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The article deals with the problem of calculating the volume calendar plan of a paper mill. The presented mathematical model and methods make it possible to schedule paper production orders between several paper machines (PM) to even their loading, devise cutting plans for each winder and arrange the order of their implementation. When forming cutting plans, orders are grouped in accordance with such parameters as grammage, roll diameter, core diameter, product type and number of layers. Deadlines and volumes in customer orders are taken into account. The cutting plans for each winder account for the allowable roll width limits and the maximum number of knives. To find the optimal schedule, a combination of the following criteria is used: minimal trim loss, minimal changes to the knives' setup and smooth transitions by product grades. Solution algorithms are presented that use a combination of the simplex method, the column generation, the branch and bound methods, the greedy algorithm and the local search procedure. We tested the solution approach on real production data from a paper mill in European Russia and obtained the production sequence that better matches deadlines in customer orders compared to the plan devised manually by production planners. [ABSTRACT FROM AUTHOR]

We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a "flattening effect" on the combustion front. [ABSTRACT FROM AUTHOR]

In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results. [ABSTRACT FROM AUTHOR]

The quest for cost-effective and thermal efficient structural materials onto beating the high cost of construction is gaining more attention among researchers. This study focused on the blending of cement and sand with waste paper pulp into cost-effective structural materials. The composites were prepared in four mix groups with each containing a fixed amount of sand at 5, 10, 15, and 20 wt.% (by weight of pulp). Cement was varied at 10, 20, 30, and 40 wt.% in each group, and curing was done for 28 days. Properties evaluated are compressive, bending, and splitting strengths. It was observed that increasing cement and sand contents enhanced strengths; howbeit, the blend of 30 wt.% cement/15 wt.% sand resulted in a reduction in bending strength even as 30 wt.% cement/20 wt.% sand engendered a decrease in bending and splitting strength. The microstructural features showed that inherent fibers of the pulp were well bonded with hydration products and sand content yielding good performance in the composites. The optimization procedure carried out depicted a combination of 35.27% cement and 20% sand as the optimum composition. Experimental outcomes were modelled for the purpose of prediction of responses. The models were confirmed statistically fit showing how varying cement content affected strength responses at fixed sand proportion. ANOVA affirmed the significant contribution of cement and sand on the strength responses. Compliance reliability was observed to be dependent on the interactive pattern between cement and sand. Going by the standard prescription for the strength properties, cement and sand content of 35.27 and sand 20 wt.% satisfied all strength requirements for low-cost construction having a compliance reliability of 1.31. [ABSTRACT FROM AUTHOR]

Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context. [ABSTRACT FROM AUTHOR]

To enhance the quality and efficiency of computer-enabled generation of papers for Test for English Majors Band 8 (TEM-8), a paper generation model supported by sparrow search algorithm-genetic algorithm was studied. First, a simplified test paper generation mathematical model was set up after analyzing and studying types and characteristics of TEM-8 tasks. In the model, quantity, type, difficulty, discrimination degree, scores, exposure, and answering time of test questions were taken into consideration. To enhance the optimizing effect of the genetic algorithm for searching test questions, the traditional genetic algorithm was improved by introducing the sparrow search algorithm into the model to achieve a better crossover rate, variance rate, optimization precision, and speed of the genetic algorithm. A new sparrow search-genetic algorithm (SSA-GA) was designed, and the optimizing effect of SSA-GA was verified to be ideal through optimizing six standard test functions. Then, SSA-GA was applied to conduct experimentation with test paper generation, and comparison with traditional genetic algorithms was also made. The values of best and average fitness of SSA-GA were better than those of the traditional genetic algorithm (GA) in the paper generation. Exposure rate and success rate in TEM-8 paper generation of SSA-GA were higher than those of traditional GA in TEM-8 paper generation. Results showed that the studied SSA-GA could implement test paper generation with higher speed and better quality. [ABSTRACT FROM AUTHOR]

This work examines the impact of multi pre-exponential factors on the lifetime modelling of the paper in oil-immersed transformers. First, the corresponding pre-exponential factor was determined based on the concentrations of the three parameters known as oxygen, moisture and acid. Next, the pre-exponential factor for each of the parameters at different concentrations was combined based on the summative approach to obtain the overall impact on the lifetime of the paper. It is found that the expected life of the paper for overall multi pre-exponential factors is higher than either single or double pre-exponential factors. For a single pre-exponential factor, the expected life of the paper decreases by a factor of 59.8 as the oxygen concentration increases from 15,000 ppm to 210,000 ppm. Moisture can decrease the expected life of the paper by a factor of 34 as it increases from 0.5% to 5%. Low molecular weight acid (LMA) has a higher impact than high molecular weight acid (HMA), whereby its impact is further enhanced through multi pre-exponential factor effect whereby the expected life of the paper decreases by a factor of 7.9 as the moisture content increases from 0.5% to 5% and oxygen increases from 300 ppm to 20,000 ppm. [ABSTRACT FROM AUTHOR]

