Mathematical Basis Research Articles

An Overview of Dyscalculia from the Perspective of Mathematics Teachers

This study was conducted using the phenomenological research design to examine mathematics teachers’ common experiences who were aware of dyscalculia and who thought they had students with dyscalculia diagnosed with learning disabilities.The study also aimed to reveal the common perception. The participants were seven elementary mathematics teachers from public schools in the provinces Van and Urfa. Ethical permission was obtained from the Scientific Ethical Evaluation Committee of the Dean of the Faculty of Education of Yüzüncü Yıl University on: 24.03.2024 with the number: 21788. Semi-structured interview was used, supported by video and audio recordings. The data were analyzed using descriptive and content analyses. Reflecting on their experiences, the teachers said students with dyscalculia were mostly introverted and asocial and they had problems in many areas of mathematics like performing four operations, rhythmic counting, multiplication tables, reading clock and expressing place and direction. As the most appropriate teaching approach to be applied to students with dyscalculia, the teachers mentioned demonstrating and teaching how to do, teaching mathematics through games, individualized teaching, associating with daily life, applying activity-based and technology-supported teaching approaches. Moreover, the teachers reported they needed family and expert support regarding the interventions for the development of children's mathematical skills.

Developing an instruments to measure prospective teacher beliefs about mathematical problem-solving using the Rasch model

Beliefs in solving mathematical problems become the basis for action, the basis for change, and the basis for learning mathematics. This research describes the development of an instrument for measuring prospective teachers beliefs in solving mathematical problems. One hundred sixty prospective teachers’ with experience in problem-solving and learning mathematics became research respondents. The research data was analysed using the Rasch model. The results of the data analysis show that the instrument developed is considered reliable and valid. Fifty-five items can be used to measure prospective teachers’ beliefs about solving mathematical problems. The instruments that have been developed can be used as initial assessments in implementing problem-based learning to help students develop problem-solving skills to face challenges in real life.

Preparing Elementary Preservice Teachers for Antiracist Mathematics Teaching

I describe a unit on antiracist mathematics teaching I developed and implemented in an elementary mathematics methods course. It may serve as an example to other mathematics teacher educators on how to incorporate antiracist mathematics teaching in their courses. I report on the unit's components, its impact on the preservice teachers in my course, my reflections about the unit (including possible modifications), and implications for other mathematics teacher educators.

분수와 소수 지도를 위해 2015 개정 초등 수학 교과서에 제시된 시각적 모델 및 연관성 학습 경험 기회 분석

분수와 소수 지도를 위해 2015 개정 초등 수학 교과서에 제시된 시각적 모델 및 연관성 학습 경험 기회 분석

A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment.

The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method. Various parameter copula models and models without considering dependency relationships are introduced and compared with this approach. The results indicate a significant advantage of employing the nonparametric copula model for fitting joint probability distributions of both wind speed and wind direction, as well as conducting correlation analyses. By utilizing the proposed KDE-COP-CV model, it becomes possible to accurately and reliably analyze how wind power density fluctuates in relation to wind direction. This study reveals the researched region possesses abundant wind resources, with the highest wind power density being highly dependent on wind direction at maximum speeds. Wind resources in selected regions of Inner Mongolia are predominantly concentrated in the northwest and west directions. These findings can contribute to improving the accuracy of micro-siting for wind farms, as well as optimizing the design and capacity of wind turbine generators.

An application of Rumor Propagation In Google trends

Daley and Kendle’s pioneering mathematical basis for modelling rumor propagation around 1965 has paved a strong platform for researchers to come up with new generalizations for practical scenarios of rumor spreading in social networks. In this study, we use a generalization of original DK model, Ignorant-Spreader-Stifler (ISS) model to analyze the cricket related searches in Sri Lanka on Google.The secondary data used for the study were obtained from Google trends for a five-year period from 2012 to 2017, targeting the three t20 matches held during the period. We introduce two algorithms on Maple mathematical software to estimate the parameters of the ISS model numerically. We observe that the way people search on web about cricket is roughly analogous to spreading a rumour and forecasting is better when modelling with most recent data than considering more data back in time and we also find that the predicting accuracy is significantly equal of the two models built considering the data in 2012 and 2014.

