Mathematical Modeling Skills Research Articles

Developing modelling competencies in pre-service mathematics teachers through reflective thinking skills

Background: Ghana’s commitment to quality education has been reflected in its goal of providing equal access to high-quality education, leading to the reforms of the New Common Core Mathematics Curriculum for Basic Schools. The study explored the integration of mathematical modelling using reflective thinking skills, which are not currently core competencies in Ghanaian basic school curriculum.Aim: The study examined the modelling proficiency of pre-service mathematics teachers by assessing their reflective thinking abilities in a modelling laboratory context.Setting: The study focussed on pre-service mathematics teachers from two education colleges in Ghana.Methods: Using purposive sampling to select participants, a quasi-experimental design with pre- and post-test interventions was employed. Data were analysed through content and inferential analysis, supplemented by interviews.Findings: The findings indicated that the comparison group lacked prior knowledge of modelling problems and struggled with comprehension tasks. In contrast, the experimental group successfully translated real-world problems into mathematical models.Conclusion: Providing pre-service mathematics teachers access to a modelling laboratory and modelling-eliciting activities was essential for developing future modellers. This approach would enhance their effectiveness in teaching foundational mathematics in Ghanaian education.Contribution: This study advocated for re-orienting the mathematics curriculum at both Basic schools and Colleges of Education in Ghana to include mathematical modelling and reflective thinking skills as core components.

Implementation of the practice-oriented mathematics teaching methodology to future rescue engineers

Introduction. In modern conditions, the practice-oriented training of rescue engineers, whose professional activities are associated with high-risk situations, is being updated. The purpose of the study is to describe the implementation of the author's methodology of practical-oriented training in mathematics of future specialists in fire and technosphere safety and experimental verification of efficiency. Materials and methods. The experimental training was attended by 685 students of the Donetsk Institute of the State Fire Service (Russian Federation), studying in the specialty "Fire safety" and the areas of training "Technosphere safety" (321 students in experimental groups, 347 in control groups). Methods of mathematical statistics: Wilcoxon signed-rank test, Fisher's exact test, Chi square test, Student's t-test. Results. The methodology of practice-oriented teaching mathematics to future rescue engineers has been developed. Mathematical training of students based on a practice-oriented approach ensures the formation of students' practice-oriented skills and mathematical modeling skills in the field of civil protection, as well as the development of personal qualities of a rescuer. Practice-oriented learning technologies are used: integration of educational and future professional activities of students, educational and practice-oriented research activities. Practice-oriented teaching methods are used (imitation of the practical activities of rescue engineers, "rapid response" and practice-oriented visualization of mathematical objects). The implementation of the developed teaching methodology contributes to the effective formation of practice-oriented mathematical competence among students (T = 0.32, α = 0.05). Conclusions. The implementation of practical-oriented training in mathematics of future specialists methodology in fire and technosphere safety contributes to increasing the level of development of practical-oriented mathematical competence due to the formation of personal qualities of the rescue engineer and his value orientations, knowledge of mathematical and practical-oriented knowledge, skills and methods of activity in mathematical and computer modeling.

Metacognition and Mathematical Modeling Skills: The Mediating Roles of Computational Thinking in High School Students.

This study was to investigate the relationship between metacognition and the mathematical modeling skills of high school students, as well as the mediating role of computational thinking. A cluster sampling method was adopted to investigate 661 high school students, using the metacognition scale, computational thinking scale, and mathematical modeling skill test questions. The results showed that metacognitive knowledge and metacognitive monitoring had a direct and positive correlation with high school students' mathematical modeling skills. Additionally, the critical thinking dimension of computational thinking mediated the relationship between metacognitive knowledge, experience, monitoring, and mathematical modeling skills. These findings indicated that sufficient metacognition could improve the critical thinking of high school students' computational thinking and enhance their mathematical modeling skills.

