Mathematical Situations Research Articles

Implementation of Discovery Learning Model with Window Shopping Approach to Improve Mathematical Communication Ability of High School Students

The low ability of students' mathematical communication in learning mathematics, especially in expressing mathematical situations or problems in the form of pictures, diagrams, language or mathematical symbols, or mathematical models makes students less active in learning and their learning motivation decreases. This study aims to determine the achievement of students' mathematical communication skills through the discovery learning model with a window shopping approach. The method in this study is a quasi-experimental research type consisting of 2 classes, namely the experimental class that uses the discovery learning model with the window shopping approach and the control class that uses ordinary learning at school with a total of 70 students from class XI SMA in one of the public high schools in Bandung. The research test instrument was in the form of a test that would be analyzed using SPSS 21 to compare learning outcomes between the experimental class and the control class. The result of the study was that the achievement of the students' mathematical communication skills in the experimental class was better than that of the control class at a significance level of 0.05 where the average communication ability of the experimental class was 81.74 and that of the control class was 77.31. The effectiveness of learning in the experimental class showed that it was more active in group discussions as indicated by the interaction and creativity of students in presenting learning material in each group, and almost 85% of students enjoyed learning using the discovery learning model with the window shopping approach.

Residual growth control for general maps and an approximate inverse function result

The need to control the residual of a potentially nonlinear function F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}$$\\end{document} arises in several situations in mathematics. For example, computing the zeros of a given map, or the reduction of some cost function during an optimization process are such situations. In this note, we discuss the existence of a curve t↦x(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\mapsto x(t)$$\\end{document} in the domain of the nonlinear map F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}$$\\end{document} leading from some initial value x0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_0$$\\end{document} to a value u such that we are able to control the residual F(x(t))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}(x(t))$$\\end{document} based on the value F(x0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}(x_0)$$\\end{document}. More precisely, we slightly extend an existing result from J.W. Neuberger by proving the existence of such a curve, assuming that the directional derivative of F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}$$\\end{document} can be represented by x↦A(x)F(x0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x \\mapsto \\mathcal {A}(x)\\mathcal {F}(x_0)$$\\end{document}, where A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}$$\\end{document} is a suitable defined operator. The presented approach covers, in case of A(x)=-Id\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}(x) = -\ extsf{Id}$$\\end{document}, some well known results from the theory of so-called continuous Newton methods. Moreover, based on the presented results, we discover an approximate inverse function result.

Ward identities in a two-dimensional gravitational model: anomalous amplitude revisited using a completely regularization-independent mathematical strategy

We present a detailed investigation of the anomalous gravitational amplitude in a simple two-dimensional model with Weyl fermions. We employ a mathematical strategy that completely avoids any regularization prescription for handling divergent perturbative amplitudes. This strategy relies solely on the validity of the linearity of the integration operation and avoids modifying the amplitudes during intermediate calculations, unlike studies using regularization methods. Additionally, we adopt arbitrary routings for internal loop momenta, representing the most general analysis scenario. As expected, we show that surface terms play a crucial role in both preserving the symmetry properties of the amplitude and ensuring the mathematical consistency of the results. Notably, our final perturbative amplitude can be converted into the form obtained using any specific regularization prescription. We consider three common scenarios, one of which recovers the traditional results for gravitational anomalies. However, we demonstrate that this scenario inevitably breaks the linearity of integration, leading to an undesirable mathematical situation. This clean and transparent conclusion, enabled by the general nature of our strategy, would not be apparent in similar studies using regularization techniques.

Using the UTAUT-TPACK model to explain digital teaching behaviour of elementary school mathematics teacher

ABSTRACT The appropriate use of digital technology in the classroom is very helpful to improve mathematics teaching in elementary school. However, the current situation of elementary school mathematics teachers’ digital teaching behaviour is not optimistic. This study analysed the factors influencing elementary school mathematics teachers’ digital teaching behaviour. A revised unified theory of acceptance and use of technology (UTAUT) model with technological pedagogical content knowledge (TPACK) was used to understand elementary school mathematics teachers’ digital teaching behaviour. A questionnaire survey was conducted in Hunan province of China. Three hundred elementary school mathematics teachers provided valid questionnaire data. The partial least squares structural equation modelling (PLS-SEM) approach was used to analyse the data. It was found that TPACK and facilitating conditions positively and significantly affected digital teaching behaviour of elementary school mathematics teachers, and TPACK was the biggest influential factor. The research results have important implications for improving digital teaching behaviour of elementary school mathematics teachers and promoting digital transformation of elementary school mathematics education.

