Mathematical Language Research Articles

Mobile Adventure: RIAMOS to Strengthen the Development of Mathematical Logic and Language in Early Education in Rural Contexts

In the development of the substantive function of the link with society of the National University of Education (UNAE), the Mobile Adventure: RIAMOS project arises from the career of Early Childhood Education (EI), with the aim of building experiential learning experiences, from educational contexts that promote the comprehensive training of children in early childhood in rural contexts. Therefore, this research analyses the impact of Aventura Móvil: RIAMOS on the development of the areas of logical-mathematical relations, comprehension and expression of language in early education in rural contexts. We worked with a methodology based on a mixed approach, with a prevalence of a qualitative, descriptive and interpretative approach and a quantitative approach focused on the pre- and post-tests applied to children in rural parishes in Cañar and Azuay. Mobile Adventure: RIAMOS is a space that integrates different actors: students, parents, authorities, teachers, students in training for comprehensive education. Through the pre-test, educational needs were identified, which were strengthened throughout the class sessions through the implementation of innovative planning, relevant to reality. The post-test reflected the advances and progress made by each child with the application of the didactic strategies and activities. In summary, Mobile Adventure: RIAMOS proves to be an effective initiative to enhance the reinforcement and integral learning of children in rural environments.

Analisis Kesulitan dalam Menyelesaikan Soal Persamaan Linear Satu Variabel dengan Metode Demonstrasi untuk Siswa Kelas VII SMP Negeri 5 Lamboya

This study aims to find out the difficulties of students in solving PLSV problems using the demonstration method for grade VII students of SMP Negeri 5 Lamboya. This study uses a qualitative approach with a descriptive method. 14 students as subjects to be researched to the extent to which the students can work on one-variable lienar equation problems. The data collection methods used are tests, interviews, and documentation. Data analysis is carried out qualitatively with the stages of data reduction, data presentation, and conclusion drawing. The results of the study showed that there was still a lack of ability of students to solve PLSV questions that answered the questions correctly and incorrectly. The results of the analysis for problems number 1, 2 and 3 were at the stage of difficulty in interpreting mathematical language (59.66%), the stage of difficulty in using data (64.33%), the stage of difficulty in mastering concepts correctly (66.66%), the stage of difficulty in using calculation operations (66.66%), and the stage of difficulty in drawing conclusions (83.33%). The cause of incompetence is that students do not read the questions carefully so that they make mistakes in writing down what is known and what is asked, so that they are less able to solve problems, in a hurry so that others are incomplete.

Analysis of the Application of Game Theory from Multiple Aspects: Economics, Business, and Education

In the late 20th century and early 21st century, there has been extensive literature published regarding proposals of the utilization of game theory from different academic aspects, which are tedious and unnecessary work for scholars who only wish to simply learn about some of the applications of game theory. This paper summarizes and organizes a few examples of the applications of game theory using prominent existing literature from three aspects: business, economics, and education, hoping to spark scholars’ interests and provide a broad understanding for readers as to when and how game theory may be used. When applying game theory to a real-world issue in business, economics, or education, the development and design of a “game” with certain selected constraints and variables is used to replicate the real-world model using mathematical languages. Depending on the real-world conflict these models are portraying, they might be novel concepts or variations of already-existing models. The summarization of some applications of game theory may spark interest for scholars interested in the various fields explored such as business management, economics, and optimization and quickly understand current progress in the area of game theory.

Examining high school students' conception of the function concept from a theoretical thinking perspective

This study explores the conceptions of functions among high school students through the lens of theoretical thinking, encompassing three core components: reflective, systemic and analytical thinking. A case study methodology was employed in this research. The data were gathered through interviews with 11 senior high school students and analysed using deductive content analysis techniques. The findings reveal that students needing more reflective thinking tend to resort to practical methods and quickly gave up when facing challenges. Those who showed limited systemic thinking often relied on incorrect or inadequate criteria to determine if an expression constituted a function and struggled to connect the function concept with other concepts. Students needing more analytical thinking faced challenges in employing mathematical language and representations for functions, verifying if an expression is a function or transforming representations and frequently overlooked quantifiers or logical connectors related to variables in definitional properties. In this study, the theoretical thinking framework, mainly used for university-level mathematical concepts, provided a broad perspective in determining high-school students' understanding of the concept of function. Future research should extend this approach to various educational levels and concepts to enhance our understanding of students' conceptions and enrich the theoretical thinking framework.