Promoting teaching improvement in elementary mathematics: A case with inverse relations

In this study, we examine two U.S. elementary teachers’ use of worked examples, representations, and deep questions in elementary mathematics lessons both before and after a project intervention designed to promote teaching improvement. This intervention was guided by a cognitive construct containing these three aspects, which were demonstrated via cross-cultural video lessons of both U.S. and Chinese teachers. We specifically analyze two teachers (Ann and Bea) who taught first-grade lessons on the topic of inverse relations. Although their lessons were rated similarly in year 1, the rating of their lessons in year 4, post-intervention, demonstrated different patterns of change. While Ann's use of worked examples and representations underwent no significant improvement, Bea spent more time unpacking a single worked example with a representational sequence fading from concrete to abstract (also called “concreteness fading”). Neither teacher showed improvement in asking deep questions. An analysis of the teachers’ responses to the project intervention revealed that their video noticing skills and personal takeaways were related to the areas of teaching where they improved. Other factors such as teachers’ prior knowledge, beliefs, and textbook resources, also played a role in teaching changes. These findings shed light on a recent endeavor called the “science of improvement” in mathematics teaching, which seeks to document teaching changes and the underlying mechanisms that might induce these changes. Implications for both research and practice are discussed.

Electrostatic body forces in cracked dielectrics and their implication on Maxwell stress tensors

In solid mechanics, Maxwell stresses are known to be induced if a body is exposed to magnetic and, in the case of dielectrics, electric fields. Acting as tractions at outer or inner surfaces as well as volume forces, they are superimposed with tractions and stresses due to mechanical loads and provide a more or less significant contribution, depending on loading, material properties and geometric aspects. The Maxwell stress tensor, constituting the physical and mathematical basis, however, is controversially discussed to date. Several formulations are known, most of them having been suggested more than 100 years ago. Being equivalent in vacuum, they differ qualitatively just as quantitatively in solid or fluidic matter. In particular, the dissimilar effect of body forces, emanating from a choice of established Maxwell stress tensor approaches, on crack tip loading in dielectric solids is investigated theoretically in this paper. Due to the singularity of fields involved, their impact is basically non-negligible compared to external mechanical loading. The findings obtained indicate that fracture mechanics could be the basis of an experimental validation of Maxwell stress tensors.

Implementation of an Academic Software for Children from 6 to 8 Years Old for Easy Learning in Basic Mathematics and Reading Comprehension

Nowadays teaching has not improved talking about the methods to get to interest the studentor want to learn, it is not common for schools to have a didactic and innovative curriculum, we continue to maintain in do the same learning format of years ago and it is one of the areas in which we do not evolve compared to others. As we well know, among the most important foundations in education are the reading comprehension and mathematics courses, because these are the pillars to have facilities in learning with other courses in the future and that is why it is important to ensure the knowledge of these courses in childhood so that these students do not present difficulties to learn in the future. That is why in the part of basic education we see important the implementation of an educational software for children, to improve their motor capacity in terms of learning the area of mathematics and reading comprehension, since relying on statistical data we realized that the levels of knowledge in these courses, They are not the desired ones, therefore, we agreed to project a new way of learning so that children can be interested in wanting to learn, for this we develop a plan in which it is proposed to implement educational games, memory games, didactic reading, among others, all this to ensure that children improve their learning through new learning methodologies.

Unconstrained lightweight control interface for robot-assisted minimally invasive surgery using MediaPipe framework and head-mounted display