In this paper, we continue describing the project and the experimentation of "Ricerca Operativa Applicazioni Reali" (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools, introduced. ROAR is composed of three teaching units, addressed to Grades 10, 11, and 12, respectively, having the main aim to improve students' interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. In a previous paper, we reported on the design and implementation of the first unit, started in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy), in a Grade-10 class. Here, we focus on the second unit, carried out in Winter/Spring 2022 with the same students, now in a Grade-11 class. In particular, we describe objectives, prerequisites, topics and methods, the organization of the lectures, digital technologies used, and a challenging final project. Moreover, we analyze the feedback from students and teachers involved in the experimentation.

Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area, particularly models involving only two or three coupled differential equations. These models were amenable to students as well as interesting and relevant to students because they came from real research papers. I will describe the use of scenarios and case studies in lectures, and group projects for assessment. The scenarios and case studies were published in a textbook that I wrote. Scenarios, case studies and projects provided an opportunity to expose students to some novel applications of differential equations. One example is developed here as a "Classroom Note": modelling the dynastic cycles in Chinese history.

The student experience with mathematical modelling has the potential to differ in nature to the experience of a typical mathematics student. The research reported in this paper forms part of a broader study looking into tertiary learning experiences for mathematical modelling. This paper reports on: What are the student experiences when learning to mathematically model? How might these experiences inform mathematics education? Data were collected across two different tertiary mathematical modelling courses in the form of student interviews. Student interviews were analysed, using reflective thematic analysis, to identify themes relating to the collective student learning experience. The results show that modelling provides an opportunity for students to be actively involved with their learning. Being open-minded was a key behaviour for a productive student experience.

Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically included in most curricula of higher secondary schools (i.e. Grades 9-12), but it is usually presented mainly at university level. To show how OR could be significant for these school students' education, the authors of this paper developed an educational project consisting of three teaching units. In this paper, we share the result of the teaching experiment related to the first unit, addressed to Grade 10. Qualitative and quantitative analyses show how it is appropriate to include OR and its typology of problems in regular school mathematics lectures. Second, these data also show how modelling and problem-solving skills, developed working with OR, can be fostered by implementing a collaborative way of working, also by making use of digital technologies. Last but not least, we demonstrate the positive impact such activities have on students' appreciation of OR.

This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for Initial Value Problems and Boundary Value Problems. The students are asked to formalise the mathematical model and build their own experiments using the information provided in the papers. Additionally, a parameter estimation experiment is organised, which involves generating synthetic data and computing noisy data to estimate the natural death rate of sensitive yeast. The results show that data noise significantly affects the parameter estimate and that scaling the data can help reduce the impact of measurement errors. The presented results can be used to investigate other possible assignments, such as how the evaluation of the Jacobian affects the estimation performance and compare different optimisation algorithms.

The generation and distribution of furfural are significantly affected by moisture content in the insulating paper. However, the diffusion mechanism of furfural under moisture effect is not clear, hence, this study investigates the effect of moisture on the diffusion characteristics of furfural by combining macro experiment and micro molecular dynamics simulation. The simulation results demonstrate that the increased moisture content in paper accelerates the diffusion of furfural from paper to oil, which is also proved by the experimental data. Then, the results of interaction energy analysis indicate that the increase of moisture enhances the van der Waals force between oil and furfural. The present findings are expected to improve the theoretical level of furfural analysis, which will facilitate the aging evaluation of the transformer insulating paper based on furfural. [ABSTRACT FROM AUTHOR]

