Types Of Mathematical Problems Research Articles

How the relationship between individual and social factors informs the narrowing of gender gaps in elementary mathematical achievements

Few scholarly studies have examined gender gaps vis-à-vis various types of mathematical problems by controlling for individual factors (e.g., general intelligence and self-regulated learning [SRL]) and social factors (e.g., the school’s socioeconomic status [SES]) among elementary school students, as addressed in this study. Achievements on three types of mathematical tasks (operations with numbers, geometry, and word problems) and general intelligence scores were obtained from elementary school students. Information regarding students’ SRL was obtained from a rating scale designed for the teachers. Results showed that boys’ achievements were significantly higher in word problem-solving and geometry tests but not in operation with numbers tests. The results concerning word problems suggest that the effect of the school’s SES level on the gender gap decreased in accordance with the increase in the school’s SES level. The significant interaction between gender and SRL indicated that the effect of students’ SRL level on the gender difference in the students’ performance on the geometry test increased in accordance with the increase in the SRL level. General intelligence contributed to individual differences in word problems and geometry, but not on operations with numbers. The analyses showed that SRL contributed to mathematical performance in all tasks. Directions for future research and implications for narrowing these gender gaps are discussed.

Validation of an Instrument to Assess Deductive Reasoning in Solving Types of Problems

The accelerated pace of knowledge generation requires engineering students to develop differenttypes of reasoning during their education. Deductive reasoning is essential to establishingself-regulated judgments based on reasoned argumentation. This paper aims to describeand illustrate the process by which a test of multiple-choice, open-response verbal mathematicalproblems was designed, applied, and validated to assess the deductive reasoning ofsecond-semester students of two engineering degrees from a university in a region of southernChile. The research used a non-experimental, cross-sectional approach focused on psychometricaspects. The evaluation instrument was developed on the basis of a typology ofmathematical problems and a model of deductive reasoning. The resolutions of types of problemsare classified according to their nature, routine and non-routine, and according to theircontext, real, realistic, fantasy, and purely mathematical, while the deductive argumentativemodel comprises the phases of data, claim, and warrant. The results guarantee sufficient contentand construct validity, item discrimination, and reliability; therefore, they represent auseful tool for measuring the level of deductive reasoning among first-year engineering studentsduring the process of solving a type of mathematical problem.

Adapting a virtual manipulative-based instructional sequence to target maintenance

The ability to maintain mathematical skills learned is critical for students to successfully engage in advanced mathematics and promote independence in daily living skills. The purpose of this study was to evaluate the effectiveness of a graduated manipulative sequence consisting of virtual, representational, abstract, and an extended abstract phase (VRAEa) to teach various types of mathematical problems to three students with autism and mild intellectual disability using a multiple probe across behavior single case design. This study extended previous research on the virtual, representational, abstract sequence (VRA) to address deficiency in maintenance results through incorporating the extended abstract phase. The results indicate the intervention was effective, however, maintenance was variable. Implications for practice and ideas for future research to support the learning needs of students with developmental disabilities are discussed.

Teaching the methods of solving mathematical problems

Following questions was affected in this article - types of mathematical problems, role and meaning of solving problems in men’s life (pupil, student), difficulties in solving  mathematical problems, classification of mathematical problems due to the way of solving key. Tasks of arithmetics are various according to the contents and on difficulty of the decision. At the solution of some tasks doesn't meet difficulties in a choice of this or that action. The choice of arithmetic actions and at the solution of many tasks is carried out on the basis of the communications existing between these sizes. Solution of each task purely arithmetic actions and logical conclusions, but not to the same extent: in one tasks arithmetic actions prevail, and reasonings and logical conclusions play so prevailing role others, after the logical conclusions the solution of a task is consolidated to thought tension. If the necessary data on arithmetics are acquired and problems of detailed type are already sorted, other problems of this sort are solved without effort. The article presents the results of a survey of teachers on the methodology of teaching mathematics and solving problems by schoolchildren. Keywords: quantily , problem, teaching the methods of problem solving , types of arithmetical problems , ways of problem solving.

Quantitative modelling demonstrates format-invariant representations of mathematical problems in the brain.

Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel-wise encoding models. Both intra- and cross-format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format-invariant manner.

