formalized mathematics

Fundamental Law of Information: Proved by Both Numbers and Characters in Conjugate Matrices

Article • Proceedings of the IS4SI 2017 Summit DIGITALISATION FOR A SUSTAINABLE SOCIETY, Gothenburg, Sweden, 12–16 June 2017.

first_pagesettingsOrder Article Reprints Open AccessProceeding Paper Fundamental Law of Information: Proved by Both Numbers and Characters in Conjugate Matrices † by Xiaohui Zou 1,2,*,Shunpeng Zou 1,2 andLijun Ke 2 1 China University of Geosciences, Beijing 100083, China 2 Searle Research Center, University of California Berkeley, Berkeley, CA 94720, USA * Author to whom correspondence should be addressed. † Presented at the IS4SI 2017 Summit DIGITALISATION FOR A SUSTAINABLE SOCIETY, Gothenburg, Sweden, 12–16 June 2017. Proceedings 2017, 1(3), 60; https://doi.org/10.3390/IS4SI-2017-03927 Published: 8 June 2017 (This article belongs to the Proceedings of Proceedings of the IS4SI 2017 Summit DIGITALISATION FOR A SUSTAINABLE SOCIETY, Gothenburg, Sweden, 12–16 June 2017.) Downloadkeyboard_arrow_down Browse Figures Versions Notes Abstract Its purpose is to prove information law by logic, mathematics and translation. The method involves: the generalized bilingual logic established on both Aristotle’s formal logic and Frege’s mathematical logic, the linkage function established on both Turing’ strong artificial intelligence using numbers and Searle’s weak artificial intelligence using characters, the ontological knowledge established on both Saussure’s general linguistics and Chomsky’s formal linguistics. The result is that the basic law can be proved by digital and textual twin matrices. Its significance lies in that the global positioning system should be regarded as a special case of the generalized bilingual system.

Neutral approach at dividend policy modeling

Article • Research Journal of Finance and Accounting

The article treats a concept of the formalized modeling of the dividend policy scores and company marketing performance scores derived (stock market position) within neutral dividend policy implementation approach conditions as an instrument of the scores analysis and forecasting. The methodology of the research consists of the Dividend Irrelevance theory, Dividend Policy Significance theory and sustainable company development concept. It has been stated that a formalized approach of the dividend policy implementation presumes a construction of the basic relevent scores models characterizing the company dividend policy and its marketing performance as Dividend Payout, Dividend Cover, expected Share Price, Dividend Yield, Price / Earnings Ratio (common stock price/earnings ratio).

A Book Review Of Fernando Orejuela's "Rap and Hip Hop Culture"

Article • Popular Music

This article is a book review of a recent textbook made for in-classroom use by Dr. Fernando Orejuela of Indiana University. This review explains the materials and resources available in the textbook, as well as connects this textbook project back to earlier, similar formalized and non-formalized projects in rap.

When Trust and Shared Goals Spark Entrepreneurial Thinking

Article • Entrepreneurship Theory and Practice

This study explores how trust and shared goals within organizations drive their entrepreneurial orientation (EO)—the willingness to innovate, take risks, and act proactively. It focuses on how internal knowledge sharing acts as a bridge between social relationships and entrepreneurial outcomes, and how this process depends on the degree of formalization in organizational structures. Using data from Canadian firms, the research shows that when employees trust each other and share aligned goals, they exchange knowledge more freely across departments, which in turn strengthens the organization’s entrepreneurial mindset. However, this positive chain of effects varies with the level of formalization—that is, how rigidly work procedures and rules are defined. In highly formalized settings, the benefits of trust and shared goals on knowledge exchange and entrepreneurship may be partially constrained. For practitioners, the study highlights the importance of creating trusting relationships and shared purpose to enhance knowledge sharing and foster entrepreneurial thinking. Managers should strive for a balance: enough structure to coordinate effectively, but not so much that it hinders collaboration and innovation.

Accounting and accountability in grassroots voluntary sports organizations

Article • Sport Business and Management An International Journal

This study describes the professionalization process experienced by the amateur sport of volleyball in Ontario. This process involved the transformation of amateur/volunteer-based organizations to pluralistic organizations as professional practices were adopted over time. While professionalization occurred sporadically for some time, significant growth and the formalization of accountability requirements at the field level accelerated professionalization. Professionalization has taken the shape of moving from volunteer to paid staff positions, adopting standardized, formal accounting processes to report to constituents, and revenue-generating activities. Accounting acted as a carrier of the professional logic, both in terms of the adoption of formal accounting practices and the requirement of accounting professionals. Across the sport, the introduction of the professional logic became formalized through the demands of the provincial and federal sport organizations. This led to the forced adoption of certain accountability practices by grassroots organizations. Formal accounting practices were required to support accountability requirements and compliance to standards, further entrenching these practices. This formalization of professionalization affected the organizational field as pressure was exerted upon organizations to comply to participate in provincial and national competitions. The adoption of formal accounting practices in response to demands from below (the fee-paying members) and above (the PSO and NSO) contributed to the professionalization of grassroots organization.

Paradigm Evolution and Sustainability Thinking under Win-Win and No Win-Win Situations

Article • British Journal of Economics Management & Trade

The history of science is one based on revolutions and discourse where a new paradigm arrives challenging the status quo with the promise of progress and if the evidence is there to justify paradigm shift on the basis of that promise the consensus will be to shift paradigms. Apparently the shift from Adam Smith’s traditional market paradigm to the eco-economic or green market paradigm formalized in 2012/RIO conference meets all the requirements for paradigm shift listed above, but it was based on the accumulated environmental evidence for change only (e.g. pollution and degradation) leaving out the accumulated social evidence for change (e.g. poverty and inequality), but a progress towards sustainability none the less. Not much seems to be written from the point of view of sustainability about paradigm changes such as paradigm death, paradigm shift and paradigm mergers. General goals of this paper are a) to introduce a sustainability inversegram that can be used to state paradigm death and shift expectations under win-win and under no win-win situations; and b) to use this expectation framework to show the structure before and after the paradigm shift from the traditional market to the green market under win-win eco-economic conditions.

Semantic modeling of the “Publisher-Subscriber” scheme of the IoT network for choosing broker settings

Article • AIP Conference Proceedings

This article reviews the features of the Internet of Things network operation in the Publisher-Subscriber scheme via the Message Queuing Telemetry Transport (MQTT) protocol. The study has been conducted using the example of the IoT designed for monitoring of technological premises with telecommunication equipment, consisting of measurement devices, telecommunication environment, virtual and physical servers and applied software solutions. We have formalized a semantic description and have built the ontology of the subject area in order to study the IoT network’s architectural solutions, define criteria of analysis for the devices’ network activity and the physical phenomena properties under their supervision. The ontology contains the calculated indicators, responsible for network activity at different settings of the security policy, including the statistics of package volumes, time of setting and holding the connection. It includes the ranges of fluctuation of parameters and its critical values. Each of the objects in the ontology has its own digital presentation in the data bases, contains the results of measurements, statistical and spectral characteristics of data and serves practical task solution. Based on the ontology, the way for configure of the publoshers and brockers performing data collection and transmission was suggested. For this not only the statistics of requests from network logs is used, but also the characteristics obtained through the analysis of the processes monitored by IoT devices.

Combining Quantitative Cyber Intelligence with Traditional Qualitative Intelligence Analysis

Article • ACM Transactions on Privacy and Security

Cyber threats are becoming more frequent and increasingly menacing. To cope with this, cyber security researchers have created novel ways of automating both detection and analysis of cyber threats using Artificial Intelligence (AI) and Machine Learning (ML). One important application of this is Cyber Threat Intelligence (CTI) where AI and ML methods provide algorithms that automatically analyze huge volumes of leads, traces, and intelligence reports, speeding up the otherwise time-consuming human intelligence analysis process. The quality of automated CTI tends however to be decreasing in realistic settings where evidence can be incomplete and ambiguous, and where threat actors may use deceptive tactics. In practice, AI- and ML-driven approaches to CTI often need to be complemented with human intelligence analysis for achieving high enough quality. This article presents AMBARGO, which is a quantitative framework that combines the efficiency of AI and ML with the contextual and hypothesis-driven nature of human intelligence analysis. What AMBARGO adds is an ability to reason with multiple interpretations of evidence, and to keep multiple possible hypotheses, without committing too early to one of them. This ability, formalized mathematically in AMBARGO, is one of traits that makes the human analyst indispensable for achieving high quality intelligence, namely assessing incomplete, ambiguous, and potentially deceptive evidence.

Design of an Ontology to Represent the Elaboration of the Annual Operational Plan

Article • Proceedings of the 16th International Conference on Theory and Practice of Electronic Governance

This article focuses on designing an ontology for the Annual Operational Plan in Ecuador, a process within the Planning area of the Decentralized Autonomous Governments. We propose a set of activities and tasks for ontology development based on the Methontology methodology. Following development, we formalized the proposed ontology using Protégé. The primary theoretical contribution lies in defining an ontology within a specific government area. Moreover, from a practical perspective, we have developed a tool facilitating the analysis and processing of data for budget planning in Ecuador.

Topic-oriented Adversarial Attacks against Black-box Neural Ranking Models

Article • Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval

Neural ranking models (NRMs) have attracted considerable attention in information retrieval. Unfortunately, NRMs may inherit the adversarial vulnerabilities of general neural networks, which might be leveraged by black-hat search engine optimization practitioners. Recently, adversarial attacks against NRMs have been explored in the paired attack setting, generating an adversarial perturbation to a target document for a specific query. In this paper, we focus on a more general type of perturbation and introduce the topic-oriented adversarial ranking attack task against NRMs, which aims to find an imperceptible perturbation that can promote a target document in ranking for a group of queries with the same topic. We define both static and dynamic settings for the task and focus on decision-based black-box attacks. We propose a novel framework to improve topic-oriented attack performance based on a surrogate ranking model. The attack problem is formalized as a Markov decision process (MDP) and addressed using reinforcement learning. Specifically, a topic-oriented reward function guides the policy to find a successful adversarial example that can be promoted in rankings to as many queries as possible in a group. Experimental results demonstrate that the proposed framework can significantly outperform existing attack strategies, and we conclude by re-iterating that there exist potential risks for applying NRMs in the real world.

Maximal and minimal dynamic Petri net slicing

Article • Fundamenta Informaticae

This paper is about Petri net slicing, a technique to reduce the size of a Petri net to ease the analysis or understanding of the original Petri net. The paper presents two new Petri net slicing algorithms to isolate those places and transitions of a Petri net (the slice) that may contribute tokens to one or more places given (the slicing criterion). The two algorithms proposed are formalized. The maximality of the first algorithm and the minimality of the second algorithm are formally proven. Both algorithms, together with three other state-of-the-art algorithms, have been implemented and integrated into a single tool so that we have been able to carry out a fair empirical evaluation. Besides the two new Petri net slicing algorithms, a public, free, and open-source implementation of five algorithms is reported. The results of an empirical evaluation of the new algorithms and the slices they produce are also presented. The first algorithm collects all places and transitions that may contribute tokens (in any computation) to the slicing criterion. In contrast, the second algorithm collects the places and transitions needed to fire the shortest transition sequence that contributes tokens to some place in the slicing criterion. Therefore, the net computed by the first algorithm can reproduce any computation that contributes tokens to any place of interest. In contrast, the second algorithm loses this possibility, but it often produces a much more reduced subnet (which still can reproduce some computations that contribute tokens to some places of interest). The first algorithm is proven maximal, and the second one is proven minimal.

Advocacy education and training in psychology

Article • The Counseling Psychologist

This article describes how to develop or improve social justice, advocacy, and public policy education and training for psychologists and psychology trainees. Although advocacy is one of the core competencies in counseling psychology training, historically, lack of formalized advocacy training served as a barrier to psychologists engaging in advocacy efforts.

A theory of higher-order subtyping with type intervals

Article • Proceedings of the ACM on Programming Languages

The Scala programming language has a powerful and expressive type system. This helps programmers write flexible and highly reusable code without giving up the benefits of static typing. Static types provide both a human-readable high-level specification for the code and allow the compiler to catch many potential bugs. But while programmers enjoy the expressiveness of Scala's type system, it complicates the job of compiler developers. Like any piece of complex software, the Scala compiler is itself prone to bugs. One way to reduce the number of such bugs is to create a mathematical model of the type system and prove its correctness. The model can then be used as a blueprint for implementing the compiler. Previous work has developed such a model, called the calculus of Dependent Object Types (DOT). But that model did not cover the full Scala type language. In particular, it was missing a blueprint for Scala's so-called Higher-Kinded (HK) types. This paper develops a formal mathematical model of HK types and proves that it has the crucial property of "type safety" and other desirable properties. The corresponding mathematical proofs are complex. We have therefore formalized and checked them using a special software called a "proof assistant" (the Agda interactive theorem prover).

