Nature Of Mathematics Research Articles

Are Mathematics and Writing Skills Related? Evidence from Meta-Analysis

Writing and mathematics are essential in academic achievement. In the present study, we investigated whether writing skills and mathematics skills are related and if so, whether their relation is moderated by participants’ grade level (a proxy for developmental phase), subskills of mathematics and writing skills, and assessment characteristics (normed and standardized nature of mathematics and writing tasks, and reliability of mathematics and writing measures), using a meta-analysis. A total of 211 studies (k = 564, N = 1,207,983) met inclusion criteria. Overall, mathematics and writing were moderately related (r = .48). The overall magnitude of their relation differed as a function of grade level such that the relation was stronger for students in primary grade levels compared to those in university and above. When explored by higher order and lower order writing and mathematics skills and grade levels, lower order writing and mathematics (.59) and higher order writing and mathematics (.48) had substantial relations in primary grades, whereas higher order writing and mathematics were weakly related in adulthood (.25). The relation also differed by the reliability of mathematics tasks such that the magnitude was stronger for mathematics tasks with higher reliability. For writing, the relation was stronger for writing tasks that were normed and standardized compared to those that were not. These results confirm not only a mathematics–writing relation but also factors that influence this relation. Future work is warranted to investigate mechanisms of the relation and potential practical implications.

Synergy as the Failure of Distributivity

The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. For the trivial case of discrete random variables, we explore whether and how it is possible to get more information out of lesser parts. The approach is inspired by the role of set theory as the fundamental description of part–whole relations. If taken unaltered, synergistic behavior is forbidden by the set-theoretic axioms. However, random variables are not a perfect analogy of sets: we formalize the distinction, highlighting a single broken axiom—union/intersection distributivity. Nevertheless, it remains possible to describe information using Venn-type diagrams. The proposed multivariate theory resolves the persistent self-contradiction of partial information decomposition and reinstates it as a primary route toward a rigorous definition of emergence. Our results suggest that non-distributive variants of set theory may be used to describe emergent physical systems.

Assessing the Effectiveness of Different Kinetic Models in Simulating the Soil Nitrification Process of Ammonium Fertilizers

ABSTRACTPrecise estimation of the soil nitrification process of ammonium fertilizers is crucial to improving soil fertility and reducing environmental pollution since nitrification is closely related to ammonia volatilization and nitrate leaching. However, the applicability and effectiveness of different kinetic models in simulating the soil nitrification process have not been systematically evaluated in previous studies. Here, we compared the effectiveness of one self‐established model (T‐function) and three commonly‐used kinetic models (L‐function, zero‐order kinetic model, and first‐order kinetic model) using data extracted from peer‐reviewed publications. Results showed that the average determination coefficients (R2) of the T‐function and L‐function were 3% higher than that of the first‐order kinetic model, while the average root mean square errors (RMSE) of the T‐function and L‐function were 30% lower than that of the first‐order kinetic model. In addition, first‐order kinetic model could not function properly when it was applied to simulate linear data. Zero‐order kinetic model was not suitable for predicting soil nitrification process because its mathematical nature was inconsistent with the actual soil nitrification process. Further investigations of the parameters of the T‐function and L‐function revealed that p1 (parameter 1) represented the soil net nitrate production of the applied N fertilizer, while p1 × p3 represented the soil nitrification rate. The response of the parameters of the T‐function was more sensitive to soil pH, TN, and C/N ratio changes than those of the L‐function. Therefore, the T‐function is slightly more accurate than the L‐function, but it requires more data points to achieve the best performance. In general, T‐function and L‐function are the most suitable models for simulating the soil nitrification process of N fertilizers and have the potential to be incorporated into soil N cycling models.

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.

Modelling and Analysing Routing Protocols Diagrammatically with Bigraphs

As more end-user applications depend on Internet of Things (IoT) technology, it is essential the networking protocols underpinning these applications are reliable. Using Formal Methods to reason about protocol specifications is an established technique, but, due to their perceived difficulty and mathematical nature, receive limited use in practice. We propose an approach based on Milner’s bigraphs—a flexible diagrammatic modelling language—that allows developers to “draw” the protocol updates as a way to increase use of formal methods in protocol design. To show bigraphs in action, we model part of the Routing Protocol for low-power and Lossy Networks (RPL), popular in wireless sensor networks, and verify it using model checking. We compare our approach with the more common simulation approach and show that analysing the bigraph model often finds more valid routes than simulation (which usually returns only a single routing tree even with 500 simulations) and that it has comparable performance. The model is open to extension, with less implementation effort than simulation, and we show this through two examples: a security attack and physical link drops. Bigraphs seem a promising approach to protocol design, and this is the first step in promoting their use.