Design and Validation of a Test for the Types of Mathematical Problems Associated with Reading Comprehension

Being able to understand a written text is an essential life skill, as is solving a problem, which configures a bidirectional relationship between both skills. With regard to reading comprehension, at least three specific levels are required to achieve a full understanding of a text: literal, inferential, and critical. For its part, mathematics has changed substantially in recent decades, prioritizing problem-solving as the central axis of the teaching process as it constitutes a resource for learning. This study connects both skills and aims to design and validate a mathematical problem-solving test contextualized to the quadratic function, to assess the level of reading comprehension of secondary school students. The study is nonexperimental, cross-sectional, and focused on psychometric aspects since it aims to validate a measurement instrument. It was applied on a pilot basis to three municipal secondary education courses in Chile. The content, construct, discrimination, and reliability validation tests carried out allowed us to demonstrate that the problem-solving test contextualized to the quadratic function is a reliable instrument to produce knowledge in educational research.

KAJIAN TINGKAT KOMPLEKSITAS MASALAH PADA BUKU PEMBELAJARAN MATEMATIKA BERBASIS TAKSONOMI SOLO

Mathematics is an important subject in schools, as well as among other complex subjects. Of the various difficulties of research, it is always difficult for mathematics to be the most important subject for every student. Students have difficulties that can make mistakes when working on math problems. One way to identify the appropriateness of students' responses to math problems is the SOLO taxonomy. SOLO taxonomy plays a role in determining the quality of student responses to the problems faced. Researchers used a Student Textbook entitled "Senang Belajar Matematika Untuk Siswa SD/MI Kelas 5" to classify math problems based on the SOLO taxonomy. This research is a qualitative study using content analysis. The results of the study resulted in prestructural 0%, unistructural 14.1%, multistructural 32%, relational 42.9%, and extended abstract 10.8%. The research result is also a type of mathematical problem with a scale of 156 questions. Not many types of questions with prestructural level are found in this book because the types of questions, in general, are at the beginning of the lesson which is made by the teacher himself. However, the results also show that the level of complexity of questions that are extended to abstract is not too much found in the examples of questions presented in this textbook. It is advisable to add variations to the extended abstract level question, because at this age students are already able to work on questions with a more difficult level of thinking.

Development of logical thinking of high school students through a problem-based approach to teaching mathematics

This article considers the search for new methodological approaches to teaching high school students mathematics that will promote the development of their logical thinking. Based on the analysis conducted by the authors of the study identified an urgent need to develop the logical thinking of students in mathematics lessons through various methods of solving problems. The authors of the article set out to investigate the factors that will ensure the implementation of a problem-based approach to teaching mathematics. These factors include the choice of a certain type of mathematical problem; selection of a method for solving mathematical problems; compiling a system of problems of one type that require the selection of methods for solving them. The authors reveal the introduction of the problem approach as a method of developing students’ logical thinking in the article on the example of solving irrational equations with parameters. The authors of the study explain the value of problems with parameters by the fact that the process of solving them contributes to the formation of students’ research skills. In the study, the authors focused on the analytical method of solving problems with parameters. Structural analysis of problems allowed the authors to formulate the following didactic requirements for the system of mathematical problems such as compliance with the problems of the course content and the principle of gradual increase in complexity; the rational relationship between the logical and heuristic components of educational activities; the presence of ideological and technical complexity, etc. To confirm the effectiveness of the introduction of the problem-based approach to the educational process, as a method of developing students’ logical thinking, an experiment was conducted. The main objectives of the experiment were to identify the level of logical thinking of students; development and implementation in the educational process of a system of problems with parameters in the study of the topic “Irrational equations”, which contribute to the development of logical thinking of students; analysis of the results of the experiment. The obtained results and their statistical processing confirmed significant differences in the levels of development of logical thinking in the control and experimental groups, respectively. This proved the effectiveness of a problem-based approach to teaching mathematics and the development of logical thinking of students.

Covid-19 data modelling using hybrid conjugate gradient method

Optimization problem is a type of mathematical problem with several uses in real life. As one of the commonly applied methods for solving optimization problem, the conjugate gradient (CG) method has undergone numerous modifications in order to improve its efficiency. The hybrid CG is one of the best CG methods which can also be applied for data fitting [1]. Nowadays, Corona Virus Disease (Covid-19) has been extensively studied by many researchers worldwide due to the rising number of infected cases and deaths resulting from contracting the virus. In 2020, the Malaysian government enforced the first ‘Movement Control Order (MCO)’ in order to significantly lower the infection rate. However, the number of cases rose again at the end of year 2020, leading to the necessity to implement the second MCO in January 2021. In this study, a new hybrid conjugate gradient method is introduced to analyse the Covid-19 cases in Malaysia before MCO 2.0. This new hybrid method yields a better numerical result compared to classical and other hybrid CG methods.