Industrial progress in papermaking in the early nineteenth century led to the technologies that resulted in more acidic papers, which was caused mainly by the exploitation of alum (KAl(SO4)2) and rosin as sizing agents. The papers prepared by such technologies have degraded more quickly. From the 1930s various deacidification and preservation processes with basic agents have been developed. The most widespread deacidification process is with the aerosol (spray system) consisting of microscale particles MgO and perfluoroheptane (PFH) as a carrier (the so-called Bookkeeper process). The shortcomings of this process are the low dissolution of solid MgO particles and the transport to the interior of acidic paper. We have developed a theoretical two-level model of the Bookkeeper process suitable for prediction of deacidification extent. The model involves both the dissolution/reaction of the solid particles and transport of solvated ions and solid particles inside the bulk of paper. The developed model coincides with the results of the performed deacidification experiment. The model is also in good agreement with the Lucas–Washburn equation, which is usually used for the description of the penetration of a deacidifying agent into the paper. [ABSTRACT FROM AUTHOR]

Howard Rachlin's widely influential behavioral economic approach to self‐control and related issues provides the model for this submission. The topic is overconsumption. Current human consumption levels are unsustainable. Explanations typically focus on societal factors, such as the seductive power of advertising and/or misguided tax policies. However, the effectiveness of these factors depends on the degree to which individuals are susceptible to the message: "consume more." Humans are not blank slates. This paper argues that how individuals frame their choices establishes the susceptibility to overconsume. According to economic theory, consumers frame their options as bundles, composed of different combinations of the available items and activities. This leads to maximizing. In experiments, participants tend to frame their options as "either‐or" choices. This leads to the matching law. Mathematical models of concurrent schedule choice procedures show that (1) the matching law implies overconsumption of the most preferred option and (2) that individuals will persist in preferring their favorite option even when doing so reduces overall reward rates. Given that the matching law better describes how individuals choose than does maximizing, the mathematical models of widely used choice procedures help explain why efforts to increase consumption have been more influential than efforts to control consumption. [ABSTRACT FROM AUTHOR]

Due to rapid temperature rise and insulation moisture, bubbles can generate in the oil-paper insulation of oil-immersed power transformers, which can reduce the dielectric strength of oil-paper insulation and even bring about the risk of insulation breakdown. In order to accurately evaluate the conditions of bubble formation, the physical process of bubble formation in oil-paper insulation is studied in this article. Considering the effects of water vaporization, gas dissolution in oil, and moisture migration on bubble formation, a bubble formation prediction model is constructed. Based on Henry’s law, the dissolution equilibrium of gas in oil is taken into consideration and the upper boundary of the initial temperature of bubble effect (ITBE) envelope is obtained in this model. Based on the moisture equilibrium in oil-paper insulation, the bubble formation process caused by the emergence and rapid evaporation of free water is analyzed, and then, the lower boundary of the ITBE envelope is obtained in this model. The model results show that the moisture content of the pressboard and the presence of free water have a great impact on ITBE. Specifically, the higher the moisture content, the lower the ITBE value. In addition, with the further increase of moisture content, the upper and lower boundaries of the ITBE envelope gradually tend to be the same. However, once free water is present on the surface of cellulose, ITBE decreases rapidly to below 120 °C. The model built in this article is of great significance to study the temperature limit of the power transformer. Hence the ITBE envelope can provide an important theoretical reference for reducing the risk of bubble formation during power transformer operation. [ABSTRACT FROM AUTHOR]

The space charge effect of transformer insulating paper will distort its internal electric field, and its space charge effect will be more prominent under extremely complex working conditions. At present, the micromechanism of charge transport and electric field distortion characteristics of paperboard are not clear under complex working conditions. So in this article, based on the bipolar carrier transport (BCT) model and the dynamic carrier balance model, the effects of high temperature, aging degree, moisture content, and bent degree on charges accumulation in paperboard are studied under dc high voltage by numerical simulation and the measured data needed for simulation. The results show that the higher temperature strengthens the carrier migration, deepens the injection depth of the charge, and aggravates the distortion of electric field intensity in paperboard. The more extended the aging time of paperboard, the greater the internal trap density and the deeper the trap depth, which lead to charges migration difficultly. Increasing water content in the paperboard will accelerate space charges to reach a steady state, while further increasing it will slow down this process, which is related to the shallow trap getting deeper. When the critical part of paperboard is extruded, many traps are introduced, resulting in charges accumulation seriously. The research results can reference the design of paperboard and the maintenance of transformer insulation system. [ABSTRACT FROM AUTHOR]

The mathematics of budgeting and space can lead to a justice-oriented experience for elementary students as they design a proposal for an inclusive playground. The authors' work focused on creating the space for elementary children to see the interconnectedness between mathematics and a community social injustice, lack of inclusive playground access, through community-based mathematical modeling (CBMM). This article highlights how third- and fourth-grade teachers, a math coach, and a university professor (also authors of this paper) collaboratively and thoughtfully engaged in the CBMM cycle.