MOVEMENT OF EVIDENCE IN THE EUROPEAN UNION: CHALLENGES FOR THE EUROPEAN INVESTIGATION ORDER

Article • Baltic Journal of Law & Politics

The issue of international cooperation in criminal matters has interested legal theorists and practitioners for decades. In this area of law there are certain challenges that can only be tackled by using the joint efforts of the States, which is different from the national law of the States. For this reason, certain principles of law are specific for international cooperation, and on the basis of these principles States provide legal assistance requests to each other or else create preconditions to ensure the efficient and unimpeded criminal proceedings. It is true that the principles of mutual legal assistance and recognition, and the influence of their alternation are not identical to all segments of international cooperation, including the development of the evidence law in the European Union. With regard to the evidence and their admissibility in Member States of the European Union, it should be noted that this issue is still relevant, because the biggest concern of some Member States is the admissibility of evidence, when evidence is collected in one State and the admissibility of them is assessed in the other State. It would seem like a more formalized "concern", but basically it is a quite significant impulse for searching of new legal instruments in the European Union, which would be able not only ensure the acceptability (admissibility) of evidence that was collected in the foreign State in accordance with the relevant procedural form, and in the court of the State which obtained this evidence, but also the sovereignty of the State, the authenticity of the national law, and the respect for the legal culture and traditions of this State. .

Applying Universal Design for Learning to library peer professional development: a case study acknowledging adults as learners

Article • Reference Services Review

The research surrounding Universal Design for Learning beyond standard educational contexts does not currently exist, inside or outside of the library literature. This paper presents a new paradigm in expanding accessible and inclusive learning practices to include less formalized learning spaces.

Wind Tunnel Testing of Tethered Inflatable Wings

Article • Journal of Aircraft

Kite-like high-altitude aerial platforms provide a large number of applications from airborne wind energy generation, to weather monitoring, etc. However, they require lightweight and durable wings which result in complications in estimating the performance of the system. We provide for the first time formalized experimental data for such a tethered kite constructed from an inflatable wing and show that it is possible to passively tailor the wing to achieve the desired aerodynamic performance.

AI ethics strategies and practices in organizations: a scoping review

Article • International Journal of Ethics and Systems

This scoping review aims to categorize and analyze the academic literature on promoting the implementation of artificial intelligence (AI) ethics within organizations. We discovered that the healthcare sector is at the forefront of the discussion compared to other areas, such as business ethics and organizational management. Our results also reveal a gap in translating theoretical and conceptual propositions into practice. Supporting our endorsement of a pluralistic ethical perspective, our findings illustrate the various approaches organizations can adopt to enhance their implementation of AI ethics. Although we deliberately excluded publications that solely focused on policy solutions without including organizational ones, nearly 25% of the recommendations addressed AI ethics initiatives established, formalized, imposed, and regulated by an external entity relative to the organization. These results may mitigate the risk of AI ethics-washing and highlight the critical role of public engagement and social license in monitoring this risk.

Electrochemical analysis of anticancer and antibiotic drugs in water and biological specimens

Article • RSC Advances

It is about electrochemical sensors as a versatile tool for the detection of low level hazardous pharmaceuticals and their metabolites. It explores advances in nanomaterial-based electrochemical sensors for detecting health hazardous pharmaceutical contaminants and provides valuable insights into their mechanistic details. A list of highly hazardous anticancer and antibiotics has been published by the Environmental Quality Standards Directive, European Union and the WHO. A variety of standard analytical methods for detecting contaminants in environmental samples are available, however most of them are expensive, require bulky instrumentation, more time and expert manpower. To address these shortcomings, electrochemical sensors are developed for on-site detection pharmaceutical residues. The World Health Organization has formalized the ASSURED criteria as a bench mark for sensing analytics to produce robust sensing platform for real time monitoring. In this review the recent trends in detecting various pharmaceutical residues for on-site detection are evoked by applying nanomaterials based electrochemical sensing platforms.

“Try to keep them dumb and under the thumb”: exploring the “darker side” of psychological contracts in “overly embedded” immigrant enterprises

Article • Employee Relations

This study explores how immigrant entrepreneurs, particularly Pakistani business owners in Northern England, manage relationships with their employees and the challenges that arise from informal agreements based on family and cultural ties. Unlike formal employment contracts, these relationships rely heavily on trust and ethnic connections, which can create both advantages and problems. While close-knit ties promote loyalty, they also lead to unexpected issues, such as skill gaps and even competition within the family. By combining psychological contract theory with the mixed embeddedness framework, this study shows how relying too much on informal agreements can hurt business stability and growth. The findings suggest that immigrant entrepreneurs could benefit from formalized management practices and clearer role definitions, and that training programs could help these businesses thrive more sustainably. This research contributes a fresh perspective on the complexities of immigrant entrepreneurship and the need for more structured employment practices in culturally embedded enterprises.

Pre-Hispanic ritual use of psychoactive plants at Chavín de Huántar, Peru

Article • Proceedings of the National Academy of Sciences

At the 1st millennium BCE monumental center of Chavín de Huántar, archaeologists have for decades interpreted carved stone art to mean that ritual included the use of psychoactive plants. However, neither psychoactive plant remains nor chemical traces of psychoactive compounds in likely ritual contexts have ever been identified. Recently excavated deposits sealed in an underground gallery at Chavín contained included bone tubes, artifacts associated with consumption of psychoactive plants elsewhere in the region. This paper reports microbotanical and chemical analyses of residues in those tubes that provides evidence that psychoactive plants were used in institutionalized ritual at Chavín. This is compelling evidence that psychoactive plants were part of formalized rituals controlled by particular individuals or groups, rather than exploratory vision-quests or shamanic healing practices. As such, they argue that rituals involving psychoactive plants were an important element of the long-term transition from small egalitarian societies to large stratified ones. Such rituals apparently contributed to the creation of societies where social, political, and economic inequality were thought of as normal and to be expected.

Institutional logics, social interactions and management of tensions in public-private partnership organizations

Article • Journal of Health Organization and Management

Tensions that arise between the public and private actors in PPPOs are primarily responded to by private actors mainly with avoidance, defiance, or decoupling and subsequently resolved by their joint efforts through informal collaboration, formalization, formalized collaboration, enforcement, or coercive pressure, depending on how the state and market logics are enacted within the hospitals and how social interactions and relationships between public and private side actors are formed accordingly.

How to Understand: Three Types of Bilingual Information Processing?

Article • Communications in Computer and Information Science

The major idea of our proposed approach is both human and the machine can cooperate or interact with each other according to their characteristics. Concretely, it is composed of the following three steps: First, find issues from the Chinese-English bilingual translation at phrase sentence level alignment. The challenge in Chinese-English translation lies in an inconsistency of the meanings between the Chinese characters and the English words. Then, analyze the problems from the view of interdisciplinary, cross-domain and cross-industry. Finally, address leveraging human-machine to divide the task and coordinate with each other. As a result, not only we discover both parallel dual formalized approach of big and small strings, but also find and validate both the superiority and followed scientific principles of generalized bilingual information processing method.

The Formal Understanding Models

Article • Communications in Computer and Information Science

The method steps are as follows: 1. Obtain a complete all equal formal understanding model (A) by constructing a twin Turing machine between numbers and numbers. 2. Obtain an approximately equal intelligent understanding model (B) by constructing a twin Turing machine between numbers and symbols. 3. Obtain a similar socialized understanding model (C) by constructing a twin Turing machine between numbers and characters, which is characterized by: the model A to B and then C gradually converge. As a result, it was found that the machine formal information processing and the human content information processing are opposite in convergence. It is clear that the combination of the three formalized understanding models and the bilingual model of interpretative translation is the key to formal understanding, intelligent understanding and social understanding. Based on them, ambiguity, misunderstanding and understanding are all well understood.

The Relationship Between Language and Speech: Formal Understanding of Natural Symbology

Article • Chinese Language and Literature

The method is: First, it is clear that monosyllabic Chinese characters have two basic attributes of language and text, English letters and morphemes, words, phrases and sentences, which belong to another type of text and language; It is found that in the past Chinese was regarded as a monosyllabic language and English was regarded as a polysyllabic language which is a complete misjudgment; Finally, it is further clarified that monosyllabic and mixed syllables not only have unique interpersonal communication in Chinese, but also have human-computer interaction and even automated batch processing with uniqueness, its fundamental feature is that the monosyllabic Chinese characters meet a certain arithmetic base that is indirectly formalized, that is, the typical P base. Its result is that, it was unexpectedly discovered that arithmetic and language have rigid constraints on the underlying sequence-position logic and surface linkage functions, but there are flexible rules for broad interpretation or translation for the symbolic objects of their division and combination.

A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations

Article • Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017

Interactive Theorem Provers (ITPs) are complex tools allowing one to encode mathematical theories and algorithms in a formal language, formulate theorems on these algorithms, develop proofs for these theorems, and mechanically check the formalized proofs with a high level of guarantee. In this work, we specifically rely on the Coq tool, of the most used tools in the ITP community. It has a very expressive logic, several tactic languages focusing on proof development, builtin support for computation, as well as support for proof reflection (roughly, the ability to perform proofs by computation). In this paper, we present the validsdp library - https://github.com/validsdp/validsdp/ - which gathers Coq tactics that can automatically and formally prove inequalities on multivariate polynomials involving real-valued variables and rational constants. These tactics internally rely on proof reflection, floating-point arithmetic, and SDP solvers (using semidefinite programming), following a certifying-based methodology that ensures we can fully trust the automatic proofs, despite the fact the external solvers are unverified and produce approximate solutions.

An approach to determine vehicle idle time at unloading points

Article • TRANSPORT, ECOLOGY - SUSTAINABLE DEVELOPMENT EKO VARNA 2021

The paper represents an analysis of current methods for determining the vehicle idle time at loading and unloading points. The features of servicing cargo flows in transport hubs are defined. The total idle time of vehicles at unloading points, which consists of maneuvering time, service queueing time, direct service time, cargo acceptance time and time for paperwork has been formalized in the paper. The factors influencing the components of the total time have been revealed. An approach to queue management at unloading points is presented. It takes into account the existing relative priorities in traffic maintenance. The suggested approach is based on the principles of queuing and scheduling theories. The characteristics of three types of traffic flow with different priorities such as service time, the arrival rate of the traffic flow and workload of the unloading point are determined. According to the results of statistical data processing, it is found that the distribution of service time for vehicles with different priorities is in agreement with the theoretical normal distribution of a random variable with specific parameters. The results of the study can be used for planning the work of road transport and also by specialists in planning the work of the unloading point in terms of optimizing the work to prevent idle time and excessive costs, which will increase the level of enterprise production efficiency.

Risk-based internal audit: factors related to its implementation

Article • Corporate Governance The International Journal of Business in Society

This study empirically investigates the factors associated with the implementation of risk-based internal audit (RBIA). First, a literature review of the relevant literature is performed, and five potential factors related to the implementation of risk-based internal audit are identified. Based on that, we construct a questionnaire survey sent out to 185 internal auditors, executives, and accountants in Greece to receive 90 responses during November 2019-January 2020. Multiple regression analysis is conducted to identify the factors related to the implementation of RBIA. We show that there is a statistically significant positive relationship between the implementation of RBIA and 1) the provision of risk management training, 2) an active audit committee role, and 3) the establishment of a formalized risk management system. Empirical studies on the factors related to the implementation of risk-based internal audit are rare. This is the first study to create empirical variables based on a thorough review of the relevant literature to empirically investigate the factors that are related to the implementation of RBIA in an emerging economy. By focusing on the Greek context, this study also sheds light to other countries with similar CG systems, thus providing insights to settings where the Type II agency problem exists (La Porta et. al., 1999). The identification of factors related to RBIA enhances internal audit effectiveness through proper risk assessment, and effectively enhances the accuracy and quality of financial information.

Hutz Limhitzato as Matter Out of Place: From Mary Douglas to the Stam

Article • Journal of Ancient Judaism

The Bible prohibitions the consumption of a tereifah, or a mauled animal, at Exodus 22:30. This prohibition is interpreted and expanded in a variety of ways in early Jewish biblical interpretation. This paper considers a heretofore mostly neglected approach that extrapolates from this prohibition a rule that "once X goes outside of its (proper) bounds it is prohibited," which it applies to a limb partially born, sacrificial flesh that exits the sacred bounds in a variety of scenarios, and several other cases. The paper demonstrates how, although some of these applications existed in earlier, Tannaitic material, they only became conceptualized and formalized as a rule in late, anonymous material of the Babylonian Talmud. The paper reconstructs the logic of extrapolating from the prohibition of a torn animal to the prohibition of items that have left their bounds on the basis of Mary Douglas' insight that "matter out of place" is often seen as transgressive and ruled out by ritual systems. The paper includes an excursus demonstrating that, although an apparent case of the conceptualized rule appears in an early, Tannaitic source, this passage actually stems from a medieval source that was incorrectly included in editions of the early source.

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Article • 2012 IEEE Colloquium on Humanities, Science and Engineering (CHUSER)

In the management literature great emphasis has been put on the concept of transaction costs, whereas firms' very capacity to carry out economic transactions has received less attention. Western Norway has numerous small- and medium-sized machining enterprises (SMEs), but these lack capacity to collaborate in complex and large-scale projects with the supplying companies for the operators at the oil fields in the North Sea. As a consequence, this decreases the potential for value creation in the region. In this paper we argue that SMEs in particular face a dual challenge of horizontal- and vertical integration to pursue inter-firm collaboration. Qualitative interview data indicate that the SMEs perceive the managing of human resources to be the greatest challenge in this regard. To overcome the lack of collaborative capacity they report that inter-firm agreements should be relatively formalized through some kind of common ownership, such as joint ventures.

