Mathematical Provision Research Articles

Capacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)

This report describes the final meeting of the project "Capacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)" held at the Tomas Bata University in Zlín, Czech Republic (June 12-14, 2023). Provision of mathematics and statistics learning support (MSLS) is developing rapidly in many parts of the world and activity in Norway and the Czech Republic has been accelerated significantly through this EEA Grants funded project. Representatives of each of the five partner institutions worked on creating a summary of good practices in tutor training, designing learning resources, and in delivering, monitoring and evaluation of mathematics and statistics support. Provision varied considerably across the institutions and the centres represented demonstrated diverse and innovative ways in which mathematics support is evolving. Outputs from the project include a Handbook on good practice and a booklet concerned with mathematics support centre tutor training, including pedagogic training and learning resources for the development of the tutors as described below. Finally, consideration turned to the value of establishing a professional network to continue this important work. The report will be relevant to other international groups interested in working in university level mathematics and statistics support.

Auditoria operacional dos sistemas previdenciários: achados do Tribunal de Contas do Estado do Ceará

The national public administration is preceded by being monitored and supervised given the large resources that are allocated to the provision of services that society needs, leaving the courts of accounts to their control and measurement. With regard to the management programs of the private pension systems, the courts began to audit actuarial management and the accounting entries referring to long-term provisions for the payment of retirement and pension benefits. The Federal Court of Auditors presented irregularities and the Court of Auditors of the State of Ceará carried out operational audits related to the municipal regimes, and asked: what were the findings of the operational audit? The answer came through research of an interpretive nature with a qualitative approach and a case study in two municipalities of the six audited. It was concluded that: the municipal social security management in the State is recurrent in the irregularities and vices in the processes of acquisition of goods, products, or services; actuarial estimates are defective and incapable of assessing the sustainability capacity of the social security system, with indications of the absence of adherence tests for the workforce, actuarial cash flow incompatible with future execution, and inconstancy in results; absence of recording mathematical provisions in the balance sheets, originating from actuarial estimates; and absence of projections of actuarial liabilities in the tax statements. The audits studied pointed out recommendations and determinations to managers, which must be monitored by the body with the possibility of sanctioning and returning resources to public coffers.

Optimising the blend of in-person and online mathematics support: the student perspective

This paper explores the provision of online and in-person mathematics support from the student perspective. We compare and contrast online, in-person and hybrid formats of mathematics support offerings between two universities from opposite sides of the globe by presenting analysis of 227 student responses to six surveys. Three surveys were conducted at each institution, based on students’ use of mathematics support in both in-person and the wholly online settings, and those who had used only online or only in-person support. Students rated the quality and importance of eleven support aspects based on their experience of online and/or in-person support, and indicated their future format preference across a range of scenarios. Students’ suggestions for improvements to both formats were also gathered. Results highlight the differences and similarities of the online and in-person experiences, with statistically significant differences between support formats found in four quality ratings, two importance ratings, and in seven of the ten questions on future format preferences. Findings suggest a hybrid model of support is desired by students going forward. The discussion of students’ views presented will enhance practitioners’ efforts in optimising the blend of online and in-person mathematics support.

Computer Science Students’ Perspectives on the Study of Mathematics

In 2019, the Department of Mathematics and Statistics at Maynooth University commenced a project which sought to address, through the provision of mathematics learning supports, the issues of poor engagement and retention of computer science students studying mathematics. In this paper, we present preliminary engagement and performance data along with interviews conducted with eight students. We discuss how the quantitative data seemed to indicate that computer science students were engaging at similar levels to their peers, but several factors, including the quality of this engagement and their mathematical backgrounds may explain their poor exam performance. It also emerged that, while students were largely negative about their experiences in large lectures and their awareness of the relevance of mathematics to computer science, they were generally positive about smaller teaching situations such as tutorials, mathematics support drop-in and opportunities to work with their peers.

