Mathematical Processing Research Articles

How are the cognitive mathematical modelling processes of third grade elementary school students?

How are the cognitive mathematical modelling processes of third grade elementary school students?

Analysis of the ion mobility spectra of chloroacetophenone, tris(2-chloroethyl)amine, and methanethiol

Objectives. To determine the ion mobilities of chloroacetophenone, tris(2-chloroethyl)amine, and methanethiol; the structure of ions corresponding to characteristic signals; the detection limits of chloroacetophenone, tris(2-chloroethyl)amine, and methanethiol with the Kerber-T ion drift detector and the Segment automatic stationary gas detector.Methods. Ion mobility spectrometry was used in order to determine the ion mobilities and detect analytes. The enthalpies of reactions of ion formation were calculated using the ORCA 4.1.1 software by means of the B3LYP density functional method with the 6-31G(d,p) basis set.Results. The ion mobilities of chloroacetophenone, tris(2-chloroethyl)amine, and methanethiol were determined. A method for recording ion mobility spectra and their mathematical processing was developed. The dependencies of the change in ion mobility spectra on the analyte concentration were also studied. Possible mechanisms were proposed for the formation of the ion mobility spectra observed, in accordance with the ionization features of chloroacetophenone, tris(2-chloroethyl)amine, and methanethiol. The enthalpies of ion formation were calculated. The ionization schemes of the compounds were shown. The generalized results of experimental studies were presented, as were the features of compound identification taking into account the structure of the spectra, the concentrations of substances, and the detection conditions.Conclusions. Characteristic signals of chloroacetophenone, tris(2-chloroethyl)amine, and methanethiol were identified. All studied hazardous substances can be detected with an ion mobility spectrometer at concentrations at the ppm level. The following detection limits of the substances were determined with the Segment gas detector: chloroacetophenone, 245 mg/m3; tris(2-chloroethyl)amine, 0.01 mg/m3; and methanethiol, 0.8 mg/m3.

Інноваційні методологічні підходи до оцінки психофізичних здібностей гандболістів на етапі попередньої базової підготовки

The article deals with the psychophysical abilities of young handball players at the stage of preliminary basic training. Particular attention is paid to the analysis of the level of formation of such abilities as reaction speed, coordination of movements, concentration of attention and the ability to make decisions in stressful situations. The scientific relevance of the study is due to the need to improve training methods aimed at increasing the effectiveness of athletes' preparation for competitions. The purpose of the study is to analyze and evaluate the psychophysical abilities of young handball players, which will help to determine the effectiveness of the applied training methods and contribute to the development of new approaches to the training of athletes. Material and methods of research. Handball players at the stage of preliminary basic training (103 people) at the age of 15-16 years old, involved in the championship of Ukraine among boys, took part in the pedagogical experiment. To implement the goals and objectives of the study used a set of methods: theoretical analysis, synthesis and generalization; pedagogical observation; pedagogical testing; mathematical and statistical data processing. Research Results. It was found that the psychophysical abilities of young handball players who are at the stage of preliminary basic training correspond to a satisfactory level. However, in order to achieve high results in the future it is necessary to improve training programs taking into account the individual characteristics of each athlete. Analysis of the test results showed that the majority of handball players, both from the experimental and control groups, demonstrate similar results on the complex index of psychophysical abilities, which allowed us to conclude that there were no significant differences in the levels of development of psychophysical abilities between the groups at the beginning of the study. It was revealed that the average characteristics of different psychophysical tests in the majority of athletes correspond to a satisfactory level. For example, the speed of reaction to visual stimuli, reaction speed in game conditions, as well as the results of specialized handball tests showed that the level of formation of these abilities is sufficient for participation in competitions, but requires improvement to achieve high results. It is important to note that the highest average values of complex indicators of psychophysical abilities were observed in point guard players, which corresponds to the average level of formation. Line players also showed the results corresponding to the average level, while half-middle and edge players showed slightly lower values corresponding to the satisfactory level. Conclusions. The conducted study showed that at the stage of preliminary basic training most young handball players have a satisfactory level of development of psychophysical abilities, which indicates that there is a potential to improve their sports training by improving training methods. Given that different players demonstrate different levels of development of psychophysical abilities, especially among midfield and edge players, it is necessary to develop and implement individual training programs, which will optimize the training of each player in accordance with his individual characteristics and increase the overall effectiveness of the team.