Simplified Formulation of Mechanics of Structure Genome

Article • AIAA Journal

This paper presents a simplified formulation of mechanics of structure genome (MSG). MSG is a unified theory for multiscale constitutive modeling for all types of composite structures. It is generalized from the previous research works based on the variational asymptotic method (VAM) including the variational asymptotic beam sectional analysis, the variational asymptotic plate and shell analysis, and variational asymptotic method for unit cell homogenization. In this paper, the original complex formulation of MSG is simplified and the principle of minimum information loss underpinning MSG is formalized. The simplified formulation of MSG is applied to construct the linear elastic Euler-Bernoulli beam model, Kirchhoff plate model, and 3D Cauchy continuum model. The connections of MSG to previous VAM-based theories are clearly pointed out.

Who Aspires to be a Partner in a Public Accounting firm? A Study of Individual Characteristics and Gender Differences

Article • Accounting Horizons

Based on a survey of a large number of public accountants we examine factors associated with aspirations to become a partner in a public accounting firm with a focus on gender differences. Prior research on gender disparity at the partner level speculates that preferences, structural barriers or a combination of both inhibit women from progressing to the partner level. While firms have responded with work-life initiaitives such as formalized alternative work arrangements, our survey results provide evidence that the proportion of females aspiring to be partners is significantly less than the proportion of males. Our analysis of the factors relating to aspirations reveals several interesting similarities and differences between genders with implications for public accounting firms wishing to eliminate the perception of a "glass ceiling," encouraging more female represenation at the partner level.

How does regulatory framework impact sectoral performance? A systematic literature review

Article • International Journal of Productivity and Performance Management

The regulatory framework is the supporting infrastructure that controls and implement a proposed course of law, rule, or action. The regulatory order is now more formalized, expert-driven, transparent, independent, and pervasive across countries and sectors. As a result, regulatory reforms enable markets to function efficiently by providing a supportive environment for increased investment, private sector growth, and market-led economic growth. This study aims to review previous literature for understanding the impact of sectoral regulatory framework on sectoral performance.

Women Deacons in the Maronite Church

Article • Theological Studies

The study investigates the inclusion of women deacons in the canons of the National Synod of Mount Lebanon of 1736, which formalized Latinization of the Maronite Church, providing for codification of its particular law. The canons were approved in forma specifica by Pope Clement XII and have never been modified or overruled, thereby giving evidence of the liceity of ordaining women deacons in the Catholic Church.

Applying Medical Device Informatics to Enable Safe and Secure Interoperable Systems: Medical Device Interface Data Sheets

Article • Anesthesia & Analgesia

Medical Device Interface Data Sheets (MDIDS) are a formalized method to document the information from a device that is 1) at the user interaction level (e.g. displayed values or key presses), 2) information that can be "streamed" from the electronic data interfaces, and 3) information that reflects the internal status of the device and context of use. Capturing context within the MDIDS is essential to make sure the information is used correctly and safely. Standardized information exchange between medical devices (interoperability) can lead to improved patient safety by enabling applications that interact with devices from different manufacturers and facilitate more rapid development by enabling the reuse of existing devices for novel clinical applications. Capturing and making explicit information that is input to and outputted from a device can support the development of safety applications that detect and prevent medical errors or enable “smart” applications based on data fusion.

The bridging role of regional headquarters. Multinational companies in the Asia-Pacific region

Article • Multinational Business Review

Large multinational companies (MNCs) are strongly formalized, often standardized, and complex with multiple hierarchical levels. Over the past few decades, MNCs have strengthened their coordination and control systems by creating regional headquarters (RHQs). This research investigates how MNCs rearticulate control dimensions at RHQs, to coordinate and exert control over subsidiaries in the Asia-Pacific region. Based on a survey of 86 French MNCs in the Asia-Pacific region, this research applies a structural equation model in order to determine RHQs’ roles in the field of regional decision making, coordination and control. We find that large MNCs, with significant presence in Asia, transfer coordination and control to RHQs, in a way that leads us to propose the use of the expression “regio-centralization”. RHQs become socialization hubs, where most regional decisions are taken and where international managers meet. MNCs mobilize at the same time expatriates, short-term assignees, and local managers who intensively interact at RHQs. Thus, informal control at RHQs increases, partly substituting formal control by HQs. Smaller MNCs, without RHQs, on the contrary, base their control and coordination on the formalization of HQs-subsidiary relations, especially through strong reporting, in combination with centralized decision-making at HQs

(Responding to) Youth epistemologies to create a third space: a reclamation of learning in an English language arts classroom

Article • English Teaching Practice & Critique

This article focuses on the construction of a third space within a high school. Third space theory emphasizes the integration of the first space of home/local community with the second space of more formalized institutions. We consider how urban youth of color engage the educational context as a basis for (re)imagining their history, culture, and themselves in order to construct counter-narratives away from framing them as failures, deficient, and depicted in “damage-centered” ways.

The '60s Kids in the Corporation: More Than Just “Daydream Believers”

Article • Academy of Management Perspectives

Did the '60s kids drop out? No. Are they different? Somewhat. Professor Raelin of Boston College has devoted a number of years to studying the '60s kids, defined as those who were between the ages of 12 and 20 in 1963, the year he believes best represents the beginning of an impactful decade. The fact is that '60s kids, compared with those a decade before and a decade after, more frequently chose professions as their career. They did not necessarily "hang out a shingle," but have opted for professional occupations (engineers, lawyers, scientists, doctors, social workers, etc.) within organizations. Moreover, they have tended to avoid taking a position in management. This "new class professional," Raelin believes, while obviously not radical, does maintain stronger values regarding professional behavior. Their loyalty is more to the standards of their profession than to the dictates of their employing organization. Raelin, a '60s kid himself, advises that to manage these '60s kids best, executives need to create an organizational climate that will encourage individual initiative, autonomy, some degree of participation in decision making, and a quality of life that fosters more of a human touch rather than a highly formalized, bureaucratic relationship.

Private Property and Collective Action: Cooperation as a Means of Reappropriating the World

Article • SSRN Electronic Journal

This paper reconsiders commonly held views on the ownership and management of private property, contrasting capitalist and simple property, particularly as it relates to the impact of the firm shareholder governance model on the shape of society. I contrast an exchange value standpoint with a use value perspective to explicate current conditions under which neither the state nor the market prevail in organizing economic activity (i.e., the cooperative form of governance and community created brand value). This consideration is motivated by the scale and scope of the modern global crisis which combines financial, economic, social and cultural dimensions to produce world disenchantment (Fischbach, 2009a; Rosa, 2012). Dismissing the alternative of individuals simply forsaking engagement with society as it stands, it becomes necessary to revisit at this historical moment, the ideals on which modern societies are built, including the philosophy of freedom for all. This utopian concept has produced an ideology limited by capitalist notions of private property, motivating this inquiry. This paper offers mechanisms and recommendations regarding the formalized conditions for collective action and definitions of common guiding principles to facilitate new expressions of the principles of co-ordination. Such behaviour will allow for the development of common resources the purpose being a re-appropriation of the world.

Private property and collective action: co-operation instead of competition

Article • EuroMed Journal of Business

Purpose – The purpose of this paper is to reconsider commonly held views on the ownership and management of private property, contrasting capitalist and simple property, particularly as it relates to the impact of the firm shareholder governance model on the shape of society. Design/methodology/approach – The author contrasts an exchange value standpoint with a use value perspective to explicate current conditions under which neither the state nor the market prevail in organizing economic activity (i.e. the co-operative form of governance and community-created brand value). Findings – This paper offers mechanisms and recommendations regarding the formalized conditions for collective action and definitions of common guiding principles to facilitate new expressions of the principles of co-ordination. Such behaviour will allow for the development of common resources the purpose being a re-appropriation of the world. Originality/value – This consideration is motivated by the scale and scope of the modern global crisis which combines financial, economic, social and cultural dimensions to produce world disenchantment. Dismissing the alternative of individuals simply forsaking engagement with society as it stands, it becomes necessary to revisit at this historical moment, the ideals on which modern societies are built, including the philosophy of freedom for all. This utopian concept has produced an ideology limited by capitalist notions of private property, motivating this inquiry.

Tribal Medicine Practices in Kadugolla Tribes : A Sociological Study of Chitradurga District

Article • International Journal of Trend in Scientific Research and Development

Traditional medicine may include formalized aspects of folk medicine, that is to say longstanding remedies passed on and practiced by lay people. Folk medicine consists of the healing practices and ideas of body physiology and health preservation known to some in a culture, transmitted informally as indigenous knowledge, and practiced or applied by anyone in the culture having prior experience. In this study various medicinal practices has been observed and used by families of Chitradurga district. The tribal people like kadugolla's are used these plants to treat different diseases. The use of these herbal medicines has important role in the modern medicine system like Ayurveda, unani sidda, homeopathy, etc. The use of herbal medicine is not only cost effective but also safe and almost free from serious side effects. A total 35 medicinal plant species distributed in Chitradurga district. Nomadic Semi nomadic tribal families are practicing this traditional medicinal system as an alternate occupation along with agriculture and animal rearing. These medicinal plants are used for headache, earache, stomach ache, antioxidants, liver diseases, renal disease, anti diabetic, wound infections, skin infections, fever, cough, diarrhea, eye infections, general weakness, blood purifier, to enhance immunity and other several diseases. Veeresha. M | Dr. Krupalini H S "Tribal Medicine Practices in Kadugolla Tribes : A Sociological Study of Chitradurga District" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-5 , August 2018, URL: https://www.ijtsrd.com/papers/ijtsrd16952.pdf

Agency in the case of long-term unemployment: Where to find?

Article • Arbeit

For a significant proportion of those affected, the consolidation of unemployment is often associated with multiple difficulties (low skills, illness, age 50+, language deficits, caring duties or forms of addiction). Thus, the chances of returning to employment decrease considerably. However, the SGB II pursues employment as a normative goal. Thus, the paradigm of ‘Foerdern und Fordern’ (‘Promoting and Demanding’) is inherent in the formalized processes of job placement and is oriented towards maximized effectiveness. Job center professionals are measured according to placement metrics and long-term unemployed according to their efforts to find and take up work. There is a lot of formal support available to end long-term unemployment as quickly as possible through employment. Nevertheless, the numbers of long-term unemployed persons are still high and the numbers of job placement are low. To investigate this situation, a qualitative study has been conducted. It is based on interviews with 33 long-term unemployed people who, despite the existence of multiple barriers, were able to find employment. It can be shown that these long-term unemployed often do not perceive the job placement offers as realistic, as they often do not address their specific needs. These successful job transitions and our respondents’ experiences with institutional job placement procedures gave the input for identifying four “action-traps“, which occur in the placement situation and can have a problematic effect on its success. In conclusion, consequences for job placement are discussed, in particular under the orientation towards an approach of “extended agency”.

A Critical Legal Approach to the South China Sea Territorial Dispute

Article • Journal of the History of International Law / Revue d’histoire du droit international

The ‘law of nations’ that colonial powers invoked to claim the South China Sea islands was based not on international convention or custom but on their own municipal laws on guano concession. It provides that states have the exclusive right to assert title over distant islands where their respective citizens have engaged in economic activities. It was applied selectively to advance colonial and maritime interests and to suppress the claim of China. In their own records, the United States and United Kingdom acknowledged China’s prior and exclusive economic activities on the Spratly Islands and Paracel Islands, and consolidation of title over the Paracel Islands. The records were ignored and subsequently revised, thereby excluding China from availing of the rule. The Japanese peace treaties formalized China’s exclusion by relegating its claim to the same category as the claims that emerged from recent acts of occupation, and subjecting it to resolution by convention.

A Review of Approaches to Manage Architectural Knowledge in Agile Global Software Development

Article • IET Software

Nowadays, Agile and Global Software Development (AGSD) has brought benefits and new challenges to the software industry. Among the main challenges is Architecture Knowledge Management (AKM), due to the following reasons: (1) in Agile Software Development team members prefer to convey knowledge in a face to face manner, over transmitting it through formal documents; and (2) an efficient AKM in Global Software Development involves managing explicit knowledge. These opposite paradigms turn AKM into an unsolved issue in AGSD. In this paper we present a systematic mapping review about AKM in AGSD. From this review, we identified nine approaches that AGSD companies use to overcome the AKM challenge, which are grouped in three areas: (1) documentation artifact-based, (2) communication-based, and (3) methodological-based. Also, we found that the selected papers evenly support the three phases of the integrated knowledge management cycle (creation/capture, sharing/dissemination and acquisition/application), although only 7% of them support the capture of architectural knowledge in a formalized way. Finally, we conclude proposing critical points to consider in the implementation of AKM solutions in AGSD, and presenting our directions of future work.

Social Capital Formed in Conflict Resolution in Bangka Belitung

Article • Society

Three potential conflicts that need to be anticipated in the reality of the life of the Bangka Belitung community in the future. The results of qualitative research through conflict mapping in seven districts/cities showed the potential for economic conflict in fighting for tin resources, agrarian conflicts with development dimensions related to land expansion for large-scale oil palm plantations, and inter-village and interethnic youth conflicts became the dominant issue. The mechanism of the savety valve as a damper of potential recurring conflicts must be institutionalized through functional and sustainable formalized social capital.

Quality assessment of medical care using an automated information system

Article • 2018 9th International Conference on Information, Intelligence, Systems and Applications (IISA)

The aim of this work is the evaluation of the quality of medical care provided in the hospitals of the Volgograd region for 2014-2016. A unified formalized expert questionnaire for assessing the quality of medical care which includes different groups of procedural indicators and an integrated indicator had been developed.

Immaterial public order : legal response to social crisis ?

