Learning Of Mathematical Concepts Research Articles

Understanding The Concept Of Pythagoras In Junior High School Students Using PMRI

This research aims to determine students' conceptual understanding using the PMRI learning approach with the context of cotton rope in the Pythagorean theorem material on students' conceptual understanding in class VIII SMP NEGERI 2 Pagaralam. The obstacle faced by students in studying the Pythagorean Theorem is a lack of understanding of the basic concepts in the Pythagorean theorem material. One method that can strengthen understanding of concepts in learning mathematics is Indonesian Realistic Mathematics Education (PMRI). The research method used was experimental using a control group Pre-test - Post-test design. This research involved 2 classes, namely the experimental and control classes. Data collection techniques include observation and tests, the analysis techniques used are documentation, observation and tests. Based on test data analysis, the average student score in the experimental class was 78.8, while the control class had a score of 72.50. From the research results, students' conceptual understanding was found to be better using PMRI with comparison results in the experimental class being better than in the control class.

TRANSTORNOS ESPECÍFICOS DE APRENDIZAGEM: DISLEXIA, DISGRAFIA, DISORTOGRAFIA E DISCALCULIA EM FOCO

Educational legislation emphasizes the need to promote the full development of reading, writing and calculation skills, highlighting these skills as essential for the individual’s insertion and meaningful action in society. However, it is not uncommon for students to complete elementary school without mastering these essential skills for professional life. This article aims to investigate the difficulties faced by some students in the process of learning reading, writing and mathematical skills. Based on theoretical research, the article addresses Specific Functional Learning Disorders — Dyslexia, Dysgraphia, Dysorthography and Dyscalculia — as possible factors that negatively interfere with the academic development of these students. Presenting a theoretical foundation on the topic contributes to the review of pedagogical practice, suggesting the need for collective work in the search for resources and procedures that promote students’ proficiency both in reading and writing and in learning mathematical concepts and operations.

Finding an Effective Assessment Approach to Enhance the Teaching and Learning of Circle Geometry

Assessment is essential for teaching and learning mathematical concepts. Teachers’ and learners’ understanding of how assessment is to be conducted in mathematics classrooms will guide what is to be taught and learnt and how teaching and learning will be conducted. The researchers’ assertion is that circle geometry lessons require thinking-based instructions. This necessitates that an associated assessment approach that elicits learners’ thinking must be formulated. Circle geometry requires rigorous logical, creative, critical, and reflective thinking, thus an assessment approach that will nurture learners’ thinking is essential. This exploration was a qualitative case study, conducted at a high school in South Africa involving two groups of grade 11 mathematics learners; both the control group and the experimental group had 34 participants. Data were gathered through classroom observations, a standardised test, and activities/investigation tasks. APOS theory (actions, processes, objects, schemas) was adopted as the theoretical framework and also as data analysis tool and circle geometry lessons were carried out in a collaborative classroom setting. Circle geometry lessons were conducted in line with the four APOS mental conception levels to evoke participants’ thinking, namely action lesson, process lesson, object lesson, and schema lesson. This study ascertained that the interactive didactic assessment was appropriate, as it enhanced participants’ metacognitive development and participants’ conceptual understanding and mathematical reasoning skills were developed. The researchers, therefore, recommend that this formulated assessment approach be implemented for the teaching and learning of mathematics, especially circle geometry, in schools in South Africa.

Teaching mathematical concepts based on the principle of "Consistency in Explanation"

This paper explores the importance and methods of achieving "self-consistency" in the teaching of mathematical concepts. It first emphasizes the central role of mathematical concepts in learning mathematics and, through the example of teaching the eccentricity of an ellipse, points out the complexity of understanding mathematical concepts. Then, by exploring the history of "eccentricity," the paper demonstrates the human conventions and historical development behind mathematical concepts, highlighting the need for teachers to delve into the origins and meanings of concepts in their teaching. The paper proposes four strategies to achieve "self-consistency": sorting out the history of mathematical development, finding applications of mathematics in daily life, rebuilding connections between mathematical knowledge, and utilizing perspectives from other disciplines. Finally, the paper argues that "self-consistency" is not only a teaching method but also a teaching philosophy, aimed at helping students gain a deep understanding of mathematical concepts.

