Mathematical Reasoning Research Articles

Enhancing mathematical reasoning: role of the search, solve, create, and share learning

Enhancing mathematical reasoning: role of the search, solve, create, and share learning

THE EFFECTIVENESS OF MATHEMATICS LEARNING THROUGH A REALISTIC MATHEMATICS EDUCATION APPROACH IN ELEMENTARY SCHOOLS

The research aims to analyze the effectiveness of mathematics learning through the realistic mathematics education approach in learning the concept of counting integers in grade VI elementary school students. The research used a quasi-experiment with one pretest postets design. The research involved 32 grade VI students at SDN 205 Neglasari, Coblong District, Bandung City. The research instrument is in the form of a multiple-choice test that includes addition and subtraction of decimal numbers. Research shows that the RME approach is effective in producing a significant improvement in students' learning completeness in the addition and subtraction of decimal integers, as well as improving mathematical problem-solving, self-efficacy, reasoning, and mathematical literacy. RME encourages students to recognize the practical application of mathematical concepts through real-world contexts and cultural elements, as well as to cultivate creative and imaginative thinking skills so that they can be an important strategy in improving mathematics education in primary schools.

The Montessori method in preprimary classrooms: logical-mathematical thinking with sensory material

When choosing a methodology for the teaching-learning process of logical-mathematical thinking, the possibilities available to the teacher are immense. The Montessori method is known for being based on freedom and spontaneous activity, as well as for the characteristic material used. The main objective of this research is to show the pedagogical possibilities of the Montessori method for the learning of the logical-mathematical competence in Second Cycle classes of Preprimary Education. Participants were 39 children. Three didactic activities based on the Montessori method were designed for the purpose of the study, and the instrument used to gather information was a Likert scale check list composed by a number of measurable items related to addition, subtraction, and operations on inequalities. The results of the study encourage both practicing and future teachers to apply the Montessori method in the classrooms as it is an attractive methodology for preprimary students and motivates them to learn contents. It can be concluded that endless contents can be developed with this method, not only logical-mathematical ones, but also any aspect that can be dealt with in the classroom.

Diagnostic study of mathematical reasoning in novice university students

This paper presents the results of a study aimed at diagnosing how newly enrolled mathematics majors reason from a mathematical standpoint when they are required to perform inductive and deductive processes and validate or refute claims of a general nature. The theoretical framework underpinning this research comprises studies and investigations related to mathematical reasoning. The results of this diagnostic reveal that students lack mathematical reasoning skills that would allow them to justify statements of a general nature. In addition, they face difficulties in the development of deductive reasoning, are prone to generalize based on specific cases and lack skills in mathematical argumentation. On the other hand, they lack basic algebra skills such as developing square binomials and factoring. These findings highlight the need to design and implement a didactic proposal that fosters the development of reasoning and argumentation in students.

Covariational reasoning of field dependent prospective mathematics teacher in solving covariance problem

This study aims to analyze the coordination and construction aspects of covariational reasoning of field dependent students’ prospective mathematics teachers in solving covariation problems. This research is qualitative research with the subject of research being field dependent prospective mathematics teachers of STKIP PGRI Jombang. The instruments in this study are the main instrument (the researcher himself) and supporting instruments in the form of GEFT, Covariation Test, and interview guidelines. Data analysis uses data reduction steps, data presentation, and conclusions. Based on the results of the study, the subjects coordinate the magnitude of variable changes and determine the pattern of change for linear covariation problems based on calculations from the results of the representation of covariation task-based problems to compile their change patterns, for linear students using students' own understanding without doing calculations. In the construction aspect, the subject constructs through the representation of the relationship of two variables into a graph by determining the coordinate axis with known variables and drawing a graph from the results of calculating the pattern of change in the relationship of two variables. From the depicted graph, the direction of the chart can be determined. The resulting graph corresponds to a given covariation task-based problem.