MAC: A Proposal for Consistent Actuarial Interest Rates in Pension Funds

ABSTRACT Objective: this article proposes the meta atuarial consistente (MAC) (consistent actuarial rate), which is a method that adjusts incompatible actuarial rates in pension funds, after investigating and proving that the rate dissociates from the general rule in current regulations (which binds this rate to the expected return of the investments of pension funds). Methodology: a sample with data from 22 defined-benefit plans was collected, and MAC was applied to produce consistent actuarial rates, after panel data methods have identified the elements that influence the definition of the actuarial rate by the pension fund board of trustees. Results: the use of MAC, adjusting actuarial rates of 2018 based on systematic biases in previous rates, enabled a positive effect that unfolds in more reliable estimates for the plans’ mathematical provision, while identifying elements that influence the determination of the annual rate, causing its non-compliance to the general rule. Conclusion: the adoption of MAC by the Brazilian supervisory authority Previc would improve the rules and provide subsidies to better adjust the contribution levels practiced in the plans, making their solvency levels more reliable, which would benefit the development of the insurance and pension market.

MAC: A Proposal for Consistent Actuarial Interest Rates in Pension Funds

ABSTRACT Objective: this article proposes the meta atuarial consistente (MAC) (consistent actuarial rate), which is a method that adjusts incompatible actuarial rates in pension funds, after investigating and proving that the rate dissociates from the general rule in current regulations (which binds this rate to the expected return of the investments of pension funds). Methodology: a sample with data from 22 defined-benefit plans was collected, and MAC was applied to produce consistent actuarial rates, after panel data methods have identified the elements that influence the definition of the actuarial rate by the pension fund board of trustees. Results: the use of MAC, adjusting actuarial rates of 2018 based on systematic biases in previous rates, enabled a positive effect that unfolds in more reliable estimates for the plans’ mathematical provision, while identifying elements that influence the determination of the annual rate, causing its non-compliance to the general rule. Conclusion: the adoption of MAC by the Brazilian supervisory authority Previc would improve the rules and provide subsidies to better adjust the contribution levels practiced in the plans, making their solvency levels more reliable, which would benefit the development of the insurance and pension market.

INTERPOLATION OF TABULAR FUNCTIONS FROM ONE INDEPENDENT VARIABLE USING THE TAYLOR POLYNOMIAL

A method of local interpolation of tabular functions from one independent variable using the Taylor polynomial of the nth degree in arbitrarily located interpolation nodes has been developed. This makes it possible to calculate intermediate values of tabular functions between interpolation nodes. The conducted analysis of the latest research and publications in the field of interpolation of tabular functions showed that the main part of the research is a strict theory of interpolation, i.e. clarification of its fundamental mathematical provisions. Some features of the interpolation of tabular functions from one independent variable using the Taylor polynomial of the nth degree are considered, namely: the solution algorithm and mathematical formulation of the interpolation problem are given; its formalized notation is given, as well as the matrix notation of interpolation procedures for certain values of the argument. A scalar algorithm for solving the problem of interpolation of tabular functions from one independent variable using the Taylor polynomial of the 2nd, 3rd, and 4th degrees has been developed. The simplicity and clarity of this algorithm is one of its advantages, but the algorithm is inconvenient for software implementation. The mathematical formulation of the problem of interpolation of tabular functions in terms of matrix algebra is given. The interpolation task is reduced to performing the following actions: based on the values of nodal points known from the table, it is necessary to calculate the Taylor matrix of the nth degree; based on the function values specified in the table a column vector of interpolation nodes should be formed; solve a linear system of algebraic equations, the root of which is the numerical coefficients of the Taylor polynomial of the nth degree. A method of calculating the coefficients of the interpolant, given by the Taylor polynomial of the nth degree for one independent variable has been developed. The essence of the method reduces to the product of the matrix, inverse of the Taylor matrix, which is determined by the nodal points of the tabular function, by a column vector containing the values of the interpolation nodes. Specific examples demonstrate the peculiarities of calculating the interpolant coefficients of the 2nd, 3rd and 4th degrees for one independent variable, and for each of them the interpolated value of the function at a given point is calculated. Calculations were performed in the Excel environment, which by analogy can be successfully implemented in any other computing environment.