A New Music Composition Technique Using Natural Science Data

The relationship of music and mathematics are well documented since the time of ancient Greece, and this relationship is evidenced in the mathematical or quasi-mathematical nature of compositional approaches by composers such as Xenakis, Schoenberg, Charles Dodge, and composers who employ computer-assisted-composition techniques in their work. This study is an attempt to create a composition with data collected over the course 32 years from melting glaciers in seven areas in Greenland, and at the same time produce a work that is expressive and expands my compositional palette. To begin with, numeric values from data were rounded to four-digits and converted into frequencies in Hz. Moreover, the other data are rounded to two-digit values that determine note durations. Using these transformations, a prototype composition was developed, with data from each of the seven Greenland-glacier areas used to compose individual instrument parts in a septet. The composition <i>Contrast and Conflict</i> is a pilot study based on 20 data sets. Serves as a practical example of the methods the author used to develop and transform data. One of the author’s significant findings is that data analysis, albeit sometimes painful and time-consuming, reduced his overall composing time. The variety and richness of data that exists from all academic areas and disciplines conceivably provide a rich reservoir of material from which to fashion compositions. As more composers explore this avenue of work, different methodologies will develop, and the value of works produced by this method will be evaluated.

About properties and the monomiality principle of Bell-based Apostol-Bernoulli-type polynomials

This article investigates the properties and monomiality principle within Bell-based Apostol-Bernoulli-type polynomials. Beginning with the establishment of a generating function, the study proceeds to derive explicit expressions for these polynomials, providing insight into their structural characteristics. Summation formulae are then derived, facilitating efficient computation and manipulation. Implicit formulae are also examined, revealing underlying patterns and relationships. Through the lens of the monomiality principle, connections between various polynomial aspects are elucidated, uncovering hidden symmetries and algebraic properties. Moreover, connection formulae are derived, enabling seamless transitions between different polynomial representations. This analysis contributes to a comprehensive understanding of Bell-based Apostol-Bernoulli-type polynomials, offering valuable insights into their mathematical nature and applications.

Primary education students’ beliefs about the nature of mathematics, self-efficacy, and mathematics educators; a descriptive study from Indonesia

ABSTRACT The significant role of mathematical belief studies has been recognised several decades later. These beliefs have been found to be significantly associated with performance and problem-solving. However, empirical studies of these beliefs in Indonesia are scarce. This study investigates students’ beliefs on the nature of mathematics, self-efficacy, and their perceptions of mathematics educators. The findings of this study revealed that Indonesian students strongly believe anyone could attain proficiency in mathematics. At the same time, students had less confidence that they could understand difficult mathematical tasks and less confidence in showing that they were good at mathematics. Notably, boys’ students exhibit stronger beliefs in their understanding of the course, including the most challenging topics in mathematics, compared to their girls’ counterparts. The implications of this study significantly contribute to the existing literature and inform teaching practices.

БАШТАЛГЫЧ МЕКТЕПТЕ 10 ГО ЧЕЙИНКИ САНДАРДЫ КОШУУ ЖАНА КЕМИТҮҮНҮ ОКУТУУНУН ТЕХНОЛОГИЯСЫ

The article deals with the technologies used for teaching primary school students addition and subtraction concepts namely teaching technologies based on ready-made tasks presented in the Toytheater app. This app sparks an interest in mathematics. The reason for this lies in the intrinsic nature of mathematics: the ability for high-level generalization, abstract, precise language, and logical apparatus allow studying any object of reality, phenomena of the micro- and macro-world. Mathematics also implies a certain style of thinking. Moreover, studying any phenomenon requires clarity, logical research aimed at establishing initial positions, completeness of classifications, and logical conclusion. Teaching mathematics in school plays a key role in developing students' functional properties of their senses, particularly attention, abilities, will, and, most importantly, thinking. Learning addition and subtraction methods involve reading models of specific, graphical, abstract methods, which require students to observe the corresponding situation, analyze it, draw conclusions, notice graphical representations, and draw conclusions about the correct use of the abstract model.

Considering Opportunities for Mathematical Magic

Mathematical magic, or experiences of beauty and creativity for K-12 mathematics students, can contribute to deepened content understanding. However, creating opportunities for mathematical magic. in mathematics classrooms has been a challenge for classroom practitioners. To support development of these experiences in classrooms, we deployed a bi-directional support program between a college-level mathematician and an early-career secondary teacher. Based on data collected from this project, we have identified four principles that will promote mathematical magic. We conclude that mathematicians and early career teachers can work together to a) leverage understandings of the nature of mathematics, b) apply meta-mathematical reasoning, c) share knowledge of content and students across contexts, and d) recognize students’ mathematical development to design learning experiences for mathematical magic.