• Combined effects of extruded brick compositions with paper sludge and expanded perlite were characterized. • The use of additives in bricks has significantly affected their thermo-physical and mechanical properties. • The effects of process parameters on brick properties were investigated with a new mathematical modeling approach. • Fired brick samples showed good thermal insulation performance. • Produced exruded bricks have good potential for energy saving. Lightweight bricks produced with addition of different additive materials such as expanded perlite (EP) and recycling paper sludge (RPS) waste have been accomplished by a pug mill. Porous fired bricks were produced by using organic and inorganic additives such as paper waste and expanded perlite as pore-makers. In the experimental study, the seventeen mixture sets were prepared with Box-Behnken experimental design procedure of two additive ratios and firing temperatures. The brick samples were produced with shaping by extrusion method and firing at 850, 950 and 1050 °C for two hours after drying. Physical characteristics such as bulk density, apparent porosity and water absorption, and also, compressive strength, thermal conductivity and microstructural properties of brick samples were studied. Influences of process parameters on brick properties were investigated with a detailed neuro-regression analysis. In conclusion, the best brick composition (10 % EP + 10 %RPS by weight) in terms of thermal conductivity corresponding to acceptable mechanical properties was optimized. Accordingly, the compressive strength values of all samples are around 10 to 27 MPa. Also, the samples with high additive content (especially 10 %RPS + 5 %EP sample) exhibited the lowest thermal conductivity value (0.432 W/mK) due to the low firing temperature. [ABSTRACT FROM AUTHOR]

This article is aimed at quantifying the health condition of the power transformer insulation system through its frequency-domain dielectric characteristic by using the concept of the resistor and fractional calculus. In this regard, the dielectric model of the fractional Poynting–Thomson (PT) is proposed, and a mathematical model for parameter identification of the proposed model is presented. The shuffled frog leaping algorithm (SFLA) is used to realize the parameter identification and the fractional PT model parameters of the oil-paper samples under different insulation health conditions. The influence of moisture and aging on the fractional PT dielectric model parameters is experimentally studied. Results show that, with the increase in the water content within the insulation system, the parameters of the fractional PT model gradually decrease, and there is a strong correlation between the relaxation time and the water content. This facilitates the employment of the fractional PT model parameters to quantify the aging and moisture content of the power transformer insulation system. [ABSTRACT FROM AUTHOR]

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Methanol concentration as an aging indicator can assess cellulose aging and estimate cellulose degree of polymerization (DP). Despite the advantages of methanol (MeOH), its major disadvantage is that its concentration in the oil decreases after some time. This point is called the MeOH peak in this article. Therefore, using this indicator when MeOH concentration is reduced leads to incorrect results. When using methanol, the main problem is that whenever the methanol concentration in a transformer is measured, it cannot be identified that the measured concentration belongs to the left or right side of the MeOH peak. If the measured concentration belongs to the right side of the MeOH peak, the estimated DP is incorrect. In this article, an empirical equation is established to estimate the DP value as a function of methanol concentration when methanol concentration belongs to the left side of the MeOH peak. Then, a new index called methanol peak detector index (MPDI) composed of a 2-furfural/MeOH ratio and normalized DP is presented to ensure the validity of the calculated DP value. If it is found that the measured concentration belongs to the left side of the MeOH peak, then the estimated DP by the presented equation is valid. Finally, the application of this method is verified by applying it to measurement data samples indicating the validity of the method. [ABSTRACT FROM AUTHOR]

The traditional method for transformer moisture diagnosis is to establish empirical equations between feature parameters extracted from frequency domain spectroscopy (FDS) and the transformer’s moisture content. However, the established empirical equation may not be applicable to a novel testing environment, resulting in an unreliable evaluation result. In this regard, it is acknowledged that FDS combined with machine learning is more suitable for estimating moisture content in a variety of test environments. Nonetheless, the accuracy of the estimation results obtained using the existing method is limited by the algorithm’s inability to generalize. To address this issue, we propose an AdaBoost algorithm-enhanced back-propagation neural network (BP_AdaBoost). This study creates a database by extracting feature parameters from the FDS that characterize the insulation states of the prepared samples. Then, using the BP_AdaBoost algorithm and the newly constructed database, the moisture estimation models are trained. Finally, the results of the estimation are discussed in terms of laboratory and field transformers. By comparing the proposed BP_AdaBoost algorithm to other intelligence algorithms, it is demonstrated that it not only performs better in generalization, but also maintains a high level of accuracy. [ABSTRACT FROM AUTHOR]