An analysis on the Elementary Students’ Mathematical Representations according to the Types of Mathematical Problems

수학적 표현은 수학적인 생각을 구체화하고 의사소통하는 기능을 가지고 있으며, 수학문제해결에서도 중요한 역할을 하기 때문에 문제 유형에 따라 학생들이 주로 이용하는 수학적 표현 양식을 확인할 필요가 있다. 본 연구에서는 정형화된 문제와 비정형화된 문제로 구성된 질문지를 이용하여 초등학생들의 수학적 표현을 분석하였다. 연구 결과, 정형화된 문제의 평균 정답률이 비정형화된 문제의 평균 정답률보다 높았으며, 정형화된 문제에서는 정답자 대부분이 수식 표현을 이용하였고, 시각적 표현을 시도한 경우가 적었을 뿐만 아니라 그 경우에도 모두 오답이었다. 이에 비해 비정형화된 문제에서는 시각적 표현과 언어 표현을 이용한 사례가 다수 나타났다. 연구 대상자들이 이용한 시각적 표현에서는 관계 그림을 이용하여 답을 한 것으로 나타났다. 이를 통해 문제해결에 다양한 표현 양식을 활용하도록 지도하고, 문제와 수학적 표현 유형에 따른 문제해결 지도 방안을 제시하였다.

Elementary school students’ mathematical connection in problem-posing activities

The ability of mathematical connections possessed by students can be seen from the ability of students to compile math problems. This study aims to determine the type of mathematical connection made by elementary school students in problem-posing activities. The research was conducted using a qualitative descriptive method. The participants were 34 fifth grade students (male =16 female =18) of one of the public elementary schools in Mataram, West Nusa Tenggara. Data were collected from the results of student work and interviews. The analysis was carried out qualitatively according to the indicators of the complexity of the problem through problem posing learning. The results showed that there were four types of mathematical problems and their relatedness that occurred in student problem-posing activities, including (1) unsolvable math problems, (2) incorrectly solved math problems, (3) neglected math problems contextual information, and (4) mathematical problems that have complexity and relevance. Based on these results, it can be recommended for further research to determine strategies to improve students' mathematical connections in problem-posing activities.

Using Lagrange’s Multiplier Method to Solve Mathematical Contest Problem

“Most people study mathematics to satisfy some requirements .Some Study Math to learn the tricks of nature so they may find out how to make things bigger or smaller or faster or more sensitive . But a few ,a very few ,study math because they wonder -not how things work ,but why they work .They wonder what is at the bottom of things -the very bottom ,if there is a bottom . This paper will be very useful to them .”-M.A.Rusho. Remember when you first participate any math contest or olympiad maybe national or International you see some terrible function and the question state that you have to find this function maximum or minimum value. You become frustrated thinking I have to take the derivative first then equalising it to 0 , then find the optimal value of X blah blah blah……. . now it’s time to reconstruct your mind for solving this type of Mathematical problem in a suitably way . First we have to think that is the difference between School textbook math problem And Olympiad Math Problem . The core difference is problem solving . But you may think that in school mathematics we all solve problem . But this problem solving is different like you can solve it by GUIDE or may a teacher can help or this problem may directly solved by any standard formula like( a+b)^2 . But in Olympiad problem You are totally in a new place , totally difference problem you didn’t see it . But you have too slove it now Many people find this difficulty .BUT IT IS not difficult if you solve it by making some useful strategies . This paper although written for High School Student’s but those who will read it thoroughly they will understand it is for useful for undergraduate or beg gainer of a graduate student from engineering background . Though Calculus , linear algebra , partial differential equation is not included in Math Olympiad Syllabus . But if you are really a Math Enthusiast I believe you already learn it !!! If you didn’t don’t be hesitate . Learn It from any book or course . Then came here to read this thesis paper . Best Wishes to all !!! Happy Problem Solving !!

A Visual Approach for Solving Problems with Fractions

This article discusses the importance of visual models in problem solving, in the scope of rational numbers. We seek to highlight the potential of this approach, as a structuring theme in the mathematical development of students in elementary education and the connections it allows to establish. In order for students to be mathematically competent and creative, they must be able not only to solve traditional computational problems but also to use models/visual representations when solving all types of mathematical problems, including those in which the visual component is not evident. We developed a qualitative study based on a didactical experience involving 14 future teachers who were attending a Didactics of Mathematics unit course that included a module about problem solving with emphasizes in visual approaches. The main purpose of the study was to identify the strategies used by the future teachers when solving problems with multiple solutions, before and after that module. Data was collected through observation and the written productions of the participants. It was possible to conclude that they tended to privilege analytical approaches before the intervention and, after the teaching experience, they started to value visual approaches, which generated an increase of the productions involving this type of solutions.