Development of cognitive capacities in 6-7 year-old children through problem situations in mathematics

Problem and objective. The relevance of the study is determined by the need for the development of cognitive capacities in the senior preschool age since they form a basis for general giftedness. However, there is no generally accepted point of view in the scientific and pedagogical community as to understanding the essence of children’s cognitive capacities and defining their structure. One of the means to develop these abilities is represented by problem situations which, in the process of their solution, have a positive effect on cognitive capacities. The purpose of the study: modelling the component structure of cognitive capacities and their practical development in children of senior preschool age using problem situations. Materials and methods. A system analysis of scientific sources was carried out; a pedagogical experiment was carried out covering 48 children of the Municipal state-run preschool educational institution “Kindergarten No. 72” of Kirov; a set of variable problem situations in mathematics aimed at the development of cognitive capacities in children aged 6-7 was developed and tested. The Wilcoxon rank sum test was used in the processing of the results. Results. The component structure of senior preschool children’s cognitive capacities was developed which includes cognitive processes as well as the forms and properties of intellection. Problem situations of four types are used for the development of cognitive capacities: a problem question, an entertaining question, an entertaining task and a joke task. Their use contributes to the effective development of all structural components of cognitive capacities: a statistically significant shift was recorded in the experimental group at a significance level of p<0.01, while it was absent in the control group. Conclusion. The author’s concept of children’s cognitive capacities is formulated; a model of cognitive capacities component structure in senior preschool children was developed; preschool children’s specific skills for each substantive component of cognitive capacities were identified; the expediency of using problem situations in mathematics for the development of intellection processes as one of the components of senior preschool children’s cognitive capacities was experimentally proved.

A survey of congruences and quotients of partially ordered sets

A quotient of a poset P is a partial order obtained on the equivalence classes of an equivalence relation \theta on P ; \theta is then called a congruence if it satisfies certain conditions, which vary according to different theories. The literature on congruences and quotients of partially ordered sets contains a large and proliferating array of approaches, but little in the way of systematic exposition and examination of the subject. We seek to rectify this by surveying the different theories in the literature and providing philosophical discussion on requirements for notions of congruences of posets. We advocate a pluralist approach which recognises that different types of congruence arise naturally in different mathematical situations. There are some notions of congruence which are very general, whilst others capture specific structure which often appears in examples. Indeed, we finish by giving several examples where quotients of posets appear naturally in mathematics.

Development and Research on the Development of Junior High School Mathematical Situation Teaching Materials Based on Chinese Excellent Traditional Culture

Development and Research on the Development of Junior High School Mathematical Situation Teaching Materials Based on Chinese Excellent Traditional Culture

Charged Cavitation Multibubbles Dynamics Model: Growth Process

The nonlinear dynamics of charged cavitation bubbles are investigated theoretically and analytically in this study through the Rayleigh–Plesset model in dielectric liquids. The physical and mathematical situations consist of two models: the first one is noninteracting charged cavitation bubbles (like single cavitation bubble) and the second one is interacting charged cavitation bubbles. The proposed models are formulated and solved analytically based on the Plesset–Zwick technique. The study examines the behaviour of charged cavitation bubble growth processes under the influence of the polytropic exponent, the number of bubbles N, and the distance between the bubbles. From our analysis, it is observed that the radius of charged cavitation bubbles increases with increases in the distance between the bubbles, dimensionless phase transition criteria, and thermal diffusivity, and is inversely proportional to the polytropic exponent and the number of bubbles N. Additionally, it is evident that the growth process of charged cavitation bubbles is enhanced significantly when the number of bubbles is reduced. The electric charges and polytropic exponent weakens the growth process of charged bubbles in dielectric liquids. The obtained results are compared with experimental and theoretical previous works to validate the given solutions of the presented models of noninteraction and interparticle interaction of charged cavitation bubbles.

Progressive mathematics of functions in secondary school students using a free-fall activity

This article aims to analyze the process of the progressive mathematization of the concept of the function by secondary school students through the resolution of a free fall situation. A free-fall mathematical situation was designed and experimented using the Tracker software to obtain movement data. Worksheets and conversations were collected between students and the teacher, and experiments and class discussions were filmed. The analysis consisted of identifying the development from informal strategies associated with the context of the problem to formal procedures. The results show that the process brings meanings to mathematical ideas such as variation, variables, and the relationship between variables, allows coordination and transition between representations and contributes to the learning of functions as a representation of the variation of physical phenomena.