Article • Hungarian Journal of Legal Studies

It is about the notion of the immaterial public order and its use in law and jurisprudence in the context of social crises. Immaterial public order is an ancient response becoming part of the formalized legal order. It helps the normative authorities to respond to many challenges which cannot be solved by regular tools. Immaterial public order is also useful not only to regulate the relationship between different legal orders but also to settle the relationship between the legislator and the constitutional judge. The analysis offers a general doctrinal approach while focusing on the French case.

Revisiting the Reliability Assessment of frame constructions of Industrial Building

Article • Applied Mechanics and Materials

Article proposes a comprehensive approach to the formation of the program sequence surveys of industrial buildings equipped with overhead cranes. Authors formalized synthesis algorithm that reveals the concept essence of the probabilistic method application to the study of changes in the stress-strain state of the industrial building frame during its operation taking into account the variability impacts. The calculation of the reliability and durability is based on the method of limiting states. The implementation of this method makes it possible to take into account the random nature of not only the combination of existing loads, but also the strength properties of building materials by constructing a system of safety factors.

SPR and ASPR Untangled

Article • IFAC Proceedings Volumes

The theory, proofs, use and implementation of robust adaptive control algorithms require the understanding of the concepts of Strictly Positive Real (SPR) and Almost Strictly Positive Real (ASPR) plants. Although these concepts are defined in the existing literature, both in time and frequency domains, their grasp is not straight forward for the practicing control engineer that deals with real-world plants. Here, we attempt to present the interpretation and meaning of these concepts in a more intuitive way for the practicing control engineer. That is, we use the Bode, Nyquist, Nichols and Root-Locus domains that may help the control engineer better grasp their implications. The paper is oriented towards the practitioner and therefore any proof that already appears in the literature is only cited. An important result that is formalized and proved is that any stable system can be made ASPR. An example is also given in order to demonstrate these concepts.

Workplace Learning, Financial Support, and Organizational Commitment of Non-Regular Employees

Article • The Korean Journal of Human Resource Development Quarterly

This study empirically examines the effect of ‘participation in institutionalized formal training and institutionalized informal-relational learning’, as formalized workplace learning, and ‘financial support for learning of business organizations’ on ‘organizational commitment’ of non-regular employees. Using the 2009 Human Capital Corporate Panel collected by the Korea Research Institute for Vocational Education & Training, surveys of 205 non-regular employees from 85 companies were analyzed. Liner-regression modeling analysis revealed that non-regular employees’participatory experiences in institutionalized informal-relational learning improved their organizational commitment. However, their participation in institutionalized non-formal training and employer’s financial support for learning had no effect on organizational commitment. The participatory experience in institutionalized informal-relational learning of non-regular employees had stronger impacts on organizational commitment relatively.

Computerization as a Means of Cultural Change: Information theories and the information society

Article • AI & Society

Since World War II the concept of Information has received several new definitions. Information can be understood as knowledge in general, as theoretical, formalized knowledge in general or as knowledge related to specific domains or specific representational forms. Because of these mutually inconsistent concepts the common traits are to be found in a perspective transcendent to those theories. The central cultural changes, it is argued, take place on the level of the societal knowledge infrastructure, evolving from the knowledge infrastructure of the industrial societies as a long-term secularization process, resulting in new forms for representation and manipulation of knowledge. The process is seen as rooted in changes of the primary domains for knowledge extraction and in a change in the human relations to the languages in which we interpret the relations to nature. Keywords: Computerization; Information theory; Information society; Language; Knowledge representation systems; Writing technologies

Simple implementation of Almost Passivity in PID controlled systems

Article • Melecon 2010 - 2010 15th IEEE Mediterranean Electrotechnical Conference

The theory, use and implementation of robust adaptive control algorithms require the understanding of Passivity and Almost Passivity. For LTI system these are the Strictly Positive Realness (SPR) and Almost Strictly Positive Realness (ASPR) concepts. Although these concepts have been defined in the existing literature, their grasp is not straightforward for the practicing control engineer that deals with real-world plants. In an attempt to present the interpretation and meaning of these concepts in a more intuitive way, in this paper we use various frequency domains illustrations that may help the control engineer better grasp their implications. An important result that is formalized and proved is that any system controlled by PID controller can be made to become ASPR and thus, robust adaptive control can be used towards improvement of performance. An example is also given in order to demonstrate these concepts.

Pipeline balance problem, with long wire load, formalized with logical effort.

Article • Electronics Letters

In logic circuit design, when there is a large, isolated wire load in the critical path, pipelining may be not trivial because the pipeline stage that contain the long wire is intrinsically slower. In principle, such penalty should be compensated by fewer logic depth in the overloaded stage, and/or by partitioning the large load among multiple pipeline stages. This work formalize the problem to obtain the optimal solution.

Importance of formalized relief in the pre-modern period

Article • The Economic History Review

The results show that in this period a substantial share of GDP, up to 3 per cent, could be spent on formal relief, offering subsistence to up to 8–9 per cent of the population, with a gradual rise over time and the highest figures being reached in the Netherlands in the eighteenth century. The three cases show a steep decline around 1800, a pattern found more generally in Europe. Next, these results are placed in a broader geographical perspective. This highlights the sharp differences within countries—which could be even larger than those between countries—and the high levels reached in the regions bordering the southern shores of the North Sea. In the last section, the results are used to discuss the possible causes underlying these long‐run patterns and geographical differences, including urbanization, wealth, religion, and social‐organizational features.

The Zero Concept in Ancient Egypt

Article • The Origin and Significance of Zero

Ancient Egyptian numerals and their zero concept are part of the non-European foundations of classical Greek mathematics and provide valuable materials for the mathematics classroom. However, non-Western achievements are little known due to European and North American rewriting of history to justify slavery and colonial occupations. That rewritten version of history flatly stated that mathematics began in classical Greece (about 500 BCE). But that date was more than 2000 years later than the development of significant mathematics in North Africa and West Asia. Also, scholars in South and East Asia had developed valuable mathematics at an early date. Throughout history, cultures around the world have independently developed distinct number systems and distinct systems of recording numerals. In pre-Columbian Peru and Central America, astronomers and mathematicians developed positional-value systems of numerals that used different methods to indicate an empty or zero-valued position. Others, as in Ancient Egypt, used an additive numeral system, without place value. In that case, they had no need for a zero-placeholder. But ancient Egyptian mathematics did use zero as a number, as a magnitude in bookkeeping records containing zero balances. Also labels on construction guidelines, still visible at pyramid and mastaba construction sites, show use of a system of integers including zero. Humanity has moved from tally records to our modern numerals in several stages. A basic concept of modern numerals includes use of a single, abstract symbol to stand for a given number of tallies. For example, the artifact known as the Metropolitan Museum knife handle, crafted c.3100 BCE, showed one lotus blossom representing the value, 1000. One cipher, the lotus blossom, was used instead of 1000 tally marks. For everyday non-monument applications, cursive hieratic numerals were written, instead of hieroglyphic. It was the hieratic numerals that the much later classical Greeks used as a model for their numerals. The concept of infinity was also explored in the papyri and may have been developed because Ancient Egyptians made much use of series of numbers.

Female Mathematics Role Models and Girls Performance in Mathematics in the South West Region of Cameroon: A Gender Issue

Article • International Journal of Trend in Scientific Research and Development

In Cameroon just like other countries in the world, Mathematics is an important subject with its skills very much needed in applying science and technology for development. There is growing demand for professionals in Science, Technology, Mathematics and Engineering STEM to meet up with significant labor shortage in the market. Women are often underrepresented in STEM and it has been noticed generally that females mathematics role models are lacking in the society. The low presence of female mathematicians Teachers professionals and others who stand for role models are lacking in the schools and society as a whole. This tendency seem to have combined with other environmental and other socioeconomic factors to give the girls a negative attitudes towards mathematics, visible in their lack of interest and low participation in its lessons. This attitude affects their ability to engage with Math related content, leads to poor performance and consequently fewer females pursuing degrees in fields that require a strong mathematics background. This paper seeks to determine how lack of female role models in mathematics negatively affect female student's participation and general performance in mathematics and also to show how female mathematics role models in the schools and society as a whole can be used to improve on the participation and performance of girls in mathematics. Research questions were constructed feminist theories and other theories in education were employed to guide the study. The study is descriptive and utilized 450 form four students and 44mathematics teachers from 158 public secondary schools in the South West Region of Cameroon. Statistical Package for social science SPSS version 12 was used to analyze data collected by research instruments. The findings shows that when girls are exposed to a female mathematics role models including the female mathematics teachers in schools, there is a positive impact that shows up in their motivation to study mathematics. To improve on the participation and performance of girls, the Researcher recommends that while school administration and other stakeholders in education work hard on making the pedagogy for secondary school mathematics gender sensitive, there should be heavy emphasis to expose students in secondary schools to female mathematics role models who will motivate their participation in mathematics and consequently improve their performance in the subject. Bisong Clara Bate AshuMbuoben (Ph.D) "Female Mathematics Role Models and Girls Performance in Mathematics in the South West Region of Cameroon: A Gender Issue" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: https://www.ijtsrd.com/papers/ijtsrd15621.pdf

Kleene's Readability and “Divides” Notions for Formalized Intuitionistic Mathematics

Article • Studies in Logic and the Foundations of Mathematics

High-Level Verification Using Theorem Proving and Formalized Mathematics

Article • Lecture Notes in Computer Science

On the Integrity of a Repository of Formalized Mathematics

Article • Lecture Notes in Computer Science

Formalized Music: Thought and Mathematics in Composition

Article • Notes

Flexary Operators for Formalized Mathematics

Article • Lecture Notes in Computer Science

An experimental library of formalized Mathematics based on the univalent foundations

Article • Mathematical Structures in Computer Science

Update on "Supersymmetry Via EDM (Electric Dipole Moment)", which ANY person is welcome to review.