The effects of mathematical ability and motivational beliefs on students’ perceptions of feedback usefulness

Research has shown that students’ learning gains in mathematics are greater when they work with problems rather than routine tasks. These learning gains from problem-solving activities may be enhanced by providing feedback that does not give away the solutions to the problems, but helps students construct their solution methods themselves and anchor their reasoning in intrinsic properties of the mathematical components involved in the reasoning. However, in order to use feedback, students would need to perceive it as useful, and not all students may find such feedback useful. In this study, we investigate how students’ ability and motivational beliefs affect how useful they perceive feedback aimed at supporting mathematical reasoning to be. In the study, students worked with mathematical problems and received metacognitive and heuristic feedback when they needed help. We used structural equation modeling (SEM) to analyze the effects. The results show that students’ mastery goals had a direct effect on the perceived usefulness of the feedback, but no such effects were found for students’ national test grades, self-efficacy beliefs, performance goals, or intrinsic or extrinsic forms of motivation. The proportion of successful use of feedback did not mediate the effects.

Investigating the Complexity in Elementary Teachers’ Noticing of Children’s Mathematical Thinking in Written Work

ABSTRACT This study investigated upper elementary teachers’ framings of their students’ mathematical thinking in written across the three component skills of noticing. Drawing on a situated perspective, the research examines the influences of teachers’ culturalhistorical backgrounds, attitudes, dispositions, interactions with students, and other situated elements of teaching on noticing mathematical thinking. Interviews used a think-aloud method to capture real-time framing as teachers observed children’s thinking on the same problem, using written work from their own and unfamiliar classrooms. Analysis of transcripts involved iterative coding to identify frames and determine their prevalence across noticing skills (attending, interpreting, deciding). Results show teachers used multiple frames beyond focusing on the mathematical thinking present in the work, such as past performance, affective traits, and curricular expectations. The prevalence of these frames appeared primarily in the interpretation and deciding how to respond. Findings highlight the situated nature of noticing, as interpretations were impacted by teachers’ sociohistorical interactions and perceptions. Implications point to explicitly addressing teacher framing in professional development, as deficit views of children’s capabilities can limit productive noticing. Considering teachers’ lenses and co-constructing frameworks can promote growth towards equitable noticing practices that privilege children’s mathematical reasoning. Implications for research and practice are explored and discussed.

Exploring group concepts in abstract algebra through ChatGPT

Traditional methods often struggle to engage students and effectively communicate the intricacies of abstract algebra. This study aims to explore the future of mathematics teaching, with a focus on integrating group theory concepts into Abstract Algebra using ChatGPT, an advanced language processing AI. Chat transcripts edited with ChatGPT were analyzed to gain insights into the evolving landscape of mathematics education, specifically concerning group theory. Group theory is a fundamental branch of Abstract Algebra poised to shape the future of mathematics instruction. ChatGPT facilitates interactive discussions and problem-solving tasks related to group operations, properties, and theorems, offering personalized explanations and guidance tailored to individual student needs. The study highlights the potential of AI-driven platforms like ChatGPT to revolutionize mathematics education by providing dynamic and engaging learning experiences centered around group theory. Furthermore, the study emphasizes the importance of incorporating group theory into mathematics curricula to foster critical thinking, problem-solving skills, and interdisciplinary connections. Educators are urged to leverage innovative tools like ChatGPT alongside traditional pedagogical approaches to ensure effective teaching and learning. Through thoughtful implementation and ongoing professional development, educators can harness AI's power to create inclusive, equitable, and enriching learning environments, empowering students in abstract mathematical reasoning and analysis.

Pengaruh Gaya Belajar Terhadap Kemampuan Penalaran Matematis Siswa SD 5 Mejobo

This research aims to examine the influence of learning styles on students' mathematical reasoning abilities at SDN 5 Mejobo. The learning styles studied include three main categories, namely auditory, kinesthetic and visual. Mathematical reasoning abilities are measured through tests that cover various aspects of reasoning such as identifying patterns, making generalizations, and solving mathematical problems logistically. This research uses quantitative methods with a survey approach. The research population was all 6th grade students at SDN 5 Mejobo, totaling 12 students, and the entire population was used as a sample population using saturated sampling techniques. Data was collected through a learning style questionnaire adapted from the VARK model and a mathematical reasoning test that refers to NCTM standards. Data analysis was carried out using regression and correlation analysis techniques with the help of SPSS software. The research results show that learning style does not have a significant influence on students' mathematical reasoning abilities (value 0.030 > 0.05). These findings indicate that individuals' learning style preferences do not determine their mathematical reasoning abilities. Therefore, it is recommended that other factors such as teaching methods, learning motivation, and learning environment be considered in an effort to strengthen students' mathematical reasoning abilities. It is hoped that this research will provide insight into the development of learning strategies that are more efficient and meet student needs.

