Mathematical Language Research Articles

Türkiye’s Educational Journey: Evaluating the Skills of Mathematics, Science, Reading, and Foreign Language in The Light of International Competition

Education has always been significant for sustainable development all around the world. However, it is not possible to achieve development without considering the international standards in this globalized world. Countries can be successful only if they interact with other societies without losing their cultural identities. The European Union is an organisation that fosters cooperation and harmony among countries for development. In this context, it has identified four main areas and sixteen indicators for these areas in order to improve the quality of education. Being one of the candidate countries, Türkiye has declared will to harmonize with the educational policies suggested by the European Union. Therefore, the question of how compatible and competitive Türkiye’s education system has become with international standards remains on the agenda in today’s world of increasing international competition in every area. In this line, this study aims at analysing the current situation of Turkish education system according to four key indicators, which are mathematics, science, reading skills and foreign language. For this purpose, the study employs the method of document analysis. Therefore, we analysed PISA 2022 report and EF EPI (EF English Proficiency Index) 2023 report in this line. The study findings show that Türkiye ranks 39th with an average score of 453 in mathematics, 34th with an average score of 476 in science, and 36th with an average score of 456 in reading skills among 81 countries in PISA 2022. Also, Türkiye ranks 66th among 113 countries with an EF EPI score of 493 in English.

“Searching for order at all levels”. Antonio Lima-de-Faria (July 4, 1921 – December 27, 2023)

“Searching for order at all levels”. Antonio Lima-de-Faria (July 4, 1921 – December 27, 2023)

Adversarial Robustness of Neural Networks From the Perspective of Lipschitz Calculus: A Survey

We survey the adversarial robustness of neural networks from the perspective of Lipschitz calculus in a unifying fashion by expressing models, attacks and safety guarantees, that is, a notion of measurable trustworthiness, in a mathematical language. After an intuitive motivation, we discuss algorithms to estimate a network’s Lipschitz constant, Lipschitz regularisation techniques, robustness guarantees, and the connection between a model’s Lipschitz constant and its generalisation capabilities. Afterwards, we present a new vantage point regarding minimal Lipschitz extensions, corroborate its value empirically and discuss possible research directions. Finally, we add a toolbox containing mathematical prerequisites for navigating the field (Appendix).

A tensor network view of multilayer multiconfiguration time-dependent Hartree methods

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalisation group (DMRG) are powerful workhorses applied mostly in different scientific fields. Although both methods are based on tensor network states, very different mathematical languages are used for describing them. This severely limits knowledge transfer and sometimes leads to re-inventions of ideas well known in the other field. Here, we review ML-MCTDH and DMRG theory using both MCTDH expressions and tensor network diagrams. We derive the ML-MCTDH equations of motions using diagrams and compare them with time-dependent and time-independent DMRG algorithms. We further review two selected recent advancements. The first advancement is related to optimising unoccupied single-particle functions in MCTDH, which corresponds to subspace enrichment in the DMRG. The second advancement is related to finding optimal tree structures and on highlighting similarities and differences of tensor networks used in MCTDH and DMRG theories. We hope that this contribution will foster more fruitful cross-fertilisation of ideas between ML-MCTDH and DMRG.

Mathematical argumentation of three-year-old children on a classroom experience based on two STEAM domains

In the last decades, the importance of argumentation as a human competence in general and its close relationship with mathematical comprehension in particular has been highlighted. Thus, in this paper we focus our interest on analyzing the argumentation skills shown by three-year-old children in a STEAM classroom experience. For this purpose, a qualitative study was carried out. For data collection, a STEAM task has been designed in which mathematics and science are worked together from the study of the physical properties of water. Specifically, what color and taste of water has by means of two experiments and, subsequently, photos and video-recordings have been collected during the implementation carried out in a classroom with 20 children of three-year-old. All data collect have subsequently been transcribed and categorized. The results indicate that the children, during the experiments done, mainly use arguments based on mathematical language, numerical figures, or make use of words or spelling, although with considerable imprecision in the type of language used. In addition, the experiments carried out have allowed a high percentage of children to change their previous ideas and have a more comprehensive approach to the concepts introduced, highlighting the importance of working on argumentation in early childhood education through contexts, in this case STEAM, which encourage reasoning and proof.