DUDA: a digital didactic learning unit based on educational escape rooms and multisensory learning activities for primary school children during COVID-19 lockdown

AbstractThe COVID-19 pandemic has accelerated digitization, access to IT resources, and digital inclusion in the Italian school system. This paper presents D-UDA (i.e., “unità didattica di apprendimento digitale”, in Italian), a digital didactic unit for learning mathematics concepts. The presented approach combines teaching methodologies and game-based activities (e.g., the escape room) with a multisensory approach to designing and developing digital and multimodal technologies. D-UDA is divided into two parts: the first part consists of logic puzzles that adhere to the guidelines set by INVALSI (the Italian Istituto Nazionale per la Valutazione del Sistema educativo di Istruzione e di formazione) for mathematics learning, while the second part involves a series of multisensory games designed to promote the development of transversal competencies, such as cooperation and engagement. Moreover, D-UDA encourages children to create their own adventure using the same tools employed by the designers to develop the experience. The children who participated in testing D-UDA in June 2020 were asked to complete usability questionnaires after the experience. Preliminary results indicate the effectiveness of the educational intervention presented, which integrates recent pedagogical theories and teaching methodologies with a multisensory perspective and a technological design.

DEVELOPMENTAL CURRICULUM AS A SOURCE OF LEARNING STRATEGIES IN THE FORMATION OF MATHEMATICAL CONCEPTS IN PRESCHOOL CHILDREN

The development curriculum was created as a supplement to the long-known teaching plan and program according to which educators are guided in planning teaching and the goals to be achieved. The work is based on the positive and necessary properties of compiling and using the curriculum within the planning of strategies for learning mathematical concepts in preschool children, as knowledge and skills that are difficult to master and present in a natural and spontaneous way.

Learning by Doing: Hands-on Activities for Learning Mathematical Concepts at ECE Level

This study was designed to examine the effects of hands-on activities on mathematical concepts at ECE level. The main objective of this study was to increase students’ understanding about early mathematical concepts through hands-on activities. Nursery class of Government Primary School Kotkay Puran Shangla KPK was selected for the study as a sample. The nature of the study demanded an experimental research design and one-group pre-test post-test design was used. The test was conducted before teaching through hands-on activities and after to see the effects. In 45 classes the treatment was completed. Pre-test and post-test were the same. The results of paired sample t-test provide evidence of significant differences which show that students’ learning of mathematical concepts was raised when taught through hands-on activities. This study recommends emphasizing the importance of hands-on activities while teaching at ECE level.

Onto-semiotic analysis of Colombian engineering students’ mathematical connections to problems-solving on vectors: A contribution to the natural and exact sciences

The mathematical connections Colombian engineering students activated when they solved vector problems were explored. The study was based on the extended theory of connections and the onto-semiotic approach. We followed a qualitative methodology that consisted of three stages: (1) selection of engineering students as participants; (2) application of a questionnaire with 15 tasks on vectors to the participating students; and (3) analysis of these data based on the theoretical articulation. The results show that students perform arithmetic operations with vectors, find the scalar and vector product, the norm of a vector, the angle between vectors, and unit vector based on mathematical connections (<i>procedural, meaning, different representations, </i>and<i> implication</i>), detail from an onto-semiotic point of view. However, some students have difficulty finding the angle between vectors because they misuse the norm. Furthermore, the new metaphorical connection based on mnemonics activated by the “<i>law of the ear</i>” is reported. The connections activated by engineering students to solve problems about vectors may have been influenced by the explanations provided by their calculus teacher, who promotes connections for the teaching and learning mathematical concepts.

The Effectiveness of Learning Google Meet Assisted by the Geogebra Application to Improve Students' Understanding of Mathematical Concepts

Due to the Covid-19 pandemic, online learning has decreased the comprehension of students’ mathematical concepts.. It is very important to instill conceptual understanding in students, in order for them to think and solve problems correctly and appropriately. Students experience difficulties in learning and understanding mathematical concepts, especially when the material provides changes to different problems. This paper aims to find out how far the effectiveness of Google Meet learning is achieved with the help of the GeoGebra application to improve students’ understanding of mathematical concepts. This study uses a quasi-experimental method with sampling using a simple random sampling technique. This research was conducted in one of the high schools in the city of Bandung with the selected sample being class XI MIA 5 as the experimental class, while XI MIA 3 as the conventional class. The instrument used was the Mathematics Preliminary Knowledge test, which is a test of the ability to understand mathematical concepts. This shows that there is an increase in the ability to understand students’ mathematical concepts between the experimental class and the control class. Learning mathematics through Google Meet assisted by the GeoGebra application provides opportunities for students to be able to actively participate in mathematics learning activities through graphic visualization media. It also fosters interest, enthusiasm, and motivates the students in improving their conceptual understanding of mathematics.
 Keywords: geogebra application, google meet, understanding of mathematical concepts