A complex methodology for the development of mathematical modeling skills in engineering education

AbstractToday, the role of humans is changing rapidly in both industrial production activities and services. Mediocre, easy-to-learn activities can be performed more efficiently by machines; mediocre knowledge is being devalued while the importance of high-level skills is increasing. As a result, in all sectors of the economy, and especially in engineering, new approaches to expert training are needed; people must learn to hand over certain decision-making roles and to control the processes supported by AI rather than compete with it. STEM education has a responsibility to achieve these goals and must develop appropriate tools for engineering education. This paper presents a complex didactic methodology for competency-based education in engineering bachelor programs. An important element is the mathematical competency map, which shows the importance and place of mathematical and algorithmic (coding) knowledge in engineering topics. Another element is the systematic testing of mathematical knowledge in non-mathematical contexts in engineering courses. We provide an overview of our achievements in applying the developed toolset and improving the efficiency of mathematics teaching in engineering bachelor programs.

Training for high school teachers to develop learning modules based on mathematical modeling in Magetan, East Java

Preparing teaching modules that lead to AKM requires skills in framing abstract mathematical material into a situation or problem context known to students. This is a new challenge for teachers. The process of arranging mathematical material into a context familiar to students is called mathematical modeling. However, in practice, teachers often overlook the importance of modeling skills in teaching. This activity aims to equip mathematics teachers with mathematical modeling skills to enhance their teaching, particularly in preparing students for AKM. The activity, attended by 25 MGMP Mathematics High School teachers in Magetan Regency, was conducted in a hybrid manner (offline and online). Based on the analysis of questionnaire data, it can be concluded that there is an improvement in teachers' understanding of the Independent Curriculum, mathematical modeling, and the application of mathematical modeling in preparing teaching modules for mathematics topics. Similarly, there is an increase in awareness of self-development as professional teachers.

The Effect of Mathematical Habits of Mind and Early Mathematical Ability on Modeling Ability of High School Students

Modeling mathematics serves as a bridge between the processes of translating real-world problems into mathematics. In reality, however, students' mathematical modeling skills, including their knowledge of derivative applications, remain subpar. This study is intended to determine the relationship between mathematical modeling skills, mathematical habits of mind (MHoM), and early mathematical ability (EMA). This research employed a quantitative methodology with mix method sequential explanatory design. The method used a quantitative and qualitative approach. The first quantitative phase is used, then explained more deeply through the qualitative phase. Sample in this study were 36 eleventh-grade students from one of Tasikmalaya's senior high schools. In this investigation, the EMA was the previous semester's math report card grade. A mathematical modeling ability test question and an MHoM questionnaire were administered to students, and the quantitative analysis of the results followed. This study demonstrates that the relationship between MHoM and EMA has a 31.2% modeling capability. In addition, a one-point increase in MHoM and EMA increases the average mathematical modeling ability of pupils by 1,570 and 2,241. Therefore, it can be concluded that MHoM and EMA have a positive effect on mathematical modeling ability.

Examining the Building and Coding Tasks Developed by Pre-service Mathematics Teachers in Terms of Curriculum Integration

Interdisciplinary approach recommended for use in the teaching mathematics in the last decade, the related literature shows that limited study focused on the reflection of the interdisciplinary approach in teaching practice. The aim of this study is to evaluate pre-service mathematics teachers’ task development processes on interdisciplinary approaches through building and coding tasks. Research was conducted with 28 pre-service mathematics teachers studying at a mathematics education department in Turkey. Data were gathered from the analysis of lesson plans and semi-structured interviews. The findings that were obtained through the lesson plans of the participants indicated that participants were able to associate building tasks more with numbers content domain and mathematical modeling skills, and coding tasks with geometry content domain and algorithmic thinking skills. The participants stated that tasks involving coding in their lesson plans would be more useful in terms of teaching mathematics and listed the factors limiting the use of building tasks as technical knowledge and cost.