Outcomes of distance education in Mathematics at secondary technical school: a case study

Education at secondary vocational schools has an important role in preparing graduates to perform professional activities in practice. These schools provide a complete secondary education, and Mathematics is also a part of the study plan. In this paper, we focused on the success of students in solving selected types of mathematical problems during the school year 2020/2021, when the study process at secondary schools was carried out in a distance form. The main goal was to evaluate the mathematical knowledge of the secondary school students through a set of selected tasks. The research sample consisted of 21 students of the 3rd year of the secondary technical school with a focus on civil engineering study program, for which we analyzed tasks of online tests in the first and second half of the school year. Using methods of mathematical statistics, we compared and evaluated the success of students in solving problems that were part of the tests from the mathematics curriculum. The results show that students have mastered the necessary electronic tools and methods of distance learning in acquiring mathematical knowledge.

Solving One-Dimensional Porous Medium Equation Using Unconditionally Stable Half-Sweep Finite Difference and SOR Method

A porous medium equation is a nonlinear parabolic partial differential equation that presents many physical occurrences. The solutions of the porous medium equation are important to facilitate the investigation on nonlinear processes involving fluid flow, heat transfer, diffusion of gas-particles or population dynamics. As part of the development of a family of efficient iterative methods to solve the porous medium equation, the Half-Sweep technique has been adopted. Prior works in the existing literature on the application of Half-Sweep to successfully approximate the solutions of several types of mathematical problems are the underlying motivation of this research. This work aims to solve the one-dimensional porous medium equation efficiently by incorporating the Half-Sweep technique in the formulation of an unconditionally-stable implicit finite difference scheme. The noticeable unique property of Half-Sweep is its ability to secure a low computational complexity in computing numerical solutions. This work involves the application of the Half-Sweep finite difference scheme on the general porous medium equation, until the formulation of a nonlinear approximation function. The Newton method is used to linearize the formulated Half-Sweep finite difference approximation, so that the linear system in the form of a matrix can be constructed. Next, the Successive Over Relaxation method with a single parameter was applied to efficiently solve the generated linear system per time step. Next, to evaluate the efficiency of the developed method, deemed as the Half-Sweep Newton Successive Over Relaxation (HSNSOR) method, the criteria such as the number of iterations, the program execution time and the magnitude of absolute errors were investigated. According to the numerical results, the numerical solutions obtained by the HSNSOR are as accurate as those of the Half-Sweep Newton Gauss-Seidel (HSNGS), which is under the same family of Half-Sweep iterations, and the benchmark, Newton-Gauss-Seidel (NGS) method. The improvement in the numerical results produced by the HSNSOR is significant, and requires a lesser number of iterations and a shorter program execution time, as compared to the HSNGS and NGS methods.

Evaluation and orientations to Grade 10 mathematics in schools differentiated by social class

In South Africa, differential performance in school mathematics with respect to social class remains an enduring concern as reflected in national and international large-scale assessments. The article examines the implications of evaluation for orientations to mathematics in a school populated by learners from upper-middle-class or elite backgrounds and a school populated by learners from working-class backgrounds. The particular focus is on mathematics problems featured in tests used by two Grade 10 teachers in each school and teachers’ marking of learners’ test scripts. A distinction between single-topic and multi-topic mathematics problem types is refracted through an analysis that draws on the adaptation by Davis of Lotman’s distinction between content orientation and expression orientation with respect to the reproduction of texts.The analysis reveals a preponderance of single-topic mathematics problems and the absence of multi-topic mathematics problems employed in the school populated by learners from working-class backgrounds and the presence of both single-topic and multi-topic problem types in the school populated by learners from middle-class or elite backgrounds. Differences in the types of mathematical problems suggest differences in mathematical demand expected of learners and differences in their preparation for examinations in the two social class contexts.The selection of test problems and the marking of test scripts as instances of evaluation construct an orientation to mathematics that is expression oriented in the working-class context whereas both expression and content orientations are evident in the middle-class or elite context. The analysis provides a potential explanation for the persistent disparity in mathematics performance along social class lines in South African secondary schools.