Meaningful learning in mathematics: a study on motivation for learning and development of computational thinking using educational robotics

ABSTRACT This research arises within the scope of the Postgraduate Course of Specialization in Technologies and Robotics in Elementary School. Its aim is to analyze the impact of robotics and programming on the motivation and involvement of students in the development of computational thinking, in the learning of mathematical concepts. The study was conducted with 36 elementary school students, where two game-based activities were designed and applied by using different technological tools (mBot and micro:bit). Data were collected from the participants using qualitative instruments, such as participant observation and semi-structured interviews. The data treatment technique selected was content analysis. The results establish evidence that the practice of these activities enabled students to learn while having fun and constructing knowledge from previous knowledge, consolidating contents. The dialogues and interviews with the students allowed us to identify that the educational use of robots encourages students’ participation. The results revealed it remains central to wager on initial and continuing teacher training to transfer this knowledge into their pedagogical practices, promoting meaningful learning.

Understanding Problem-Based Learning and its Application in Learning Mathematics Concepts Among Pre-Service Teachers

Learning to teach mathematics has become crucial since its application in real life cannot go unmentioned. The desire of mathematics education researchers to make mathematics concepts easier for pre-service teachers to easily understand has attracted attention. This has become indispensable since after college, pre-service teachers are deployed from K-12 to assist learners in understanding mathematics concepts. The study aimed to ascertain how improvement in the learning of mathematics concepts using the Problem-based learning (PBL) approach could be understood and/or explained among pre-service teachers. This was viewed in two folds: how improvement in learning outcomes using the PBL approach could be explained; and how pre-service teachers’ disposition about the PBL could be explained/understood. Exploratory case study design involving qualitative and quantitative data was concurrently gathered and used. This involved the use of data collection instruments such as focus group discussion, pre-post-test scores, PBL observation protocol, and PBL disposition questionnaire. The study showed that the PBL method improved the learning of mathematics concepts among pre-service teachers. Pre-service teachers also showed a positive disposition (interest, belief, and attitude) toward the PBL intervention. The authors advocated for the conduct of a longitudinal study to understand the direction of change over time.

"Now I Get It!": Eureka Experiences During the Acquisition of Mathematical Concepts.

Many famous scientists have reported anecdotes where a new understanding occurred to them suddenly, in an unexpected flash. Do people generally experience such "Eureka" moments when learning science concepts? And if so, do these episodes truly vehicle sudden insights, or is this impression illusory? To address these questions, we developed a paradigm where participants were taught the mathematical concept of geodesic, which generalizes the common notion of straight line to straight trajectories drawn on curved surfaces. After studying lessons introducing this concept on the sphere, participants (N = 56) were tested on their understanding of geodesics on the sphere and on other surfaces. Our findings indicate that Eureka experiences are common when learning mathematics, with reports by 34 (61%) participants. Moreover, Eureka experiences proved an accurate description of participants' learning, in two respects. First, Eureka experiences were associated with learning and generalization: the participants who reported experiencing Eurekas performed better at identifying counterintuitive geodesics on new surfaces. Second, and in line with the firstperson experience of a sudden insight, our findings suggest that the learning mechanisms responsible for Eureka experiences are inaccessible to reflective introspection. Specifically, reports of Eureka experiences and of participants' confidence in their own understanding were associated with different profiles of performance, indicating that the mechanisms bringing about Eureka experiences and those informing reflective confidence were at least partially dissociated. Learning mathematical concepts thus appears to involve mechanisms that operate unconsciously, except when a key computational step is reached and a sudden insight breaks into consciousness.

Analyzing the level of interest of high school students in solving mathematical problems in the modular and face-to-face learning

As schools continue to adjust to changing circumstances, it is essential to use strategies that not only help students learn, but also interest and inspire them. More effective and engaging learning experiences can be created with the use of knowledge on how different strategies affect students’ levels of interest. This quantitative study aimed to analyze the interest levels of students in solving mathematical problems as mediated by different teaching ideas/strategies i.e., with gamification, with graphic and visuals, and with digital resources. Likert-scale was used to code and assign weight for the questionnaire. Findings indicated that interest levels of students were high during distance learning because they can access online resources (e.g., search engines, YouTube, e-books) to be used for independent learning. In face-to-face classes, students reported high level of interest in solving mathematical problems if there are learning aids (e.g., graphs, pictures, charts) presented to them and access to online resources. As suggested, teaching strategies require teachers to focus more on visual and online-assisted learning to make students feel interested in solving mathematical problems and in learning mathematical concepts. The findings offered teachers an opportunity to integrate more on innovative teaching through adapting to resources which their students have access to. Such instructional direction required in-depth assessment to establish some novel instructional strategies that stimulate students to learn more.