Pengaruh Tingkat Kecemasan Matematika terhadap Hasil Tes Penalaran Matematis pada Siswa Kelas V SD 5 Mejobo

This research aims to determine the effect of mathematical anxiety on the results of mathematical reasoning tests. This is motivated by the emergence of anxiety experienced by students when learning mathematics which affects the results of students' mathematical reasoning tests. The research method used in this research is a quantitative research method with the aim of testing a predetermined hypothesis and the data analysis technique used is an inferential statistical analysis technique with a simple linear regression test. The population of this study were 18 fifth grade students at SD 5 Mejobo, consisting of 11 boys and 7 girls. The data used is secondary data in the form of student anxiety questionnaire data and data from mathematical reasoning results. Class V anxiety is in the average category, the calculation results are included in the anxiety category. Mathematics anxiety has a negative effect on the results of fifth grade students' mathematical reasoning tests and the effect is 70.9%.

Mathematics Teaching-Learning Methodology and Its Impact on Academic Performance

Mathematical logical thinking is essential for the development of cognitive constructs of complexity, where the symbolic and abstract take shape, hence the importance of teaching-learning of mathematics, however the strategies in the educational process are not always diverse. which may have an impact on academic performance. Objectives: identify the main methodological elements of teaching-learning mathematics and their relationship with academic performance. Methodology: the research was developed based on a quantitative, non-experimental and descriptive approach. An instrument designed with 12 questions was used, whose Cronbach's Alpha validity was .890, indicating internal consistency. The sample was 383 teachers from public and private educational entities, characterized by not having normality with a value of p .000. Results: The type of classes in public and private educational institutions is generally synthetic-analytical libraries, the institutional guide text and sources from institutional are used as guide materials, in addition, educators reinforce memory and understanding in students to enhance learning significantly, they implement problem solving and presentations, and evaluating through tests and projects. Conclusions: the mathematics teaching-learning methodology that the educators of the Sierra regime apply implies a synthetic-analytical modality, in addition, strategies are used that vary according to the type of educational entity.

Neurobiological Definition of Intelligence: A Neuroscience Review

Abstract Intelligence is a complex cognitive trait that has long intrigued researchers across disciplines. Recent advances in neuroscience have provided insights into the neurobiological underpinnings of intelligence. This review examines the neurobiological definition of intelligence, focusing on the neural processes and brain regions associated with cognitive functions such as reasoning, problem-solving, memory, and learning. Key findings include: (I) prefrontal cortex plays a crucial role in higher cognitive functions such as decision-making, planning, and working memory, with larger prefrontal cortex volume correlating with better fluid intelligence performance; (II) parietal cortex is implicated in mathematical reasoning and spatial processing, essential for problem-solving and abstract thinking; (III) hippocampus, critical for memory formation and retrieval, is linked to intelligence through its role in cognitive task performance; and (IV) neuroimaging studies reveal that higher intelligence scores are associated with increased connectivity between brain regions, suggesting more efficient information processing. Understanding the neurobiological basis of intelligence can provide valuable insights into human cognition and inform interventions to enhance cognitive functioning. Further research is needed to unravel the complexities of intelligence and its neural substrates.

DEVELOPMENT OF AUGMENTED REALITY-BASED LEARNING ON FLAT-SIDED SPACE BUILDING MATERIALSVERSION

Nowadays, technology is developing rapidly. Augmented reality is one of the technologies frequently used in the learning process. The purpose of augmented reality-based learning is to improve mathematical reasoning skills by providing interesting and appropriate learning media. This study aims to develop mathematics learning media for flat-sided spatial geometry material based on augmented reality that can be tested on grade VII students of SMPN 16 Tangerang City. This research uses the ADDIE development model, which includes analysis, design, development, implementation, and evaluation. The research data includes both qualitative and quantitative data. The instruments used are media validity expert assessments, media practitioner assessments, and respondent responses. The results of the study showed a significant increase in students' knowledge and skills during the learning process of mathematics on cube and cuboid materials based on augmented reality in grade VII students of SMPN 16 Tangerang City. This is indicated by the expert assessment results, which rated it as "valid," the media expert assessment results, which rated it as "very practical," and the respondents' answers, which were categorized as "moderate." Students' knowledge and skills increased significantly due to the application of augmented reality-based mathematics learning on cubes and cuboids. The application of this learning method provides an effective increase in students' knowledge and skills and helps achieve learning objectives.