Developing TPACK through task design: exploring the use of multiple modes of representation and the promotion of mathematical processes

ABSTRACT This research considers the need to train teachers who can effectively integrate technology for teaching and learning mathematics. The primary goal of this research is to showcase a successful training experience by identifying and describing some indicators of the technological pedagogical content knowledge acquired by pre-service early childhood education teachers during their participation in this initial training programme. Specifically, we focus on the different ways of representing mathematical concepts and the mathematical processes that can be activated by including such modes of representation. The participants in this research were 28 PECTs, who were organised into groups that planned a set of tasks using technology to teach geometric concepts. The results show that the groups employed a variety of modes of representation, translations and transformations (connections), fostering the emergence of different mathematical processes. Thus, our proposal to integrate technology was satisfactory in this sense, suggesting its potential applicability across diverse subjects, particularly those in which the ways of representing concepts play a relevant role. Also, the analysis conducted may be extrapolated to subjects others than mathematics.

Исследование работы термической опреснительной установки с контактным испарителем и компрессией паровоздушной смеси

One of the global issues of our time is the shortage of freshwater resources. Desalination of marine and brackish waters is a promising solution to this problem. The most common desalination technologies are thermal (distillation) and baromembrane (reverse osmosis and nanofiltration) processes. When designing demineralization stations with reverse osmosis units, it is necessary to consider a number of limitations associated with higher requirements for pretreatment of water entering the unit. The use of thermal desalination plants makes it possible to obtain fresh water of higher quality, and less stringent requirements are imposed on the preliminary preparation of water for this type of unit. However, during the operation of desalination plants of this type, scale forms on the heating surfaces, which negatively affects the efficiency of the unit. Scale is formed less intensively in the units with contact vapors, since in this case the evaporation process occurs in volume. Thus, the development of thermal scheme of such unit and the study of their operation is relevant. The tasks have been solved using the methods of experimental studies of heat and mass transfer processes, mathematical processing of experimental data, and balance calculations of power plants. A thermal scheme of a thermal desalination plant with a contact evaporator with compression of a vapor-air mixture has been developed. Thermal and material balance has been compiled, on the basis of which energy costs have been determined to obtain m3 of fresh water. The authors have proved the determining influence of the temperature of desalinated water in the bubbling zone on the productivity of desalination plants with a contact evaporator. An amendment has been obtained that allows the initial salinity of water and brine to be considered when calculating the operating cycle of the unit. As a result of the analysis of the results obtained, it is found that an increase in the water temperature in the bubbling zone allows us to increase the productivity of the unit, and an increase of the drying temperature of the vapor-air mixture leads to a decrease of the energy consumption of the desalination plant. The introduction of an amendment considering the salinity of the source water and brine makes it possible to increase the accuracy of calculating air humidification up to 15 %.

The process of pre-service mathematics teachers reaching spatial visualisation generalisations

The process of pre-service mathematics teachers reaching spatial visualisation generalisations

Preface: 2024 International Conference on Mathematical Modeling, Algorithms and Data Processing (MMADP 2024)

The 2024 International Conference on Mathematical Modeling, Algorithms and Data Processing (MMADP 2024) was held in Abu Dhabi, United Arab Emirates during September 14-15, 2024. The conference is devoted to mathematical modeling, algorithms application, data processing, computer simulation, artificial intelligence, and scientific computing. It is an opportunity to academics, scientists, engineers, researchers, and scholars to discuss, to present, and to assess the results of their research work on recent developments. The primary goal of the conference is to promote research and developmental activities. Another goal is to promote scientific information interchange worldwide. The success of MMADP 2024 is due to the high scientific level of all the contributions as well as to the enthusiasm of all the attendees. The member of the technical committee did a precious job in selecting the papers that were accepted for presentation and for inclusion in this book of proceedings among those that were initially submitted. We hope MMADP 2024 can develop into persistent success in future years, involving participants and speakers from all corners of the world. MMADP Organizing Committees Abu Dhabi, United Arab Emirates

On the Relationship Between Bilingualism and Mathematical Performance: A Systematic Review