ChatGPT in didactical tetrahedron, does it make an exception? A case study in mathematics teaching and learning

The didactical tetrahedron model proposes a framework for integrating technology into the previous didactical triangle. This study addresses this issue through examining the role of ChatGPT in educational settings. This quantitative and qualitative study reveals differences among three groups. We observed that students relying solely on ChatGPT for learning resulted in lower performance compared to those receiving instruction from teachers, either alone or supported by ChatGPT. The findings highlight the potential of ChatGPT in enhancing mathematical understanding, yet also underscore the indispensable role of instructors. While students generally perceive ChatGPT as a beneficial tool for learning mathematical concepts, there are concerns regarding over-reliance and the ethical implications of its use. The integration of ChatGPT into educational frameworks remains questionable within a didactic context, particularly due to its limitations in fostering deep information comprehension, stimulating critical thinking, and providing human-like guidance. The study advocates for a balanced approach, suggesting that ChatGPT can augment the learning process effectively when used in conjunction with guidance. Thus, positioning technology as an independent focal point in transforming the didactic triangle into a didactical tetrahedron is not appropriate, even when represented by ChatGPT.

Changes in the Ghanaian schools’ mathematics curriculum – Exploring the need to raise awareness in the integration of the history of mathematical concepts as a pedagogical tool

There have been frequent changes to the Ghanaian mathematics curriculum content but with little or no regard for the pedagogical strategies to deliver the content. It was, therefore, important to explore teachers' awareness of integrating the history of mathematical concepts as a pedagogical strategy in teaching mathematics. The study employed the interpretive paradigm, using the qualitative inductive approach of an explorative case study with eight participating secondary school mathematics teachers. The interviews were conducted and transcribed for analysis using content analysis. The results indicated that while most teachers were enthusiastic about the use of the history of mathematical concepts as a strategy, they hardly employed it as a critical approach to teaching mathematics, and those who were aware of it merely used it as a form of introduction to their lessons. This limited the level of engagement of learners in the history of mathematical concepts in learning mathematics. Conclusions and recommendations were discussed.

ChatGPT and other AIs: Personal relief and limitations among mathematics-oriented learners

Mathematics utilizes symbolic language, logics, relationships, and numerical connections that made it challenging for students to learn and develop their computational skills. Recently, artificial intelligence emerged as a supplement tool for education and learning because of its ability to detect relationships and logics. Academic institutions are looking on how to implement AI-assisted learning specifically for mathematics to aid in increasing the quantitative competence of students. This study analyzed the relief and limitations of AI chat models in learning among mathematics-oriented students in higher education. Fifteen students participated in this study from mathematics-oriented courses e.g., engineering, statistics, and education. Interviews were conducted on how students used AI chat models to assist in learning mathematical concepts and methods. Narratives indicated that AI chat models like ChatGPT and Bard were capable of accurately responding to chat prompts in problem solving, proving, and explanations. It was prominent that these AI models understood the mathematical language and use of symbols for integration, derivatives, limit, fractions, exponentials, and intervals. At some instances, AI models could give inaccurate results or incorrect methods for solving; they also sometimes give correct answers on second run of chat prompts after these mistakes. These results had promising implications in education as these accessible AI models could reinforce the firsthand learning of mathematical foundations. This preliminary study offered important usability of AI models in mathematics in assisting students and monitoring their learning progress.