The bridging understanding of language and mathematical symbols between teachers and students: An effort to increase mathematical literacy

The research aims to analyze the gap between teachers' and students' understanding of language literacy and mathematical symbols. The study was designed with a concurrent triangulation strategy. The research respondents consisted of 20 teachers and 120 class VII students. Data collection through questionnaires, interviews, and cognitive tests. Qualitative data was analyzed descriptively, and quantitative data was analyzed inferentially. The results of the analysis of quantitative data show that there is a linear (significant) relationship between understanding language and mathematical symbols and mathematical literacy skills. The results of the qualitative data analysis describe that the teacher's understanding of language and mathematical symbols (high criterion) does not necessarily support the students' understanding of language and mathematical symbols. We confirm the suspicion that there is a gap in the ability of teachers and students to understand language and mathematical symbols. Students need to improve their understanding of mathematical language and symbols. The pattern of errors is based on the teacher's conception of learning in the previous class, so the process of transitioning the teacher's knowledge to students' understanding of mathematics experiences obstacles. The implication is that the process of transitioning meaning from mathematical symbols to written and spoken language must be carried out when the teacher introduces or teaches new topics to students, and the context in which mathematical symbols are used must be followed by clarification.

Investigating Models for the Transcription of Mathematical Formulas in Images

The automated transcription of mathematical formulas represents a complex challenge that is of great importance for digital processing and comprehensibility of mathematical content. Consequently, our goal was to analyze state-of-the-art approaches for the transcription of printed mathematical formulas on images into spoken English text. We focused on two approaches: (1) The combination of mathematical expression recognition (MER) models and natural language processing (NLP) models to convert formula images first into LaTeX code and then into text, and (2) the direct conversion of formula images into text using vision-language (VL) models. Since no dataset with printed mathematical formulas and corresponding English transcriptions existed, we created a new dataset, Formula2Text, for fine-tuning and evaluating our systems. Our best system for (1) combines the MER model LaTeX-OCR and the NLP model BART-Base, achieving a translation error rate of 36.14% compared with our reference transcriptions. In the task of converting LaTeX code to text, BART-Base, T5-Base, and FLAN-T5-Base even outperformed ChatGPT, GPT-3.5 Turbo, and GPT-4. For (2), the best VL model, TrOCR, achieves a translation error rate of 42.09%. This demonstrates that VL models, predominantly employed for classical image captioning tasks, possess significant potential for the transcription of mathematical formulas in images.

Применение цифровых инструментов обработки естественного языка для оптимизации подготовки учителя-предметника в полилингвальной образовательной среде

The aim of the research is to automate the analysis process of the most common grammatical forms and syntactic structures of a foreign or second language to optimize the content and acquisition of English language programs in the training of future Mathematics teachers for professional activities in a multilingual educational environment. The paper theoretically justifies the necessity of a comprehensive frequency analysis of language structures. Software tools for natural language processing (the Python programming language and the spaCy library) were developed, which were subsequently applied in the course “Methods of Mathematical Data Processing” to identify the most frequent grammatical forms and syntactic structures characteristic of the English language of Mathematics. Based on the data obtained, methodological recommendations were formulated for the content and outcomes of English language programs for future Mathematics teachers in a multilingual educational environment. The scientific novelty of the research lies in using digital natural language processing (NLP) tools for a quantitative and statistical analysis of language data, necessary for the development of methodological recommendations for the content and outcomes of foreign/second language programs for subject teacher training. As a result of the research, it was found that digital natural language processing tools can be used to improve the language training of subject teachers in a multilingual educational environment.

