores GeoGebra’s use in mathematics, its effects on student performance, and the correlation between its usage and academic outcomes. A sample of 7,916 participants was surveyed, including 69 math teachers, 309 students, and three headteachers. Data were collected through questionnaires, interviews, and observations, using purposive, stratified, and simple random sampling. The study revealed that 87.4% of participants agreed that GeoGebra enhanced students’ mathematical problem-solving abilities, while 94.1% agreed that it improved class participation. Additionally, 89.9% noted improvement in mathematics exam and test performance, with 91.3% observing better homework completion rates. GeoGebra use correlated with higher test scores and increased engagement in mathematical analysis, including trigonometry, transformations, and equation-solving. Although correlations with some outcomes were statistically minor (p > 0.05), the tool consistently supported mathematical independence and exploration. GeoGebra’s interactive features, including graphs, charts, and 3D models, facilitate students’ understanding of complex concepts, fostering improved memory and problem-solving skills. It enables collaborative learning, which promotes critical thinking, and highlights real-world applications of mathematics, increasing engagement. Personalized feedback features allow students to progress at their own pace, suggesting GeoGebra as an effective tool for enhancing mathematical comprehension and performance in secondary education.

Leveraging ChatGPT for Scoring Students' Subjective Tests

Assessing students' understanding of circle-related material through subjective tests is effective, though grading these tests can be challenging and often requires technological support. ChatGPT has shown promise in providing reliable and objective evaluations. Many teachers in Indonesia, however, continue to face difficulties integrating technology into assessments, highlighting the need for research on leveraging ChatGPT for scoring subjective tests. This study explores the potential of ChatGPT in mathematics education, specifically for evaluating students’ answers on subjective tests related to circles. Using a qualitative case study approach, the research investigates how ChatGPT analyzes student responses. The findings reveal that ChatGPT effectively processes the answers of 15 vocational school students, delivering results that are logical and well-structured. ChatGPT aids teachers by offering a comprehensive evaluation focused on accuracy, clarity, completeness, and technical terminology. This approach supports effective feedback and objective assessment, making ChatGPT a valuable tool for understanding and addressing students' mathematical comprehension issues.

Peran Orang Tua Dalam Mendukung Pembelajaran Matematika di Rumah Bagi Siswa Sekolah Dasar

This study aims to understand the critical role of parents in supporting children's mathematics learning at the elementary school level. In this context, the research employs a qualitative approach with a case study design to explore parental involvement in facilitating mathematics comprehension at home and collaboration with teachers. Data were collected through in-depth interviews, participatory observations, and document analysis of ten purposively selected families. The results indicate that effective communication between parents and teachers, as well as the support provided at home, plays a significant role in enhancing children's understanding and motivation in learning mathematics. Parents who are actively involved in their children's learning, both through direct interaction with teachers and by facilitating learning activities at home, are proven to help children overcome challenges in learning mathematics. The study also emphasizes the importance of consistent collaboration between home and school to create a supportive learning environment. The implications of this study suggest that active parental involvement and collaboration with teachers are crucial for achieving optimal mathematics learning outcomes.

The Effect Of Multy Reprecentacy Discourse Learning Assisted By Liveworksheet On Students' Mathematical Comprehension Ability

The discourse multy reprecentacy (DMR) model is one of the models that are able to improve students' mathematical understanding by collaborating in groups in class and using the Liveworksheet application. This study aims to determine the influence of students' mathematical knowledge after verifying the DMR model with the Liveworksheet application. This study uses a quantitative approach. Using a sample of grade VII students at SMPN 1 Cikeusik, class VIIA as an experimental class and VIIB as a control class were taken using a purposive sampling technique. The data collection techniques used in this study are observation and tests. This study uses statistical data analysis, but previously, a prerequisite test was carried out to conduct data analysis with parametric statistics using the polled variance formula. Based on the research, it can be concluded that the influence of the DMR model with the Liveworksheet application on the mathematical comprehension ability of junior high school students. Keywords: Multy Reprecentacy Discourse Model; Liveworksheet app; Understanding Mathematics

Augmented Reality for Mathematics Learning: A Study for Enhancing Mathematical Comprehension in High School Students