Asynchronous online mathematics learning support: an exploration of interaction data to inform future provision

Over the past 30 years, higher education institutions (HEIs) worldwide have been grappling with the difficulties experienced by many students entering higher education due to their poor pre-entry core mathematical skills. In the Republic of Ireland and the UK, the provision of mathematics learning support (MLS) is the approach most commonly adopted by HEIs to deal with this problem, providing free one-to-one mathematical support and/or workshops for students. However, despite the availability of such supports and research that suggests that engagement with these supports can have a positive impact on student retention and progression, ensuring high levels of student engagement with these supports remains a significant challenge. In more recent years, some institutions have started to provide online MLS which takes many different forms but mainly provide links to websites, revision notes, past exam papers, etc. In light of the COVID-19 pandemic and the need for many to resort to remote teaching, it would appear the successful provision of online mathematics support is set to become increasingly important over the coming years. This paper will examine student interaction data with one such online MLS provision, hosted within a virtual learning environment. The interaction data will be analysed in order to gain a better understanding of the level of student engagement with this resource and the content most frequently accessed. This analysis will be used to inform the future development and enhancement of the resource so as to encourage student engagement.

ANALISIS VIDEO PEMBELAJARAN MATEMATIKA UNTUK MENINGKATKAN KEMAMPUAN PENYELESAIAN MASALAH BILANGAN PECAHAN SISWA SD

Lack of problem solving ability elementary school students in learning mathematics with fractions. The application of solving mathematical problems of fractions has not been carried out optimally. The provision of mathematics learning media is still very minimal, especially in problem solving, so that it becomes an obstacle to increasing problem solving abilities. Learning media is now not only visual media, there are many kinds of media that can be accessed, such as audio-visual media. Video is one of the audio-visual media that can help the learning process. Now it has been widely circulated on various social media, YouTube channels and learning applications making it easier for students primary schools can access learning. However, not all learning videos are in accordance with the learning objectives, many mathematics learning videos have not achieved the basic competence of mathematics, namely solving mathematical problems. Students' difficulties in solving fractional number problems. The study aims to analyze the feasibility of mathematics learning videos in improving the problem solving abilities of elementary school students. This research approach uses descriptive qualitative. Data collection techniques are through literature studies and documentation studies. Data analysis uses data reduction, data presentation and conclusion drawing. The result of this research is a video feasibility analysis of students' fractional number completion.

Measuring the Success of Mathematics and Statistics Support Sessions at UWS

Following a review of the provision of mathematics and statistics support across Scottish Higher Education Institutions, academics at the University of the West of Scotland initiated weekly mathematics and statistics support sessions. These sessions were open to all students and staff across the institution, but primarily aimed at the science and engineering students with a high degree of numerate work in their study programmes. After two years of operation, previous attendees and students within key demographics were canvassed on their knowledge of, and opinion of, these support sessions. Four key points were uncovered: advertising of the existence of the sessions should be increased; the use of PhD students overseeing the sessions should be investigated; the centralisation of the sessions should be investigated; and more formal tutorial engagement should be encouraged.