Pelaksanaan Diagnostik Kesulitan Belajar Peserta Didik oleh Guru SD di Kota Salatiga

Elementary school students who experience learning difficulties need help from teachers because it disrupts the learning process and affects learning success. This research is in the form of descriptive research with the aim of describing the implementation of diagnostics for learning difficulties by teachers. The subjects in the research were 23 elementary school teachers spread across four sub-districts of the city of Salatiga, both public and private elementary schools. The variable of this research is the implementation of the diagnosis of students' learning difficulties by elementary school teachers. This research method is in the form of a survey, collecting data on the implementation of the diagnosis of learning difficulties for elementary school students in the city of Salatiga. Data collection used a questionnaire supplemented by interviews. The analysis technique used is descriptive qualitative. The research results found that all teachers had carried out diagnostics for learning difficulties, and there were always students who experienced learning difficulties. Students' learning difficulties are more related to academic activities. Diagnostics of learning difficulties is carried out at the end of learning, using observation and learning results tests, as well as interview guides. The learning difficulties experienced by students in elementary school are predominantly in the form of Mathematics and Indonesian language subjects. Almost all teachers identify students' learning difficulties and determine the factors that cause their learning difficulties. The assistance provided by teachers to deal with students' learning difficulties generally takes the form of assisting students' learning and providing additional study time (tutoring) to students, as well as providing advice or referrals to parents to consult with experts. Barriers to carrying out diagnostics for learning difficulties in general are that complete diagnostic instruments for learning difficulties are not yet available, and teachers are not yet skilled in using diagnostic instruments for learning difficulties.

Algebra is the Language of Mathematics & Algebraic Philosophy is the Luggage of Mathematics

Algebra is the Language of Mathematics & Algebraic Philosophy is the Luggage of Mathematics

Discovering interpretable physical models using symbolic regression and discrete exterior calculus

Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of machine learning to recover physical models from experiments and increase the accuracy of physical simulations, purely data-driven models have limited generalization and interpretability. To overcome these limitations, we propose a framework that combines symbolic regression (SR) and discrete exterior calculus (DEC) for the automated discovery of physical models starting from experimental data. Since these models consist of mathematical expressions, they are interpretable and amenable to analysis, and the use of a natural, general-purpose discrete mathematical language for physics favors generalization with limited input data. Importantly, DEC provides building blocks for the discrete analog of field theories, which are beyond the state-of-the-art applications of SR to physical problems. Further, we show that DEC allows to implement a strongly-typed SR procedure that guarantees the mathematical consistency of the recovered models and reduces the search space of symbolic expressions. Finally, we prove the effectiveness of our methodology by re-discovering three models of continuum physics from synthetic experimental data: Poisson equation, the Euler’s elastica and the equations of linear elasticity. Thanks to their general-purpose nature, the methods developed in this paper may be applied to diverse contexts of physical modeling.

Methodical conditions which are conducive to improving the education of pupils to solve their context-based mathematics task

Relevance. The research's relevance is due to the need to explore optimal ways to improve the education of pupils in mathematics for the formation of mathematical literacy, by independently solving text-based tasks in mathematics regardless of the orientation of their interests and the chosen specialty. Purpose. The purpose of the article is the characterization of methodical conditions conducive to teaching pupils to solve mathematical tasks on their own. Methodology. The methodology of the research consisted of the use of a set of theoretical methods (general scientific, specific-scientific), which allowed processing of the scientific literature, distributing the information array, studying and clarifying terms and concepts, and structuring the collected information. And empirical methods – interviews and sociological surveys with teachers and experts in the field under study. The participants in this study were 70 primary school mathematics teachers in 2-5 grades. Results. The article analyzes the process of the collaboration between teacher and students during solving textual problems in various ways, which allows students to form not only knowledge and skills on the relevant issue, and also to develop such elements of mathematical literacy as logical thinking and form a literate mathematical language. Conclusions. The study's applied value is that the main points, factual materials, and conclusions can be used in the school system by teachers, methodologists, and research educators to develop recommendations for improving the teaching of schoolchildren's autonomy in solving text-based problems in mathematics.