Numerous initiatives have sought to incorporate novel learning environments or technology, including Augmented Reality, into delivering more comprehensive education. But it's crucial to look at how this technology or settings impact different types of students. Research purposes: the main purposes of this study are the degree to which students are receptive to adopting augmented reality software as a learning tool and the effectiveness of such software in improving students' comprehension of probability and statistics in junior high school. Seventy-seventh graders from Purwokerto City, Indonesia's junior highs bordering urban and rural areas, participated. Research methods: two groups of students could be selected: one for the experiment and another for control purposes. In contrast to the control group, who stuck with tried-and-true teaching techniques, the experimental group conducted additional exploration of probability concepts either alone or in small groups using custom-built augmented reality software. While the control group continued to use more traditional methods of education, the experimental group utilised custom-built augmented reality software to explore probability concepts further, either individually or in small groups. All three courses met for a total of sixty-two days. Research results: The findings from the study showed that students' grasp of mathematical ideas can be improved by around 25.6% with the help of augmented reality learning apps. Furthermore, we analyse the differences in student learning and inquiry behaviours between two experimental conditions that differ in the complexity of augmented reality information. Furthermore, the results of the attitude questionnaire and the open-ended questions (5 items questions) corroborate the students' good opinions towards applications. However, in the future, researchers may look at how augmented reality affects students' more subjective characteristics, such as learning anxiety, and broaden the demographic of those who use these apps.

Discovering Ethnomathematics in Sundanese Gamelan: Explore Mathematics Aspect in Gamelan

Ethnomathematics is important in recent decades, specifically in the production of gamelan instruments. Therefore, this research aimed to examine the intricate relationship between mathematics and cultural craftsmanship in Sundanese gamelan instruments made at Gong Factory in Bogor, West Java. Ethnographic methods were used to observe and describe the practices of gamelan craftsmen and the data collection process comprised carefully selected artists. These individuals actively acquire data by reviewing relevant material, observing, analyzing, and interviewing. Miles and Huberman's framework for data analysis included data reduction, presentation, inference, and verification. The procedures understood the delicate relationship between mathematics and culture in the investigated setting. The results showed that Gong Factory in Bogor preserved and promoted a unique musical heritage. Furthermore, the instruments were known for exceptional sound quality, serving as cultural relics and didactic tools, as well as teaching visitors about the manufacturing process. The factory preserved culture through the manufacture of gamelan instruments including gong, bonang, and saron. In this context, the craftsmanship used mathematical principles, specifically precise proportions and ratios. The instruments' visual and auditory qualities depended on geometry. The results significantly impacted mathematics education by enhancing cross-cultural connections, improving proportional reasoning and mathematical comprehension, and recognizing the wider relevance of principles. Culture, mathematics, and education were connected, showing that conserving Indonesian musical tradition benefited local and global populations.

Solving Intuitionistic Fuzzy Unconstrained Optimization Problems Using Interval Newton’s Method

This research work studies the optimization of intuitionistic fuzzy valued functions in unconstrained problems. The Interval Newton's Method using an Intuitionistic approach addresses both single and multivariable optimization problems. The study incorporates a mathematical comprehension of interval intuitionistic fuzzy valued problems, as well as real-world examples to demonstrate their effectiveness. Furthermore, MATLAB code is provided to demonstrate the implementation of the Interval Newton's Method.

Innovative Strategies in Math Education: The Impact of PBL and TaRL on Concept Mastery and Classroom Dynamics

In scrutinizing the amalgamation of Problem-Based Learning (PBL) and Teaching at the Right Level (TaRL) approach within mathematics pedagogy, extant scholarship scarcely offers a holistic evaluation of their synergistic efficacy. Prior research predominantly accentuates scholastic outcomes, frequently neglecting the ramifications of these models on classroom dynamics, including the nuances of student-teacher interactions and student engagement and participation levels. This study probes the integration of PBL and TaRL models to augment students' comprehension of mathematical principles, employing a mixed-methods research design encompassing qualitative and quantitative methodologies. The investigation centered on seventh-grade students in junior high school, utilizing test instruments to evaluate mathematical comprehension and observational protocols to document student and teacher engagement for enriched insights. Comprehensive qualitative and quantitative data analyses were executed. The findings disclosed significant advancements in students' grasp of mathematical concepts, with observations revealing heightened student engagement and more favorable teacher-student interactions. Statistical analyses evidenced substantial disparities between pre-test and post-test scores (p < 0.05). The results proffer recommendations and pragmatic implications for enhancing mathematics education, underscoring the imperative for teacher professional development in deploying this integrative pedagogical model to elevate the quality of mathematics instruction at the secondary school echelon.