КОМП’ЮТЕРНА РЕАЛІЗАЦІЯ АЛГОРИТМУ РЕКУРСІЇ ПРИ ВИЗНАЧЕННІ НАТЯГУ НИТОК ПРИ ФОРМУВАННІ БАГАТОШАРОВИХ ТКАНИН З ПОЛІЕТИЛЕНОВИХ НИТОК

Multilayer fabrics made of polyethylene threads are widely used for products of real property and tactical equipment of servicemen capable of protecting the human body from the influence of firearm, cold, cutting, spiny weapons, shock and shock-fractional influences. Optimization of the process of their manufacture is to optimize the tension of the main polyethylene threads in front of the formation zone. To do this, it is necessary to determine the change in relative tension on zones of filling of polyethylene threads on a loop. The execution of this complex task should be based on the use of specially designed computer programs. Taking into account the specifics of the processing of threads on a weaving machine, when determining the relative tension in each individual zone, it is necessary to use a recursion algorithm when the initial tension of the thread from the previous zone will be input for the next zone. Designing new and improvement of existing technological processes of processing polyethylene complex threads on weaving machines requires a change in relative tension on zones of refueling of basic threads. The execution of this complex task should be based on the use of specially designed computer programs using a recursion algorithm. Determination of the change in relative tension on zones of filling of polyethylene complex threads on weaving machines, taking into account the material of the guide, will improve the technology of manufacturing multilayer fabrics that are used to manufacture products of real property and tactical equipment of servicemen capable of protecting the human body from the influence of firearms, cold, cutting, spiny weapons, shock and shock-fractional influences. Improvement of existing technological processes of processing polyethylene complex threads on weaving machines will reduce the downtime that arise when breaking the threads. This negatively affects the productivity of weaving machine tools, reduces the quality of multilayer tissues. Minimization of tension in each line of refueling line of basic polyethylene complex threads will reduce the likelihood of a cliff of the thread, which is important for improving technological processes from the position of increasing the productivity of weaving machine tools and the quality of multilayer tissues. Mathematical provision of a computer program requires the development of thread interaction models with surfaces of scala, framing guides, holes of the remission framework taking into account the real physical and mechanical properties of complex threads and yarns and their real geometric and constructive parameters. The main factor affects the growth of the tension of polyethylene complex threads is the force of friction. It characterizes the friction properties of the threads and conditions of their interaction with the surfaces of the scala, framing guides, holes of the striped frames.

Modeling the Probability of the Detection Process of Tax Evasion Taking into Account Quality and Quantity Indicators

Aims: In contrast to the classical approaches of the standard model of tax evasion based on game theory, our manuscript has considered the detection of tax evasion as one of the main function of tax administration and has proposed a model for assessing the probability of tax evasion taking into consideration qualitative and quantitative indicators.
 Study Design: This investigation has been carried out on the basis of research methods such as scientific abstraction and systematic analysis, expert evaluation, logical generalization, statistical analysis.
 Place and Duration of Study: Department of Mathematical provision of economic researches, between November 2019 and May 2020.
 Methodology: For the evaluating of the probability of tax evasion’s detection firstly, efficiency indicators of tax administration were selected including 3 groups such as internal environmental, external micro, and external macro-environmental factors. These indicators consist of both quantitative as well as qualitative indicators. Quantitative indicators were assessed on the base on statistics information base. Quantitative indicators were assessed on the base of expert skills, knowledge, and experiences in accordance with under investigation countries. The objectiveness of obtained data that characterize qualitative indicators was checked and used both these as well as quantitative indicators for formulating the tax efficiency index. The next step is consists of using these formulations for evaluating the probability of detection of tax evasion under uncertainty. The impact degrees (membership functions) of the parameters that characterize the influence of 3 groups-environmental factors, in the detection of tax evasion were defined, and taking them into account in the fuzzy inference system probability of detection of tax evasion was assessed.
 Limitations: Lack or uncertainties of the information base cause difficulties in applying our model.
 Results: The probability of detection of tax evasion in the Republic of Azerbaijan was assessed with the proposed model and depends on the results recommendations have been consulted for improving appropriate tax system. As a result of model the probability of detection of tax evasion was defined 29%. The result shows that tax administration mechanism in Azerbaijan Republic need to be improved.
 Conclusion: Proposed model drives practical significance as a providing effective activity of tax institutions by defining the level of tax administration, as well as, as an impacting remarkably the revenue of state budget by determining the probability of tax evasion's detection.

