Mathematical Ideas Research Articles

A Capstone Course in Public Writing About Mathematics

This article describes a major capstone course centered on public writing, whose underlying pedagogical principles are transferable to courses across the curriculum. The course aims to strengthen students' mathematical agency and their ability to effectively communicate mathematical ideas. In its unique format, students repeatedly take turns writing articles aimed at a variety of audiences and editing peers' work. Student reflections and survey data demonstrate that this collaborative, active format builds students' confidence in math and writing and their sense of belonging in the mathematical community. The last section offers suggestions for getting started with implementing aspects of this pedagogy.

Literature Review on the Teaching Engineering Mathematics: Issues and Solutions for Student Engagement

Engineering mathematics is essential for fostering analytical and problem-solving abilities in engineering education, especially in Malaysia, where it plays a crucial role in the nation's technical and industrial ambitions. Nevertheless, students encounter substantial obstacles such as the need to strike a balance between grasping abstract concepts and acquiring practical skills, surmounting feelings of apprehension about mathematics, actively participating in crowded classrooms, and adapting to the demands of online education and self-directed study. This paper examines the difficulties and suggests remedies, with a focus on incorporating active learning methods, creating supportive learning environments, and using digital resources to improve student involvement and understanding. The study emphasizes the significance of visualizing abstract mathematical ideas and establishing connections with practical engineering applications. These strategies are important to maintain the sustainable development of engineering education. By using these strategies, instructors may enhance pupils' readiness for prosperous engineering jobs, guaranteeing that they grasp mathematical ideas, and possess the ability to apply them proficiently in real-world situations.

The tasty world of irrational numbers – explorative mathematical visualizations generated by AI image models

In this paper, images containing mathematical ideas that were generated by different image-generating AI models (DALL-E 2, Leonardo.Ai, and Midjourney) are comparatively interpreted from a mathematics aesthetical perspective. Our exploratory study aimed to scrutinize how AI image models visualize abstract mathematical ideas and whether this imagination holds any potential for use in the context of learning mathematics. Two different mathematics-containing prompts, representing different aspects of mathematics, were used as input. Our results show that based on our examples, currently, Midjourney generates the most detailed outcome that can be used as an initial point for discussing mathematical ideas with students in the classroom.

Design and implementation in power-efficient and thermal conductivity of vedic processor for embedded applications

An embedded system that handles critical applications requires power economy, performance and thermal management, and an efficient Vedic processor with highly efficienct thermal conductivity. The proposed contemporary processor architecture has been designed to use Vedic mathematics and elaborate power and thermal optimization approaches to formulate an Arithmetic Logic Unit (ALU). This ALU is based on Vedic Sutras to enable quick computation, high precision floating point operations, and low power consumption. Since thermal management leads to energy loss in the form of heat, the embedded processor’s thermal conductivity is enhanced using novel materials and unique ways of heat dissipation. This improves performance as well as power efficiency. The proposed approach uses extensive simulation thermal analysis by EDA tools to build an optimised embedded processor that consumes 35% less power, has 40% high thermal conductivity, is 25% faster, and utilizes 15% less area when compared to conventional embedded processors. This paper helps in furthering embedded systems research by showing how old mathematical ideas can be used in a new engineering approach to solve current technology issues. The suggested novel embedded system is more efficient and thermally resistant for IOT, mobile computing, and industrial control systems.

Ethno-Science, Technology, Engineering, and Mathematics (EthnoSTEM) Ideas in the Sama Mat-Weaving

Mat weaving has been culturally and economically significant among the Sama ethnolinguistic group since time immemorial. This study sought to find concepts and processes of ethnoscience, ethnotechnology, ethnoengineering, and ethnomathematics (ethnoSTEM) present in weaving tepo, a hand-woven mat of the Sama, made from indigenously processed leaves of pandan or screw pine (Pandanus tectorius). To determine ethnoSTEM ideas, concepts, and processes in tepo weaving, an ethnography was conducted involving five female mat weavers in a coastal village in Tawi-Tawi’s major producer of tepo, the Municipality of Tandubas. Data were gathered primarily through observations during a monthlong community immersion. Results revealed that Ethnotechnology tools were in the form of bolo, pandan-presser, pandan slitter, traditional stove, bamboo scalp scratcher, and other local cooking tools, with each tool exhibiting unique characteristics and functions needed for weaving. Ethnoengineering was evident in preparing pandan strips to create, bleach, and dye pandan strips for weaving and fastening the tepo. Ethnomathematics comprised primitive length measurement, arithmetic calculations, ratio and proportion, linear and quadratic equations, sinusoidal functions, basic geometric concepts, circles, symmetries, and isometries. Ethnoscience was observed in the processes determining the dyeability of pandan strips, as well as in the procedures employed in its softening and bleaching. It is concluded that the concepts and ideas of ethnoSTEM found in Sama weaving of tepo are loaded with scientific affluence that should be preserved to preclude them from fading to oblivion.

