Mathematical Language Research Articles

ChatGPT on the Mathematical Language in Physics

This is my first attempt to communicate with the ChatGPT on the mathematical language in physics. Chat GPT during our half hour conversation reacted promptly to explain to me the Heraclitus quote “Nature loves to hide”. Chat GPT communicated many examples from the history of physics and astronomy on the application of the mathematical language and the continuous development of those mathematical models to describe the true events in Nature. In some situations, it is very difficult to choose the correct mathematical description – a possible danger of the “mathematical camouflage” protecting the secrets of Nature. Chat GPT recommended continuing further research even for cases where the mathematical language describes the observed events on a very high confidence level.

ChatGPT and other AIs: Personal relief and limitations among mathematics-oriented learners

Mathematics utilizes symbolic language, logics, relationships, and numerical connections that made it challenging for students to learn and develop their computational skills. Recently, artificial intelligence emerged as a supplement tool for education and learning because of its ability to detect relationships and logics. Academic institutions are looking on how to implement AI-assisted learning specifically for mathematics to aid in increasing the quantitative competence of students. This study analyzed the relief and limitations of AI chat models in learning among mathematics-oriented students in higher education. Fifteen students participated in this study from mathematics-oriented courses e.g., engineering, statistics, and education. Interviews were conducted on how students used AI chat models to assist in learning mathematical concepts and methods. Narratives indicated that AI chat models like ChatGPT and Bard were capable of accurately responding to chat prompts in problem solving, proving, and explanations. It was prominent that these AI models understood the mathematical language and use of symbols for integration, derivatives, limit, fractions, exponentials, and intervals. At some instances, AI models could give inaccurate results or incorrect methods for solving; they also sometimes give correct answers on second run of chat prompts after these mistakes. These results had promising implications in education as these accessible AI models could reinforce the firsthand learning of mathematical foundations. This preliminary study offered important usability of AI models in mathematics in assisting students and monitoring their learning progress.

Multiple-Criteria Decision-Making (MCDM) techniques to study the behavior of dendrimers using topological indices.

Topological indices provide a mathematical language for capturing molecular structure, symmetry, and predicting properties. Dendrimers are microscopic bilaterally symmetrical molecules with a well-defined homogeneous nanoparticles structure, often consisting of a symmetric center, inner shell, and outer shell. In this work, first we compute some degree-based topological indices of Porphyrin (DnPn),Poly (Propyl) Ether Imine(PETIM), Zinc porphyrin (DPZn), and Polyamidoamine (PAMAM) dendrimers. Then, we use multi-criteria decision making (MCDM) techniques to establish the weighted evaluation of dendrimer classes based on certain topological indices. For weighted analysis we correlate the properties of benzene derivatives with topological invariants. Finally, based on the multi-criteria decision making techniques namely TOPSIS, SAW and MOORA method, we have ranked the dendrimer structures based on their properties.

Ethnomathematics of Lahbako Dance Movement In The Perspective Of Mathematical Literacy Of Geometry Concept

Movement in a dance is a visual symbol full of meaning conveyed to be accepted by dance lovers from the whole dance performed. The selection of dance movements is related to the mathematical concept of illustrating its meaning (ethnomathematics). In addition, there is a mathematical literacy process of geometry concepts revealed in dance movements. This becomes a meaningful symbol that becomes a wealth of dance movements that are increasingly interesting to present. The purpose of this research is to identify the ethnomathematics of lahbako dance in the perspective of mathematical literacy of geometry concepts. qualitative research with a descriptive approach to explain the data and its discussion. Data collection methods of interviews, observation, and documentation with data validity test source triangulation. Subjects 2 people from Arutala dance studio and Hastarini. The results obtained are dance movements that come from different habits and interpretations of dancers but the actual meaning of the movements is the same. Ethnomathematics in lahbako dance successfully illustrates the meaning of the movements conveyed in lahbako dance through hand, finger, foot, and body movements that modify into lines, acute and obtuse angles, and triangular and rectangular fields. The mathematical literacy perspective of the geometric concepts of lines, angles, and fields is visualized conceptually, the application of real contexts of daily life, geometric thinking, and the delivery of mathematical language helps in illustrating the message conveyed in a lahbako dance, namely the activities of tobacco farmers. Further research recommendations for dance movements that jump or repeatedly back and forth and the count used by dancers in each movement.