Analytics Modules for Business Students

Data science is a relatively new requirement for business students. Historically, many business students shied away from business statistics and quantitative or operational research (OR) modules believing them to be boring and irrelevant. The high-profile use of analytics and modelling during the COVID pandemic has drawn awareness to the relevance of analytics. Greater availability of data and modelling tools afford business students an opportunity to re-engage with operational research and analytics and to enjoy the satisfaction of modelling and solving real-world problems, but the challenge of the mathematical modelling skills gap of business students remains. In this paper, we describe a learning pathway of modules in business analytics that can enhance business students’ confidence and capabilities in performing statistical and analytical business tasks. We recommend modelling tools and incremental innovative mathematical modelling teaching approaches that are pedagogically sound and suitable for business students with varying quantitative backgrounds.

The Effect of Mathematical Modelling Activities on Students' Mathematical Modelling Skills in the Context of STEM Education

This study was conducted to examine the effect of mathematical modelling activities on the mathematical modelling skills of secondary school students in the context of STEM education. The study was designed according to the embedded design, one of the mixed research methods. The study group of research consists of 66 eighth-grade students studying in a public school in the central district of a large province in the south of Turkey in the 2020-2021 academic year. While the criterion sampling method, one of the purposeful sampling methods, was used to determine the quantitative study group of the research, the maximum variation sampling method was used to determine the qualitative study group. On the other hand, in the context of STEM education, mathematical modelling problems, evaluation rubric and semi-structured interview forms were used as data collection tools in the research. As a result of the research; It was concluded that mathematical modelling activities in the context of STEM education positively improved the mathematical modelling skills of secondary school students. In addition, it has been concluded that the students who receive education with mathematical modelling activities applied in the context of STEM education gain different interdisciplinary perspectives, experience positive developments in their thinking skills, adapt to group work more easily, and increase their interest in engineering and technology.

Adaptations to Support the Flint Water Task

This Perspectives on Practice manuscript focuses on an innovation associated with “ Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task ” from Volume 7, Issue 2 of MTE . The Flint Water Task has shown great promise in achieving the dual goals of exploring mathematical modeling while building awareness of social justice issues. This Perspectives on Practice article focuses on two adaptations of the task—gallery walks and What I Know, What I Wonder, What I Learned (KWL) charts—that we have found to enhance these learning opportunities. We found that the inclusion of a gallery walk supported our students in the development of their mathematical modeling skills by enhancing both the mathematical analyses of the models and the unpacking of assumptions. The KWL chart helps students document their increase in knowledge of the social justice issues surrounding the water crisis. Using the mathematical modeling cycle to explore social justice issues allows instructors to bring humanity into the mathematics classroom.

Enhancing mathematical modeling skills for sustainable livestock production.

Enhancing mathematical modeling skills for sustainable livestock production.

A Hybrid Method for Assessing Student Mathematical Modelling Skills under Fuzzy Conditions

Mathematical modelling (MM) appears today as a valuable tool in mathematics education, which connects mathematics with everyday life situations on the purpose of increasing the student interest on the subject. In this paper a hybrid method is applied for the assessment of student groups’ MM skills with qualitative grades (i.e. under fuzzy conditions). Namely, soft sets are used as tools for a parametric assessment of a group’s performance, the calculation of the GPA index and the Rectangular Fuzzy Assessment Model are applied for evaluating the group’s qualitative performance, grey numbers are used as tools for assessing the group’s mean performance and neutrosophic sets are utilized when the teacher is not sure about the individual grades assigned to some (or all) students of the group.

Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies

STEM education has been promoted in schools worldwide to cultivate students’ 21st-century skills. Mathematical modelling is a valuable method for developing STEM education. However, in this respect, more attention is given to secondary level or above compared with kindergarten or primary level. Teaching mathematics at the primary level is closely related to authentic problems, which is a crucial characteristic of mathematical modelling activities. After screening 239 publications from various databases, we reviewed 10 empirical studies on mathematical modelling at the primary level. In this systematic review, we analysed the following three aspects: (1) the use of professional development intervention methods/strategies to enhance the intervention effects and the competencies of primary teachers to utilize mathematical modelling; (2) the effects of mathematical modelling on primary students and methods of improving their mathematical modelling skills; and (3) methods used to assess the modelling skills of primary school teachers and students. The results indicate that professional development interventions can enhance the teaching quality of mathematical modelling. The components of the interventions should include an introduction to the pedagogy of mathematical modelling, clarifying the role of the teacher and the student in mathematical modelling activities. Through mathematical modelling, students can generate mathematical ideas, explore mathematical theorems independently, develop critical thinking, and improve their metacognitive and communicative skills. The competency of mathematical modelling is often determined using formative assessments of teachers and students. Because limitations still exist in conducting primary-level modelling activities, schools should utilise more standardised assessment methods, provide universal teacher training, and grant more opportunities for primary school students to participate in mathematical modelling activities. The lack of research on cross-cultural contexts should draw the attention of future research.

Geomorphological Analysis of Ayad River Basin, Udaipur (India) using Remote Sensing and GIS Techniques

Geomorphological analysis is useful for managing land resources and aid in resource inventory, mapping, and management for a variety of purposes. The science of geomorphology is now better able to comprehend surface dynamics because to recent improvements in remote sensing and GIS, the availability of satellite-based DEM, and improvements in mathematical modelling skills. The study is emphasis on utilization of secondary data which have been compiled from different sources e.g. SOI, USGS, NBSS&LUP, GSI. LULC, drainage, river-lake link, soil, geology, landform, geomorphology have been analyzed based on satellite imagery, DEM, toposheet, and other secondary data. Dendritic and sub-dendritic drainage pattern is common in Ayad basin and drainage density is ranging between 0.46 and 3.45 (Km/Km2). Eight artificial lakes are linked together in a chain in the saucer-shaped valley, which is the first historic river linking project in India. Lithology ranging in age from Archaean to Upper Proterozoic are present and belong to three geological cycles - Bhilwara, Aravalli, and Delhi supergroups. Landforms of the area are mainly lower-flat, and ridge cover only 13% of the area. A very detailed geomorphological map has developed by visual image interpretation of satellite imagery, DEM data, toposheets, geological map and classified in 13 broad geomorphic units, and 63 micro-geomorphic units. Through the percentage hypsometric curve method, the hypsometric integral is 27% which indicates the old stage of the basin.

Modeling with Differential Equations and Geogebra in High School Mathematics Education

The integration of technology in mathematics education is still much slower despite the benefits of using technology. Dynamic Geometry Computer Software (DGCS), like GeoGebra, makes mathematical modeling alive and more attractive. They allow dynamic graphical representations and support an in-depth understanding of abstract mathematical concepts. From this perspective, the purpose of this study is to design activities (which include the use of mathematical software Geogebra), where the students manipulate, observe, analyse, and generalize mathematical concepts. With GeoGebra, solving more interesting and difficult problems will evidently be more feasible for students. To evaluate the contribution of GeoGebra in the learning of mathematical modeling, we carried out an experimental study in two groups for the 12th grade students. Experimental group (using GeoGebra) and control group (not using GeoGebra). The intervention lasted five weeks on the subject of differential equations. Based on the results, students in the experimental group achieved higher scores on the Mathematical Modeling Skills Rating Scale.
 
 Received: 20 February 2022 / Accepted: 16 April 2022 / Published: 5 May 2022

Experience in training specialists with mathematical computer modeling skills, taking into account the needs of the modern labor market

Today in most countries there is a lack of qualifications in areas, which require specialists with mathematical competencies, despite the high unemployment rate in many countries. At the same time, it is generally recognized that most likely those sciences are developing, the fundamental results of which can be formulated mathematically. Using mathematical methods, researchers draw important conclusions that could hardly be obtained otherwise. Digital transformation of all industries requires specialists with a sufficient level of mathematical competence and skills in ICT tools, including computer modeling using the approach called Inquiry-Based Mathematics Education (IBME).