Article • Qeios

Also, scroll to the article's end and read my reply to the review by Alessandro Rizzo. It contains thoughts about the infinite and eternal universe, something I call the Mobius Matrix, as well as the shape or geometry of spacetime. PRELIMINARY NOTE #1 - My approach may be called quantum-gravitational. I take "educated guesses", using the present state of scientific knowledge, at what might be revealed by a future union of General Relativity and Quantum Mechanics. Educated guesses sound remote from real science, but it's the best that can be done with a theory which doesn't exist yet. Of course, the maths accompanying that theory doesn't exist either - so formal mathematics can't be used. The quantum-gravitational approach isn't meant to be purely mathematical but also physical, with the binary digits and Mobius strips that compose every fermion and boson being linked - a state at odds with our human frame of reference of seeing objects and events as separated. As the movie "Interstellar" pointed out, people will oneday be able to build things they can't build now. Let's scientifically explore a few of those things. (Thanks go to Penny from TV's "Big Bang Theory" for inspiring Interstellar-related thoughts!) At the start of the 20th century, physicist Max Planck assumed that electromagnetic radiation can only be emitted or absorbed in discrete packets, called quanta. He thought of his discovery as nothing more than a math device ... a kind of trickery. Albert Einstein developed his explanation of the photoelectric effect from this “mathematical convenience”. So it appears entirely possible that another supposed mathematical trickery (Wick rotation) will find practical application in the future. Imagine the universe actually is a holographic projection or a computer simulation where every fermion and boson is linked by the AI-generating BITS (binary digits) of 1 and 0. What happens to formal mathematical definitions when every fermion and boson is linked? The linkage means everything throughout time and space can be regarded as one particle. This is reminiscent of John Wheeler's and Richard Feynman's speculation that the entire universe consists of just one electron, zigzagging through time (the weirdness of quantum physics vanishes and no particle can exist in two places at once since the unification of everything in space and time - possibly achieved with Quantum Gravity - means only one place or event can ever exist in the universal, co-moving frame of reference where observer and observed are united). If the universe can be regarded as one particle, how can one thing be added to another thing? Then 1+1=2 cannot be true in an absolute or quantum-gravity sense. 1+1=2 would only be true in the human frame of reference (it would also be true in the technology and mathematics which the human frame of reference developed). These conclusions regarding 1+1=2 may be compatible not only with a QG (quantum-gravitational) approach but also with an LF (Leonardo-Faraday) one. Neither Leonardo da Vinci nor Michael Faraday appear to have trained in the formal mathematics of their time but that lack never stopped them from discovering great things. 1+1 would equal 2 if human mathematics and technology from the 21st century used general relativity's curvature of time - made circular by Wick rotation and warping spacetime - to create the universe. But I look around and see that our tech/maths is not advanced enough yet. In forwards time travel, the waves composing mass in the x-axis and y-axis rotate in the counter-clockwise direction. Compare Wick rotation to a DVD that has no end. The future destination is reached by a computer using tensor calculus to change the present coordinates in the Cosmic DVD to ones in the future. To use a simple example confined to two dimensions: -1,+ i becomes +1, -i. This is interdimensional travel since it incorporates both the time and space elements of the time-space unity i.e. Wick rotation residing in the Mobius strips and figure-8 Klein bottles * composing space and mass. Backwards travel in time is identical to forward trips except for the coordinates being different and belonging to points in the past. * 1-dimensional BITS encode two-dimensional (2D) Mobius bands instead of the untwisted Strings of String Theory or Loop Quantum Gravity (also, binary digits may be thought of as strings of 1’s and 0’s). A Mobius band, with its undulations and single surface, must be travelled around twice to reach the starting point. This raises the possibility that billions or trillions of Mobius strips compose every particle of matter since such particles must be turned 720 degrees (completely rotated twice) to look the same. If photons and gravitons share EDM with neutrons, it’s reasonable to conclude the symmetry means photons and gravitons are also composed of Mobius loops. Electromagnetism and gravitation aren’t identical, so a photon might be simply constructed from billions of Mobius bands while a more complex graviton might be based on a pair of Mobius strips uniting into a figure-8 Klein bottle which is immersed in the 3rd dimension. Billions, or more, of these “Mobius Doublets” form a graviton. Photon-graviton momentum and interaction would not only produce a matter particle’s, and black hole's, quantum spin but a pressure that’s equivalent to what we call mass or solidity. Any particle’s mass, including the Higgs boson’s or that of the bosons belonging to the nuclear forces, would be created this way. Possessing an electric dipole moment, every massive or force-carrying particle would have both positive and negative charge – capable of cancelling to produce neutrality. The imaginary numbers - essential to quantum physics - in Wick rotation would combine with Wick's real numbers to produce time, and rotation of gravitational and electromagnetic waves would be energy forming mass on the x-axis plus dark energy forming dark matter on the y-axis. PRELIMINARY NOTE #2 - The photoelectric effect, plus imaginary and complex numbers, say the universe never Started with a Bang In A Brief History of Time, Stephen Hawking said there are no boundaries or singularities in imaginary time. I know Wick rotation is regarded as mathematical convenience or trickery. But Max Planck thought of his idea of quanta as a math convenience. And Albert Einstein seems to have developed the photoelectric effect's explanation from Planck's quanta. So could Wick rotation also end up having practical application, with our so-called real time existing on the X-axis and imaginary time on the y-axis. In that case, would the lack of boundaries and singularities mean the universe has no beginning or end? The relevance of imaginary numbers to the cosmos is that complex numbers have uses in quantum field theory, special and general relativity, and spinors. Real time and real numbers are still present, so we can't get rid of an initial singularity through a Wick rotation. This reflects the fact that Wick rotation isn't so useful in General Relativity. But Einstein's theory, though the best theory we have of gravity and the universe, is incomplete. It needs to be combined with quantum physics. In such a theory of quantum gravity, it's possible that Wick rotation is extremely useful, just as it's a very useful mathematical technique in quantum field theory. We don't live in a universe that is merely real (governed by real numbers) or exclusively imaginary but is complex, embodying a union of real plus imaginary. Then Wick rotation means there could be an additional time dimension - time and space are inseparable, so another space dimension also exists - as California Prof. Itzhak Bars has said (https://phys.org/news/2007-05-two-time-universe-physicist-explores-dimension.html). Just as E=mc^2 describes energy producing mass in known space-time, dark energy might not be the cause of alleged cosmic expansion but could account for the formation of dark matter. Thanks to astrophysicist Ethan Siegel for inspiring this paragraph. I'm reading an article titled "Scientists Seek Life Across the Multiverse" and it says, "If the multiverse hypothesis is correct, physicists would no longer have to find explanations for the absurdly improbable fine-tuning of the laws of nature that has made our existence possible. We are just lucky to live in a good universe among many different ones. One universe fine-tuned for life is an unlikely fluke. But one habitable universe among many is to be expected." Another way of phrasing this is - Scientists are so eager to avoid any notion of Intelligent Design of the cosmos that they're willing to deny Earth's own scientific potential ... and their own intelligence. Evolution can be observed in the form of adaptation of structure and function to the environment but there’s no reason to extrapolate this theory in order for it to account for life’s origin. In future centuries, human technology will develop terraforming and incredibly advanced bioengineering of cells - amino acids, proteins, water, nucleic acids, etc which were gathered in space or on planets and combined (science already knows these molecules exist out there). This could account for life’s origin since it agrees with 19th-century chemist Louis Pasteur’s proving that life can only originate from life. The origin-of-life hypothesis presented here obviously needs time travel back to a time when there was no life. This is feasible using General Relativity's concept of curved time (which is made circular via Wick rotation and future warping of space-time). It's convenient to say Wick rotation is a form of mathematical trickery but explanation of the photoelectric effect seems to have sprung directly from Max Planck's idea of quanta - now called photons - which was also regarded for years as a mathematical convenience. Could an extension of evolution spring directly from the supposed math trickery of Wick rotation? We only need to be open to our current interpretations of science and maths not being set in stone. History has shown that presently accepted theories always change. And we are not the endpoint of history - we're simply one more step passing through it. ABSTRACT The article begins by mentioning the accepted correlation between Albert Einstein’s relativistic equations, as well as James Clerk Maxwell’s electromagnetic waves, with the Prandtl-Glauert equations for fluid flow. These topics are explored in the article - Rizzo, A. (2024). On the Vacuum Hydrodynamics of Moving Bodies (The Theory of General Singularity). *Journal of High Energy Physics, Gravitation and Cosmology, 10*(3), 875-905. http://dx.doi.org/10.4236/jhepgc.2024.103054 The equation-free mention at the start of SUSY VIA EDM nevertheless ends with 180° ΔO = + => - (180 Degree Change in Orientation Equals Positive Becomes Negative). Of course, it also means negative can become positive: 180° ΔO = - => +. Using this article’s new equations, the Electric Dipole Moment is introduced and the charges of the quarks composing a neutron are transformed. EDM’s undetectability is explained from the perspective of a hypothetical someone who doesn’t accept the Big Bang but believes the universe is literally infinite and eternal. Then quantum spin of matter particles is discussed, and extended to astronomy’s black holes, in terms of photons and gravitons not being elementary force-carrying particles but being in possession of EDM. The photon-graviton interaction producing quantum spin is proposed as electromagnetic and gravitational vectors in a figure that might be called “Vector-Tensor-Scalar Geometry”, as well as being related to quaternions plus the Higgs boson and field. Then the article returns to black holes, showing how the inability of light to escape them leads to a 4-dimensional space-time: via binary digits or base 2 mathematics, Mobius bands, figure-8 Klein bottles, and Wick rotation. The electric potential of photons and gravitons is then interpreted not strictly as a neutron-identical Electric Dipole Moment but as a vast array of pulses sharing similarities with modern computers and electronics – the binary digits of the previous sentence. As a consequence of the electric force-carriers bringing them into existence, particles of matter and antimatter are symmetrical with bosons in the sense that every boson or fermion is, at its most fundamental level, composed of binary digits. Imaginary numbers are essential to quantum mechanics, and this article connects the imaginary numbers of Wick rotation to the nature of time. Therefore, the words here are not painting a classical picture of space-time. The 1’s and 0’s of binary digits are compatible with quantum mechanics and may be referred to as the Hidden Variables which Einstein advocated to complete quantum physics, and to give its calculations an exactness which would bring a hidden order to its chaotic randomness and superficial uncertainty. If the universe can be quantized and viewed as comprised of infinitesimal ones and zeros, how could it not obey quantum physics? And if those ones and zeros are all ultimately connected by Quantum Gravity, waves and particles could never be separated but wave-particle duality would rule. To finish, many thanks to Albert Einstein for laying the foundations of this article 105 years ago when he published a paper titled “Do gravitational fields play an essential role in the structure of elementary particles?” Immediately before submission for publication, a few topics were added to this article - dark matter, precession, the Hodge conjecture, and the Riemann hypothesis. Keywords: electric dipole moment, quantum spin, mass, symmetry, black holes, vector-tensor-scalar geometry, photon-graviton interaction, 4-dimensional space-time, BITS, binary digits, topology, Mobius band, figure-8 Klein bottle, Wick rotation, imaginary numbers, hidden variables, quaternions, dark matter, precession, Hodge conjecture, Riemann hypothesis.

In-service mathematics teachers’ knowledge of differentiated instruction

Article • JRAMathEdu (Journal of Research and Advances in Mathematics Education)

This study sought to investigate in-service mathematics teachers’ knowledge of differentiated instruction in junior high schools in Tano South Municipality of Ghana. The study adopted an explanatory sequential mixed methods design. We employed a sample of 50 JHS mathematics teachers comprising 41 general in-service teachers and 9 special in-service teachers in the quantitative study through a proportionate stratified sampling technique. In the qualitative phase, 6 JHS mathematics teachers comprising 4 general in-service teachers and 2 special in-service teachers were purposively selected and interviewed. In line with the design adopted, the quantitative data obtained through a questionnaire was first collected and analysed. This was followed by the qualitative data obtained through semi-structured interviews. The quantitative data were analysed using both descriptive statistical tools (such as frequency counts, percentages, mean, standard deviation, and average per item rating), and inferential statistical tools (independent samples t-test). Qualitative data used inductive content analysis. Among the findings, we found no statistically significant difference in the knowledge scores on differentiated instruction for general in-service teachers and special in-service teachers (t = -0.80, df = 48, p > 0.05). We, therefore, recommend teacher education institutions review their mathematics curriculum to reflect the use of differentiated instructional approaches among mathematics teachers.

Values in college mathematics learning: Student teachers' preference

Article • Asian Journal for Mathematics Education

This study explored what Ghanaian student teachers value in college mathematics learning. A cross-sectional survey involving 180 student teachers from College of Education in Ghana was conducted using the What I Find Important (WIFI) in mathematics learning questionnaire. The study employed principal component analysis with Oblimin rotation and one-way multivariate analysis of variance in analyzing the data gathered. Among the findings, it was found that student teachers value exploration, connections, understanding, and fluency in their study of college mathematics. Also, the findings of the study revealed a statistically significant difference in what student teachers value in college mathematics learning across college class levels. To facilitate a clearer understanding of valuing in the colleges of education in Ghana, it is considered important to establish through research the values of teacher educators regarding college mathematics learning and teaching, and how these values reflect what student teachers value and those values espoused in the new 4-year Bachelor of Education (B.Ed.) curriculum in Ghana.

How to Develop an Evidence-based Mathematics Vocabulary Test in Multilingual Context?

Article • Developmental Psychology

Children with a limited mathematics-related vocabulary (with words such as more, after, first and empty) often develop mathematical learning difficulties that may be related to their vocabulary. Educators and researchers need valid and reliable tests to identify such children. This is important because after identification, at risk children’s mathematics vocabulary can be developed to prevent learning difficulties to increase. Several mathematics vocabulary measures for young children have been developed in northern English-speaking countries, but reliable and easy-to-use measures for early grades mathematics vocabulary are lacking in African countries, including South Africa. A test to assess children’s mathematics vocabulary is especially important in multilingual countries where many children learn mathematics in a language that is not their home language. Developing an instrument in several languages requires a team of translators and reviewers, together with thorough statistical analysis and planning. We developed the Mathematics Vocabulary Test (MVT) - an instrument to measure young children’s mathematics vocabulary in several South African languages. The study, with children aged 3-8.5 years (N=988, ngirls = 429), consisted of two phases. In the first phase, the original MVT, with 26 items, was developed by a team of teachers, parents and researchers and used in a small group of children who used four languages in their home environment. Children with the home languages of isiZulu– (n=229), Sesotho– (n=83), English– (n=89) and Afrikaans (n=216) participated in the pilot study to determine how well the test works. Based on the results, the MVT was revised and improved. In the second phase, additional children were assessed with the revised versions of the English (n=270) and isiZulu (n=101) MVT. Phase 2 analyses showed that 20 items of the English test and 16 items of the isiZulu test worked well. The analysis of the English MVT also showed that the test identified the same children to be at risk five months later. This paper explains how educators and researchers can use the total score of the test to describe young children’s mathematics vocabulary knowledge. Our findings also showed that the MVT was able to detect the same children at risk in their mathematics learning as in another early numeracy test. By using the English MVT in our study, it was possible to predict the performance in mathematics vocabulary and early numeracy six months later. Taken together, our results showed that the English and isiZulu MVT can reliably be used to identify children with a limited mathematics vocabulary. Ultimately, the purpose of such identification is to know which children need additional support in their mathematics learning, especially in multilingual schools and countries. Next, we plan to evaluate the reliability of the Sesotho and Afrikaans MVT.