Topological defect lines in two dimensional fermionic CFTs

We consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of TDLs, called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing feature is an extra one-dimensional Majorana fermion living on the worldline of the TDLs. The properties of TDLs in fermionic CFTs are captured in the mathematical language of the super fusion category. We propose a classification of the rank-2 super fusion categories generalizing the \mathbb{Z}_8ℤ8 classification for the anomalies of \mathbb{Z}_2ℤ2 symmetries. We explicitly solve the F-moves for all the nontrivial categories, and derive the corresponding spin selection rules that constrain the spectrum of the defect operators. We find the full set of TDLs in the standard fermionic minimal models and a partial set of TDLs in the two exceptional models, which give CFT realizations to the rank-2 super fusion categories. Finally, we discuss a constraint on the renormalization group flow that preserves a q-type TDL.

Can mathematics-unrelated reading intervention improve children’s mathematical performance?

This study aims to examine whether a maths-unrelated reading intervention can improve children’s mathematical performance and to compare the effects of maths-related and maths-unrelated reading interventions. Furthermore, this study examines whether the effects of reading interventions are moderated by individual differences, including gender, pre-test maths performance and general cognitive ability. One hundred thirty-four second-grade Chinese children were recruited into three different groups. In the control group, the children received business as usual teaching, while in the two experimental groups, the children received a maths-related or maths-unrelated reading intervention. The results showed that the maths-unrelated reading intervention could significantly improve children’s mathematical performance, and the beneficial effect did not differ from the maths-related intervention. Moreover, the effects of the two reading interventions were not moderated by children’s individual differences. These findings support the function hypothesis of language for mathematics.

Middle Level Mathematics Teachers’ Problems on Linear Relationships in a Semi-Structured Problem Posing Situation

This study examines in-service mathematics teachers’ problems on linear relationships that they posed in a semi-structured problem posing situation with a group and their ideas about the factors affecting the quality of the posed problems. Eight groups of 24 teachers participated in the study. Teachers' problems, written group work, and class discussion all served as sources of data for this study. The data was mainly analyzed through qualitative methods. The results demonstrate that seven groups’ problems were invalid because the problems did not meet the given conditions in the problem posing task. Their problems mostly lacked key mathematical concepts related to linear graphs, such as linearity, slopes, and y-intercepts. In class discussion, teachers dealt with the following factors that affect the quality of posed problems: misunderstanding of the problem posing situation, making inappropriate mathematical decisions, and using improper mathematical language. This study revealed that more content-focused practices are necessary to support teachers’ problem posing skills.

An Examination of Mathematics Teachers’ Mathematical Language Usage

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

Examining YouTube Videos with Counting and Numbers Content for Preschool Children

Children, who are introduced to technology as soon as they are born, have access to internet-based videos as young as one year old. These colourful, animated cartoon/animation content supported by songs have turned into informal learning tools for children. Some of these videos, which families do not hesitate to present as educational content, are math videos. These videos reach millions of views. These videos with mathematical content prepared for children, mostly shared with the label of children's songs, are the subject of this study. In this study, we focused on Turkish number and counting videos from the open access YouTube content provider. Document analysis method was used in this study. As a result of the analysis, it was observed that only a few videos were adequate in terms of mathematical language, content and number teaching, and almost all of the other videos included incorrect or inaccurate mathematical representations. While counting, it was observed that number symbols were used as "ordinal numbers". In addition, it was observed that there were scenes where the amount counted and the number did not match. It was thought that these situations could lead to false learning. Based on all these findings, it can be concluded that the mathematical language used in YouTube video content is weak.