Assessment of Executive Function Skills in Children with Isolated Growth Hormone Deficiency: A Cross-sectional Study

The aim of this study was to evaluate executive function (EF), such as inhibition and working memory, in children with isolated growth hormone deficiency (IGHD) using performance-based tests and parent-report scales. A total of seventy children between the ages of 7 and 12 years were included in the study. Half (n=35) had children with IGHD and half were healthy controls. To evaluate the EF performances of the participants, the Visual Aural Digit Span Test-B Form (VADS-B) and Stroop task were applied. EF was also evaluated using the Behavior Rating Inventory of Executive Function (BRIEF). Children with IGHD scored lower on the VADS-B form for short-term memory (p<0.05) compared to healthy controls. In addition, the completion time for the Stroop-color/word test was significantly longer in children with IGHD (p<0.05). For children with IGHD, their parents reported higher scores on all sub-scales of the BRIEF scale, with statistically significant differences for all sub-scales with the exception of “organization of materials” (p<0.05). In this study, children with IGHD had poorer EF skills compared to unaffected peers. EF skills may influence academic success by affecting children’s language skills, mathematical comprehension, cognitive flexibility, and hypothetical thinking. We believe that psychiatric evaluation of children with IGHD before and during treatment may positively contribute to both their academic performance and social relationships.

Layers of Student Understanding Based on Pirie Kieren's theory in Solving Story Problems in Terms of Cognitive Style

Objective: Understanding lines and angles serves as the foundation for further mathematical topics such as trigonometry, geometry, calculus, etc. Students may struggle with advanced mathematical reasoning and problem-solving without a firm grasp of these basic concepts. This study aims to investigate how students' mathematical understanding processes are based on the folding back theory. Method: The research utilizes a qualitative approach with descriptive eksploratif design. Two subjects were selected from 28 seventh-grade students, each representing the field-dependent and field-independent cognitive style. Data was collected through mathematical comprehension tests, GEFT tests, and interviews. Data were analyzed through data reduction, data presentation, and verification stages, with each subject being interviewed to verify the processes. Results: Based on the research results, students in the field-independent cognitive style were much more active and better understood the problem-solving process than those in the field-dependent. However, both subjects still required learning assistance. Novelty: This research explores the folding back theory in the mathematical understanding process based on cognitive styles, whereas previous studies have mainly focused on mathematical comprehension abilities. Therefore, further research would benefit from using instructional media to better engage students in understanding the material.

The Effect of Motivation and Interaction Effects on Improving Mathematical Comprehension Skills through Problem and Inquiry-Based Learning

This study investigates the influence of motivation levels and interaction effects on students' Mathematical Comprehension Ability (KPM) while utilizing Problem-Based Learning (PBL) and Inquiry-Based Learning (IBL). Employing a quasi-experimental with the 3x2 factorial design, the research was conducted with fourth-grade students in Ciamis Regency, West Java. The findings indicated that the average KPM increase for students using PBL was 53%, which is considered moderate, whereas for IBL, it was 29%, which is categorized as low. Significantly, there were variations in learning effects between PBL and IBL (p 0.001), with PBL demonstrating a more pronounced impact on KPM improvement. However, the influence of motivation level on KPM improvement was deemed insignificant (p = 0.192), as was the interaction effect between learning methods and motivation level on KPM improvement (p = 0.057). In conclusion, the study suggests that PBL is more effective than IBL in enhancing students' KPM. At the same time, motivation level does not significantly influence KPM improvement, and there is no interaction effect between the type of learning method and motivation level on KPM improvement.