Identifying Key Instructional Practices in Rational Number Interventions: A Systematic Review and Meta-Analysis

Impacts of rational number interventions among U.S. students in Grades 3 through 9 with mathematics difficulties are examined using a systematic review and meta-analysis. The primary goal of the meta-analysis was to identify instructional practices that are key drivers of student impacts. From approximately 1,200 published and unpublished study records, we identified 28 studies that met our inclusion criteria and coded the interventions for their instructional practices, intervention characteristics, and study design features. The random-effects mean effect size across all 28 studies (90 effect sizes) was 0.68 ( SE = 0.08, p < .001, 95% confidence interval [CI]: [0.51, 0.85]). The 95% prediction interval was −0.36 to 1.8. Using meta-regression techniques, we found the teaching of mathematical language ( β = 0.50) and the use of the number line ( β = 0.47) during intervention to be significantly associated with positive impacts when adjusted for controls. We discuss implications for intervention practice and study limitations along with the challenges of examining complex, multifaceted interventions.

The associations between mathematical skills, cognitive performance, and language background in elementary school children. a two-year follow-up study

ABSTRACT Early mathematical skills contribute to later school performance and socio-economic status. Working memory is related to mathematical skills, but spatial and language skills have independent effects on separate areas of mathematical skills such as solving word problems or arithmetic skills. In this study, 9- to 10-year-old children's (N = 57) cognitive and mathematical skills were assessed three times over 2 years. Spatial reasoning was associated with performance in solving word problems and working memory with performance in the arithmetic test. Regarding word problems, girls outperformed boys. Also, the second-language learners performed similarly to the native speakers in the beginning and in the end of the third grade, but worse in the end of the fourth grade. The results suggest that the students’ inadequate mastery of the school language may lead to underachievement in mathematics, implying that further efforts should be invested in supporting their language learning.

Computational Thinking Processes in Solving the Corona Epidemic Model: Pre-service Maths Teachers

In the 21st century, pre-service mathematics teachers are expected to have problem-solving skills that are effective, efficient, and solutive and are in line with the mindset of computer experts. In learning mathematics, the concept of computational thinking (CT) is also needed and at this time, many still have difficulty solving mathematical problems in general, especially in solving problems in epidemic mathematical models. The subjects of this study were twenty-seven pre-service mathematics teacher students who took mathematical modeling courses. The researcher used the purposive sampling technique to select two research samples. The research method used was a descriptive qualitative research method in exploring the thinking process of pre-service mathematics teacher students in solving the problem of modeling the epidemic spread of disease. The results showed that the thinking process of the first subject began with identifying the problem and existing information by writing down the data in the form of a graph so as to get a certain pattern, which was then used as the basis for the process of transforming the problem into mathematical language. By adding assumptions related to the existence of environmental limitations in the next epidemic model, the concept of differential equations, in which there are integral properties and natural logarithms, can be used to find the solution to the epidemic model. The second subject was unable to solve the integral at hand. The researcher discovered that pre-service mathematics teacher students who correctly solved the problem in the mathematical model used CT components, namely decomposition, abstraction, pattern recognition, algorithm and mathematical literacy.

Misconceptions and Errors Among Grade 12 Students When Learning Differentiation Rules: A Case Study

t is an established fact that some grade 12 students learning differentiation in calculus are found struggling with the rule of differentiation and these rules include power rule, quotient rule, chain rule and product rule. Because of these, some students came up with some misconceptions which eventually resulted to the students having multiple errors when learning rules of differentiation. The reason associated with these common errors are not far from their failure to model some prerequisite knowledge in the laws of logarithm into their learning of the laws of differentiation. And this has resulted to the poor performance of some students in mathematics (calculus) since calculus carries about 40% in the overall grade in mathematics as a subject at grade 12 level. On this note, this paper presents an analysis of students’ errors and misconceptions in learning differentiation rule. The study was conducted among grade 12 students preparing for NSC examination in a high school in Limpopo province in South Africa. And the data was initially collected using 35 test scripts of grade 12 on the topic of differentiation and differentiation rule. A qualitative approach was considered, and the data collected was analysed, focusing on product rules, quotient rules and chain rules and the errors committed. The result of the study indicated that some grade 12 students make some errors and misconceptions in differentiation rules. And these were because of poor conceptual understanding, poor mathematics language understanding, and some other error. It was confirmed that the results of this study highlight the common mistakes and errors students make when learning differentiation rules, and these errors are; conceptual, systemic, language, and generalization errors.