A Digital Storytelling Application for Resolving Errors in the Use of Mathematical Field Language by Eighth-Grade Students

Bu araştırma, sekizinci sınıf öğrencilerinin matematiksel alan dilini kullanmalarına ilişkin hatalarının dijital öykülerle giderilmesini amaçlamaktadır. Araştırma, bir devlet ortaokulunda sekizinci sınıfta öğrenim gören toplam 24 öğrenci ile yürütülmüştür. Araştırmada eylem araştırması esas alınmıştır. Veri toplama aracı olarak, Matematiksel Alan Bilgisini Tespit Etme Formları ve Öğrenci Görüşme Formu kullanılmıştır. Formların analizinde, betimsel ve içerik analiz teknikleri kullanılmıştır. Araştırmanın sonunda öğrencilerin çoğunun uygulama öncesinde matematiksel alan dilini yanlış kullandıkları özellikle de ayrıt-kenar, açı-açı ölçüsü, doğru-doğru parçası-ışın, cisim-şekil, eş-eşitlik arasındaki farkı bilmedikleri ya da bu farkı uygun matematiksel dille vurgulamaya dikkat etmedikleri görülmüştür. Uygulama sonrasında ise öğrencilerin çoğu bu hatalarının farkına vararak matematiksel alan dilini doğru kullanabilmişlerdir. Görüşmelere yönelik sonuçlar incelendiğinde de öğrencilerin çoğunun uygulamada kullanılan dijital öyküleri beğendikleri ve öğretici buldukları ortaya çıkmıştır.

Optimizing a Multi Period Deterministic Inventory Routing Problem in Agriculture Industries

This paper develops a solving model for multi-period deterministic inventory routing problem (MP-DIRP) in supply chain focus on agriculture industries. The issue is how to improve the perishable product delivery process from a distribution centre (DC) to a collection of customers over a planning horizon. This paper proposed a model to achieve optimization in terms of costs respectively. The transportation problem is solved by using a simulation technique and developed using an algebraic modelling language which is known as a mathematical programming language (AMPL) to find an optimal solution within the period. The route for a distribution centre (DC) is set up by a supplier depending on the number of products assigned to each customer, which contributes to determining the best inventory routing problem (IRP) for each period. As a result, by applying the transportation model developed in this study, it is expected that the industries can achieve optimization by minimizing their total inventory and transportation costs.

GeoGebra Software on the Mathematical Language Developments and Self-Efficacy Perceptions of Students

The aim of the study is to investigate the effects of using GeoGebra in teaching functions on mathematical language development and self-efficacy perceptions of tenth grade students. The study, which used the action research method, changes in participants’ language structures were examined with the worksheets, mathematical language questions, researcher’s logs and participant’s logs; participants' self-efficacy perceptions were also examined with the self-efficacy perception scale. The ability of the participants to switch between the sub-dimensions of mathematical language was observed. The research showed that GeoGebra-Assisted Education improved the participants’ perceptions of mathematical self-efficacy and positively affected their mathematical language skills. Since the effective use of mathematical language is an important component of mathematics lessons, the results present important findings.

Implications from a Modelling based Flipped Mathematics Course

The present study investigated the effect of the flipped classroom model, which was practiced in an undergraduate mathematics class, on pre-service primary school teachers’ ability to solve problems related to real life and modelling. This study was designed as an action research study exploring the implementation of a new teaching technique. The participants were 16 pre-service teachers who voluntarily took part in the study. The implementation period, which lasted for five weeks, included the following topics: ordered pairs, Cartesian product, relation and its characteristics, the concept of function, types of functions, and linear relation. The data in this study consisted of worksheets that had problem-solving processes, video records of classroom practices, participant journals, and field notes taken by the researcher. The data were analyzed through content analysis. It was observed that the flipped classroom model in the study enabled students to develop their mathematics language, conceptual knowledge, and the use of multiple representations by providing them with an opportunity to work on modelling and real-life problems. This model allowed students to take responsibility for their learning and also provided the teacher with an opportunity to prevent mistakes and misconceptions of students. In addition, it was observed in the data collected from classroom practices and student journals that student–student and student–teacher interactions developed as a result of the classes taught in the flipped classroom model.