Quantile regression model on how logical and rewarding is learning mathematics in the new normal

Learning mathematics through distance education can be challenging, with the “logical” and “rewarding” nature proving difficult to measure. This article aimed to articulate an argument explaining the “logical” and “rewarding” nature of online mathematics learning, elucidating their causal factors. Existing data from the literature that involving students at Visayas State University, Philippines, were utilized in this study. The study used statistical measures to capture descriptions from the data, and quantile regression analysis was employed to forecast the predictors of the logicality and rewarding nature of learning mathematics at a distance. Results indicate that learning mathematics in the new normal is perceived as “logical” and moderately “rewarding”. The regression and correlation analyses revealed a significant positive association between the perceived “logical” nature and the rewarding experience of learning mathematics. The constructed statistical models depicted that the determinants of logicality in learning mathematics include family income, money spent on the internet, learning environment, household size, social status, and health. Moreover, causal factors such as family income, money spent on the internet, learning environment, leisure activities, social status, and health significantly determine the rewarding nature of learning mathematics online. Conclusively, institution must support college students with their online learning needs. Furthermore, mathematics instructors should create lively and exciting online discussions that boost their logical thinking. Providing problem-solving task that are intrinsically rewarding can contribute to a more fulfilling learning experience.

An examination of pre-service mathematics teachers’ course-taking, beliefs, and preferred assessment practices

AbstractThis study uses structural equation modeling to investigate the relationships between pre-service teachers’ (PSTs’) course-taking history, beliefs about mathematics, beliefs about students’ mathematical ability, and opinions about (1) how student errors should be addressed when they occur and (2) how much emphasis should be given to various forms of assessment. The results indicate that some types of courses are strongly associated with beliefs about the nature of mathematics. Specifically, PSTs who have taken more mathematics courses are more likely to see mathematics as a set of rules. PSTs’ views about mathematics strongly predict their beliefs about who can do high-level mathematics, how they think student errors should be addressed, and which forms of assessment they think are most appropriate. Implications for teacher preparation programs are discussed.

The Mathematical Thinking Among Muslims and Its Impact on the Science of Inheritance

The challenge I faced while teaching the inheritance course to students unfamiliar with this field and its terminology was evident in their difficulty in easily understanding the scientific material, requiring considerable time for explanation. This situation prompted me to seek a way to simplify their understanding of inheritance. Given the mathematical nature of the course and the students' familiarity with this area, so I decided to utilize this aspect to achieve my teaching objectives, eventually developing mathematical rules that clarify the distribution of inheritance among heirs. This approach not only helped me achieve my goals but also led me to connect the efforts of Muslims with mathematics, highlighting their creativity in this domain, which continues to this day. Therefore, in my teaching methodology, I relied on both library research and mathematical approaches. The research highlighted the contributions of Muslims to mathematics and I introduced some of my own rules, applying them specifically to the topic of intersex cases.

Understanding the physics of eigenvalue-eigenfunction problems: Rotating beam problem

Eigenvalue-eigenfunction problems frequently appear in many physical areas. Some mathematical experience is needed to identify whether the differential system is an eigenvalue-eigenfunction problem or not. Apart from the mathematical nature of the problem, the eigenvalue-eigenfunction solutions have physical interpretations which have to be addressed properly for real problems. The rotating beam problem is treated to exploit the mathematical and physical nature of such problems and the conditions to divert from the eigenvalue-eigenfunction problem. The rotation of a beam about its symmetry axis along its length and about another axis parallel to its symmetry axis changes the nature of the problem. While the former is an eigenvalue-eigenfunction problem, the latter is not. The interpretations of the physical consequences of the solutions are discussed in detail. The problem can be used as supplementary material in undergraduate courses such as differential equations, mechanics and dynamics.

Relative Effectiveness Of Reading Activities In The Pakistani ESL Context

The quality of reading determines the quality of both content and language learning. Reading plays a key role in developing advanced grammatical skill and academic vocabulary necessary for creating written discourse and thus raising learners’ level of language proficiency. However, a substantial body of ESL college learners in Pakistan are reported to be struggling for attaining a satisfactory level in reading proficiency. Notably, the scrutiny of underachievement reveals that indiscriminate insistence on GTM and consequent failure to actively engage learners for cognitive development are included in major issues. For addressing these problems, a promising alternative is suggested in Task-Based Learning (activities-based learning). A 40-minute task-based class, 3 days a week, was run for four weeks. The sample comprised 111 students of Intermediate Level. The researcher-created videos on reading activities uploaded on his YouTube channel were watched by the learners.[1] Listening to the recorded lecture was followed by a set of activities in which the participants were engaged before they showed their work in the physical classroom. Subsequently, relative effectiveness of ten prevalent reading activities was studied through written tests. Quantitative data analysis was made by SPSS. Furthermore, qualitative data collected through interviews were analyzed by inductive approach thematic analysis. Mathematical nature of activities, such as Main Idea Formula, Students Created Quizzes & Tests and Cause & Effect Grid made them relatively more effective.