BioModME for building and simulating dynamic computational models of complex biological systems.

Molecular mechanisms of biological functions and disease processes are exceptionally complex, and our ability to interrogate and understand relationships is becoming increasingly dependent on the use of computational modeling. We have developed "BioModME," a standalone R-based web application package, providing an intuitive and comprehensive graphical user interface to help investigators build, solve, visualize, and analyze computational models of complex biological systems. Some important features of the application package include multi-region system modeling, custom reaction rate laws and equations, unit conversion, model parameter estimation utilizing experimental data, and import and export of model information in the Systems Biology Matkup Language format. The users can also export models to MATLAB, R, and Python languages and the equations to LaTeX and Mathematical Markup Language formats. Other important features include an online model development platform, multi-modality visualization tool, and efficient numerical solvers for differential-algebraic equations and optimization. All relevant software information including documentation and tutorials can be found at https://mcw.marquette.edu/biomedical-engineering/computational-systems-biology-lab/biomodme.php. Deployed software can be accessed at https://biomodme.ctsi.mcw.edu/. Source code is freely available for download at https://github.com/MCWComputationalBiologyLab/BioModME.

Evaluation of school achievements in adolescents with primary hypertension.

Primary hypertension (HT) is a global public health problem with increasing prevalence in recent years. HT may have caused decreased neurocognitive functions and learning difficulties. In this study, clinical characteristics of adolescents with primary HT were examined and the relationship between semester grade point average (GPA) and HT was evaluated. This is an observational, cross-sectional, descriptive study conducted on adolescents with primary HT attending high school. Patient records (number of hospital visits, HT-related complaints, blood pressure measurements, and laboratory tests) were evaluated retrospectively. End-of-semester report card grades of Mathematics, Turkish Language and Literature and English courses were noted, and compared with the clinical characteristics of the patients. The study included 83 patients with a mean age of 15.6±1.2 years. Patients with higher body mass index had lower grades in Mathematics (p=0.007) and Turkish Language and Literature (p=0.004). Patients with HT-related symptoms such as headache, epistaxis and palpitations had lower GPAs for all courses. Also, patients with hyperuricemia or proteinuria had lower semester GPAs compared to patients with normal serum uric acid levels or without proteinuria (p<0.05). GPAs for Mathematics (p=0.000) and Turkish Language and Literature (p=0.006) decrease as the number of hospital visits increases. HT may cause not only cardiovascular complications but also decreased neurocognitive functions through various mechanisms and may have a negative impact on academic skills. Therefore, HT should be followed up with a multidisciplinary approach and intensive efforts should be made to approach the goal of normotension.

Application Strategies of Computer Technology in the Field of Mathematical Modeling

The era of big data has arrived in society, and the technology behind com-puter networks has not only raised the general level of people's living stand-ards but is also making steady headway in the direction of artificial intelli-gence. The most important theoretical basis for it is mathematics. The pro-cess of abstracting and synthesizing the laws of reality through the use of mathematical techniques is known as mathematical modeling. The applica-tion of mathematical modeling in the natural sciences seeks to approach a problem with more precision by employing mathematical rigor and a mathe-matical language that is systematically complete. At this point in time, the progression of mathematical modeling just can't happen without the assis-tance of advances in computer technology. The significance of computer technology in mathematical modeling is demonstrated by a detailed examina-tion of the formula underlying the computer technology model. After con-ducting research on the results of the mathematical modeling competition held over the course of several years, utilizing the artificial neural network (ANN) algorithm to analyze the data, and coming to the conclusion that the implementation of computer technology plays a role in the dissemination of mathematical modeling, we say that computer technology has a part to play in the dissemination of mathematical modeling.

Machine learning and deep learning-based approach to categorize Bengali comments on social networks using fused dataset.