Difficulties in mathematical language and representation among elementary school students when solving word problems

Difficulties in mathematical language and representation were the dominant difficulties in solving word problems for students in elementary school. The research aims to analyze students' mathematical language and representation difficulties when solving word problems. The research subjects were 114 fifth-grade elementary school students selected using a purposive sampling technique with different mathematical abilities. The research was conducted at an elementary school in Sumbawa District, West Nusa Tenggara, Indonesia. Data collection techniques included tests, questionnaires, and interviews. The research results show that students' difficulties in mathematical language were dominant indicators of sentences. Students had difficulties in mathematical representation indicators, which were dominant in symbols. The factors that cause difficulty for high, middle, and lower ability students are unaccustomed to solving word problems and using problem-solving procedures, difficulty with concepts, difficulty with reasoning, difficulty understanding what is known and what is being asked, not being careful in reading the problem, and difficulty with long sentences. Student word problem-solving is in the low category.

Mastery of the Concept of Percentage and Its Representations in Finnish Comprehensive School Grades 7–9

This research was conducted in 2019 in collaboration with Japanese colleagues, with the research tasks translated from the original Japanese. In Finland, a total of 1112 students from grades 7–9 in primary school participated in the study. In our article, we examine Finnish students’ mastery of the concept of percentages and how they express their mathematical thinking about percentages in a multimodal way. A multimodal expression of mathematical thinking can typically take the form of natural language, written mathematics, pictorial representations, mathematical symbolic language, or combinations of these, which can be used to manage information, such as through tables. Our focus is on Finnish primary-school students’ mastery of the concept of percentages, and we then narrow our analysis to tasks where students have used a multimodal approach. We analyze the representations of the concept of percentages and the related thought processes. The concept of percentages was best mastered in grade 9 and weakest in grade 7. Students mostly used a combination of pictorial language, natural language, and mathematical symbolic language to describe their solution processes. However, describing their thinking in different ways did not necessarily highlight possible errors in their reasoning.

The professional practice of designing tasks: how do pre-service early childhood teachers promote mathematical processes in early algebra?

AbstractSpanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers’ professional practice of designing tasks. According to this, our aim is to analyze the ways in which pre-service early childhood teachers understand the mathematical processes in the professional practice of designing early algebra tasks and to identify how they intend to promote these processes through the tasks. Content analysis techniques were used to examine the designed tasks. To illustrate the data analysis and results, six tasks are presented. As a result, pre-service early childhood teachers associate problem solving with challenges and questions. They understand problems as unfamiliar situations but ignore the relationships between students and tasks. Moreover, they do not encourage exploration of phases of problem solving and tend to use strategies more suitable for routine tasks. Communication is identified in all the tasks designed, encouraging interaction and discussion. However, only one task explicitly promotes mathematical language. For reasoning and proof, pre-service teachers begin to use questions to elicit explanations and justifications, but do not encourage verification strategies and various modes of reasoning. The process of connections is only present in one task, reflecting the fragmented nature of mathematics teaching. We conclude that the professional practice of designing mathematical tasks is a powerful in teacher education. However, training programs should place greater emphasis on the meaningful use of mathematical processes.

A mathematical model of the combination of lateral tilt and rotation of the vertebra