Factors Influencing Pupils’ Performance in Mathematics at Kenya Certificate of Primary Education in Turkana Central Sub-County, Kenya

Article • International Journal of Trend in Scientific Research and Development

The purpose of the study was to investigate factors influencing pupils' performance in Mathematics at Kenya Certificate of primary education KCPE in Turkana Central Sub County, Kenya. The study was informed by the following objectives to determine the influence of teaching resources in pupils' performance in Mathematics at KCPE, to examine the relationship between teachers qualification and pupils' performance in Mathematics at KCPE, determine the influence of parents on pupils' performance in Mathematics at KCPE and to establish pupils' attitudes in Mathematics at KCPE Turkana Central Sub County. The study adopted descriptive survey design. The study adopted a sample size of 266 respondents. Stratified, random and purposive sampling techniques were used by the researcher to sample out the population basing on capacities, group characteristics and progressive records for all the respondents. Questionnaire was administered to the head teachers, teachers and pupils. The questionnaire was issued to the head teachers, teachers and learners. The findings of the study were as follows that the teaching resources influenced performance in Mathematics that there was a relationship between teachers' qualification and pupils' performance in Mathematics that parents influenced pupils' Mathematics performance and that pupil' attitudes influenced performance in Mathematics at KCPE. The study came up with the following recommendations that the schools should have a well established library so that pupils have enough teaching and learning resources the government should increase Mathematics teachers in schools the government and well wishers to assist the schools by providing them with more learning and teaching resources, parents should be encouraged to assist their children in Mathematics achievements by buying them text books and pupils should have a positive attitude so that they may do well in Mathematics. Lewis Ngesu | Moses Jamin Simotwo "Factors Influencing Pupils' Performance in Mathematics at Kenya Certificate of Primary Education in Turkana Central Sub-County, Kenya" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-1 , December 2018, URL: https://www.ijtsrd.com/papers/ijtsrd18984.pdf

The Effects of Cooperative Learning Strategies and Attitudes on Performance in Secondary School Mathematics in the South West Region of the Republic of Cameroon

Article • International Journal of Trend in Scientific Research and Development

This study examined, "The Effects of Cooperative Learning Strategies and Attitudes on Performance in Secondary School Mathematics in the South West Region of Cameroon. The researcher's concern about the study emerged from his observations over a period of more than five consecutive years on the very poor performance of students at the General Certificate of Education, Ordinary Level. This made him to ask a number of questions, from which one general research question was formulated. This was To what extent do cooperative learning strategies and attitudes affect performance of students in secondary school mathematics This general research question gave rise to four specific research questions which were translated to a general hypothesis and four specific hypotheses respectively. A combined quasi experimental and survey research design was used for the study. The target population of the study consisted of 5,671 Form Three students in the entire South West Region. From this population, a sample of 359 Form Three students was selected for the survey study, and 65 students in their intact groups of 34 and 31 students were used for the quasi experimental study. Both probability, in particular, simple random sampling technique and the non probability sampling, in particular, purposive sampling techniques were used in the study to select the subjects. The questionnaire, pre test and post test, instrument for focus group discussion were the instruments used for data collection. Validation of the instruments was done through face, content and constructs validity. Reliability was achieved through the test re test method. The hypotheses were tested through inferential statistics. In particular, through the t test and Pearson Correlation r coefficient product moment. The results rejected all the null hypotheses while retaining their alternative forms. This led to the following conclusions 1. The mean performance of students exposed to peer tutoring in the study of mathematics is significantly better than that of those who study individually. 2. The mean performance of students exposed to positive interdependence in the study of mathematics, is significantly better than that of those who study individually. 3. There is a significant relationship between interest in secondary school mathematics and performance. 4. There is a significant relationship between participation in mathematics lesson and performance in secondary school mathematics. Based on these results, recommendations were made to teachers to regularly use cooperative learning strategies so as to raise the interest of learners and their participation in mathematics, with the results being improved performance. Nkengasu William Oben "The Effects of Cooperative Learning Strategies and Attitudes on Performance in Secondary School Mathematics in the South West Region of the Republic of Cameroon" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-1 , December 2018, URL: https://www.ijtsrd.com/papers/ijtsrd18970.pdf

The Influence of the use of Instructional Resources in the Teaching of Mathematics on Students Performance in Mathematics in Public English Speaking Secondary Schools

Article • International Journal of Trend in Scientific Research and Development

It has been suggested that teachers' instructional practices mediate the relationship between teacher background variables and student learning FennemaandFranke, 1992 Mewborn and Cross, 2007 . One instructional practice that has been supported as a way to help build students' mathematical understanding is the use of instructional resources e.g., Hiebertet al., 1997 . In this dissertation, it is investigated the influence of the use of instructional resources on the teaching of mathematics as a mediator of the relationship between teacher variables and students' mathematics learning. A survey design employing a mixed method approach, quantitative and qualitative, was used. In this research, 408 students sampled from both urban and rural areas in the six divisions that make up the South West region of Cameroon, 8 focus group discussions were organized and 12 observations were done. Instruments for data collection were a semi structured questionnaire, a focus group discussion guide and an observational guide. As concerns questionnaire and observation, the data for the closed ended questions were described using frequency, proportion and Multiple Responses Analysis to aggregate score within conceptual components while hypotheses were tested using logistic regression model with the statistical package of social science version 21.0. SPSS . Qualitative data were analysed following the thematic approach. Though the study revealed that the performance of students in mathematics was generally good 80.6 329 , the contribution of instructional resources was perceived to be weak and statistically non significant. From both students and observation perspectives, print media were not effectively used, as only 22.9 weight from the observation and 19.4 79 of students agreed that they were used to a high extent. Only 15.7 64 of the students acknowledged that they were effectively available. In the same line, 68.9 281 students were of the opinion that mathematic laboratories were not used at all while 73.5 300 denounced the fact that computer laboratories were not used at all. Though students for the majority agreed that libraries equipped with books are available in schools for the teaching of mathematics 65.2 266 , only 15.2 62 stated that they were effectively used for the teaching of mathematics. it was perceived that projected audio visual instructional resources in the teaching of mathematics were not at all used, as generally perceived by the students 82.4 336 . It was then recommended that teachers and students should be drilled on the importance and usage of instructional resources. Those instructional resources should be made available to make the teaching of mathematics more practical and take advantage from the assets offered by ICTs, notably computer based simulations and modeling. Besong Francis Mbeng "The Influence of the use of Instructional Resources in the Teaching of Mathematics on Students' Performance in Mathematics in Public English Speaking Secondary Schools" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: https://www.ijtsrd.com/papers/ijtsrd14570.pdf

Learning Mathematics (LM) Model

Article • Asian Research Journal of Mathematics

The LM model establishes the role of teaching competence in improving mathematics performance. The outcomes of the study would help establish the basis for education administrators and leaders to understand the need to guarantee that teachers proceed to more training and professional growth as a milestone to improve performance in mathematics. These findings may also serve as the basis for educational policymakers, internal and external stakeholders, specifically mathematics teachers, to always consider and strengthen learners’ problem-solving skills and their teaching competence to ensure the attainment of positive and excellent mathematics performance among learners.

STEM major choice of Cambodian university freshmen

Article • Research in Science & Technological Education

Background: STEM (science, technology, engineering, mathematics) education is attracting increasing public interest and policy attention and being promoted at different educational levels in Cambodia. Purpose: The study seeks to identify factors associated with Cambodian university freshmen’s choice of STEM major and how significant associations differ by gender and university location. Sample: The study draws on primary data collected from a survey of 2,016 freshmen at 15 universities across Cambodia. Design and method: Binary logistic regression was applied to detect correlates of major choice (dichotomized into STEM major and non-STEM major). Results: Students who choose a STEM major are likely to be male, have clearly prioritized the major since high school, have high self-efficacy in the chosen major, want a career in STEM, enrol at a Phnom Penh-based university, excel at mathematics at high school, excel at science at high school, have no job while studying, and value the importance of science and technology to society. When moderated by gender and university location, only excellence in mathematics, excellence in science, and STEM career prospects remained significantly associated with STEM major choice. Conclusion: Student experience in learning mathematics and science subjects at high school and their exposure to career information and guidance are vital in widening participation in STEM disciplines at higher education level in Cambodia.

God and the Infinite: Bridging Theology and Mathematics

Article • Divined Explanations. The Theological and Philosophical Context for the Development of the Sciences (1600-2000)

Infinity has fascinated thinkers for centuries, sparking debates in mathematics, philosophy, and theology. In mathematics, infinity describes endless processes, like unending numbers or limitless space. Philosophers and theologians, however, have asked whether infinity is real or just a concept we use to make sense of complex ideas. Bernard Bolzano, a 19th-century philosopher, mathematician, and theologian, argued that infinity is not just abstract—it is real. He based this claim on the idea that God exists as an unconditioned, infinite being. For Bolzano, God’s infinite nature—His boundless knowledge, power, and goodness—proves the reality of infinity. Bolzano also presents a philosophical argument for the existence of God, grounded in logic and metaphysical principles, asserting that God is the ultimate foundation of reality and the source of all conditions. Historically, many thinkers, like Aristotle, rejected the existence of an actual infinite, claiming it could only exist as a potential—something that could never be fully realized. Bolzano, however, challenged this view by demonstrating how infinity can be understood as complete and real, particularly in the context of divine attributes and the structure of reality. Bolzano’s work also reveals that some key principles in modern mathematics, such as the axiom of infinity in set theory (which assumes the existence of infinite sets), may have historical and philosophical roots in theological discussions. By connecting these fields, he highlights how the concept of infinity bridges mathematical rigor and deep metaphysical inquiry. In his work, Bolzano not only defends the existence of an actual infinite but also provides a unique argument for God’s existence, emphasizing how infinity and the divine are intertwined. His insights continue to offer a valuable perspective on how abstract ideas influence both our understanding of mathematics and the nature of existence.

Students’ and lecturers’ perceptions of online mathematics instruction during the lockdown

Article • African Journal of Educational Studies in Mathematics and Sciences

This study sought to assess the nature of online mathematics teaching and learning, the associated challenges and the support system put in place for students due to COVID-19 at the University of Education, Winneba (UEW), Ghana. The study employed concurrent mixed method design. A sample size of 507 comprising 490 students and 17 lecturers respectively were used for the study. In the study, proportionate stratified sampling, and list-based sampling frame were employed by the researchers to select the sample of mathematics students whereas census was used to include lecturers. Data for the quantitative phase were garnered using questionnaire while interview was used for collecting data for the qualitative phase. Descriptive statistics and thematic analysis were used to analyse the quantitative and qualitative data respectively. From the study it was deduced that, among the challenges facing students and lecturers in the online teaching and learning of Mathematics are; high cost of internet data bundle, unreliable internet connection, unfamiliarity with some online platforms, difficulty in accessing some online platforms using smartphones, and difficulty in teaching some topics online. In addressing the issue of encountering difficulty in teaching some topics online, we recommend the University’s Management to partner with agencies that host learning resources platforms to provide mathematics contents to help students explore. Again, we recommend that University’s Management commences discussions with telecom providers to allow zero charges on the use of smartphones for content download from the university’s learning sites.

Functional Mathematics Education

Article • Contemporary Mathematics and Science Education

There is the need to inculcate in the students entrepreneurial skills through functional mathematics to enable students to be self-employed. There is need for the government to lay more emphasis on the teaching of mathematics to make it more functional so that the students can acquire mathematics skills that will assist them to be an entrepreneur and become self-reliance. Nigeria as a nation need functional mathematics and entrepreneurship skills in their various schools to enable her citizens acquire practical skills for sustainable self-reliance.

Intuition and understanding of the world in mathematics

Article • Kairos Journal of Philosophy & Science

Mathematics is not a set of formal rules for the manipulation of symbols and the mere calculation of numbers. Mathematics has primarily to do with ideas, intuition, imagination and with the understanding of the more hidden and profound aspects of the world. Moreover, mathematics is a a way of exploring new unknown territories of the world, and a particular way of uncovering new possible worlds. Mathematics is, likewise somehow music or philosophy, an art of human understanding.

Forecasting in Mathematics - Recent Advances, New Perspectives and Applications

Article

This book is titled Forecasting in Mathematics – Recent Advances, New Perspectives and Applications. Additionally, each time I work on the field of mathematical probability and statistics I find the pleasure to tackle the knowledge, the theorems, the proofs, and the applications of the theory. In fact, each problem is like a riddle to be solved, a conquest to be won, and I become relieved and extremely happy when I reach the end of the solution. This verily proves two important facts: firstly, the power of mathematics and its models to deal with such kind of problems and secondly the power of the human mind that is able to understand such class of problems and to tame such a wild concept that is randomness, probability, stochasticity, uncertainty, chaos, chance, nondeterminism. Mathematical probability and statistics are an attractive, thriving, and respectable part of mathematics. Some mathematicians and philosophers of science say the gateway to mathematics deepest mysteries. Moreover, mathematical probability and statistics denotes an accumulation of mathematical discussions connected with the efforts to most efficiently collect and use numerical data subject to random or deterministic variations. In the twentieth century and present time, the concept of probability and mathematical statistics has become one of the fundamental notions of modern science and philosophy of nature. This was accomplished after a long history of efforts done by prominent and distinguished mathematicians and philosophers like the famous French Blaise Pascal and Pierre de Fermat, the Dutch Christiaan Huyghens, the Swiss Jakob Bernoulli, the German Carl Friedrich Gauss, the French Siméon-Denis Poisson, the English Thomas Bayes, the French Joseph Louis Lagrange and Pierre-Simon de Laplace, the English Karl Pearson and Ronald Aylmer Fisher, the Russian Andrey Nikolaevich Kolmogorov, the American John von Neumann, etc… As a matter of fact, each time I read or meditate these outstanding giants I feel the respect, the admiration, and the esteem to these magnificent men and giants of science who most of them were mathematicians, physicists, astronomers, statisticians, philosophers, etc... at the same time. They were, as we call them today: Universalists. Moreover, the book develops methods for simulating simple or complicated processes or phenomena. If the computer can be made to imitate an experiment or a process, then by repeating the computer simulation with different data, we can draw statistical conclusions. Thus, a simulation of a spectrum of mathematical processes on computers was done. The result and accuracy of all the algorithms are truly amazing and delightful; hence, this confirms two complementary accomplishments: first the triumphs of the theoretical calculations already established using different theorems and second the power and success of modern computers to verify them. To conclude, due to its universality, mathematics is the most positive and certain branch of science. It is successfully called by philosophers the Esperanto of all sciences since it is the common, the logical, and the exact language of understanding, capable of expressing accurately all scientific endeavor. Although Probability and Statistics are approximate sciences that deal with rough guesses, hypotheses tests, estimated computations, expected calculations, and uncertain results, they still keep in them the spirit of “exact” sciences through their numbers, proofs, figures, and graphs, since they remain to be a branch of mathematics. Surely, the pleasure of working and doing mathematics is everlasting. I hope that the reader will benefit from it and share the pleasure of examining the present book. Sincerely, I am truly astonished by the power of probability and statistics to deal with deterministic or random data and phenomena, and this feeling and impression never left me from the first time I was introduced to this branch of science and mathematics. I hope that in the present book I will convey and share this feeling with the reader. I hope also that he will discover and learn about the concepts and applications of the probability and statistics paradigm.