Exploring new geometric contraction mappings and their applications in fractional metric spaces

<abstract><p>This article delves deeply into some mathematical basic theorems and their diverse applications in a variety of domains. The major issue of interest is the Banach Fixed Point Theorem (BFPT), which states the existence of a unique fixed point in fractional metric spaces. The significance of this theorem stems from its utility in a variety of mathematical situations for approximating solutions and resolving iterative problems. On this foundational basis, the study expands by introducing the concept of fractional geometric contraction mappings, which provide a new perspective on how convergence develops in fractional metric spaces.</p></abstract>

PENINGKATAN KEMAMPUAN BERPIKIR KRITIS MATEMATIS SISWA DENGAN MENGGUNAKAN PENDEKATAN PROBLEM POSING

The purpose of the study was to determine how the problem posing approach in learning mathematics can improve mathematical critical thinking skills. This type of research is Quasi experimental with Post Test Only Control Group design. The population in this study were VIII grade students of SMP Negeri 12 Bandar Lampung. The cluster random sampling method was used to select sample members from the population without considering the students' ability level. The results showed that the problem posing approach with steps to create mathematical situations, formulate mathematical questions, solve mathematical problems, and apply mathematical concepts has a relationship with indicators of mathematical critical thinking skills. Indicators of critical thinking skills include interpretation, analysis, evaluation, inference, explanation, and self-regulation. So, it can be concluded, students' mathematical critical thinking skills can be improved using the problem posing approach.

Modelagem matemática e saberes da complexidade

In this investigation, the results of a modeling activity are discussed, with multiple themes and their relationship with Edgar Morin's seven complex knowledge. The production of the data was obtained by means of a bibliographic review, on the drakes (Dendrocygna autumnalis), and the production of infographics, by means of a short course held in online meetings. The themes of drakes were dealt with in their various contexts, the covid-19 pandemic, deforestation, infographics, social networks, fake news and scientific dissemination. The selection of the data was inspired by the content analysis, and the description and discussion of the results were organized in two Modeling cycles. In this experience, students were not invited to model a mathematical situation, but to dialogue about local and global issues, and go further, giving contributions to society, in order to make scientific knowledge accessible through social networks.

The Construction of Definitions Through Padovan’s Combinatorial Model: An Investigation With Didactic Engineering in an Initial Education Course for Mathematics Teachers

Background: Given the oversight of specific topics in the history of mathematics books, this research was motivated by the extensive coverage of the Fibonacci sequence. In addition, the existence of the Padovan sequence, which is considered a Fibonacci cousin, stands out. Objectives: Investigating the Padovan sequence, building its definition through a combinatorial model using manipulative materials based on the theory of didactical situations in the initial mathematics teacher education course context. Design: The research methodological design follows didactic engineering, and a didactic teaching situation is created to investigate the Padovan sequence. Thus, manipulative material was developed to facilitate the teaching process and the construction of the sequence definition. Settings and participants: The interventions were done in the mathematics degree course of a higher education institution in Fortaleza. Five students enrolled in the component of History of Mathematics participated in the study. Data collection and analysis: Data were collected during classes, recorded through photos and audio recordings, based on didactic engineering and the theory of didactical situations. Results: The most relevant result of this study is constructing the definition of the Padovan sequence through the manipulative material. Conclusions: We concluded that the research allowed an investigation of the Padovan sequence, enabling the visualisation of its terms and their integration with other mathematical contents, contributing to teaching these numbers.

An Examination of Mathematics Teachers’ Mathematical Language Usage

The aim of this research is to examine the mathematical language use of mathematics teachers in detail within the framework of the theoretical approach of “Three Worlds of Mathematics” put forward by Tall (2007). The research was carried out in the case study pattern, which is one of the qualitative research methods. The study group of the research consists of 27 math teachers. In the research, “Worksheet for the Use of Mathematical Language”, which includes four mathematical situations, was used as a data collection tool. In the analysis of the data collected within the scope of the research, the interpretation of the “Three Worlds of Mathematics” theoretical approach towards the use of mathematical language was adopted. As a result of the research, it was seen that mathematics teachers used mathematical language mostly in the context of the “conceptual-embodied world”, and least in the context of the “axiomatic-formal world”. At the same time, while the mathematical world in which the mathematical situation is presented affects the mathematical language used by the teachers for that situation, the teachers could not fully reflect the mathematical language to different worlds whilst working on mathematical situations. Finally, based on the conclusion that teachers use mathematical language in a more qualified way while performing high-level skills, it is suggested to include activities that allow the development of high-level skills in mathematics lessons and that serve to understand and develop mathematics

Dezvoltarea reprezentărilor despre operațiile aritmetice la copiii de vârstă preșcolară mare prin prisma metodei exercițiului

Solving arithmetic operations requires an unusual mental work that corresponds to a real action, characterized by mathematical transformations. Any arithmetic operation starts from a mathematical situation, random or provoked, which through observation, discovery, action that triggers a rational act of thinking. The most effective way to form representations about the arithmetic operations, addition and subtraction, is exercise, because only by repeating some actions can certain results be obtained.