An important section of spinal biomechanics is the analysis of various types of movements in spinal segments, which are difficult to observe, and setting up experiments is quite complex. There are few articles devoted to this topic, and the methodological approaches outlined in these studies are so heterogeneous that they do not allow for a comparative analysis. In this situation, the abstract language of mathematics allows us to objectively answer the questions that arise. Aim of the study was to develop a mathematical model of a spinal segment to calculate the combination of rotation angles and lateral inclination of the vertebra, as well as to identify factors influencing these parameters. Material and methods. The developed mathematical model of the motion segment of the spine was used as the main tool for the study. The initial data for this model were the coordinates of the reference points of the vertebrae, which makes it possible to determine a number of parameters describing their complex structure. Using this model, the parameters of the combination of vertebral movement in the frontal and horizontal planes were calculated. Results and discussion. The developed model of the combination of movements in the spinal segment is adequate to the ideas about the nature of movements in the spinal segments. The coefficient of combination of lateral tilt and rotation of the vertebra for the cervical vertebrae is from 0.5 to 0.7, for the thoracic vertebrae from 0.3 to 0.5, and for the lumbar vertebrae from 0.0 to 0.1. Fluctuations in the value of this coefficient depend on the angle of inclination of the upper articular surfaces of the underlying vertebra. Reducing the size of the articular surfaces leads to a decrease in the magnitude of the angular movements of the vertebra, and their convergence leads to an increase in mobility in the spinal segments. A negative angle of inclination of the articular surfaces causes opposite rotation of the vertebra.

Mathematical endeavours to explain biological phenomena

The use of mathematical methods and models is continually increasing in many areas of contemporary biological research: in genomics, molecular modelling, structural biology, neurobiology, biology of systems and so on. In this paper we discuss the importance of Mathematics, mathematical modelling and dynamic visualization, with the aid of technology, in the field of Biology and Medicine. We emphasize that the language of Mathematics and the graphical display is remarkably powerful and flexible, and the modes of understanding and thinking about phenomena can yield deep insight into it that pervades the modern life.

Enhancing Distribution Networks with Optimal BESS Sitting and Operation: A Weekly Horizon Optimization Approach

The optimal sitting and operation of Battery Energy Storage Systems (BESS) plays a key role in energy transition and sustainability. This paper presents an optimization framework based on a Multi-period Optimal Power Flow (MOPF) for the optimal sitting and operation of BESS alongside PV in active distribution grids. The model was implemented in AMPL (A Mathematical Programming Language) and solved using the Knitro solver to minimize power losses over one week, divided into hourly intervals. To demonstrate the applicability of the proposed model, various analyses were conducted on a benchmark 33-bus distribution network considering 1, 2 and 3 BESS. Along with the reduction in power losses of up to 17.95%, 26% and 29%, respectively. In all cases, there was an improvement in the voltage profile and a more uniform generation curve at the substation. An additional study showed that operating over a one-week horizon results in an energy gain of 1.08 MWh per day compared to single daily operations. The findings suggest that the proposed model for optimal sitting and operation of BESS in the presence of Renewable Energy Sources (RES) applies to real-world scenarios.

Influence of Social Economic Status and Interest on Students’ Academic Performance

The positioning of any economy in the global light is anchored on the growth and development of its educational institutions hence the more developed these institutions are, the more advanced such economy will be to handle issues related to technological advancements, development of military arsenals, robust & global economy and scientific breakthroughs et. The performance of these institutions is dependent on the impact of both informal and formal education on the academic performance of students influenced by certain key factors amongst which includes; Socio-economic Status (SES) and Interest. This paper seeks not to only investigate the impact of these two factors but also observe amongst them which has a greater impact on academic performance while steering its attention on two core subjects; Mathematics and English Language. On this premises, let’s consider the performance of 210 students in the Senior Secondary One (SS1) spanning across six (6) different Schools within the city of Jos. The data collected were analyzed and tabulated using Microsoft Excel. Results showed that though both factors impact academic performance (either positively or negatively) however SES seems to have a much greater influence on academic performance than interest.

Mathematical Concept Representations in the Early Years of School: Analyzing Student’s Errors

In this paper we analyze students’ mathematics errors in the early years of Brazilian school. To achieve this goal, we developed a questionnaire with eight math problems that included basic operations. This instrument was distributed to 76 third-grade students in three different classes from three different schools. To comprehend what caused the errors, we analyzed each question. To perform these analyzes we used the following categories: Errors due to language difficulties; Errors due to difficulties in obtaining spatial information; Errors due to incorrect associations or rigidity of thinking; Errors due to the application of irrelevant rules or strategies; Errors due to deficient mastery of prerequisite skills, facts, and concepts; Incorrect reproduction of the task; Error of counting; Errors in the assemblage of the arithmetic operations; Errors in the summing up with values bigger than ten; and Specific errors of subtraction. We believe that using errors as motivation could improve students' understanding of mathematics. We seek to help teachers (and researchers) identify most of the mistakes made by students in order to recognize them in their classrooms. The results indicated that some of the students' most common errors are in line with what the literature points out, that is, difficulty in translating the problem into mathematical language; difficulties in using the operations algorithms and difficulties in understanding what the problem is asking.