Mathematical Modeling Skills for Data on the Spread of the COVID-19 and Some Observations Using Statistical Models: Case Study of Arab Countries

Mathematical Modeling Skills for Data on the Spread of the COVID-19 and Some Observations Using Statistical Models: Case Study of Arab Countries

APPLICATION OF SOFT SETS TO ASSESSMENT OF MATHEMATICAL MODELLING SKILLS

Formulation of the problem. Formulation of the problem. Mathematical modelling is a very important component of mathematics education, because by applying the mathematical theories to practical needs of our everyday life increases the student interest for mathematics. The main steps of the mathematical modelling process include analysis of the given real world problem, formulation of the problem and construction of the mathematical model (mathematization), solution and control of the model and implementation of the final mathematical results to the real situation. Mathematization possesses the greatest difficulty among the steps of the MM process, because it involves a deep abstracting process, which is not always easy to be achieved by a non-expert. It is sometimes, however, the transition from the solution of the model to the real world (control and/or implementation of the model) that presents difficulties for students too. An example is given to illustrate this remark.
 Materials and methods. In this paper soft sets are used as tools for developing a model for assessing human activities in a parametric manner and an example is presented (assessment of football players performance) to illustrate its applicability under real situations. A soft set, being a parametrized family of subsets of the universal set of the discourse, is a generalization of the concept of fuzzy set designed on the purpose of dealing with the existing uncertainty in a parametric manner. The theory of soft sets has found many and important applications to several sectors of the human activity like decision making, parameter reduction, data clustering and data dealing with incompleteness, etc. 
 Results. The soft set assessment model is applied for evaluating student mathematical modelling skills with respect to the parameters excellent, very good, good, mediocre, and failed. It serves both for assessing the general performance of a student class and the individual performance of each student with respect to the steps of the mathematical modelling process. 
 Conclusions. The constructed in this paper model is very useful in cases where the assessment has qualitative rather than quantitative characteristics and could also be applied to a variety of other cases for assessing human and/or machine (e.g. computer programs) activities.

CHALLENGES OF SOLVING VISUALLY PRESENTED PROBLEMS

Organization of the teaching process which enables the acquisition of quality and effective mathematical knowledge applicable in different life situations and which lays the foundation for lifelong learning is based on problem-solving. Teaching how to solve visually presented problems is one objective that contributes to these overall goals. The main research goal of this paper is an experimental examination of the effects of problem-based teaching in the development of mathematical modeling skills involving visually presented problems. The effectiveness of teaching visually presented problems for the development of mathematical modeling skills in solving equations and inequalities in the fourth grade of primary school is examined. The descriptive method was used for the analysis, processing, and interpretation of the research results to investigate the type of errors pupils make when dealing with the visually presented information. Participants in the experimental program showed a higher level of knowledge when solving simple and complex equations and inequalities as well as in compos- ing texts based on given iconic representations of equations and inequalities, as opposed to the pupils not influenced by the experimental model. Given its positive effects on the development of mathematical modeling skills, teaching visually presented problems is justified during the early years of mathematics education.

Kemampuan Pemodelan Matematika Melalui Pendekatan Pendidikan Matematika Realistik Indonesia (PMRI) di SMK Yayasan Bakti Prabumulih

This study aims to determine and describe the ability of mathematical modeling through the Indonesian Realistic Mathematics Education approach. The Indonesian Realistic Mathematical Education approach is a learning approach that uses real problems as the beginning of learning mathematics so that it is skilled in solving problems, so as to obtain essential knowledge and concepts from the learning material. The research method used in this research is a one-shot case study experiment. This research was conducted in class XI.TKJ SMK Yayasan Bakti Prabumulih Foundation in the 2020/2021 academic year, totaling 30 students. This type of research is descriptive quantitative. Data collection in this study used a test instrument in the form of description questions based on indicators of mathematical modeling ability. Based on the results of the study, it was found that the mathematical modeling skills of students through the Indonesian Realistic Mathematics Education approach reached an average percentage of 75.96%.