Mathematical modeling (MM) -- a cyclical process that involves using mathematics to make-sense of and analyze relevant, real-world situations -- has the potential to advance equity and challenge spaces of marginalization in the elementary mathematics classroom. When informed by culturally responsive teaching practices, MM creates opportunities to center the knowledge and experiences that students from diverse racial, cultural, and linguistic backgrounds bring to the classroom as valuable resources to support learning and inform action. It can disrupt power and status hierarchies in the classroom that contribute to structural and ideological marginalization. This paper describes ways teachers connected their teaching of MM with key components of a culturally responsive mathematics teaching framework. Analysis synthesizes data from an innovative, research-based professional development for elementary teachers to support teacher learning of equity-centered, culturally responsive MM instruction. Data sources include end of year teacher interviews, and professional development discussions from 19 teachers at four geographically, racially, and culturally diverse sites. Findings focus on how teachers connected their teaching of MM with key dimensions of culturally responsive mathematics teaching, and affordances and challenges related to resisting ideological and structural forms of marginalization.

Literature screening is the process of identifying all relevant records from a pool of candidate paper records in systematic review, meta-analysis, and other research synthesis tasks. This process is time consuming, expensive, and prone to human error. Screening prioritization methods attempt to help reviewers identify most relevant records while only screening a proportion of candidate records with high priority. In previous studies, screening prioritization is often referred to as automatic literature screening or automatic literature identification. Numerous screening prioritization methods have been proposed in recent years. However, there is a lack of screening prioritization methods with reliable performance. Our objective is to develop a screening prioritization algorithm with reliable performance for practical use, for example, an algorithm that guarantees an 80% chance of identifying at least 80% of the relevant records. Based on a target-based method proposed in Cormack and Grossman, we propose a screening prioritization algorithm using sampling with replacement. The algorithm is a wrapper algorithm that can work with any current screening prioritization algorithm to guarantee the performance. We prove, with mathematics and probability theory, that the algorithm guarantees the performance. We also run numeric experiments to test the performance of our algorithm when applied in practice. The numeric experiment results show this algorithm achieve reliable performance under different circumstances. The proposed screening prioritization algorithm can be reliably used in real world research synthesis tasks.

Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite integrals by reviewing the research literature on quantitatively-based approaches to integration, in order to pull together the ideas that are spread across many papers in many outlets. We note that the literature in this area has largely developed along two distinct paradigms, which we call "adding up pieces and accumulation from rate." While they are both based in quantitative reasoning, there are critical differences between them that have important ramifications for teaching and learning integration. We use these two paradigms to organize our review and we use the literature to discuss the meanings, formalizations, foci, reasoning, and modeling in these approaches.

The imbalance between the prevalence of patients with acute respiratory failure (ARF) and acute-on-chronic respiratory failure and the number of intensive care unit (ICU) beds requires new solutions. The increasing use of non-invasive respiratory tools to support patients at earlier stages of ARF and the increased expertise of non-ICU clinicians in other types of supportive care have led to the development of adult pulmonary intensive care units (PICUs) and pulmonary intermediate care units (PIMCUs). As in other European countries, Italian PICUs and PIMCUs provide an intermediate level of care as the setting designed for managing ARF patients without severe non-pulmonary dysfunction. The PICUs and PIMCUs may also act as step-down units for weaning patients from prolonged mechanical ventilation and for discharging patients still requiring ventilatory support at home. These units may play an important role in the on-going coronavirus disease 2019 pandemic. This position paper promoted by the Italian Thoracic Society (ITS-AIPO) describes the models, facilities, staff, equipment, and operating methods of PICUs and PIMCUs. [ABSTRACT FROM AUTHOR]

Item response theory (IRT) refers to a family of mathematical models which describe the relationship between latent continuous variables (attributes or characteristics) and their manifestations (dichotomous/polytomous observed outcomes or responses) with regard to a set of item characteristics. Researchers typically use parametric IRT (PIRT) models to measure educational and psychological latent variables. However, PIRT models are based on a set of strong assumptions that often are not satisfied. For this reason, non-parametric IRT (NIRT) models can be more desirable. An exploratory NIRT approach is kernel smoothing IRT (KS-IRT; Ramsay, 1991) which estimates option characteristic curves by non-parametric kernel smoothing technique. This approach only gives graphical representations of item characteristics in a measure and provides preliminary feedback about the performance of items and measures. Although KS-IRT is not a new approach, its application is far from widespread, and it has limited applications in psychological and educational testing. The purpose of the present paper is to give a reader-friendly introduction to the KS-IRT, and then use the KernSmoothIRT package (Mazza et al., 2014, 2022) in R to straightforwardly demonstrate the application of the approach using data of Children's Test Anxiety scale.