Components of Mathematical Language and Mathematical Ability in 5-Year-Old Dual Language Learners

ABSTRACT A growing body of research suggests that children’s understanding of mathematical language is critical for their mathematical abilities. Most of this work has been restricted to single language learners (i.e., SLLs), and used dual language learners (i.e., DLLs) as an exclusion criterion, raising questions about the generalizability of these findings to DLLs. This is particularly important given the observed differences in the association between general language and mathematics for DLLs as compared to SLLs. In our study, conducted in Belgium, we therefore investigated the associations between components of mathematical language and different mathematical abilities in 75 DLLs and compared them to 75 age- and sex-matched SLLs (M age = 4 years 8 months; 33 females in each group). Unfortunately, the two groups could not be matched on socioeconomic status (i.e., SES), and SES-levels of the parents of DLLs were significantly lower than SES-levels of SLLs. We assessed children’s quantitative and spatial language, their mathematical abilities (numerical competencies, geometry, and measurement), as well as their general vocabulary and spatial skills. All children, including DLLs, were only tested in the language of instruction (i.e., Dutch) in which DLLs exhibited varying levels of proficiency. Results revealed that DLLs obtained lower scores than SLLs in quantitative and spatial language, mathematical abilities, general vocabulary, but not in spatial skills. Associations between components of mathematical language and mathematical abilities were similar across DLLs and SLLs, except for the relation between spatial language and geometry, which was weaker in DLLs.

General Fractional Economic Dynamics with Memory

For the first time, a self-consistent mathematical approach to describe economic processes with a general form of a memory function is proposed. In this approach, power-type memory is a special case of such general memory. The memory is described by pairs of memory functions that satisfy the Sonin and Luchko conditions. We propose using general fractional calculus (GFC) as a mathematical language that allows us to describe a general form of memory in economic processes. The existence of memory (non-locality in time) means that the process depends on the history of changes to this process in the past. Using GFC, exactly solvable economic models of natural growth with a general form of memory are proposed. Equations of natural growth with general memory are equations with general fractional derivatives and general fractional integrals for which the fundamental theorems of GFC are satisfied. Exact solutions for these equations of models of natural growth with general memory are derived. The properties of dynamic maps with a general form of memory are described in the general form and do not depend on the choice of specific types of memory functions. Examples of these solutions for various types of memory functions are suggested.

Research on the Cultivation Strategy of Primary School Students' Mathematical Language Expression Ability

Learning mathematics is a process of learning mathematical language, which is the external manifestation of mathematical thinking, the carrier of mathematical knowledge and mathematical ideas and methods, and at the same time, mathematical knowledge also needs mathematical language as a medium to disseminate and communicate. In the study of mathematics, whether students can learn mathematics well is related to whether students have good mathematical language skills, but many studies can show that there are obvious deficiencies in the current mathematical language expression skills of primary school students. Therefore, teachers need to strengthen students' thinking training and good study habits, so as to further cultivate students' mathematical language expression ability and improve students' core literacy. To this end, this paper will elaborate on the concept and classification of mathematical language, as well as the cultivation strategies of primary school students' mathematical language expression ability.

The Contribution of the Principal's Managerial Function in Improving the Quality of Education Based on School Exam Results in High Schools in Banten Province

This study examines the contribution of the principal's managerial function in improving the quality of education in high schools in Banten Province based on school exam results. The challenges faced include disparities in access, the quality of educators, curriculum relevance, availability of facilities, parental involvement, resource management, and the utilization of technology. The research employs a quantitative method with surveys involving principals, teachers, and students from various high schools in Banten. Data were analyzed using SPSS to determine the relationship between principal leadership and exam results. The correlation test results between X (the principal's contribution) and Y (school exams) showed rcalcualted= 0.664 and rtabel = 0.514. In other words, since 0.664 > 0.514, H0 is accepted, indicating a positive relationship between variables X and Y. This demonstrates that the principal's leadership has a significant impact on improving school exam results, particularly in Mathematics and Indonesian Language subjects. These findings underscore the importance of developing principal leadership to enhance the quality of education in Banten Province.