Comparative study of means of mathematical communication in Japan, Laos, and Thailand

This comparative study analyzed the similarities and differences in the mathematical communication used by teachers and primary school students in Japanese, Lao, and Thai mathematics classrooms. It adopted a qualitative research design, and the targets were teachers and students in Grades 1 - 6 at a selected school in each of the three countries. The data were collected from one classroom at each grade level from the three schools, so eighteen classrooms were involved in the study. The research tools included video recorders, photo cameras, and a field notes form. The data were analyzed by employing the analytical descriptive method based on Pirie's conceptual framework of the means of mathematical communication (1998). The findings revealed that the means of mathematical communication in the three countries were similar in their use of ordinary, mathematical, verbal, and symbolic language—differences in the means of mathematical communication related to how varied the learning materials were. The Japanese classrooms used the most varied means of mathematical communication, demonstrating all six means, while the Thai classrooms used only 5, and the Lao PDR classrooms used only 4. The Japanese classrooms were shown to be focused on the students' diverse self-solution concepts, while some of the Thai and Lao PDR classrooms were based on question-answer interactions between the teachers and students.

Addressing Language Diversity in Early Years Mathematics: Proposed Classroom Practices through a Live Brief Assessment

There is a growing emphasis on the role of language in teaching and learning mathematics, most significantly in classrooms with increased language diversity. Consequently, teachers face considerable challenges in accommodating diverse needs and must employ strategies to support all students. It is, therefore, crucial to provide prospective teachers with opportunities to enhance their pedagogical approaches while raising their awareness of the relationship between language and mathematics. In this respect, Live Brief assessments in Higher Education, which involve students working on authentic projects/tasks from a school, may be a promising avenue. This research draws on the 19 Live Brief group presentations prepared by a total of 118 Year 1 prospective primary school teachers, specifically focusing on the language-related challenges faced by a local school in early years mathematics. The data encompassed prospective teachers’ proposed practices, including one-to-one, small group and whole class activities, that aimed to address language diversity. Data analysis was informed by Moschkovich’s three perspectives on the relation between language and teaching and learning mathematics, namely lexicon, register and situated-sociocultural perspectives. While a lexicon perspective was commonly evident in the activities, the manifestation of a situated socio-cultural perspective mainly in the one–to-one activities is noteworthy, given its social and discursive nature. Three themes encapsulated a range of practices suggested in the findings: explicit vocabulary teaching, different strategies of scaffolding and utilising multi-sensory approaches. While the lexicon and register perspectives were commonly evident, the situated socio-cultural perspective was much less commonly manifested in the practices. We offer implications to initial teacher education curriculum, future research and policies about teaching and learning mathematics.

Facing and challenging language ideologies towards a more inclusive understanding of language in mathematics education research—the case of sign languages

Research on language in mathematics education is largely dominated by a ‘normalcy’ of spoken languages. This modal hegemony does not only affect a whole group of learners in failing to provide access that is epistemologically equitable—those using sign language as their preferred mode for mathematical discourse—it also obscures our view on the roles language can play in mathematical thinking and learning. As a field, we can only win from seeking to understand Deaf learners of mathematics beyond a disability, as learners of mathematics with a specific linguistic background that influences mathematical thinking and learning in peculiar ways. In this contribution, I suggest a shift in mindset towards a more inclusive view on language in mathematics education research and practice. I propose basic principles to inform a perspective for reconsidering the role of language in mathematics thinking and learning, inspired by work of philosopher Francois Jullien. This perspective counters a perspective that merely integrates sign language into existing research and instead searches for dialogue between linguistic modalities in learning mathematics, looking beyond language as spoken or written. This approach will be illustrated by the case of the modal affordance of iconicity foregrounded in signed mathematical discourse, its role in Deaf students’ mathematics thinking and learning, and how this can inform existing research and practice dealing with language in mathematics education.