Enhancing 8th grade students' mathematical understanding

The low mathematical comprehension among 8th-grade students at MTs Al-Hidayah Purwokerto was the driving force behind this research. Factors contributing to this low ability include the use of conventional learning media, which is less attractive to students, leading them to easily become bored and encountering greater difficulty in understanding lessons. Therefore, this study aimed to evaluate the efficacy of using educational game-based learning media to enhance students' mathematical understanding skills in 8th grade. An experimental approach was employed in this study, with a population consisting of 56 students from the 8th grade at MTs Al-Hidayah Purwokerto. Saturated sampling was conducted, encompassing all 8th-grade students as the research sample. Consequently, Class 8A, comprising 28 students, was designated as the experimental group, while Class 8B, with 28 students, served as the control group. The conclusive outcomes of the research indicate that the use of educational game-based media effectively improves students' mathematical understanding abilities. The N-Gain value for the experimental group is 0.83, which falls within the high category, whereas the N-Gain value for the control group is 0.37, categorized as medium. Thus, it can be inferred that educational game-based media is effective as a learning medium for 8th-grade mathematics material at MTs Al-Hidayah Purwokerto.

Study of Academic Achievement of Mathematics Subject in the Context of Study Habits of Students

Students have different study habits from one another and from location to location. It is a crucial component of education since students' study practices have a big effect on their achievement in academics. Parents, educators, administrators, and members of the public are increasingly concerned about the poor level of mathematical comprehension in our country. Researchers and educators have worked very hard to determine the causes of the low performance in the subject. Despite all of these initiatives, the issues persist. Students' study habits are a powerful indicator of both their academic performance in mathematics and the quality of their education. It is unrealistic to expect students to acquire all there is to know about a subject from their teachers in the classroom; students' study habits are a combination of what they learn in and outside of the classroom. Sorenson (1991) listed several beneficial study habits, one of which is that the main goal of study should be understanding. One must focus on this for an extended period of time rather than rushing through. Effective study techniques, according to Crow &amp; Crow (1992), include setting up a specific workspace, creating a timetable, and taking concise, well-organized notes.

Mathematical argumentation of three-year-old children on a classroom experience based on two STEAM domains

In the last decades, the importance of argumentation as a human competence in general and its close relationship with mathematical comprehension in particular has been highlighted. Thus, in this paper we focus our interest on analyzing the argumentation skills shown by three-year-old children in a STEAM classroom experience. For this purpose, a qualitative study was carried out. For data collection, a STEAM task has been designed in which mathematics and science are worked together from the study of the physical properties of water. Specifically, what color and taste of water has by means of two experiments and, subsequently, photos and video-recordings have been collected during the implementation carried out in a classroom with 20 children of three-year-old. All data collect have subsequently been transcribed and categorized. The results indicate that the children, during the experiments done, mainly use arguments based on mathematical language, numerical figures, or make use of words or spelling, although with considerable imprecision in the type of language used. In addition, the experiments carried out have allowed a high percentage of children to change their previous ideas and have a more comprehensive approach to the concepts introduced, highlighting the importance of working on argumentation in early childhood education through contexts, in this case STEAM, which encourage reasoning and proof.

The negative theology of absolute infinity: Cantor, mathematics, and humility

Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate on absolute generality and argue that the method of diagonalization constitutes a modern version of the vianegativa. On our reading, negative theology can evoke an attitude of humility with respect to the boundedness of the human condition. Along these lines, we think that the foundational problem of mathematics concerning its domain can be addressed through a methodological attitude of humility.

A study of mathematical understanding levels in set theory based on the APOS framework by using python programming language for secondary school students

This study used the APOS theoretical framework to assess secondary school pupils’ set math knowledge. Princess Chulabhorn Science College Lopburi randomly sampled 20 8&lt;sup&gt;th&lt;/sup&gt; graders in the second semester of 2022. There are a total of six plans, with each plan comprising a 180-minute. The objectives are the instructional goals. Content is the topic. Learning materials include resources and tools. Last, activities include learning assignments and exercises. Assessment includes three subtests to assess set understanding and a test to assess mathematical comprehension. These activities increased secondary school students’ set comprehension. The result of the study indicated that they had demonstrated a strong&lt;b&gt; &lt;/b&gt;conceptual understanding of set theory to pass the criteria over 60% of the total students with a statistical significance level of .01. Furthermore, delving into all four APOS theoretical levels we found similar impressive results, with over 60% of students exceeding expectations at each level (p&amp;lt;0.01).