In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis of the two approaches. The ultimate goal of the paper is to encourage precalculus instructors teaching either version of logistic growth to consider incorporating our proposed changes in their classes. Sample classroom materials are provided in the supplemental data, along with access to preprogrammed computer spreadsheets for student use and/or classroom demonstrations.

The COVID-19 pandemic revealed that many countries have failed to provide the general population with the cognitive tools to thoroughly understand and cope with a global health crisis. While scientists and leaders worldwide have struggled to discover ways to contain the spread of the virus, this difficult task has become overwhelming due to the limited ability of many citizens to grasp the urgency of the situation. Although in today's digitized world we have endless access to data and more ways to represent information and statistics than ever before, numerous incidents have demonstrated that the frequent misapprehension of data can cause confusion rather than clarity. This opinion paper examines how issues such as the misunderstanding of large quantities, fractions, probabilities, and mathematical modeling may be affecting the way people view the current pandemic. Finally, we also discuss how numeracy can act as a protective factor against motivated reasoning, which often affects how we consume information related to the pandemic.

The main aim of this paper is to present results of an experimental test focused on the validity and effectiveness of composed methodology aimed at increasing the student's attention in Virtual Learning Environment. Areas of presented methodology which were subject of our research is students behavior during learning. The behavioral part of methodology is focused on calculating estimated time for reading/learning specific learning material based on mathematical model. The model has been created as linear regression model trained and validated with student's access logs from Moodle instance used at the university. The methodology created by us, which is the subject of the experiment, uses the mentioned mathematical model in order to more optimally calculate the time-on-task and thus assume the time required for the correct understanding of the presented curriculum in the form of e-learning. In this paper, we will focus on confirming the didactic effectiveness of our proposed methodology for monitoring student attention. We describe an experiment with which we verified the proposed methodology. Methodology itself is focused on improving students learning experiences while using e-learning platforms like Moodle.

This paper investigates students' mathematical modeling activity in data-rich modeling tasks. It aims at gaining insight into how students develop meaning when modeling data-rich situations and the mathematical models produced. A tendency to model a particular dataset, rather than the phenomenon that the dataset is a particular instance of, has been observed previously. Students concentrate on fitting mathematical objects such as functions to data, rather than using domain knowledge about the situation being modeled, mapping this to the data so as to capture the phenomenon as a whole. In other instances, students find functions that simply linearly interpolate the data and do not consider key features of the phenomenon, particularly when they have access to technological tools. The extent to which students' reasoning indicated awareness of their taking either approach was investigated in a qualitative study with Year 10/11 students. How the approach taken affected the processes students engage in whilst modeling was also investigated. The paper contributes to our currently limited literature on research into this issue and how it affects the outcome of students learning to model in classrooms at this level of schooling.

Bin packing problem (BPP) is one of the fastest-growing research issues within the field of combinatorial optimization. Over the last years, several studies carried out various BPP variants, mathematical models, and proposed methods to the BPPs. The classical BPP consists of packing a set of rectangular items in a minimum number of rectangular bins while respecting some constraints.Throughout the years, an improved typology was introduced by Wäscher et al. (2007), providing an excellent instrument for the organization and categorization criteria that defined the problem categories different from those of Dyckhoff (1990). Several early literature reviews have been conducted on various aspects of related packing problem variants.The contribution of this paper is to provide a comprehensive and refined taxonomy intended for BPPs. In addition to that, it is an up-to-date review based on a chronological taxonomy of the literature and depicts further research horizons.This systematic review allowed us to identify other characteristics and constraints, based on Wäscher's original ideas, mainly distinguished according to real cases studies. The detailed analysis provides a valuable framework for understanding the research gaps for future studies that should be acknowledged while proposing and solving new extensions. Note: The addresses of second and third authors have been corrected online. [ABSTRACT FROM AUTHOR]

The Compulsory Education Course Standards for Mathematics 2022 have highlighted the educational objectives of junior secondary mathematics by emphasizing the development of mathematical competence and practical learning. Model consciousness, as one of the fundamental mathematical competencies to be developed at the junior secondary level, can facilitate students' comprehension of the universal application of mathematics. Teachers of mathematics in junior high school should construct effective classroom activities based on the cognitive qualities of their students in order to enhance their mathematical model consciousness and comprehension of the substance of mathematics knowledge. This paper is a lesson study of the education of Congruent Triangles, and its purpose is to investigate strategies for fostering mathematical model consciousness among junior high school pupils.