Robotic surgery is preferred over open or laparoscopic surgeries due to its intuitiveness and convenience. However, prolonged use of surgical robots can cause neck pain and joint fatigue in wrist and fingers. Also, input systems are bulky and difficult to maintain. To resolve these issues, we propose a novel input module based on real-time 3D hand tracking driven by RGB images and MediaPipe framework to control surgical robots such as patient side manipulator (PSM) and endoscopic camera manipulator (ECM) of da Vinci research kit. In this paper, we explore the mathematical basis of the proposed 3D hand tracking module and provide a proof-of-concept through user experience (UX) studies conducted in a virtual environment. End-to-end latencies for controlling PSM and ECM were 170 ± 10 ms and 270 ± 10 ms, respectively. Of fifteen novice participants recruited for the UX study, thirteen managed to reach a qualifiable level of proficiency after 50 min of practice and fatigue of hand and wrist were imperceivable. Therefore, we concluded that we have successfully developed a robust 3D hand tracking module for surgical robot control and in the future, it would hopefully reduce hardware cost and volume as well as resolve ergonomic problems. Furthermore, RGB image driven 3D hand tracking module developed in our study can be widely applicable to diverse fields such as extended reality (XR) development and remote robot control. In addition, we provide a new standard for evaluating novel input modalities of XR environments from a UX perspective.

Relationship of Attitude and Performance in Mathematics of the BEEd and BSE Students

This study aimed to determine if the attitude toward mathematics of BSE and BEED students in DMMMSU NLUC is significantly correlated to their Mathematics performance. Specifically, it seeks answers to the following questions: What is the profile of the students enrolled in Mathematics along sex, CAT Result in Mathematics and IQ level. What is the attitude of students towards Mathematics? What is performance of the respondents in Mathematics? Is there a significant relationship between profile variables and attitude towards Mathematics profile variables and performance in Mathematics, attitude toward Mathematics and Mathematics performance? Which among the variables are predictors of Mathematics performance? What action plan can be proposed to enhance the level of performance and attitude of the students in Mathematics? This study utilized the descriptive method of investigation. This is best fitted to the study because this method involves describing, recording, analyzing and interpreting conditions that exist. It also includes some forms of comparison and contrast and discovers relationship between existing non-manipulative variables. The respondents are two classes enrolled in Basic Mathematics and Contemporary Mathematics for the SY 2014-2015. Their attitude towards Mathematics were obtained using an attitude inventory, their IQ and CAT Math results were obtained from the Guidance Office and their performance were taken from their final grade in Mathematics. The attitude of students toward Mathematics and their performance in Mathematics were described, analyzed, compared, and interpreted. Mean was used to describe the attitude and performance in Mathematics. Furthermore, the relationship of the aforementioned variables will be obtained. Hence, the use of statistics of correlation under descriptive method was also used. The following are the salient findings of this study: Majority of the Mathematics students are females with fair to good performance in the Math CAT and IQ level. The students have positive to highly positive attitude towards Mathematics. The students have very good performance in Mathematics.IQ and CAT performance are significantly correlated with Mathematics performance. CAT significantly correlates with attitude and attitude is significantly correlated with Mathematics performance. In the light of the above-stated findings, the following conclusions are drawn: The Math classes are dominated with females who have only fairly satisfactory to satisfactory IQ levels and performance in the CAT along Mathematics. A greater majority of the students find mathematics enjoyable, interesting and fun. Most of the students have acquired the needed competencies in Mathematics. They are good in computation, comprehension and problem solving. Those who have high IQ and high CAT results perform excellently in Mathematics. The better is the attitude towards Mathematics the higher is the performance in the subject. Attitude has a positive impact of performance in Mathematics. Based on the conclusions, the researcher offered the following recommendations: Teachers are encouraged to customize their instruction and improve the use of modernized and innovative teaching techniques and strategies to enhance performance and attitude of students toward Mathematics. The Mathematics teachers especially the Math Club Adviser should consider the implementation of the Action Plan to improve attitude and performance in Mathematics. The administrators should support the implementation of the Action Plan by providing the opportunities and logistics for its accomplishment. The Action Plan should be considered for adoption by other HEIs in La Union with the administrators and Head of Mathematics Department planning its mechanics of implementation. A research on the effectiveness of the proposed action plan when implemented be conducted as basis for revisions and improvement.