Ethnomathematics Study: Mathematical Concepts in Bima Weaving Motifs

This study aimed to discover and investigate the mathematical concepts present in muna Mbojo (Bima weaving). This study was an ethnographic research, and employed a descriptive approach. This study's information was derived from observations and document reviews of Bima woven fabrics. The data was obtained using documentation by collecting the types or motifs of Bima weaving. Subsequently, in-depth observationswere conducted on the collected weaving. The data was analysed through reduction, presentation, and verification/conclusion. The results of the study found by the researchers namely: 1) bali motif (line motif) discovered mathematical concepts, including lines, rectangles, squares, and parallels; 2) wunta motif (flower motif) discovered mathematical concepts, including lines, sigsag lines/curves, angles, triangles, rhombuses, circles, alignments, symmetrical, translation/shifts, and reflections; and 3) kakando motif (bamboo shoots motif). Bima weaving is rich in motifs, weaving motifs that are generally produced by Bima people are bali motifs (lines), wunta motifs (flowers), and kakando motifs (bamboo shoots). In these motifs many mathematical concepts are found such as line, zigzag/curved line, angle, rectangle, square, triangle, rhombus, circle, alignment, symmetry, translation/shift, and mirroring. These mathematical concepts found in Bima weaving can be used by teachers to help or facilitate elementary school students in learning and understanding mathematical concepts. Learning mathematics will be more meaningful if teachers are able to involve students' culture in constructing their knowledge in the learning process.

Assessing ChatGPT’s Proficiency in Quantitative Risk Management

The purpose and novelty of this article is to investigate the extent to which artificial intelligence chatbot ChatGPT can grasp concepts from quantitative risk management. To this end, we enter a scholarly discussion with ChatGPT in the form of questions and answers, and analyze the responses. The questions are classics from undergraduate and graduate courses on quantitative risk management, and address risk in general, risk measures, time series, extremes and dependence. As a result, the non-technical aspects of risk (such as explanations of various types of financial risk, the driving factors underlying the financial crisis of 2007 to 2009, or a basic introduction to the Basel Framework) are well understood by ChatGPT. More technical aspects (such as mathematical facts), however, are often inaccurate or wrong, partly in rather subtle ways not obvious without expert knowledge, which we point out. The article concludes by providing guidance on the types of applications for which consulting ChatGPT can be useful in order to enhance one’s own knowledge of quantitative risk management (e.g., using ChatGPT as an educational tool to test one’s own understanding of an already grasped concept, or using ChatGPT as a practical tool for identifying risks just not on one’s own radar), and points out those applications for which the current version of ChatGPT should not be invoked (e.g., for learning mathematical concepts, or for learning entirely new concepts for which one has no basis of comparison to assess ChatGPT’s capabilities).

Rethinking Proficiency in the Language of Teaching and Learning (LoTL) as a Pillar in the Learning of School Mathematics

Although English has become the preferred language of instruction in most classrooms, including those of mathematics across the world today, it will still remain a second language (L2) to many students and their teachers for a long time to come. In mathematics language research, the attention so far given to the role of English as the Language of Teaching and Learning (LoTL) has been with the regard to the impact of levels of student proficiency in the language. This perhaps explains why those who learn in English as their first language (L1) are perceived as proficient in mathematical language, while L2 learners have to attain a level of proficiency in English first. This is in spite of the current absence of clear benchmarks for satisfactory proficiency in English for successful general learning in school mathematics. The poignant question remains: must L2 learners learn mathematics in English given the double jeopardy they face? This paper presents a critical analysis of findings of students’ interpretation of lexical vocabulary common in mathematics texts and in the classroom language typical of mathematics students in L2 contexts, to highlight the general difficulty of this language (English) to the mathematics learners. The main study from which the paper is extracted employed multiple-case study design to examine Mathematical Language (ML) usage and learners’ conceptual understanding of mathematics in secondary schools in Kenya. Data were collected by questionnaires, classroom observations and interviews. The findings of the paper indicate that a majority of L2 students have low proficiency in LoTL; socio-economic background is a factor of proficiency in the LoTL, and mathematics teachers were not aware of the importance of language in learning mathematical concepts. The main conclusion of the paper is that interpretation of mathematical concepts is language dependent which is a challenge to learners not versed in the LoTL. The paper reco

Study on Learning Difficulties of Function Concepts and Solutions

Mathematical concepts are the cornerstone of mathematics, the foundation of students’ cognition, and the carrier of students’ mathematical thinking activities. Mathematical concepts are learned in stages, and students may make errors at all stages, which in turn affect the quality of subsequent learning of related mathematical content. This paper analyzes and summarizes the difficulties in each stage of learning mathematical concepts from the student's point of view, drawing on the “Action-Process-Object-Scheme” stage of learning mathematical concepts according to the APOS theory. Combined with the corresponding teaching strategies proposed by the APOS theory, we guide and help students to feel, obtain, understand and connect the concepts, and give a case study of the application of the solution strategy of “teaching the concept of function”, in order to give some insights into the effective learning and teaching of mathematical concepts.