The aim of this study is to investigate both the planning and implementation process of a modelling task by a middle school mathematics teacher. The participant of the study, which was conducted as a single case study, is a middle school mathematics teacher who have knowledge and experience in modelling. The data collecting tools of this study were the lesson plans of the teacher, the observation notes taken by the researchers during the implementation of the modelling task,the video records of the implementation, students' solution papers and the voice records of the pre- and final-interview conducted with the teacher. Whole data were analyzed according to a framework for modelling implementations developed by the authors through descriptive analysis. The teacher planned his in-class implementation to consolidate the circle concept and revised an existing modelling task by developing appropriate materials for the task. He asked students to arrange their desks appropriate to group work, decided to enable students to evaluate both the implementation and their peers, and announced their students that they would present their group solution and evaluate each other at the end of the lesson. During the implementation, he first reminded prior knowledge about circle and then presented the materials. He shared instructions about group work in the context of sharing social norms and gave information about the peer assessment form, which the students filled at the end of the lesson. During the students were solving the task, he intervened about enabling self-assessment in the groups, considering realistic values and comparing mathematical results with the problem context. In addition, during the solution, he tried to establish socio-mathematical norms by making explanations. After the solution process ended, student groups presented their solution approaches and discussed different solutions by comparing each solutions. Peer assessment form and affective evaluation form regarding the implementation were filled by the students at the end of the implementation. This study contributed the literature regarding modelling implementations and presented a different view about teacher actions in planning and implementing a modelling task.

In this paper, we share a mentorship model we developed and implemented while collaborating with pre-service teachers (PSTs) on their Model Eliciting Activity projects and the outcomes of the mentorship model in terms of PSTs' growth as teachers as well as researchers. For their projects, PSTs designed and developed their own mathematical modeling tasks and later analyzed student work collected during task implementations to better understand their students' reasoning. The PSTs' reflections were collected to assess the effectiveness of the program and to report their professional growth. The PSTs who participated in this mentorship model identified core teaching practices (e.g., questioning, facilitating discussions) and they improved their knowledge of student thinking and reasoning. They were also able to analyze rich data and identify trends in student learning. The findings from this study affirm that engaging in undergraduate research provides PSTs with opportunities to improve their teaching practice as well as their understanding of research processes.

Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by amalgamating perceptual features confounded with the set's cardinality. In this paper, we approach the question of whether ANS representations are numerical by studying the properties they have, rather than how they are formed. Across two pre-registered within-subjects studies, we measured 189 participants' ability to multiply the numbers between 2 and 8. Participants completed symbolic and nonsymbolic versions of the task. Results showed that participants succeeded at above-chance levels when multiplying nonsymbolic representations within the subitizing range (2-4) but were at chance levels when multiplying numbers within the ANS range (5-8). We conclude that, unlike Object Tracking System (OTS) representations, two ANS representations cannot be multiplied together. We suggest that investigating which numerical properties ANS representations possess may advance the debate over whether the ANS is a genuinely numerical system.

The paper aims to propose an instrument to identify students' metacognitive strategies in mathematical modelling activities. The items were designed from a review regards metacognition and instruments already recognised in literature. This design comprises an instrument that differs from others in which the data were the self-reported students' use of metacognitive strategies. The instrument we propose is aimed at the teacher and it is he/she who, based on an analytical process, will infer whether the students use metacognitive strategies in modelling activities. An empirical research was realized and five modelling problems were solved by students of a mathematics degree. The analysis addressed the groups actions and the individual behaviour within the group when working on modelling processes. The results allow to conclude working successfully and in a goal-oriented manner on modelling problems requires metacognitive strategies and the instrument seems to be adequate for the teacher to identify these students' strategies.