HOW ARE STUDENTS' CREATIVE REASONING ABILITIES IN SOLVING STRAIGHT-LINE EQUATION PROBLEMS?

Creative reasoning is a person's ability to solve mathematical problems in a manner of thinking that deviates from the norm, yet remains logical and grounded in a strong mathematical foundation. While crucial for students, many have not yet attained proficiency in creative reasoning, necessitating comprehensive research on the subject. This study aims to elucidate students' creative reasoning abilities in tackling straight-line equation problems, focusing on indicators such as creativity, plausibility, and anchoring. Employing a qualitative approach with a case study design, the research involved three students from Madrasah Tsanawiyah who had studied straight-line equations. The primary instrument was the researcher, supported by a creative reasoning ability description test and interviews. Data collection utilized triangulation techniques, encompassing tests and interviews. Analysis of the research findings entailed describing students' creative mathematical reasoning abilities for each creative reasoning indicator in straight-line equation material. Results indicated that while students could provide correct and reasonable arguments in solving mathematical problems, they struggled to devise alternative methods and employ strategies based on mathematical concepts. Consequently, they only met the plausibility criterion, falling short in creativity and anchoring. Thus, it can be concluded that students have not yet achieved creative reasoning proficiency in solving straight-line equation problems.

English learners learn from worked example comparison in algebra

Comparison is an important mechanism for learning in general, and comparing two worked examples has garnered support over the last 15 years as an effective tool for learning algebra in mainstream classrooms. This study was aimed at improving our understanding of how Modified for Language Support-Worked Example Pairs (MLS-WEPs) contribute to effective mathematics learning in an ESOL (English to Speakers of Other Languages) context. It investigated a novel instructional approach to help English Learners (ELs) develop better understanding in mathematical reasoning, problem solving, and literacy skills (listening, reading, writing, and speaking). Findings suggest that MLS-WEPs not only enhanced ELs’ ability to solve algebra problems, but it also improved their written explanation skills and enabled them to transfer such skills to different mathematical concepts. Moreover, when controlling for ELs’ prior knowledge, the effectiveness of the MLS-WEPs intervention for performing and explaining calculations did not vary by their English proficiency.

Integration of the POE Model and Metaphoral Thinking in Student Worksheets: Improving Mathematical Reasoning Abilities in the Modern Education Era

Purpose of the study: This research aims to develop and evaluate the effectiveness of POE-based (Predict, Observe, Explain) student worksheets using a Metaphorical Thinking approach to enhance the mathematical reasoning abilities of class 9 students at Public Middle School. Methodology: This research aims to find out how to develop student worksheets based on POE (Predict, Observe, Explain) through a Metaphoral Thinking approach oriented towards the mathematical reasoning abilities of junior high school students in class 9 and find out the effectiveness of student worksheet products based on POE (Predict, Observe, Explain) through Metaphoral Thinking approach to the mathematical reasoning abilities of Public Middle School 7 Banjit students in class 9. Main Findings: Validation results showed material experts rated the worksheets at 89.4%, media experts at 94.9%, and language experts at 75%, all with high appropriateness. Small group trials averaged 86%, field trials 87%, and educator trials 97.2%, all with very good criteria. The paired t-test (thitung = 12.7 > ttabel = 2.02) confirmed the effectiveness of the POE-based worksheets using the Metaphorical Thinking approach in enhancing mathematical reasoning abilities.. Novelty/Originality of this study: The novelty of this study lies in developing and validating POE-based student worksheets integrated with a Metaphorical Thinking approach to enhance junior high students' mathematical reasoning. This innovative strategy combines cognitive and imaginative techniques, fostering deeper comprehension and problem-solving skills.