PRE-SERVICE MATHEMATICS TEACHER’S ABILITY IN DESIGNING MATHEMATICAL TASK: AN ANALYSIS OF LESSON PLANS

Mathematical tasks have an essential role in the mathematics learning process. Well-designed mathematical tasks will provide a learning opportunity for students to develop their mathematical ideas. The ability of pre-service mathematics teachers to design mathematical tasks during their academic studies significantly influences how they teach in actual learning. One of the ways to investigate pre-service mathematics teachers' ability to design tasks is by analyzing the tasks in the lesson plans they proposed. This study aims to scrutinize the level of cognitive demand for mathematics tasks designed by pre-service mathematics teachers in their lesson plans to get a thorough understanding of their ability to design tasks. This descriptive qualitative research analyzed mathematical tasks in 25 lesson plans proposed by pre-service mathematics teachers using the framework developed by Stein and Smith (1998). The results of this study show that most pre-service teachers designed tasks with a lower cognitive demand classification with types of memorization and procedures without connections. The mathematical tasks designed by pre-service mathematics teachers also have yet to lead to argumentation and the development of mathematical ideas through exploration or doing mathematics. Thus, based on the findings in this study, designing mathematics tasks with the potential to promote students' mathematical understanding remains a challenge for pre-service mathematics teachers. This article discusses and presents the implications of research results and recommendations for designing mathematical tasks.

ANALISIS KEMAMPUAN KOMUNIKASI MATEMATIK MAHASISWA PADA PEMBELAJARAN PROBLEM BASED LEARNING DITINJAU DARI GAYA BELAJAR

The purpose of this study is to describe students' mathematical communication skills in Problem Based Learning viewed from students' learning styles. The type of research used is qualitative research supported by observation data, questionnaires and interviews. Validity testing is the credibility test, transferability, dependability, and confirmability. The results of the study indicate that students' mathematical communication skills viewed from learning styles include visual learning styles (30.4%), auditory (34.8%), and kinesthetic (26.1%) and visual-kinesthetic (8.7%). Mathematical ability indicators on a scale of 0-10 include 1) The ability to express ideas orally, in writing and demonstrate them and describe them visually (8.78), 2) The ability to understand, interpret, and evaluate mathematical ideas orally, in writing and demonstrate them and describe them visually (8.21), 3) The ability to use mathematical terms, notations, and their structures to present ideas describing relationships with situation models (5.30). The appropriate learning style is the key to student success in learning. The use of learning styles that are limited to only one form can cause an imbalance in absorbing information. Therefore, in learning activities, students need to be helped and directed to recognize the learning style that suits them so that learning objectives can be achieved effectively.

Analysis of students' mathematical communication skills in terms of learning styles

The purpose of this research is to obtain a description of the mathematical communication skills in terms of the learning styles of Grade XI TKR 3 students at SMK Negeri 1 Tanara for the 2023-2024 academic year. This research is qualitative in nature. Six subjects were selected, representing each learning style, from Grade XI TKR 3 students at SMK Negeri 1 Tanara, Tanara District, Serang Regency. The data collection techniques used were observation, interviews, documentation, and tests based on the indicators of mathematical communication skills, namely: (1) the ability to express mathematical symbols through everyday events, (2) the ability to determine the solution set by relating real objects to mathematical ideas, (3) the ability to explain mathematical problems related to elimination, (4) the ability to analyze mathematical problems related to substitution, and (5) the ability to evaluate mathematical thinking and strategies used in problems according to the observed object. The results showed that (1) subjects with a visual learning style have good mathematical concept comprehension on indicators 1, 2, 3, 4, and 5; (2) subjects with an auditory learning style have good mathematical communication on indicators 1, 2, and 5, but performed poorly on indicators 3 and 4; and (3) subjects with a kinesthetic learning style have good mathematical communication skills on indicators 1 and 2, but performed poorly on indicators 3, 4, and 5.