Mathematical benefits of a language-friendly pedagogical tool: a praxeological analysis of teachers’ perceptions and practices

ABSTRACT In this paper, we report on data from 40 middle and secondary school mathematics teachers and teacher candidates as they begin to articulate the intersection of language-friendly pedagogy, mathematics teaching, and a multilingual technological tool by way of a two-hour introductory workshop. We use an Anthropological Theory of the Didactic which recognises that mathematics instruction and language instruction are done differently under distinct institutional conditions (curriculum, culture, language, etc.) to analyse our data. Our findings suggest that teachers’ beliefs and perspectives regarding their multilingual students guide their choices about how to use a powerful digital multilingual platform to either remediate what they perceive as deficits in their students or leverage the assets of multilingual learners.

Finnish pre-service teachers’ understandings of the role of language(s) in learning mathematics

ABSTRACT We examined Finnish pre-service primary school teachers’ understandings of the role of language(s) in learning mathematics and how these understandings developed during a period of teaching practice. We also examined how the participants experienced the usefulness of the ready-made multilingual digital material Binogi and how the teaching practice period influenced their thoughts on multilingual pedagogies. Our results indicate that the teacher training period increased awareness of linguistic challenges and of the importance of students’ L1s in learning. However, some participants’ views reflected monolingual ideologies, especially regarding the conditional use of L1s. Regarding linguistic support, the participants reported using visual supports and explaining vocabulary and structures. Although many participants perceived Binogi as beneficial and motivating, less than half used it. Some participants emphasised that the practice period reinforced their understanding of the importance of multilingual pedagogies. It is important to critically reflect on the language policies and practices of Finnish teacher education and support the dialogue between research and practice regarding a shared understanding of valuing linguistic diversity in teacher education.

Development of Multimodal Mathematics and Indonesian Language Books for Elementary School Learning in Bandung Barat

This study aims to (1) develop multimodal mathematics and Indonesian language books for learning in elementary schools, (2) determine the feasibility level of multimodal mathematics and Indonesian books for learning in elementary schools. This study used the Borg and Gall development model research method which consisted of (1) preliminary study, (2) initial product development, (3) expert validation and product revision, (4) limited field trials and product revision, (5) test try the field and the final product. The resulting product is an Android-based learning media in the form of multimodal books for learning mathematics and Indonesian in elementary schools with the subject, integer arithmetic operations, mixed integer arithmetic operations, determining mixed arithmetic operations with whole numbers, looking for main ideas and writing poetry in elementary schools. Based on the formulation of the problem, research results, and discussion, the results of this study can be concluded that (1) the development of Multimodal Book considered several product characteristics, namely, (a) students play an active role, (b) precise and consistent language, (c) music selection, background, buttons, types, colors, attractive letters, (d) animations and images support elementary school students' understanding, (2) multimodal Mathematics and Indonesian Language Books for Elementary School Learning are appropriate to use and can improve the learning of Mathematics and Indonesian Language for Elementary School students in West Bandung Regency.

High School Students' Mathematical Communication Skills Through Ethnomatematics-Based Realistic Mathematics Learning Approaches in Geometry Transformation Materials

Mathematical communication ability is the ability of students to use mathematics as a form of communication (the language of mathematics) and student's ability to convey the mathematics they learn as the content of the message to be conveyed. This study aims to describe the Mathematical Communication Skills of High School Students Through an Ethnomatematics-Based Realistic Mathematics Learning Approach on Geometry Transformation Materials. This research is a type of descriptive research with a qualitative approach. The selection of subjects used in this study used an interpersonal intelligence questionnaire, which involved all students of class XI IIS 3 State Islamic High School 1 Pasuruan. Based on the interpersonal intelligence questionnaire scores, three subjects were selected with high, medium, and low levels of interpersonal intelligence. Then, these three subjects will examine the student's ability to draw the correct solution, explain the answer systematically, and construct a problem into a mathematical model. The results of this study indicate that the mathematical communication skills of students with high, medium, and low levels of interpersonal intelligence have many differences in problem-solving on the questions given