Student with special needs and mathematics learning: A case study of an autistic student

The provision of mathematics for autistic students has not gained a special concern. In fact, many autistic children have good mathematical skills and some are even excellent. It imposes teachers to formulate and create effective strategies to teach autistic students. The purpose of this study was to determine teacher behavior and how to teach students with autism effectively. This study was designed as a qualitative case study research. It involved mathematics teacher, assistant teacher, student, and parents. Data were obtained through observations and interviews. The autistic student's attitude and behaviors during mathematics learning were investigated. It included examinations on the supporting and inhibiting factors in mathematics learning in a school for students with special educational needs/SLB. The result indicated that mathematics learning for students with autism as performed in inclusive education was different from regular education programs, in which teachers were required to adjust materials with students' psychological condition. It also revealed that the students had had focus issues; hence materials were mostly conveyed outside the lesson plan, particularly to introduce the basic material. The supporting factors included parents' motivation for the student to learn and behave appropriately and well-designed learning packages. Meanwhile, limited learning media and school facilities, as well as the absence of special teachers for students with autism, became the inhibiting factors for mathematics learning.

Developing computational mathematics provision in undergraduate mathematics degrees

Over the last ten years we have comprehensively embedded computational mathematics, and in doing so programming, into the undergraduate mathematics degree programmes at the University of Leeds. This case study discusses some of the practical, organisational and pedagogical issues we encountered, and how we addressed them.

Error Estimation of Indirect Measurement Results for Certain Quantities

The basic mathematical provisions that determine the necessary and sufficient conditions for the application of the method of linearization of nonlinear functions of random arguments in estimating the errors of indirect measurements are considered. The necessity of assessing the emerging systematic component of the error and the degree of approximate representation of functions is noted. Within the framework of necessary and sufficient conditions for expanding an arbitrary function into a Taylor series, a new analytical formula is obtained for approximating a nonlinear function in the form of a quotient of independent random arguments. When using this formula for estimating the errors of the results of the indicated indirect measurements, it is possible not to refine the results obtained by adding terms to the Taylor series and not to evaluate the degree of approximation of the nonlinear function from the values of the corresponding remainder terms. The proposed formula allows one to determine practical conditions under which, for estimating the errors of the corresponding results, one can use well-known and fairly simple formulas for estimating the absolute and relative errors without preliminary processing of the results of direct measurements.

Estimation of the error of the results of indirect measurements of some quantities

The basic mathematical provisions that determine the necessary and sufficient conditions for the application of the method of linearization of nonlinear functions of random arguments in the evaluation of errors of the results of indirect measurements are considered, and the need to present the assessment of the arising systematic component of the error and the degree of approximate representation of functions is noted. Within the framework of the necessary and sufficient conditions for the expansion of an arbitrary function into a Taylor series, a new analytical formula for the approximation of a nonlinear function in the form of a quotient of independent random arguments is obtained, which allows to exclude the questions of refinement of the results by adding terms to the Taylor series and estimating the degree of approximation of a nonlinear function by the values of the corresponding residual terms when evaluating the errors of indirect measurements. It is shown that the obtained new approximation for the replacement of such a function allows us to determine the practical conditions under which to estimate the errors of the corresponding results it is possible to use known, and quite simple, formulas for estimating the absolute and relative errors without preprocessing the results of direct measurements.

