Mathematical Language Research Articles

Problem Solving Process Based on the Newman Procedure in an Effort to Improve Students' Mathematical Reversible Thinking

Students' low Reversible Thinking and mathematical problem solving abilities, especially in working on mathematics problems in the form of stories. This research aims to determine and describe the increase in Reversible Thinking and problem solving abilities in mathematics problems in the form of stories after implementing the Newman Procedure in the learning and problem solving process. This type of research is the Kemmis and Taggart model of Class Action Research (PTK) which consists of 4 stages, namely planning, implementation, observation and reflection. This research was conducted in two cycles. Data collection techniques in this research are observation, tests, and documentation. The data analysis technique used is qualitative analysis to describe research results through observation and quantitative analysis techniques to analyze test assessment scores. The results of this research show an increase in students' reversible thinking abilities seen from changes in attitudes and behavior, seen from the ability to read questions quickly and clearly, able to understand the information contained in the reading, easy to transform information into mathematical language, confident to work on questions and able to take responsibility for the answers obtained.

A capturing math language use during block play: Creation of the spatial and quantitative mathematical language coding system

The goals of the current study were: 1) to modify and expand an existing spatial mathematical language coding system to include quantitative mathematical language terms and 2) to examine the extent to which preschool-aged children used spatial and quantitative mathematical language during a block play intervention. Participants included 24 preschool-aged children (Age M = 57.35 months) who were assigned to a block play intervention. Children participated in up to 14 sessions of 15-to-20-minute block play across seven weeks. Results demonstrated that spatial mathematical language terms were used with a higher raw frequency than quantitative mathematical language terms during the intervention sessions. However, once weighted frequencies were calculated to account for the number of codes in each category, spatial language was only used slightly more than quantitative language during block play. Similar patterns emerged between domains within the spatial and quantitative language categories. These findings suggest that both quantitative and spatial mathematical language usage should be evaluated when considering whether child activities can improve mathematical learning and spatial performance. Further, accounting for the number of codes within categories provided a more representative presentation of how mathematical language was used versus solely utilizing raw word counts. Implications for future research are discussed.

Theoretical and Experimental Approaches to Study of Biological Objects by Mathematical Methods Using the Example of Hormone Production in the Thyroid Gland

The study of any biological object is a complex process that involves a number of successive stages, one of which tools can be a specially created expert system. It is advisable to present the conclusion about the studied biological object in clear forms of expression – quantitative or binary, which are the results of the practical application of the principles of absorption by some researched factors of others, a compromise between them or the prevailing alternative of the studied properties. The involvement of mathematical technologies in the identification and explanation of the regularities of the activity of biological objects requires the display of the results of their research using a mathematical language. This makes it possible to establish regularities in the course of biological processes and predict their consequences. Since any living system is formed from a large number of elements, the organism has a complex hierarchy of structural and functional levels of organization. A mandatory prerequisite for the activity of a biological system is a variety of states, each of them being characterized by its own characteristics – markers of change, which, according to the degree of completeness of the one state transformation into another, should be divided into markers of primary changes, markers of prevailing majority changes, and markers of final changes. Comprehensive application of the Semi-quantitative analysis of electronograms according to Ryabukha O. (2000) and her method for determining the profiles of hormonopoietic cells’ special capacities (2003) when studying the cytophysiology of the thyroid gland in normal and pathological conditions, it is possible to determine the specific link of the follicular cell’s specialized activity, in which there was a violation of hormonopoiesis, and to assess its intensity. The developed Conceptual apparatus of functional connections between organelles of hormone-producing cells when studying them by the Method of correlation analysis by creating intra- and intersystem correlation portraits reflects the features of mutual influences and interdependencies, which deepens the understanding of the intimate mechanisms of hormonopoiesis.