Three-Parameter Electric Dipole Moment Function for the CO Molecule.

A global electric dipole moment function of the ground electronic state of carbon monoxide is constructed by morphing its best theoretical approximants from the literature to the best available experimental data within the framework of the reduced radial curve approach. The resulting functions coincide with their best many-parameter empirical counterparts so closely that they can be used as highly accurate three-parameter representations. Apparently, given the mathematical nature of the problem addressed, this approach can be applied equally well to all radial molecular functions that have similarly cumbersome shapes as the function probed. This means that the property characteristics of diatomic molecules can, in principle, be described with high precision even when as few as three pertinent experimental data points are accurately known. To date, no such functional approximants are available in the literature.

Clashing perspectives: Kantian epistemology and quantum chemistry theory

In this contribution, the role of epistemology in understanding quantum chemistry is discussed. Quantum chemistry is the study of the behavior of atoms and molecules using the principles of quantum mechanics. Epistemology helps us evaluate claims to knowledge, distinguish between justified and unjustified beliefs, and assess the reliability of scientific methods. In quantum chemistry, the epistemology of knowledge is heavily influenced by the mathematical nature of quantum mechanics, and models can be tested, proven, and validated through experimentation. This paper also discusses key concepts used in quantum chemistry, such as the wave-particle duality of matter and the uncertainty principle. This work utilizes Kant’s philosophy of science to frame debates and discussions in quantum chemistry, particularly with regard to the interplay between empirical observation and theory. Additionally, the text explores how Kant’s ideas about the role of the mind in constructing our understanding of the world can help us comprehend the counterintuitive phenomena of quantum mechanics and its applications in quantum chemistry theory.

Use of a Modified Threshold Function in Fuzzy Cognitive Maps for Improved Failure Mode Identification

Fuzzy cognitive maps (FCMs) provide a rapid and efficient approach for system modeling and simulation. The literature demonstrates numerous successful applications of FCMs in identifying failure modes. The standard process of failure mode identification using FCMs involves monitoring crucial concept/node values for excesses. Threshold functions are used to limit the value of nodes within a pre-specified range, which is usually [0, 1] or [-1, + 1]. However, traditional FCMs using the tanh threshold function possess two crucial drawbacks for this particular.Purpose(i) a tendency to reduce the values of state vector components, and (ii) the potential inability to reach a limit state with clearly identifiable failure states. The reason for this is the inherent mathematical nature of the tanh function in being asymptotic to the horizontal line demarcating the edge of the specified range. To overcome these limitations, this paper introduces a novel modified tanh threshold function that effectively addresses both issues.

Teachers’ professional development for inclusion of experimental mathematics and interactive resources in the classroom

Information technology enhances the nature of mathematics as an empirical discipline, leading to an approach called “experimental mathematics” (EM). It fosters the use of technology-based interactive resources (IRs) in mathematics education, giving mathematics an experimental dimension and reflecting a tension between the empirical-inductive nature of IRs and formal mathematics (FM). Our qualitative research focused on professional development (PD) for IR-based teaching of EM intertwined with FM based on a threefold theoretical framework that combines the mathematical knowledge required by EM, the pedagogical functionality of IRs, and instrumental orchestration. The research analyzed 14 high school teachers’ documents generated in the course of a PD program, revealing the evolution of their orientation. We argue that teachers’ evolving orientation toward IR-based EM inclusion in school mathematics is the result of meticulous dynamic PD design implementing three key aspects framed by the threefold theoretical framework: teachers playing various roles during the PD, teacher-researcher collaboration, and theoretical support. The beginning of the evolution of the teachers’ orientation toward IR-based EM inclusion in school mathematics was made possible by a design grounded in the above theoretical framework and observed through its lens.

Mathematics teachers’ beliefs about mathematics, its teaching, and learning: The case of five teachers

This study explores the views of mathematics teachers at Assosa University regarding effective mathematics teaching. The study used a case study method as a mode of inquiry through semi-structured interviews with five mathematics teachers at Assosa University. The data were analyzed thematically. The results showed that mathematics teachers view memorization, practice, and concrete experiences as ways to enhance their students’ understanding of mathematics. Teachers expressed different views on the nature of mathematics. Some teachers have an instrumental view, while others have a problem-solving view, and others have a Platonist view of the nature of mathematics. The study showed important arguments about the belief systems of mathematics teachers, showing that teachers’ beliefs about the nature of mathematics provide the basis for their mental models of mathematics teaching and learning. The study revealed those mathematics teachers’ beliefs about effective mathematics teaching influence their educational practices. The study suggests that developing the expertise of teachers in higher education institutions by changing their entrenched beliefs about mathematics needs particular attention, which ultimately affects their practice.