Assistive Learning Technologies for Students with Visual Impairments: A Critical Rehumanizing Review

Article • Investigations in Mathematics Learning

Students with Visual Impairments are often dehumanized in mathematics education based upon deficit perspectives, on the assumption that mathematics learning must be visual, and a lack of tools that allow students on the entire spectrum of vision to collaborate mathematically. The current advent of Assistive Learning Technologies holds promises in helping students with visual impairments learn mathematics, however, these emerging technologies attempt to solve this issue by translating non-textual mathematics information into auditory or haptic output, so students with visual impairments can hear or touch a graph. These technologies are impressive, but how do they actually connect with how these students learn and understand mathematics, especially since they approach mathematics from a non-sighted perspective? We, the two authors, one blind and one sighted, use a disability studies and rehumanizing mathematics education framework to examine currently available assistive learning technologies. We organize our findings using the Substitution, Augmentation, Modification, and Redefinition (SAMR) model, then offer a critical analysis of 14 studies involving assistive technology for students with visual impairments. Lastly, this review not only examines the current advancements in assistive technologies, but also connects them to learning theories from the realms of disability studies and rehumanizing mathematics education.

Exploring Paradoxes in the Development of Mathematical Thinking: a Cultural-historical Perspective

Article • Cultural-Historical Psychology

Primary school teachers are the educators responsible for introducing children into the world of mathematics. In the process of learning mathematics, children may experience negative emotions and develop negative attitudes or mathematics anxiety. Some authors approach these issues by focusing on primary teachers’ mathematics anxiety or proficiency in mathematics. In this article, we explore whether and how certain social and educational practices shape or not the development of mathemati- cal thinking in prospective primary teachers, from a cultural-historical perspective. The study’s sample consists of twelve prospective primary teachers in their last year of studies. The participants were interviewed about their experience with mathematics throughout their educational years. By examin- ing and contrasting the different developmental trajectories of the participants, we identified their “imprisonment” in situational thinking and some of the paradoxes that characterise their development. Adopting a historical perspective in analysing participants’ trajectories was crucial in uncovering the paradoxical nature of the development of mathematical thinking. We conclude by highlighting the socially mediated nature of mathematics and the obstacles posed by the competitive and exam-driven nature of educational practices.

Faculty Attempt to Incorporate Outside-of-School Geometry into Geometry Teaching in the Classroom

Article

Research has revealed a deficiency in cultural congruence in the pedagogy and acquisition of geometrical knowledge as the cause of students’ poor performance in geometry. Drawing upon the historical context of mathematics education and its evolution, incorporating ethnomathematical perspectives was introduced as a potential remedy. This embedded mixed methods study explored how mathematics teacher educators incorporate the mathematics found outside of school into geometry teaching in the classroom. Based on the findings, male and female mathematics teacher educators at the colleges of education tend to employ culturally responsive teaching (a pedagogical perspective of ethnomathematics) to integrate the mathematics found outside of school into geometry teaching in the classroom. Nonetheless, only a few mathematics teacher educators (one from each case) strove to incorporate the forms of mathematics found outside of school to teach plane geometry by citing appropriate cultural examples.

A Study on Teaching Effectiveness of Mathematics

Article • International Journal of Trend in Scientific Research and Development

Mathematics is one of the core subjects in secondary education different modern concepts and methods are introduced in the syllabus of mathematics at secondary stage. The curriculum revision is being undertaken by the state department of education SCERT and the central department of education NCERT constantly and all the modern mathematics is incorporated at the secondary stage. The teacher education programs for preparing mathematics teachers are also strength and during the past to ducats whenever the curriculum is changes different researching programs such as refresher courses, seminars, workshops etc., are conducted to make true teaching of mathematics more effective in secondary schools.Hence in this paper it is proposed to undertake teacher wise and student wise analysis for this study keeping in view of certain variables like sex, locality, qualification, experience etc., and develop a tool to measure teaching effectiveness of mathematics teachers and also to understand the type of relationship between the teaching effectiveness and its relation to student achievement. The collected is analyzed by descriptive and inferential statistics Dr. Y. Raghunatha Reddy | Dr. Shaik Thajoddin | Arif Khan, Dr. S.Makbul Hussain "A Study on Teaching Effectiveness of Mathematics" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-4 , June 2017, URL: https://www.ijtsrd.com/papers/ijtsrd141.pdf

Mobile inquiry-as-play in mathematics teacher education

Article • On the Horizon The International Journal of Learning Futures

This study describes the feasibility of designing and fostering pre-service teacher inquiry at the intersection of community and disciplinary engagement. Mapping My Math (MMM), a game-based and mobile learning activity, guided pre-service teachers in playfully exploring mathematics featured in the everyday activities of people and places and creatively representing this inquiry with digital media. This study draws from design-based research that examined the role of place, digital media and mobility in mathematics teacher education. Design narrative methods describe how MMM was created, implemented and refined to support disciplinary inquiry across settings given the evolution of tools, activities and practices. The study and design narrative address the following question: How can game-based and mobile learning be designed to support pre-service teachers’ disciplinary inquiry of everyday mathematics? Findings shared in this study’s design narrative attend to the quality of pre-service teachers’ inquiry-as-play, or expressive mobility situated among learners’ social and material relations, disciplinary concepts and the built environment. Implications from this study concern the role of mobile learning in mathematics teacher education to connect school, community and online settings; the potential of gameful design to impact pre-service teacher learning across settings; and the importance of fostering disciplinary inquiry whereby pre-service teachers can “navigate” their own learning. Originality/value – Game-based and mobile learning designs, like MMM, can create the conditions for cross-setting mobility as generative of inquiry-as-play in mathematics teacher education. MMM encouraged pre-service teachers to playfully leverage disciplinary practices that shaped new relationships with mathematics, their city and the mathematics of place and community.

Exploring the links between spatial and mathematical skills.

Article • British Journal of Educational Psychology

Spatial reasoning has been found to be closely related to mathematics achievement, yet there are so many components in both domains that researchers often don't understand the links between specific spatial and mathematical skills. In this study we explored the relationship between spatial skills and mathematics content with the goal of unpacking some of these complex relations. Furthermore, in both spatial and mathematical domains there are established gender differences in performance, therefore in this paper we also considered the role of gender. Two studies were conducted, Study 1 with 84 grade 5 students and Study 2 with 903 grade 8 students. Students completed digital assessments covering a range of spatial and mathematics skills. Spatial skills had a larger contribution to mathematics performance in the grade 5 sample compared with grade 8, and for geometry and measurement content in both studies, compared with number sense problems. A notable finding was the influence of spatial orientation on mathematics performance, this spatial skill concerns large scale spatial relations and has previously received little attention in the field of spatial-mathematical relations. The contribution of spatial orientation to mathematics performance was particularly strong for females.

Mathematics in Language

Article • Cognitive Semantics

Elementary mathematics is deeply rooted in ordinary language, which in some respects anticipates and supports the learning of mathematics, but which in other respects hinders this learning. This paper explores a number of areas of arithmetic and other elementary areas of mathematics, considering for each area whether it helps or hinders the young learner: counting and larger numbers, sets and brackets, algebra and variables, zero and negation, approximation, scales and relationships, and probability. The conclusion is that ordinary language anticipates the mathematics of counting, arithmetic, algebra, variables and brackets, zero and probability; but that negation, approximation and probability are particularly problematic because mathematics demands a different way of thinking, and different mental capacity, compared with ordinary language. School teachers should be aware of the mathematics already built into language so as to build on it; and they should also be able to offer special help in the conflict zones.

How censorship is used to suppress black achievements in math

Article • Journal of Black Studies

After the end of apartheid in South Africa, blacks got admission to South African Universities. Though they paid high fees, they are regularly failed by the faculty which is still white-dominated. This led to the agitation “Rhodes must fall” to decolonise the university. In this context, I was asked to comment on an offensive article purporting to decolonise mathematics, which started with the premise "Much, though certainly not all, mathematics is the work of dead white men". (Hence, by implication, blacks and women are bad at mathematics, and must be taught to think like the white, male creators of the subject.) I responded with a counter-article, "To decolonise math stand up to its false history and bad philosophy" which was published by the Conversation (global edition), in October 2016. Some of the points I made enraged closet racists in South Africa. For example, I said that black Africans in Egypt understood fractions since the days of the Rhind papyrus, while Greeks and Romans could not manage fractions. (How do you write a fraction in Roman numerals?) Fractions were first introduced in the European math syllabus only around 1572, three THOUSAND years after the Rhind papyrus. What mathematics did white men invent, I wondered, if they lagged so far behind blacks even as regards elementary fractions? I further said that there was nil evidence for “Euclid” the purported white Greek father of mathematics, and that my challenge prize of around USD 3000 for the slightest evidence for Euclid was standing unclaimed for a decade. I explained that the real author of “Euclid’s” Elements was a black woman who was raped and killed in a church for her advocacy of “heretical” beliefs about mathematics and religion. (The black woman appears on the cover of my 2012 book Euclid and Jesus, which tells her story.) The article in Conversation went viral but was immediately censored by its South Africa editor. Many others, across the world, who had carried the article, subsequently took it down. But, no one, until today, has pointed to any error of fact or argument in my article which is reproduced in full in this article in the Journal of Black Studies. Censorship is being used to preserve falsehoods against blacks.

Unlocking the Power of Operators: From Quantum Physics to Machine Learning

Article • Journal of Mathematical Physics

How can a single mathematical framework link vibrating strings, quantum particles, and today’s cutting-edge artificial intelligence? This is the story of operator theory—a unifying language at the heart of mathematics and physics. In this paper, the author (J. Kouneiher) traces the fascinating journey of operators, from their birth in classical mechanics and differential equations to their central role in quantum theory, spectral analysis, and noncommutative geometry. The article reveals how these abstract transformations not only underpin the mathematics of Hilbert spaces and quantum observables but also drive innovation in data science, optimization, and scientific machine learning. By weaving together historical insights and modern breakthroughs, this work shows how operator theory illuminates structure, governs dynamics, and provides powerful tools to solve problems across disciplines. From the classical foundations of Green’s functions and spectral theory to neural operators shaping the future of AI, the paper demonstrates that operator theory is more than a branch of mathematics—it is a bridge between centuries of knowledge and the technologies of tomorrow.

2010 Mathematics Subjects Classification (2010MSC)

Article • Technical Services Quarterly

A review of the 2010 Mathematics Subjects Classification (2010MSC) website is designed for librarians and library professionals. This review explains how the 2010 Mathematics Subjects Classification (2010MSC) website is relevant for technical services librarians and library staff and also provides an overview of the 2010 Mathematics Subjects Classification (2010MSC) website.

Leveraging measurement instruction to develop kindergartners’ numerical magnitude knowledge.

Article • Journal of Educational Psychology

The measurement-to-number intervention described in this study offers a promising approach for streamlining mathematics curricula in kindergarten and maximizing the efficiency of instructional time. With just 10 instructional sessions focused on developing measurement concepts, children participating in the intervention condition showed improvements in both measurement and number knowledge. In contrast, the control group participants who engaged in mathematics activities similar to their regular classroom instruction demonstrated only limited improvement in number knowledge. The results speak to the value of targeting shared concepts underlying multiple domains of mathematics and of utilizing spatial information to promote the acquisition of numerical concepts.

Rural teacher leadership in science and mathematics

Article • School Science and Mathematics

This research focused on the understanding of science and mathematics teacher leadership in rural schools. by investigating secondary science and mathematics teachers' perceptions of rural teacher leadership. We also identified patterns in science and mathematics teacher leadership that are contextually connected to teachers' instruction in rural high poverty schools.

Exploring Influential Factors and Conditions Shaping Statistical Literacy Among Undergraduate Students in Mathematics Education

Article • International Journal of Cognitive Research in Science Engineering and Education

Statistical literacy (hereafter SL) has been considered an important learning outcome in statistics learning in higher education, yet studies that focus on investigating the factors and conditions that influence students’ SL, especially mathematics education students, are still limited. This study seeks to uncover the factors and conditions that significantly contribute to the SL of mathematics education students. This survey study involved 1,287 mathematics education students from 21 higher education institutions in Indonesia. Linear regression analysis involving four predictor variables (i.e., gender, status of higher education institution, laptop ownership, and research preference) was performed to determine the variables that contributed significantly in predicting SL achievement. The results revealed that gender, higher education institution’s status, and laptop ownership contributed significantly, but research preference was not significant in predicting mathematics education students’ SL. Furthermore, laptop ownership was found to have the highest contribution in predicting mathematics education students’ SL. All findings and their implications are discussed.