More than Steepness: Introducing Slope Quantitatively with Interactive Dynamic Representations

We report on a long-term collaboration with ninth-grade mathematics teachers at a linguistically diverse high school in which we examined the intersection between mathematics and language, and how language and mathematical thinking can be developed together in a multilingual setting. We co-designed lessons that promoted conceptual understanding, increased students’ access to grade level mathematics and created opportunities for students who are classified as English learners to participate in discussions. Our content focus was linear and exponential rates of change. In this article, we focus on linear rate of change and its connection to slope. After identifying three distinct meanings for and uses of slope in a ninth-grade mathematics textbook: (a) slope as steepness, (b) slope as rate of change, and (c) slope as a property of collinearity (presented in this order) and observing student interactions around slope concepts, we considered whether it may be more beneficial for students, particularly emergent multilingual students, to develop a robust quantitative understanding of slope first, then introduce the other two meanings of slope as an application of rate of change. To achieve this, we created a series of lessons incorporating dynamic interactive technology and mathematical language routines. We share three of these lessons in this article and include a classroom vignette illustrating the classroom interactions that were achieved through using our first Desmos activity.

Comparing the Use of AI Tools in Mathematics and English Education: The Potential and Challenges of AI as Learning Assistant for FKIP UQ Students in Completing Academic Tasks

This study investigates the utilization of Artificial Intelligence (AI) among students enrolled in Mathematics and English Language Education programs at higher education in completing their academic tasks. Through a qualitative method, the study examines students' attitudes towards AI, their preferred AI tools, and the perceived benefits and challenges associated with AI integration in academic tasks. The findings reveal that the majority of students in both programs view AI as a valuable tool for enhancing learning outcomes and academic performance. Chat GPT emerges as the most favoured AI tool, particularly among Mathematics students. Moreover, students acknowledge the potential of AI to improve their motivation in learning and provide personalized feedback. However, students also express concerns regarding AI's limitations, including its inaccuracy and potential biases in data and information. Overall, this study underscores the importance of integrating AI responsibly and equitably to optimize its benefits and address potential drawbacks

Towards an advanced mathematical language task for the early primary school years: preliminary results on reliability and validity

Towards an advanced mathematical language task for the early primary school years: preliminary results on reliability and validity

Investigation of Students' Difficulties in Mathematical Language : Problem-Solving in Mathematical Word Problems at Elementary Schools

Investigation of Students' Difficulties in Mathematical Language : Problem-Solving in Mathematical Word Problems at Elementary Schools

The essence and structure of mathematical language competence of a future teacher

The essence and structure of mathematical language competence of a future teacher

Kemampuan Komunikasi Matematis Siswa SMP ditinjau dari Gaya Belajar

Taking into account auditory, visual, and kinesthetic learning modalities, this research animed to evaluate students mathematical communication abilities on the subject of Two Variable Linear Equation Systems. This qualitative study surveyed six junior high school students from the city of Sukabumi. The tools used for this study were a written exam to evaluate mathematical communication abilities and a learning style questionnaire. Mathematical communication skills are the basis of the learning style questionnaire. These skills include the ability to draw connections between mathematical ideas and real word objects, images, and diagrams to explain mathematical concepts, situations, and relationships in writing and to express events or ideas using mathematical symbols or language. Communication abilities are excellent among students with low visual learning styles, as are those with high visual learning styles, according to the study’s findings. The communication abilities of pupils whose learning style is mostly auditory are good, while those whose learning style is predominantly visual are poor. The same holds true for students communication abilities, those who learn best via movement tend to have excellent ones, while those who learn best by sitting still tend to struggle. Knowing one’s own learning style is crucial for pupils to enhance their mathematics communication abilities

Pengaruh Peran Bahasa Indonesia Dalam Konteks Soal Cerita Matematika

In this research, it was found that mathematical literacy and language literacy have an important role in students' ability to understand and solve mathematical story problems. Language literacy skills, such as the ability to read and understand text, can influence students' ability to solve mathematical problems presented in story form. Improving students' numeracy skills does not only require acceptance of mathematical material, but also the ability to understand and apply mathematical material in everyday life. This shows the importance of students being able to relate mathematical concepts to real situations in everyday life. Mathematical literacy and language literacy are closely related in the context of mathematics story problems. The type of research carried out was descriptive research with literature study. The research method used is a quantitative method by collecting data from previous research and data analysis using the SPSS application. The results of the research show that there is a correlation between Indonesian language literacy and students' mathematical numeracy literacy in solving mathematics story problems. Based on research conducted, Indonesian language scores influence mathematics scores by 54.1%. This proves that Indonesian is very important to learn to expand understanding in solving mathematical story problems. The ability to understand questions/problems of course really depends on the student's reading ability or Indonesian language literacy.