Conducting research on teacher professional development in partnership with educators: promises, tensions and opportunities

ABSTRACT This study aims to document how a research-practice partnership designed and carried out joint work between researchers and educators to support teacher instructional improvement. A district-wide research-based teacher professional program, grounded in research on student development of mathematical ideas, was adapted to the assets and needs of one elementary school. The primary source of data were field notes of meetings of the school instructional improvement team, involving researchers, the principal, and teacher leaders, and focused on the co-design of school-based settings for instructional support. A framework outlining key conditions of research-practice partnership success was used as an analytical tool to examine partnership design elements that support joint work towards both practice and research goals, partner practices, processes, and activities as they unfolded, and methodological tensions and opportunities. Findings highlight how centring relationships, shared goals, and relevance to practice supported researchers in gaining deep understanding of the local context and of the complexity involved in creating settings that facilitate instructional improvement within school systems. They also underscore the need for vulnerability and flexibility in researcher involvement. Future directions include supplementing data sources to examine co-design sessions discourse and through multiple perspectives and extending analyses to subsequent years of the partnership.

БАШТАЛГЫЧ МЕКТЕПТЕ ЖАҢЫ ПРЕДМЕТТИК СТАНДАРТТЫН НЕГИЗИНДЕ МАТЕМАТИКАНЫ ОКУТУУГА СУНУШТАЛГАН МАТЕРИАЛДАР

This article discusses the main goals of teaching mathematics in elementary school, the implementation of learning goals and objectives and subject competencies presented in the standard, the content bands specified in the subject standard of elementary school, the didactic development of scientific mathematical material included in the subject bands of mathematics, taking into account the age characteristics of younger students, the order of educational materials and ideas of mathematics, established in the primary school subject standard, we are talking about methods. The student will have to accurately determine the correct answer to the task among several answers offered in one type of test. To do this, the student must have a certain level of knowledge and skills, such as analysis, comparison and analogy. And in some tests, it is necessary for the child to have a certain level of choosing the appropriate "yes" and "no" answers.

KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN SOAL OLIMPIADE TINGKAT SMP

Mathematical representation abilities can be in the form of expressions, ideas or mathematical ideas, which originate from students' thoughts that emerge during learning in an effort to find mathematical solutions. There are three indicators of mathematical representation ability, namely verbal, pictorial and symbolic. The process of developing students' potential and thinking can be done by holding mathematics competitions or olympiads. The approach used in this research is qualitative with descriptive methods. Purposive sampling technique was used in this research to select samples with certain considerations. The aim of this research is to describe students' mathematical representation abilities in solving Olympiad questions. This research used a sample of 3 students each representing each high, medium and low representation ability group. Based on the results of research on visual representation abilities, some students already have high abilities, although there are some who are still medium or low. Meanwhile, in symbolic ability, there are many students whose abilities are high and only a few whose abilities are medium or low. For verbal representation, most students already have high abilities and only a few students have medium or low abilities

Applications of neural networking in Eyring-Powell nanofluid dynamics on a rotating surface in a porous medium

One of the fundamental aspects of solving difficult and nonlinear mathematical ideas is the use of Artificial Neural Networks due to their exceptional efficiency in handling such problems. In many complex fields such as computational fluid system, biological computation, and biotechnology, a distinct computing structure is provided by Artificial Neural Networks, which is extremely valuable. The main purpose of this article is to dig out the abilities of the Levenberg-Marquardt technique using back-propagation artificial neural networks regarding the fluid mechanics and the heat transport assessment in nanoparticles. This interdisciplinary field explores heat and mass transfer through objects and fluids, and their impacts on temperature as well as concentration distributions. With the help of mathematical modelling and numerical solution methodologies, researchers can simulate and analyze these processes. The present analysis communicates the Eyring-Powell fluid flow caused by a rotating disk placed in the horizontal direction. The fluid flow over a rotating disk through non-linear partial differential equations is modeled. After converting the partial differential equations to ordinary ones, they are tackled numerically through shooting technique. The Levenberg-Marquardt algorithm using back-propagation artificial neural networks technique is used with reference datasets, having 70 % training, 15 % testing, and 15 % to validation. The method is validated with the help of mean squared error, error histogram and comprehensive regression analysis. These figures show the accuracy of the proposed method for solving nonlinear problems. Flow features such as velocity, temperature as well as the concentration profiles are exemplified quantitatively and have been graphically discussed. Velocity of the fluid decreases for porosity and increases for fluid parameter while temperature increases for thermophoresis and Brownian motion parameters. Consistency is shown by getting a minimum absolute error approaching zero, showing the strength of the proposed approach.