A Systematic Review and Comprehensive Analysis of Pioneering AI Chatbot Models from Education to Healthcare: ChatGPT, Bard, Llama, Ernie and Grok

AI chatbots have emerged as powerful tools for providing text-based solutions to a wide range of everyday challenges. Selecting the appropriate chatbot is crucial for optimising outcomes. This paper presents a comprehensive comparative analysis of five leading chatbots: ChatGPT, Bard, Llama, Ernie, and Grok. The analysis is based on a systematic review of 28 scholarly articles. The review indicates that ChatGPT, developed by OpenAI, excels in educational, medical, humanities, and writing applications but struggles with real-time data accuracy and lacks open-source flexibility. Bard, powered by Google, leverages real-time internet data for problem solving and shows potential in competitive quiz environments, albeit with performance variability and inconsistencies in responses. Llama, an open-source model from Meta, demonstrates significant promise in medical contexts, natural language processing, and personalised educational tools, yet it requires substantial computational resources. Ernie, developed by Baidu, specialises in Chinese language tasks, thus providing localised advantages that may not extend globally due to restrictive policies. Grok, developed by Xai and still in its early stages, shows promise in providing engaging, real-time interactions, humour, and mathematical reasoning capabilities, but its full potential remains to be evaluated through further development and empirical testing. The findings underscore the context-dependent utility of each model and the absence of a singularly superior chatbot. Future research should expand to include a wider range of fields, explore practical applications, and address concerns related to data privacy, ethics, security, and the responsible deployment of these technologies.

Different Languages, Different Mathematics Learning

Culture shapes pupils’ mathematical learning, their performances and life trajectories of participation (César, 2013a, 2013b). It also contributes to the senses they attribute to mathematical learning (Bakhtin, 1929/1981). Using collaborative work and inter-empowerment mechanisms facilitates knowledge appropriation (César, 2009). This is particularly important for pupils participating in minority cultures, socially undervalued and whose L1 is not the instruction language. Bi-univocal culture mediation (César, 2017b) is important regarding empowerment. We used an instrument to evaluate pupils’ abilities and competencies (IACC), conceived by the Name of the Project team (Machado, 2014), and other mathematical tasks. The goal we address is to trace the differences between their approaches to problems, mathematical reasoning and solving strategies used by pupils whose L1 is ideographic (Creole, Cape Verde) or phonetic (Portuguese). We developed an intrinsic case study (Stake, 1995). The main participants are the pupils from almost 600 classes (all over Portugal and Cape Verde) who participated in the Name of the Project. The analysis of some examples illustrates that L1 shapes pupils’ approaches to problems, mathematical reasoning and solving strategies. This evidence plays an important role in their access to school achievement and in teachers’ understanding about how they can promote pupils’ mathematical learning.

Proposed theoretical value for TSP constant

The traveling salesman problem (TSP) involves determining the shortest length (optimal tour) for a complete circuit through an arbitrary number of points. In the special case that the points to be visited are randomly distributed in the plane within a unit square, and travel costs correspond to the Euclidean distance between points, it is known that the length of the optimal tour divided by the square root of the number of points ([Formula: see text]) asymptotically approaches a constant ([Formula: see text] as [Formula: see text] becomes large. If individual points are randomly drawn from a uniform distribution, the optimal lengths for a sufficiently large number of TSP instances of the same size ([Formula: see text] comprise a normal distribution whose mean approaches [Formula: see text] as [Formula: see text] increases. Moreover, as [Formula: see text] approaches infinity, this distribution gradually narrows such that its standard deviation asymptotically approaches zero. Although the precise value of [Formula: see text] is unknown, published studies indicate its magnitude is approximately 0.712. In this paper, possibly for the first time, precise formulae are proposed for the parameters of the underlying normal distribution and [Formula: see text], based on intuition, mathematical reasoning, and empirical fits to both published and experimentally derived data.

Embedding Mathematics in Socio-Scientific Games: The Mathematical in Grappling with Wicked Problems

This paper discusses the ways in which digitally enabled transformation in mathematics education could envisage a role for rationality in post-normal science and wicked problems. The scene is set firstly by reviewing the ways in which digital media have been designed and used in transformative mathematics education as a rationale for thinking about such media for wicked problem education. The problem is set in epistemological terms: can normal science approaches contribute to post-normal science? By considering the basic arguments regarding wicked problem education, I focus on the discussion of a specific constructionist digital tool called ‘ChoiCo: Choices with Consequences’, designed to embed mathematical ideas and facilitate mathematical reasoning, yet be about grappling with wicked problems. The final section discusses student discourse to set the scene for what such reasoning might look like in the context of grappling with wicked problems.