Автоматизація розв’язування задач з планіметрії, записаних природною українською мовою

The article focuses on developing a software solution for solving planimetry problems that are written in Ukrainian. We discuss tendencies and available abilities in Ukrainian natural language processing. Presenting a comprehensive analysis of different types of describing a problem, which shows regularities in the formulation and structure of the text representation of problems. Also, we demonstrate the similarities of writing a problem not only in Ukrainian but also in Belarusian, English, and Russian languages. The final result of the paper is a system that uses the morphosyntactic analyzer to process a problem’s text and provide the answer to it. Ukrainian natural language processing is growing rapidly and showing impressive results. Huge possibilities appear as the Gold standard annotated corpus for Ukrainian language was recently developed. The created architecture is flexible, which indicates the possibility of adding both new geometry figures and their properties, as well as the additional logic to the program. The developed system with a little reformatting can be used with other natural languages, such as English, Belarusian or Russian, as the algorithm for text processing is universal due to the globally accepted representations for presenting such types of mathematical problems. Therefore, the further development of the system is possible.

Solving Multi-Objective Linear Fractional Stochastic Transportation Problems Involving Normal Distribution using Simulation-Based Genetic Algorithm

In real-life situations, we human beings faced with multi-objective problems that are conflicting and non-commensurable with each other. Especially, when goods are transported from source to locations with a goal to keep exact relationships between a few parameters, those parameters of such problems might also arise in the form of fractions which are linear in nature such as; actual transportation fee/total transportation cost, delivery fee/desired path, total return/total investment, etc. Due to the uncertainty of nature, such a relationship is not deterministic. Mathematically such kinds of mathematical problems are characterized as a multi-objective linear fractional stochastic transportation problem. However, it is difficult to handle such types of mathematical problems. It can't be solved directly using mathematical programming approaches. In this paper, a solution procedure is proposed for the above problem using a stochastic Genetic Algorithm based simulation. The parameters in the constraint of the above problem follow a normal distribution. The probabilistic constraints are handled by stochastic simulation-based GA for the solution procedure of the proposed problem. The feasibility of probability constraints is checked by the stochastic programming through the Genetic Algorithm approach, without finding the equivalent deterministic model. The feasibility is maintained all-over the problem. The stochastic simulation-based Genetic Algorithm is considered to generate non-dominated solutions for the given problem. Then, a numerical case study is provided to illustrate the method.

Evaluation and Thinking of “IF-Problem” of Mathematics for China’s College Entrance Examination

The Mathematics Proposition of College Entrance Examination is going through a process of deepening reform. According to the requirement of mathematics education for examinee's mathematics literacy, a lot of attempts have been made in the past mathematics teaching and proposition practice. Now the new type of questions is gradually infiltrating into the proposition of mathematics in college entrance examination.“IF-Problem” is a type of mathematical problem for China’s college entrance examination, It is helpful to improve the shortcomings of the past mathematics evaluation in college entrance examination, to evaluate the innovative consciousness and practical ability of candidates in mathematics thinking, and to infiltrate the core quality of mathematics in mathematics teaching. This essay focuses on researching examples of this new type in terms of its positive, reverse, strategic, and linguistic aspects from evaluation basis, score to the establishment of evaluation criteria, from its structure, its elements, test subject and content to the interpretation of innovative examples, which may pave the way for scientific evaluation of mathematics education.

Methodological Approaches to Experimental Teaching of Mathematics to University Students

Introduction: the article imparts authors’ thoughtson a new teaching methodology for mathematical education in universities. The aim of the study is to substantiate the efficiency of the comprehensive usage of mathematical electronic courses, computer tests, original textbooks and methodologies when teaching mathematics to future agrarian engineers. The authors consider this implementation a unified educational process. Materials and Methods: the synthesis of international and domestic pedagogical experience of teaching students in university and the following methods of empirical research were used: pedagogical experiment, pedagogical measurementsand experimental teaching of mathematics. The authors applied the methodology of revealing interdisciplinary links on the continuum of mathematical problems using the key examples and exercises.Results: the online course “Mathematics” was designed and developed on the platform of Learning Management System Moodle. The article presents the results of test assignments assessing students’ intellectual abilities and analysis of solutions of various types of mathematical problems by students. The pedagogical experiment substantiated the integrated selection of textbooks, online course and online tests using the methodology of determination of the key examples and exercises. Discussion and Conclusions: the analysis of the experimental work suggested that the new methodology is able to have positive effect on the learning process. The learning programme determined the problem points for each student. The findings of this study have a number of important implications for future educational practice.