The Behavior of High Scanning Electron Voltage Electron in SEM Due to Mirror Effect

To determine the factors influencing the electron scattering process in a scanning electron microscope caused by the electron mirror, a set of physical and mathematical ideas were used. These equations, which relate the scattering of the input electron with the surface potential energy of the dielectric material under examination using a matched beam ion microscope and scanning electrons, are based on simplified engineering mathematics. After five minutes of charging the insulator to saturation with an acceleration voltage of 30 kV, the accumulated charge was 0.3 nC, from which the surface voltage across the working distance (WD = 15 mm) was determined. The scattering angle (β) was found to be inversely proportional to the incidence angle (θ) in the second stage, when scanning voltages (Vsc=2, 4, and 6 kV) were employed. This was because the angle between the incident and scattered electron (2

Global Realism with Bipolar Strings: From Bell Test to Real-World Causal-Logical Quantum Gravity and Brain-Universe Similarity for Entangled Machine Thinking and Imagination

Following Einstein’s prediction that “Physics constitutes a logical system of thought” and “Nature is the realization of the simplest conceivable mathematical ideas”, this topical review outlines a formal extension of local realism limited by the speed of light to global realism with bipolar strings (GRBS) that unifies the principle of locality with quantum nonlocality. The related literature is critically reviewed to justify GRBS which is shown as a necessary and inevitable consequence of the Bell test and an equilibrium-based axiomatization of physics and quantum information science for brain–universe similarity and human-level intelligence. With definable causality in regularity and mind–light–matter unity for quantum superposition/entanglement, bipolar universal modus ponens (BUMP) in GRBS makes quantum emergence and submergence of spacetime logically ubiquitous in both the physical and mental worlds—an unexpected but long-sought simplification of quantum gravity with complete background independence. It is shown that GRBS forms a basis for quantum intelligence (QI)—a spacetime transcendent, quantum–digital compatible, analytical quantum computing paradigm where bipolar strings lead to bipolar entropy as a nonlinear bipolar dynamic and set–theoretic unification of order and disorder as well as linearity and nonlinearity for energy/information conservation, regeneration, and degeneration toward quantum cognition and quantum biology (QCQB) as well as information-conservational blackhole keypad compression and big bang data recovery. Subsequently, GRBS is justified as a real-world quantum gravity (RWQG) theory—a bipolar relativistic causal–logical reconceptualization and unification of string theory, loop quantum gravity, and M-theory—the three roads to quantum gravity. Based on GRBS, the following is posited: (1) life is a living bipolar superstring regulated by bipolar entropy; (2) thinking with consciousness and memory growth as a prerequisite for human-level intelligence is fundamentally mind–light–matter unitary QI logically equivalent to quantum emergence (entanglement) and submergence (collapse) of spacetime. These two posits lead to a positive answer to the question “If AI machine cannot think, can QI machine think?”. Causal–logical brain modeling (CLBM) for entangled machine thinking and imagination (EMTI) is proposed and graphically illustrated. The testability and falsifiability of GRBS are discussed.

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.

Teachers’ practice of mathematical representation, and its relationship to the preschooler’s utilization of it in expressing mathematical ideas

هدفت الدراسة إلى الكشف عن العلاقة بين مستوى ممارسة المعلمات لعملية التمثيل الرياضي وتوظيف طفل ما قبل المدرسة له في التعبير عن الأفكار الرياضية. اتّبعت الدراسة المنهج الوصفي الارتباطي، واشتملت الأدوات على بطاقتي ملاحظة مغلقة لكل من المعلمة والطفل. تم اختيار العينة بطريقة قصدية، وتكونت من (15) معلمة في مرحلة ما قبل المدرسة، يعملن في مدارس رياض الأطفال التي تطبق برنامج رياضيات خلال البرنامج اليومي في مدينة الأحساء و(120) طفل من الأطفال في فصولهن، وتم معالجة البيانات إحصائيًا باستخدام البرنامج (SPSS)، خلصت النتائج إلى وجود علاقة ارتباطية موجبة دالة إحصائيًا بين درجات ممارسات المعلمات للتمثيل الرياضي وتوظيف الطفل له في التعبير عن الأفكار الرياضية، كما أظهرت أنّ مستوى ممارسات المعلمات لعملية التمثيل الرياضي جاء بمستوى منخفض، ومستوى توظيف الطفل لعملية التمثيل الرياضي في التعبير عن أفكاره الرياضية جاء بمستوى منخفض. وفي ضوء النتائج توصي الدراسة بتوفير برامج تطوير مهني لمعلمات الطفولة المبكرة تتضمن طرق استخدام التمثيلات الرياضية في تقديم وشرح مفاهيم الرياضيات، وتوفير الوقت الكافي والأنشطة الملائمة نمائيًا لجميع الأطفال للانخراط في أنشطة الرياضيات عامةً والتمثيل الرياضي خاصة.