As part of the demands of a globalized and interconnected world, studying second languages has become a major priority. Bilingual programs implemented in recent decades have motivated an educational strategy in which content area courses are taught through L2. The potential costs of this strategy in academic performance are debated, especially in challenging areas such as mathematics. The present work systematically reviewed 71 papers based on experiments measuring mathematics performance in bilinguals in order to establish if bilinguals show a (dis)advantage in mathematics compared to monolinguals. The results of a total of 305,136 participants (57,703 bilinguals and 247,503 monolinguals) show that bilingualism does not seem to affect mathematical performance, but this is dependent on whether subjects are highly proficient bilinguals. This type of bilingual may only be affected by lower reaction times depending on the testing language. On the other hand, low language proficiency negatively impacts mathematical performance. Lastly, bilingualism enhances mathematical encoding and processes in non-language-related tasks.

Parents' use of sustained shared thinking during joint mathematics activities with young children: Aninvestigation of its measurement, antecedents, and outcomes.

There is currently a dearth of tools to assess parents' use of effective interactive strategies for supporting early mathematics learning. One potential such strategy is sustained shared thinking. This study therefore constructed and validated a scale for measuring parents' use of sustained shared thinking during joint mathematics activities with young children, and examined its antecedents and outcomes. Four hundred and sixty-six parents completed a questionnaire about their conceptions of mathematics teaching and learning, home practices, as well as their kindergarten children's approach and avoidance motivation to learn mathematics. Additionally, the children were tested on numeration skills. Results showed that our new scale has three factors: exchanging ideas with children about mathematical problem-solving processes, creating a child-centred atmosphere for mathematics learning, and engaging children in mathematical thinking. Parents' uses of these three strategies were predicted by their constructivist conception of mathematics teaching and learning, and were differentially associated with the children's numeration skills, approach, and avoidance motivation to learn mathematics. Potential uses of our new scale in future home mathematics environment research are discussed.

COMPARATOR REGRESSION ANALYSIS IN CONDITIONS OF FUZZY INITIAL DATA

Abstract. The canonical task of regression analysis consists in studying the problem of estimation and mathematical description of the influence caused by one or more independent variables (predictors, explanatory variables) on the dependent (explained) variable. The subject of comparator identification problem is a specific modification of the standard regression analysis problem in the case when, for some reason, it is not possible to measure values of the dependent, explained variable. However, the problem of reconstructing a regression polynomial can be solved if it is possible to qualitatively compare the results of experiments and rank them, for example, in the order of increasing. Taking into account the results of ranking the values of the explained variable in different experiments, a corresponding system of inequalities is formed. The purpose of the research consists in developing a method for mathematical processing of the resulting system of inequalities for analytical assessment of the level of influence of explanatory variables on the explained variable. The method for solving the problem is based on transforming a system of inequalities into a system of linear algebraic equations. A significant drawback of the known approach to solving this problem consists in the fact that the resulting system of linear algebraic equations is an underdetermined one (the number of unknowns in this system exceeds the number of equations). At the same time, the system has an infinite number of solutions, among which there may be an uncontrollable number of unacceptable ones. The exhaustive search method for finding acceptable solutions is futile. In this regard, the problem of developing a correct method of comparator identification remains relevant. Another difficulty that accompanies the actual procedure of comparator identification when solving practical problems consists in the fact that measurements of values of the controlled parameters are not accurate. The uncertainty that arises in the conditions of a small sample of initial data can be removed using the tools of fuzzy mathematics. It is assumed that, based on preliminary research, a mathematical description of the corresponding membership function can be obtained for each of the controlled parameters. As a result, effective approaches to solving emerging problems have been proposed, based on the use of developed optimization procedures in the conditions of a small sample of fuzzy initial data.

Mathematical Modelling from a Semiotic-Cognitive Approach

Mathematical modelling has acquired relevance in different fields at an international level, both in education and research. This article states that, throughout the construction of the theoretical corpus of this mathematical process and competency – among others – two big issues have occurred: one of terminological nature since the definitions surrounding modelling have varied, and other of representational nature since different representations have been proposed to explain modelling as a cyclical process. These two issues occur mainly due to the diversity of positions on how modelling is understood and how this process is tried to be explained. To address the terminological issue, a position was adopted on the terminology surrounding modelling in Mathematics Education, based on the main theoretical developments of ICTMA Community. To address the representational issue, a modelling cycle from a semiotic-cognitive approach that represents this process in a non-set way is proposed, that is, without a strict separation between «real world» and «mathematical world». In this way, a proposal aligned with a system of theoretical principles (terminology and structure), a methodology (modelling cycle), and sketches of research questions (for future theoretical and empirical developments) is presented to address both issues.