Through the advancement of the contemporary web and the rapid adoption of social media platforms such as YouTube, Twitter, and Facebook, for example, life has become much easier when dealing with certain highly personal problems. The far-reaching consequences of online harassment require immediate preventative steps to safeguard psychological wellness and scholarly achievement via detection at an earlier stage. This piece of writing aims to eliminate online harassment and create a criticism-free online environment. In the paper, we have used a variety of attributes to evaluate a large number of Bengali comments. We communicate cleansed data utilizing machine learning (ML) methods and natural language processing techniques, which must be followed using term frequency and reverse document frequency (TF-IDF) with a count vectorizer. In addition, we used tokenization with padding to feed our deep learning (DL) models. Using mathematical visualization and natural language processing, online bullying could be detected quickly. Multi-layer Perceptron (MLP), K-Nearest Neighbors (K-NN), Extreme Gradient Boosting (XGBoost), Adaptive Boosting Classifier (AdaBoost), Logistic Regression Classifier (LR), Random Forest Classifier (RF), Bagging Classifier, Stochastic Gradient Descent (SGD), Voting Classifier, and Stacking are employed in the research we conducted. We expanded our investigation to include different DL frameworks. Deep Neural Networks (DNN), Convolutional Neural Networks (CNN), Convolutional-Long Short-Term Memory (C-LSTM), and Bidirectional Long Short-Term Memory (BiLSTM) are all implemented. A large amount of data is required to precisely recognize harassing behavior. To rapidly recognize internet harassment written material, we combined two sets of data, producing 94,000 Bengali comments from different points of view. After understanding the ML and DL models, we can see that a hybrid model (MLP+SGD+LR) performed more effectively when compared to other models, its evaluation accuracy is 99.34%, precision is 99.34%, recall rate is 99.33%, and F1 score is 99.34% on multi-label class. For the binary classification model, we got 99.41% of accuracy.

Terminology in the Age of AI: The Transformation of Terminology Theory and Practice

Abstract This article explores the necessary transformation of terminology theory and practice induced by advances in artificial intelligence (AI), in particular generative AI and large language models (LLMs). It underlines the centrality of terminology for accurate and efficient multilingual communication, and it studies the interaction between two different forms of language, the embodied language of humans and the algorithmic and mathematical language of AI. The analysis traces the evolution of terminology, from its normative, concept-centric origins to contemporary challenges such as the concept-context gap, multilingual conceptual modeling and enriching terminologies with contextual relations. The article then highlights how AI and LLM are revolutionizing terminology work, by proposing the construction of relations between terms around prototypical contexts. This innovative approach aims to infuse a more deterministic understanding into human-AI interactions, guiding the latter to generate responses more aligned with human intent and context. Advocating a re-evaluation of current methodologies to interact better with AI's algorithmic mathematical interpretation of natural language, the article envisions a future in which terminology science and AI co-create a framework for improving multilingual knowledge exchange and understanding.

Experimental simulation of quantum superchannels

Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe quantum evolution, while in recent years quantum superchannels have emerged as the substantial extension. Superchannels capture effects of quantum memory and non-Markovianality more precisely, and have found broad applications in universal models, algorithm, metrology, discrimination tasks, as examples. Here, we report an experimental simulation of qubit superchannels in a nuclear magnetic resonance (NMR) system with high accuracy, based on a recently developed quantum algorithm for superchannel simulation. Our algorithm applies to arbitrary target superchannels, and our experiment shows the high quality of NMR simulators for near-term usage. Our approach can also be adapted to other experimental systems and demonstrates prospects for more applications of superchannels.

Unique and combined effects of quantitative mathematical language and numeracy instruction within a picture book intervention: A registered report.

Unique and combined effects of quantitative mathematical language and numeracy instruction within a picture book intervention: A registered report.

Describing growing tissues in the language of thermodynamics

New analysis shows how key properties of biological tissues can be accurately described in the mathematical language of Onsager’s variational principle, widely used to describe continually changing systems in thermodynamics.