The Positive Impact of E-LKPD Material on Number Patterns Based on Computational Thinking with the Malay Islamic Context on Students' Mathematical Reasoning

Learners still have difficulty in using patterns and relationships to analyze mathematical situations. The purpose of this study was to positively impact E-LKPD on number pattern material based on computational thinking with Malay Islamic context on students' mathematical reasoning. This research is design research with the type of development studies that have preliminary research, prototype stage, and summative evaluation stages. Data collection techniques in this research are questionnaires, interviews, and tests. The data analysis techniques in this study are questionnaires and interviews conducted qualitatively and tests measured based on mathematical reasoning indicators. The result of this research is that the E-LKPD developed is valid which is obtained from the results of expert validation and confirmation of students who get comments and suggestions. In addition, the E-LKPD which is practical can be seen from students responding to the E-LKPD. The impact that occurs after applying E-LKPD is that it makes students able to write what is known from the problem, able to find patterns and connect them, to determine the right solution procedure. The research conclusion shows that the application of E-LKPD based on computational thinking has an impact on students' mathematical reasoning ability. The implication of this research can improve students' critical thinking skills.

A Literature Review of Indonesian Students' Mathematical Communication Ability in Geometry Materials

The purpose of this study is to identify and examine students' written mathematical communication skills in geometry subject over the last five years. This study is a literature review that was conducted by looking for and assessing similar previous studies. Several stages were completed in this research: (1) identifying articles that discussed communication skills in geometry material, (2) analyzing student mathematical communication abilities in working geometry questions, and (3) identifying similarities in mathematical communication inhibiting factors. According to the findings of the study's six articles, pupils had difficulties articulating ideas, mathematical circumstances in writing with visuals, and algebra, expressing ideas or mathematical situations in everyday life in algebraic form. Students' mathematical communication abilities have not achieved their full potential. Of course, there are numerous elements that influence this, including pupils' lack of desire to describe or comprehend the challenges or problems they confront. Students do not understand the fundamental principles involved in answering these questions. Some pupils also do not understand the context of the questions, resulting in carelessness factor in communicating it mathematically.

Komunikasi matematis siswa melalui model pembelajaran kooperatif tipe memeriksa berpasangan

Mathematical communication is one of the abilities that needs to be improved considering the number of studies that still show low students' mathematical communication skills. The purpose of this study was to describe students' mathematical communication through a cooperative learning model of the type of checking in pairs. This type of research is descriptive research with a qualitative approach. The research subjects were 10 students of class VII. The research instrument was a test question sheet which contained material on a system of linear equations with one variable in the number of 2 questions. The research steps are preparation, implementation and drawing conclusions. Preparation was carried out by studying literature and compiling research instruments. Implementation, carried out by carrying out learning and collecting data. Conclusions are drawn based on analysis through the stages of reduction, presentation, and drawing conclusions. The research findings show that students are able to write down mathematical situations by writing down the known information and being asked questions. . Students are able to write down ideas well in determining the value of variable x in a given problem.

Analisis Kemampuan Komunikasi Matematis Siswa SMP pada Materi Bangun Ruang Sisi Datar

In order to better understand how junior high school pupils solve arithmetic issues involving flat sided spaces, this study will examine their mathematical communication abilities. At SMPN 3 Tirtajaya, this research was done. There are five measures of students' ability to communicate mathematically, including the first measure, which links visuals to mathematical ideas, the second measure, which makes conjectures, gathers evidence, and formulates definitions and generalizations, the third measure, which expresses ideas, situations, and mathematical relations with visuals, the fourth measure, which turns everyday events into mathematical situations, and the fifth measure, which explains and creates q. A descriptive qualitative research methodology was used to perform the study on 21 students in class IX. The test asks students to answer five questions regarding how well they can communicate mathematical ideas. The description test method is the method utilized to collect data. According to the data analysis's findings, pupils at SMPN 3 Tirtajaya are classed as having moderate problem-solving skills.

ANALYSIS OF STUDENTS’ ERRORS IN MATHEMATICAL PROBLEM SOLVING BASED ON KASTOLAN ERROR ANALYSIS

This research is motivated by the many mistakes made by students in solving problem-solving questions. The purpose of this research was conducted to see the causes of student errors in solving problem-solving questions based on kastolan error analysis theory. The research method used is descriptive qualitative. The instrumented object in this study involved 4 students of class XI MIA 5. The sample selection technique uses purposive sampling. The instruments used in this study were tests and interviews.The test results were obtained from a problem-solving ability test through creative problem-solving learning on linear programming material. Based on the results of the many errors found in the indicator, presenting mathematical situations in various ways and knowing the differences, and developing the concepts that have been studied. The types of errors that students have made in answering the problem included conceptual error, procedural error, and technical error