The faster the better? Advanced internet access and student performance

In this paper, we study the impact of high-speed internet access on student performance. Our empirical analysis leverages a unique dataset that combines information on ultra-broadband (UBB) diffusion in Italy with data on student performance in 2nd, 5th, and 8th grades for the period 2012–2017. We exploit the staggered roll-out of UBB, starting from 2015. Through an event study approach, we find evidence of endogeneity between student performance and UBB diffusion. We deal with this issue through an instrumental variable approach that exploits plausibly exogenous variation in the diffusion of the essential UBB input. Our results suggest that advanced internet connections significantly decrease student performance in Mathematics and Italian language in the 8th grade. In contrast, we do not find any significant effect in the 2nd and 5th grades. Male students from low-educated parental backgrounds are those more adversely affected, especially if they attend schools with a low IT usage.

Comparing Power Models for circuits design with Mathematical Language Processing

The work presented in this paper is part of a project that focuses on sorting simulation models used at Intel to calculate power consumption of electronic devices. Hundreds of thousands of analytical power models have already been accumulated in a directory of files and folders, for the simulation of the consumption of thousands of products. As a first step, this work focuses on comparing and grouping together models of smaller granularity - the formulas - which consist of power equations, the definition of the parameters involved in these equations, and a description.To manage this large data problem, we follow the principles of Model Management and Analytics, to decompose the problem into the analysis of constituent fields. We believe that the equations describing power consumption are the most highly information-rich field of our models. The aim of this work is to group together the formulas models, using Mathematical Language Processing (MLP), to take advantage of the business information contained in electrical equations. We calculate the embeddings of our formulas, to enable comparisons between them, to cluster together similar equations (and therefore models).

Setting the stage for successful inclusion of students with autism spectrum disorder: Supports to generate and process mathematical language

AbstractStudents with autism spectrum disorder (ASD) are included in the general education classroom more often than ever before. Despite mathematical strengths and early success, these students experience poor outcomes (academic and employment) compared to their typically developing peers. The language of mathematics increases in complexity, use, and expectations as students age. To facilitate the development of mathematical proficiency for students with ASD, teachers can incorporate instructional strategies to support language processing and use in mathematics. This manuscript provides practical advice for teachers who want to support math language for students with ASD in the general education environment including (a) the importance of these supports, (b) specific recommendations, (c) visual and descriptive examples, and (d) additional resources.

Programming as a mediator of mathematical thinking

We report on three episodes from a case study where upper secondary students numerically explore the definite integral in a Python environment. Our research questions concern how code can mediate and support students' mathematical thinking and what kind of sociomathematical norms emerge as students work together to reach a mutual understanding of a correct solution. The main findings of our investigation are as follows. 1) Students can actively use code as a mediator of their mathematical thinking, and code can even serve as a bridge that helps students to develop their mathematical thinking collaboratively. Further, code can help students to perceive mathematical notions as objects with various properties and to communicate about these properties, even in other semiotic systems than the mathematical language. 2) For the participating students, a common norm was that an acceptable solution is a sufficient condition for the correctness of the solution method although students were aware of a problem in their code, yet also other norms emerged. This demonstrates that learning mathematics with programming can have an effect on what kind of sociomathematical norms emerge in classroom.