The Monte Carlo Methods - Recent Advances, New Perspectives and Applications

Article

This book is titled The Monte Carlo Methods - Recent Advances, New Perspectives and Applications. It illustrates the famous Monte Carlo Methods and the computer simulation of random experiments in different areas of science. As such, the book will be of interest to all scholars, researchers, and undergraduate and graduate students in mathematics and science in general. In applied mathematics, the name Monte Carlo is given to the method of solving problems by means of experiments with random numbers. This name, after the casino at Monaco, was first applied around 1944 to the method of solving deterministic problems by reformulating them in terms of a problem with random elements which could then be solved by large-scale sampling. But, by extension, the term has come to mean any simulation that uses random numbers. The development and proliferation of computers has led to the widespread use of Monte Carlo methods in virtually all branches of science, ranging from nuclear physics (where computer-aided Monte Carlo was first applied) to astrophysics, biology, engineering, medicine, operations research, and the social sciences. The Monte Carlo Method of solving problems by using random numbers in a computer – either by direct simulation of physical or statistical problems or by reformulating deterministic problems in terms of one incorporating randomness – has become one of the most important tools of applied mathematics and computer science. A significant proportion of articles in technical journals in such fields as physics, chemistry, and statistics contain articles reporting results of Monte Carlo simulations or suggestions on how they might be applied. Some journals are devoted almost entirely to Monte Carlo problems in their fields. Studies in the formation of the universe or of stars and their planetary systems use Monte Carlo techniques. Studies in genetics, the biochemistry of DNA, and the random configuration and knotting of biological molecules are studied by Monte Carlo methods. In number theory, Monte Carlo methods play an important role in determining primality or factoring of very large integers far beyond the range of deterministic methods. Several important new statistical techniques such as “bootstrapping” and “jackknifing” are based on Monte Carlo methods. Hence, the role of Monte Carlo methods and simulation in all of the sciences has increased in importance during the past several years. These methods play a central role in the rapidly developing subdisciplines of the computational physical sciences, the computational life sciences, and the other computational sciences. Therefore, the growing power of computers and the evolving simulation methodology have led to the recognition of computation as a third approach for advancing the natural sciences, together with theory and traditional experimentation. Knowing that, at the kernel of Monte Carlo simulation is random number generation. Moreover, the book develops methods for simulating simple or complicated processes or phenomena. If the computer can be made to imitate an experiment or a process, then by repeating the computer simulation with different data, we can draw statistical conclusions. Thus, a simulation of a spectrum of mathematical processes on computers was done. The result and accuracy of all the algorithms are truly amazing and delightful; hence, this confirms two complementary accomplishments: first the triumphs of the theoretical calculations already established using different theorems and second the power and success of modern computers to verify them. Additionally, each time I work on the field of mathematical probability and Monte Carlo methods I find the pleasure to tackle the knowledge, the theorems, the proofs, and the applications of the theory. In fact, each problem is like a riddle to be solved, a conquest to be won, and I become relieved and extremely happy when I reach the end of the solution. This verily proves two important facts: firstly, the power of mathematics and its models to deal with such kind of problems and secondly the power of the human mind that is able to understand such class of problems and to tame such a wild concept that is randomness, probability, stochasticity, uncertainty, chaos, chance, nondeterminism. Sincerely, I am truly astonished by the power of probability and these random techniques to deal with random data and phenomena, and this feeling and impression never left me from the first time I was introduced to this branch of science and mathematics. I hope that in the present book I will convey and share this feeling with the reader. I hope also that he will discover and learn about the concepts and applications of the probabilistic and Monte Carlo paradigm.

Teaching mathematics in an EFL context at higher education; before, during and after the COVID-19 pandemic: a comparative study

Article • Journal of Applied Research in Higher Education

Over the last few years, there has been a considerable amount of literature investigating the efficacy of the various delivery modes: on-campus delivery (face-to-face), online delivery, and blended learning (hybrid), in helping college students improve their mathematical skills. However, the extent to which one student learns best has been hotly debated among researchers. Therefore, this study aims to compare the efficacy of implementing three teaching and learning delivery modes before, while, and after the COVID-19 pandemic: on-campus delivery (face-to-face), online delivery, and blended learning (hybrid) on academic achievement in mathematics at a higher education institution in the United Arab Emirates. The main research question explores whether there is a statistically significant difference (p≤ 0.05) in students’ academic based on delivery methods: on-campus face-to-face, online, and blended learning. The results showed that there were significant differences in the mean scores in the student’s achievement in the mathematics courses favoring the blended learning delivery mode. The findings also show that the student achievement in mathematics using the on-campus face-to-face teaching and learning was better than the student achievement in mathematics using online teaching and learning delivery mode. Keywords: Mathematics, face-face learning, online learning, blended learning.

Application of Fundamental Mathematical Structure using a Self Game for Cognitive Development in Children

Article • International Journal of Trend in Scientific Research and Development

Education plays a great role in everyone's life. The whole education has been divided into Primary, Secondary, and Higher Education divisions. All the three parts of education have their own importance and benefits. The primary education consists of wonderful subjects which can be taught to better the life of child and lays foundation. Mathematics is one of the core subjects in Educational System. This Paper presents how to develop an understanding of the basic mathematics concepts specifically for children in Primary education division. This paper contains a "Snake and Ladder play way method which is an ancient Indian Board Game and enables the child to learn playfully and willingly and is a great tool for self learning. Cognitive development is a concept derived from Piaget's theory and the basic concept of mathematics is derived from Number theory. It is also called as THE QUEEN OF MATHEMATICS. Combination of these two concepts helps the child to "play and learn and in the process build an understanding of stable fundamental mathematical concepts aiding in gaining knowledge. Therefore, this innovative self play game can be used as excellent teaching learning material for people of all ages, specifically for children as this focuses on the cognitive development of students irrespective of those facing learning difficulties in mathematics. K. Suneetha Devi "Application of Fundamental Mathematical Structure using a Self Game for Cognitive Development in Children" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-3 , April 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23121.pdf

The Importance of Digital Application of Mathematics and its Application in Secondary Schools in the South West Region of Cameroon

Article • International Journal of Trend in Scientific Research and Development

This study examined the importance of digital application of mathematics and its application in secondary schools in the South West region of Cameroon. Now the question is to what extent does the educational system in Cameroon consider these contemporary challenges in the teaching of mathematics It is in this line that this study was conducted to appraise how effective the use of specialized rooms notably computer laboratories have been integrated in the teaching of mathematics in secondary schools in the South West region of Cameroon. To answer this question, a total of 12 schools were sampled through simple random sampling, stratifying for setting type urban Vs. rural and for the 6 divisions making up the South West region of Cameroon, with one school in the urban area and another one in the rural area per division. Employing a survey design, notably a mixed method approach and more specifically concurrent triangulation. As such a survey employing a semi structured questionnaire and focus group discussions were corroborated with observation, and concurrent transformative. Given that the availability and usage of specialized rooms in the teaching of mathematics were appraised through set indicators defined as closed ended questions. However, prospective response measures were assessed qualitatively through open ended questions. Altogether, 408 students sampled conveniently were involved in the study. The research procedural rigors were respected whereby administrative clearance was obtained from the University Buea. Descriptive analysis employed frequencies, proportions and MRA to aggregate scores within conceptual components while hypothesis was tested using Logistic Regression. Besong Francis Mbeng "The Importance of Digital Application of Mathematics and its Application in Secondary Schools in the South West Region of Cameroon" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-5 , August 2018, URL: https://www.ijtsrd.com/papers/ijtsrd15857.pdf

Does using mathematics support in university increases the odds of a student passing a maths exam?

Article • Teaching Mathematics and its Applications An International Journal of the IMA

Mathematics support is now offered in many higher-education institutions in Ireland, as an optional, free additional support for students studying any type of mathematics. We examined the attendance records at mathematics support for one Irish university over the past 12 years, and compared these with whether or not students passed their mathematics module. We found that, even when taking into account their previous grades and module studied, the odds of a student passing their module were higher if they used mathematics support, even if they only came one time.

Detailing a doctoral-level telehealth course for clinical psychology students

Article • Journal of Technology in Behavioral Science

The development, instructional techniques, and pilot evaluation of a doctoral-level clinical psychology-focused course are detailed. Pre- to post-class evaluation suggested increases in student self-reported telehealth-related knowledge, as well as high satisfaction. The pilot course may serve as a template for future telehealth courses.

Challenges Regarding the Integration of Ethnomathematical Perspectives into Geometry Teaching

Article

A significant gap exists, as research has revealed that teaching mathematics in classrooms is usually unrelated to the sociocultural contexts of the learners. This embedded mixed methods study explored the challenges mathematics teacher educators face in integrating ethnomathematical perspectives into Euclidean geometry teaching in the classroom. The mathematics teacher educators' accounts revealed college and educator-related challenges, including inadequate/lack of cultural examples in the geometry curriculum, a lack of clarity on how to integrate ethnomathematical approaches into geometry teaching in the curriculum, cultural diversity, financial constraints, time constraints, and gender discrimination. The quantitative study observed a statistically significant difference between the male and female cases in their response to the challenge of inadequate/lack of cultural examples in the geometry curriculum. In all, the findings obtained from the qualitative investigation revealed differences among male and female mathematics teacher educators regarding what they perceive as challenges regarding the integration of ethnomathematical perspectives.

CLIL Implementation in Elementary Mathematics Education in Indonesia

Article • KLAUSA (Kajian Linguistik Pembelajaran Bahasa dan Sastra)

This article aims to describe the fitness of Content and Language Integrated Learning (CLIL) in Mathematics subject for elementary education in Indonesia. The research was a qualitative study conducted through a case study. The case study was conducted in the context of elementary education. This research discovered that CLIL needed to be conducted in consideration of the urgency of teaching Mathematics in English, the appropriate method of teaching Mathematics in English, the appropriate duration of applying CLIL, and the impacts of CLIL on learners. Through the application of CLIL in teaching Mathematics in English, Indonesian students will be accustomed to the concept of understanding word problems in English, be accustomed to the application of higher order thinking in solving math problems, have higher interest in math and English, and have a stronger foundation for a more complex math learning at a higher level.

SUPPORTING YOUNG CHILDREN’S MATHEMATICAL DEVELOPMENT: THE ROLE OF PARENTS

Article • International Online Journal of Primary Education

Undeniably, parents remain one of the most important resources needed in children’s mathematical development since children begin education from home. The role parents play in their children’s math education is a largely untapped resource for improving the quality of mathematics education among Ghanaian children. In order to maximise this resource, there is a need for basic research on the nature of the involvement of parents in their children's mathematical growth. In view of this, we employed a case study design to explore ways by which parents involve themselves in their children’s mathematical development and how these can be harnessed to improve students’ mathematics achievement in Tano North Municipality. This study was guided by Epstein’s overlapping spheres of influence theory. A sample of 10 comprising 5 students and 5 parents was considered for the study. We employed a semi-structured interview to gather the required data which were analysed using inductive content analysis. Among the findings, it was revealed that some of the ways by which parents can help in the development of children’s mathematical development are the provision of learning resources and activities at home, helping with mathematics homework, encouraging good study habits, monitoring their school attendance, organize remedial classes, parents’ participation in school activities, and teaching appropriate behaviour for academic success. Based on the findings of the study, we recommend the Tano North Municipal Directorate of Ghana Education Service to collaborate with headteachers at the basic schools to create family engagement programmes that highlight parents’ role in the children’s mathematics development and future success.

Impact of multiple representations-based instruction on pupils’ performance in fractions

Article • Journal of Mathematics and Science Teacher

The study sought to investigate the impacts of multiple representations-based instructions (MRBI) on basic six pupils’ performance in solving problems on common fractions in the Sagnarigu Municipality of Ghana. The study employed non-equivalent control group design in which 96 pupils in one primary school were purposively sampled and assigned to experimental group (n=46) and control group (n=50). Data were gathered using tests (pre- and post-test) and analyzed using descriptive and inferential statistics (independent samples t-test). Also, pupils’ exposed to multiple representations-based instructions performed better in the post-test than in the conventional group. This suggests that MRBI positively impacted pupils’ performance in solving problems on common fractions. We conclude that MRBI is an effective approach, that mathematics teachers need to incorporate in their teaching of fractions. Therefore, we recommend the MRBI approach for basic school mathematics teachers to enhance pupils’ understanding of mathematics concepts, especially at mathematics education’s foundation (basic level).

Transforming undergraduate mathematics instruction via primary historical sources

Article • Implementation and Replication Studies in Mathematics Education

The TRIUMPHS (TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources) project is a multi-year collaboration funded by the US National Science Foundation. Its aim is to improve instruction in undergraduate mathematics by developing high-quality curricular resources known as Primary Source Projects that place students in direct contact with the writings of the historical individuals who created and shaped the mathematics they are expected to learn. Using data collected from over 100 site testers of these materials, this article employs an implementation-related research lens to explore the factors that influence adoption of innovative curricular materials such as these by university and college mathematics faculty. We consider in particular two extreme cases of adoption—instructors who have thus far limited their use of Primary Source Projects to a single course and instructors for whom Primary Source Project usage has permeated their instructional practice—as a means to gain insight into the factors that influence the nature and depth of future uses of the innovation for various profiles of (potential) adopters.

Exploring Black children’s mathematical learning in informal environments

Article • Information and Learning Sciences

Mathematics educators have often highlighted the ways in which Black students are struggling in mathematics. Although well intended, consistent reminders of their failures have done little to help them overcome challenges in the classroom. In this paper, the authors argue that in order to truly understand what Black children know mathematically, we must look at their lives outside of the classroom. If we explore the mathematics learning opportunities in their everyday lives, we may find that these children know more about mathematics than what the classroom environment allows them to share.