Transforming learning opportunities in linguistically diverse secondary classrooms through promoting discussions: results of an intervention

ABSTRACT This article presents results from a design experiment intended to develop students’ understanding of linear functions and rates of change in a linguistically diverse ninth grade classroom. The intervention focused on fostering classroom discussions. Students’ pre-post assessment gains were higher in the redesigned classrooms than in the pre-intervention classrooms. Additionally, multilingual students who were classified as English Learners (ELs) made larger gains than their non-EL peers, and the majority of student learning gains occurred on conceptually-focused items. Analysis of classroom talk showed an increase in high demand moves from the teacher and an increase in the level of teacher responsiveness to students’ mathematical ideas. We discuss implications for future research and design efforts to enhance student learning in multilingual mathematics classrooms.

Overt and Covert Participation in an Argumentative whole-class Discussion: Spread of Ideas about Quadratic Functions

AbstractMathematical ideas are developed and spread during argumentative whole class discussions between a teacher and her students. The goal of the current study is to characterize how ideas about quadratic functions emerge and are spread during a whole-class discussion among ninth graders. To this end, we recorded both discussions between pairs of students and whole-class discussions led by the teacher. We used the approach of documenting collective activities as our methodological lens. The findings show that mathematical ideas about quadratic functions, like positive and negative range, increase and decrease range, minimum or maximum point, intersection with the axes, and more were spread in two parallel layers. Students participated in an overt layer in which they uttered their ideas in a public discussion. At the same time, they also uttered mathematical ideas privately with their peers in a covert layer. That is, whole-class discussions are not identical for all participants in that the covert layer turns these discussions into a unique experience.

Introduction to the virtual special issue: Mathematics that underpins social issues

This Virtual Special Issue on Mathematics in Society: Exploring the Mathematics that Underpins Social Issues features 13 articles which expand our understanding of how people build, retain, communicate, apply, and comprehend mathematical ideas as they relate to social and societal issues. The focus is on education research that explores the ways in which mathematics and a mathematical worldview can influence choices, on educational, personal and societal levels. We take a broad view and raise questions about what it means to be mathematical in society, and we consider the multifaceted ways in which abilities to derive and interpret information presented mathematically are also necessary in and for society.

Multilingual Students’ Solution Strategies in Solving Linear Programming Problems: A Case of National Curriculum Vocational Level 3 Mathematics Students

This paper presents an exploratory case study that investigates multilingual students' solution strategies for linear programming problems at a technical vocational education and training (TVET) college in Gauteng. South Africa, like many developing nations, uses English as the language of instruction in technical vocational education and training in TVET colleges, despite the fact that many students lack the essential fluency to interact effectively with the curriculum. Where TVET lecturers and students speak the same home language, there is a disconnect between language policy and codeswitching, which is a frequent approach for achieving pedagogical goals. However, lecturers' training in multilingual realms in the classroom has frequently been framed in terms of linguistic issues, with a limited understanding of code-switching. The ability to combine two languages in the classroom in a systematic manner to promote learning has not been widely appreciated. Furthermore, codeswitching discourses are frequently veiled, with lecturers bringing the vernacular into the classroom. The authors of this study advocate for the discontinuity framework, which claims that in order to learn mathematics, pupils must first acquire the essential language. A purposive sample of 18 National Certificate (Vocational) Level 3 bilingual students was given the linear programming challenge. Data were gathered through a test and semi-structured interviews. The inductive content analysis, which was used for collection and analysis, revealed that students were unable to complete the linear programming task successfully because to a lack of relevant linear programming vocabulary (register) caused by language barriers. We thus recommend that lecturers use the mathematics register in their discussions with students about mathematics to demonstrate the complex and precise ways of expressing mathematical ideas; for example, lectures may re-voice their students' language representations so that these expressions more closely approximate the precision of the mathematics register.