Climate change put most species' survival in danger because it substantially affects the climate in which the species live, the quality of the water they drink, as well as the temperature of the air or water. When climate change increases the temperature of the climate, excessive evaporation occurs in lands, lakes, seas, and oceans. Our purpose in this paper is to introduce a mathematical modelling activity embedded in Problem Based Learning (PBL) that allows students to investigate factors related to evaporation. Mathematical modelling is a popular technique of teaching mathematic concepts and skills and a method of inquiry about scientific phenomena that interests scientists. In the present activity, students use secondary data from trusted websites to test their hypotheses. Students are engaged in analyzing and interpreting data, generating and testing models, and discussing and presenting findings with their peers. The activity allows students the opportunity to examine the relationship between variables and predict one variable using the other. The activity has the potential to foster students' computational and higher-order thinking skills.

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in educational and psychological measurement. A key component of CDMs is the Q-matrix characterizing the dependence structure between the items and the latent attributes. Additionally, researchers also assume in many applications certain hierarchical structures among the latent attributes to characterize their dependence. In most CDM applications, the attribute--attribute hierarchical structures, the item-attribute Q-matrix, the item-level diagnostic models, as well as the number of latent attributes, need to be fully or partially pre-specified, which however may be subjective and misspecified as noted by many recent studies. This paper considers the problem of jointly learning these latent and hierarchical structures in CDMs from observed data with minimal model assumptions. Specifically, a penalized likelihood approach is proposed to select the number of attributes and estimate the latent and hierarchical structures simultaneously. An expectation-maximization (EM) algorithm is developed for efficient computation, and statistical consistency theory is also established under mild conditions. The good performance of the proposed method is illustrated by simulation studies and real data applications in educational assessment.

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in a variety of contexts. The questionnaire was finalized after a trial of its pilot version on 7 students on the basis of their written scripts and interviews. After content validation by three external experts, the test was administered to a sample of 141 senior undergraduate physics students from a diverse set of colleges and national institutes. Data analysis reveals several significant student pitfalls in the topic related principally to (i) the identification of a dimensionless ratio to characterize an approximation, (ii) the notion of the order of approximation and consistent handling of a problem up to the required order, and (iii) the notion of the order of infinitesimal in calculus-based derivations. The findings are of direct pedagogic relevance.

In this paper, we discuss how a professor could have students, using rational and exponential functions, develop models for several different density-dependent populations based on characteristics of the species. Students would then need to choose an appropriate method from among three different analytic methods (find a solution, phase-line analysis, graphing approximate solutions) to analyse their models. We then discuss how to use aspects of a species' behaviour to choose an appropriate model from among the ones developed. Finally, we show how a professor could apply what students have learned to develop general principles for sustainable harvesting of such species.

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM majors approach and think about differential equations as models for real-world scenarios. Our purpose is to inform faculty who are using open, authentic, scenario-driven instructional materials about the ways their students think about what are often taken-for-granted concepts in advanced mathematics and to support faculty in ensuring their students get the most from their innovative instructional materials.

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a contextual environment. Teaching mathematics in context has the potential of giving students something to anchor the mathematics to and hence act as cognitive roots With this in mind, in what ways can lecturers use mathematical modelling to provide students with contextual learning experiences of differential equations? A New Zealand study was carried out involving three case studies. Each case study comprised of a mathematical modelling course, lecturer participant and student participants. Modelling examples and activities that involved differential equations were part of all course content. In this paper, I will present information on each course, the main modelling activities each course used, and examples of students' use of differential equations for these activities. Insights discovered into the common practices of the three lecturers regarding using mathematical modelling to teach differential equations will also be presented.

Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context.

In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi problems. In addition, we discuss a framework (called the Fermi problem activity template [FPAT] framework) for supporting the design and use of Fermi problems to facilitate students' learning within particular mathematics content areas and/or aimed at particular concepts or higher-order thinking skills. We also illustrate how the FPAT framework can be used to (i) facilitate interdisciplinary collaborations with other subjects such as the social sciences, but in particular with the other STEM subjects; and (ii) support teachers in adapting and implementing Fermi problems in their classrooms.

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook environments during real-time instruction. Each of these teaching modules employs a literate programming approach that uses the notebook environment to explain the concepts in anatural language, such as English, interspersed with snippets of macros and traditional source code on a web browser. The pedagogical approach employed is reproducible and leads to openaccess material for students to motivate and teach differential equations efficiently. We will share examples of this framework applied to teaching advanced concepts such as machine learning and neural network approaches for solving ordinary and partial differential equations as well as estimating parameters in these equations for given datasets. More details of the work can be accessed from https://aoguedao.github.io/teaching-ml-diffeq.