Optimised Congestion Management Using Curative Measures in Combined AC/DC Systems with Flexible AC Transmission Systems

Due to the increasing demand for transport of electrical energy, measures for power flow control, congestion management, and higher utilisation of the existing grid play a decisive role in the transformation of the power system. Hence, enormous efforts must be undertaken using measures of congestion management. Modelling and integration of corresponding measures in optimisation tools to support grid and system operation and therewith reduce the resulting efforts become more important. This is especially true because of the high intermittency and decentralisation of renewable generation leading to increased complexity of the power system, higher loading of assets, and a growing need for control over flexible alternating current transmission systems (FACTS) and high-voltage direct current (HVDC) converters. This work therefore describes the implementation of optimised congestion management in an A Mathematical Programming Language (AMPL)-based nonlinear optimisation problem. AMPL is an effective tool to deal with highly complex problems of optimisation and scheduling. Therefore, the modelling of assets and flexibilities for power flow control in AC/DC systems in combination with an innovative grid operation strategy using predefined curative measures for the optimised use of the existing grid is introduced. The nonlinear mathematical optimisation aims at the optimal cost selection of flexibility measures. The application of the optimisation technique in a combined AC/DC system shows the optimal preventive and curative use of measures in operational congestion management. Simulation results prove that, by using predefined curative measures, the volume of cost-intensive preventive measures can significantly be reduced, especially in association with power flow control.

Promoting 5th Grade Students’ Spontaneous Focusing on Quantitative Relations

Spontaneous focusing on quantitative relations (SFOR) is related to the development of rational number knowledge and predicts future mathematical knowledge. However, scarce evidence exists on whether and how SFOR tendency can be supported with classroom instruction. In this quasi-experimental study, 306 5th grade students participated in one of two four-lesson interventions. We investigated the relative effectiveness of both interventions on students’ SFOR tendency and their knowledge of multiplicative relations and fractions. Students in the Spot the Relations intervention (n = 142) completed activities that supported their ability to recognize and describe multiplicative relations in their everyday surroundings. Students in the Fraction Estimation Game intervention (n = 164) trained with digital game-based number line estimation tasks that supported their fraction knowledge. The results revealed that students in the first group showed larger gains in their multiplicative relations knowledge and SFOR tendency, whereas those in the second group showed larger gains in their fraction knowledge from pre- to posttest. Although SFOR tendency was supported by both interventions over time, the effect was larger for Spot the Relations, which used instructional practices that supported students’ multiplicative knowledge and mathematical language and made multiplicative relations relevant and observable parts of the world.

A CLAUSE COMPLEX ANALYSIS OF PROBLEM STATEMENT SECTIONS IN MPHIL THESES ACROSS THREE DISCIPLINES IN A GHANAIAN UNIVERSITY

Academic writing is considered persuasive (Hyland 2008) and as post-graduate-students negotiate their entry into the research community, they are expected to build a formidable argument to create a research space for themselves in their research problem statements. As such, how they build logical connections of ideas in their problem statements is key, varying from one discipline to the other. This study explores the Problem Statement sections of MPhil theses, using Halliday and Matthiessen’s (2004/2014) notion of clause complexing in Systemic Functional Linguistics (SFL). Specifically, the study focused on the tactic and the logico-semantic relations of the Problem Statements sections of three disciplines: Mathematics, Nursing, and English Language in the University of Cape Coast, Ghana. The findings reveal that regarding the basic clause complex structure of the three disciplines, English Language uses a lot of clause complexes compared to the other disciplines. Also, all three disciplines use considerable hypotactic relations and hypotactic projection of locution instead of idea since in the problem statements, writers report what others have said and not their own thoughts. In terms of relations of expansion, there are variations in the three disciplines, with English language favoring elaboration whilst Mathematics favor extension and enhancement. The use of expansion relations for Nursing is closer to that of English language. It is suggested that clause complexing is not only determined by genre and mode but also conventions of academic discipline. The findings have implication for theory and disciplinarity in academic writing.