The Mathematical Literacy Process Based on The Students' Mathematical Resilience

Mathematical literacy is very important in daily life, however, the mathematical literacy of Indonesian students is still low. Improving mathematical literacy requires a resilient and unyielding attitude known as mathematical resilience. This study aims to find out the process of mathematical literacy reviewed from the mathematical resilience of students. This research uses a qualitative method. The subject of this study is a grade VIII student at one of the junior high schools in Semarang City. Data collection uses questionnaires, written tests, interviews and documentation. Data analysis uses triangulation techniques. The results of the study show that the students' mathematical literacy process has not been optimally achieved against the existing stages of the mathematical literacy process.

Analysis of High School Students' Mathematical Literacy Skills in Solving Contextual Problems on SPtDV Material

Mathematical literacy is one of the abilities that must be possessed in today's 21st-century education. This study aims to describe the mathematical literacy skills of grade X students at one of the Yogyakarta high schools in Bantul Regency in solving contextual problems on SPtDV (System of Inequality of Two Variables) material. The method used was descriptive qualitative. Data were collected through multiple-choice tests, descriptions, and questionnaires using SPtDV material. Data analysis was done by reducing and presenting data, and drawing conclusions based on indicators of students' mathematical literacy (mathematical process). Sampling of the population was carried out using a non-purposive sampling technique. To determine the number of samples to be taken, researchers used a saturated sampling technique. The research subjects were students of class X of Yogyakarta Private Senior High School in Bantul Regency in the first semester of the 2023/2024 academic year, with a total of 20 students. The results showed that students with high ability were able to fulfill all three aspects of the indicators in mathematical literacy skills, namely formulating, using, and interpreting. While students with moderate ability were able to fulfill two aspects of the indicator, namely formulating and using. And students with low ability were only able to fulfill one aspect of the indicator, namely formulating. The percentage of results obtained is based on the Mathematical Literacy Profile Criteria, namely: 10% proficient, 60% proficient, 15% basic, and 15% need special intervention. This study implies that it is important for other researchers to explore the factors that influence the mathematical literacy skills of low-ability students, especially in high school students or equivalent.

Corrected mathematical models for inertial torques generated by a spinning sphere

The recent publications about inertial torques acting on spinning objects describe their physics by mathematical models. The several inertial torques are generated by the rotating mass which produces centrifugal, Coriolis forces, and the change in the angular momentum. The values of the inertial torques depend on the geometries of the spinning objects. The volumetric geometries of the objects request complex analytical processing of the expressions for the inertial torques. The analysis of the known publication related to the spinning sphere shows the expressions of inertial torques derived from errors in the mathematical processing of integral equations. The wrong limits of the integral equations that give incorrect values for the inertial torques of the spinning sphere present these errors. This manuscript presents the corrected mathematical model for the inertial torques generated by the rotating mass of the spinning solid and hollow sphere.

Editorial: Mathematical thinking, practices, and processes in non-formal learning environments

Editorial: Mathematical thinking, practices, and processes in non-formal learning environments

Experience of integrating lean technologies into the quality management system of a medical organization providing primary medical and sanitary care

Objective. To evaluate the effectiveness of implementation of lean production methods into the practical activity of primary health care on the example of the State Institution of Health Care «Saratov City Polycli nic № 2». Materials and methods. The study was divided into three stages: data collection through anonymous sociological surveys using phones or tablets, timing and improvement of the process, and a follow-up questioning of participants to assess their satisfaction. 296 residents of Saratov receiving primary health care at the polyclinic took part in the survey. The survey was conducted using a specially developed electronic questionnaire via Google Form. For mathematical processing, the results of the study were initially transferred into an electronic database; the results of the study were analyzed using the descriptive statistics method. Results. According to the survey, the majority of respondents are satisfied with the quality of outpatient medical care. This shows that organization of the medical care is focused on the patients` needs and desire to meet their demands. The organization of the front office and the premises of the polyclinic in accordance with the requirements for the new model of the organization providing primary medical care made it possible to achieve a high evaluation of the information stands and the waiting area. The study showed that ineffective organization of the registry office contributed significantly to the patients` low assessment. In our opinion, in order to solve the problem, it is necessary to optimize the work of the registry office by introducing modern technologies and equal distribution of duties among the employees. Conclusions. In order to improve the quality and accessibility of medical services, it is necessary to make certain changes in the organization of medical care. The level of patient satisfaction with the work of medical institutions may depend on various factors, such as waiting time for a doctor, the timing of medical services provision after the appointment, the availability of necessary diagnostic tests and specialists.