Economic-Mathematical Modeling and Forecasting of Competitiveness Level of Agricultural Sector of Ukraine by Means of The-ory of Fuzzy Sets under Conditions of Integration into European Market

The processes of integration of Ukraine into the European Economic Community, the presence of powerful com-petitors in the European markets encourage the formation of a set of measures with the distinction of tools to ensure the com-petitiveness of the agro-industrial complex of the state. The ne-cessity of ensuring the competitiveness of Ukraine's agro-industrial complex on the basis of determining the competitive advantages dictate the urgency of scientific search for new meth-ods, forms, tools for its enhancement, which will further promote the market relations in Ukraine and will have a direct impact on the well-being of the population. The aim of the work is to devel-op an innovative economic-mathematical model for assessing and forecasting the grade of competitiveness of the agricultural sector of Ukraine based on fuzzy sets, which will allow acceleration of the process of Ukraine integration into the European market. The object of the research is the process of ensuring the competi-tiveness of the Ukrainian agricultural sector. The subject of the research is methodological aspects of economic and mathemati-cal modeling of the competitiveness of the agrarian sector of Ukraine. The methodology of the study is based on the principles and mathematical provisions of fuzzy sets, which allows to use both qualitative and quantitative indicators of influence on the process under study. As a result of the research, based on fuzzy set theory, which allows taking into account both quantitative and qualitative factors of influence on the level of competitive-ness, an innovative economic-mathematical model of valuation and forecasting of the grade of competitiveness of the agricultur-al sector of Ukraine has been developed. The classification of factors influencing the level of agrarian industry competitiveness has been formed. The forecast of the grade of competitiveness of the agricultural sector of Ukraine in 2025 has been made, which will allow formulating a strategy of development of the agricultural sector of Ukraine.

The Provision of Mathematics and Statistics Support in Scottish Higher Education Institutions (2017) – A Comparative Study by the Scottish Mathematics Support Network

The Scottish Mathematics Support Network (SMSN) was formed in July 2008 with the aim of creating a support network for people working in Scottish universities who were involved with, or wished to be involved with, providing mathematical and/or statistical support for their students. The consensus of the SMSN is that increasingly more students need assistance with their basic mathematical and statistical skills than was the case in the past, and that consequently mathematics support is an area on which universities will need to focus on in future years. Through networking and professional development opportunities with other practitioners in the field of mathematics and statistics support, the SMSN have developed and maintained strong links with individual practitioners, and more broadly with like-minded groups such as the sigma Network and the Irish Mathematics Learning Support Network. With the provision of mathematics and statistics support becoming more prevalent in UK Higher Education institutions, it seemed timely to assess the current state of this provision in Scotland, and to compare with the rest of the British Isles. At the 2016 SMSN AGM, it was unanimously agreed that such a study should be carried out with the SMSN committee taking responsibility for conducting the research.

Mastering maths starts with a great deal of talking

Following the success of the Talk for Reading partnership, the natural progression was to look at how working in clusters of schools and settings can help to improve our mathematics provision for children.

Maths Advice and Revision for Chemistry (MARC)

It has been recognised for some time by Science and Engineering departments that students are entering Higher Education ill-equipped in terms of their mathematical skills, despite having in many cases, attained good grades at Higher/A level (The Engineering Council 2000; Fry, Ketteridge & Marshall 1999; Score Education 2009). In an attempt, therefore, to ensure that all students progressing on to Chemistry degrees are equally prepared (in terms of ability and confidence) to attempt the more mathematical aspects of our courses, the School of Chemistry has over recent years been sequentially introducing mathematics support into the curriculum. As part of the School’s ongoing mathematical support provision, the aim of this project was two-fold: 1) to assess the popularity and effectiveness of tailored maths support sessions and 2) in relation to the teaching of mathematical concepts to science students, collate examples of existing appropriate open educational resources to provide additional support to facilitate student learning such as RSC Discover Maths for Chemistry and Math Centre (Royal Society of Chemistry; MathCentre 2016). A pilot project has been carried out during the academic year 2015-2016, where support sessions were delivered in tutorial format by the Maths Adviser. Although the sessions were open to all 3rd year students studying on chemistry degree programmes, the expectation was that they would mainly be attended by students with little formal mathematics training and those who are less confident about their abilities. Keywords: Chemistry, Mathematics, Student Support, Maths Support