Multi-Vehicle Collaborative Trajectory Planning for Emergency Vehicle Priority at Autonomous Intersections

Emergency vehicle (EV) prioritization plays an important role in improving rescue efficiency and saving lives and property. Most existing studies have been confined to either investigating signal prioritization for EVs at intersections or focusing on clearing emergency lanes on road segments, with limited consideration for an integrated approach that combines both methods. In this study, we have developed a bi-level trajectory planning model aimed at optimizing the trajectories of EVs at intersections and road segments located within the communication range, using vehicle-to-everything technology. The upper-level model is designed to plan the entry times, speeds, and internal trajectories of vehicles within the intersection while avoiding any conflicts that may arise during their movements. In particular, to address the dimensionality of the proposed large-scale optimization problems, we introduce the equidistant discretization method to discretize the entry speeds of vehicles into a finite set of selectable values. The lower-level model focuses on optimizing the longitudinal and lateral trajectories on roadways to ensure that vehicles arrive at the stop line punctually and promptly. Both the upper- and lower-level models are formulated as mixed-integer linear programming models. The A Mathematical Programming Language and the Gurobi solver are employed for optimization. The case study demonstrates that the proposed model effectively optimizes vehicle trajectories at intersections and road segments, leading to a significant reduction in delays for EVs.

Пифагорейский аргумент разумного замысла вселенной и его критика. Статья 3: Возражения философов

The article is devoted to a critique of the Pythagorean argument, explicit and implicit, offered by philosophers of different epochs. We begin with Kant’s “critique of the physicotheological argument”, finding not a refutation of the argument, but a mixture of support and fair remarks removed by the further development of physics. We next assess objections to the Pythagorean argument which may be called “downplaying” emphasizing the incompleteness of physical conceptions of the world. We note that, despite this incompleteness, the cosmic scope and incredible precision of knowledge of modern physics require an explanation of why this turned out to be possible. Another variant of the downplay is connected with the negative attitude to the fruits of the “Pythagorean faith”, with the possibility of rejecting it according to the pragmatic criterion. We noted that, as far as we know, none of the adherents of this retrograde position have answered the question about the reason for the effectiveness of mathematics in cognition of the universe, whether the fruits of this cognition are good or not. A number of attempts to explain this efficiency are associated with a sort of omnipotence attributed to an aspect of cognition. Karl Popper suggested that the effectiveness of the language of mathematics is not surprising, because languages are generally effective in describing reality. Anatoly Akhutin explained the success of mathematical physics by the fact that mathematized methodology was originally incorporated into physics, ‘what we put in, we get out’. Ivor Grattan-Guinness and Andrei Rodin deduced the success of physics from the general way of progress. Noting the inadequacy of such explanations, we tried to respond to them correctly. One more direction of criticism of the Pythagorean argument is connected with ethical, political and politically-correct requirements of strict observance of the boundary between the ‘magisteria’ of science and religion, inadmissibility of its crossing. Our response consists in pointing out the incompatibility of such a ‘Chinese wall’ with the task of philosophical reflection of scientifi c cognition and developing a meaningful worldview. The article then moves on to a series of remarks that may seem relevant without actually being so. Finally, the role of irrational motivations in solving metaphysical problems is considered.

The Language of Spheres in Physics

Physical laws manifest themselves through the amalgamation of mathematical symbols, numbers, functions, geometries, and relationships. These intricate combinations unfold within a mathematical model devised to capture and represent the “objective reality” of the system under examination. In this symbiotic relationship between physics and mathematics, the language of mathematics becomes a powerful tool for describing and predicting the behavior of the physical world. The language used and the associated concepts are in a perpetual state of evolution, mirroring the ongoing expansion of the phenomena accessible to our scientific understanding. In this contribution, written in honor of Richard Kerner, we delve into fundamental, at times seemingly elementary, elements of the mathematical language inherent to the physical sciences, guided by the overarching principles of symmetry and group theory. Our focus turns to the captivating realm of spheres, those strikingly symmetric entities that manifest prominently within our geometric landscape. By exploring the interplay between mathematical abstraction and the tangible beauty of symmetry, we seek to deepen our understanding of the underlying structures that govern our interpretation of the physical world.