An investigation of students’ mathematical connection and metacognitive skills in the mathematical modelling process

The purpose of the study is to investigate the changing mathematical connection and metacognitive skills of students in the process of applying mathematical modelling. The data used for the study were collected from modelling activities, students’ written responses to modelling activities, audio recordings, semi-structured interviews, and observation notes. The data obtained were analysed using content analysis. As a result of the data analysis, it was found that metacognitive skills were used in each activity in the mathematical modelling process and were developed in interaction with each other. Although inter-concept and real-world connection skills are most commonly used in mathematical connection skills, modelling activities were found to enhance connection skills by allowing students to use connection skills with different disciplines and between different representations of the concept. It was found that metacognitive skills and mathematical connection skills develop interdependently, and it was found that mathematical modelling activities can be used as a tool for developing both of these skills.

Metacognitive strategies in mathematical modelling: a case study with engineering students

During the last years, mathematical modelling has been entering the field of engineering education because it is a bridge between mathematics and industry that also promotes the development of skills that require the engineer of the twenty-first century. Nevertheless, the modelling process is involved and requires the deployment of cognitive skills of superior level, particularly metacognitive skills. This contribution presents the results of a multiple qualitative case study on metacognitive strategies used by groups of engineering students associated with each transition of the mathematical modelling process. During the development of the course, observations and retrospective interviews were carried out, which evidenced the use of metacognitive planning strategies from simplification to interpretation; metacognitive monitoring strategies throughout the modelling process, metacognitive regulation strategies from mathematization to mathematical work and metacognitive evaluation strategies during simplification, mathematization and validation. The results expand the classification framework of metacognitive strategies for engineering students.

Development of coordination abilities of mentally retarded children in physical education lessons

The aim of the study to develop a methodology for improving the level of development of the coordination abilities of mentally retarded children aged 8-9 years in the lessons of adaptive physical education. Methods The study was organized at a special correctional school from September 13 to December 16, 2023. 14 schoolchildren aged 8-9 took part in the experiment. Children from the control group studied according to the usual program, and children from the experimental group performed complexes of coordination exercises and used outdoor games during lessons on adaptive physical culture. The level of development of coordination abilities of mentally retarded children aged 8-9 years was determined by three tests: 3x10m shuttle run, one-leg stand, obstacle course. The Student’s T-Test was the main method of mathematical processing of the research results. Results Prior to the start of the study, the difference in performance in control tests in both groups was not significant and not reliable (p>0.05), which indicates the homogeneity of the groups. After the end of the pedagogical experiment, the indicators of coordination abilities of children from the control group improved, but not significantly or significantly (p>0.05). Significant positive changes occurred in the experimental group for all tests. In the shuttle run, the indicators became higher by 0.5 seconds (p>0.05), in the one-leg stand test, the indicators improved by 1.1 seconds (p>0.05), and in the obstacle course test, the indicators improved by 1.2 seconds (p<0.05). An intergroup comparison showed a difference in two of the three indicators of coordination abilities when the significant difference is the shuttle run (p<0.05) and the obstacle course (p<0.05). Conclusion The developed experimental methodology for the development of coordination abilities for mentally retarded children aged 8-9 years in the lessons of adaptive physical education has proven its effectiveness and is recommended for use in correctional schools in working with mentally retarded children. Bangladesh Journal of Medical Science Vol. 23 No. 04 October’24 Page : 1219-1226

Delving into division

When teaching the multiplicative domain in New Zealand primary schools, teachers tend to spend a greater proportion of time on the meaning and processes of multiplication, to the detriment of a specific focus on understanding the concept of division. When division is taught, it tends to be by reversing the context and turning the division scenarios into multiplication problems. While this article stems from wider research based on teaching division in Years 5 and 6, it is relevant to all primary school teachers as they teach the mathematical process of division to the students in their classroom.