The inverse heat placement problem in metal additive manufacturing: Why a rational approach is needed for powder bed fusion

Powder bed fusion (PBF) uses an energy beam to scan a powder bed surface, heat it locally, and consolidate the material to form a part. The choice of energy beam paths is typically based on user experience. Simple beam path strategies (e.g., raster or spiral) are used and the thermal field analysed post hoc. We refer to this approach as solving the direct problem, which involves many modelling and experimental iterations until a close to satisfactory, but not optimal, thermal field is achieved. In contrast, we propose a rational approach, solving an inverse problem to control heat placement, which we illustrate using laser beam PBF. Starting from the desired thermal field to be induced in the powder bed, we show how to formulate and solve the Inverse Heat Placement Problem (IHPP) so that a set of time-varying beam parameters (path, scan speed, energy delivered) is obtained in a single iteration. Solving the IHPP takes the craftsmanship out of beam path planning and puts it on a sound scientific and mathematical basis. This will enable a step change in the quality and complexity of customised macro-, meso-, and microscale properties of PBF built parts.

ОДНОВИМІРНА ЗГОРТКОВА МОДЕЛЬ НЕЙРОННОЇ МЕРЕЖІ ДЛЯ ОБРОБЛЕННЯ СИГНАЛІВ З АМПЛІТУДНОЮ МОДУЛЯЦІЄЮ БАГАТЬОХ СКЛАДОВИХ

The processing of radio signals using artificial neural networks (ANNs) has great potential for research, which can be explained by the adaptability of ANNs to various transmission conditions and the ability to detect abstract patterns of changes in signal parameters. The article reviews the works of other authors devoted to different ways of using ANNs for processing radio signals. Taking into account the information in the reviewed works, the research task was formed, which consists in developing an optimized ANN model for radio signal processing. Signals with amplitude modulation of many components (AMMC) were chosen to form training samples for ANN. The choice of modulation type is justified by greater energy efficiency compared to other widely used digital modulation types, such as quadrature amplitude modulation. Mathematic basis of AMMC signal generation is described. The process of finding the coordinates of three component 8-AMMC signal constellation is explained, the formation of signals in the time plane based on the found coordinates is explained as well as their discretization and the addition of white noise. An iterative algorithm for generating initial data for ANN based on the described ratios is proposed. The general structure of one-dimensional convolutional neural network is considered. Functions of individual neurons, connections between them, the formation of layers and the convolution operation are described mathematically. On the basis of the previously given ratios, a final display of the network was formed. Specific dimensions and activation functions for layers are selected. The use of convolutional layers is justified by time invariance. Based on the reviewed mathematical models, selected activation functions and dimensions, a neural model was formed. The process of validating the effectiveness of the formed neural model is described, which is based on comparing the symbolic error probabilities of the proposed and reference models at different signal-to-noise ratios. The validation results are presented. The advantages of the obtained model over the previously proposed purely recurrent model and the AMMC reference receiver are explained.

Implementation of the Jigsaw Type Cooperative Model Using Pop Up Book Media to Increase Elementary School Students' Mathematics Learning Activeness

The aim of this research is to find out how to apply the Jigsaw Type Cooperative learning model in increasing student activity in elementary school mathematics learning. The research method used is a classroom action research method that uses the development model by Kemmis and Mc. Taggart. The subjects of this research were 32 class VI students at SD Negeri 207/IV Jambi City. Data was collected using observation techniques, questionnaires and written tests. Data analysis uses quantitative descriptive analysis. The results of the research prove that the application of the jigsaw cooperative learning model can increase the learning activity of class VI students in the mathematics subject of plane figures. The average results of observing students' learning activity in cycle I was 87.52%, in cycle II it increased to 90.00%, the results of the student learning activity questionnaire obtained an average in cycle I of 60.55% and in cycle II it increased to 89.31%.

Index Card Match Boosts Math Learning by 84.2%

This study examines the effectiveness of the Index Card Match (ICM) learning model on fifth-grade mathematics education at SDIT Ainul Yaqin. Using a pre-experimental design, 20 students were selected through purposive sampling. Test sheets were used to measure learning outcomes, and data analysis included testing for normality and calculating N-Gain scores. The results showed a significant 84.2% improvement in mathematics learning outcomes, indicating the positive impact of the ICM model on student achievement. This research contributes to understanding innovative teaching methods' efficacy in enhancing elementary mathematics education. Highlight: Effective Math Learning: Evaluating Index Card Match model in fifth-grade math education. Pre-Experimental Design: Utilizing purposive sampling to assess teaching model impact. Notable Improvement: 84.2% increase in math learning outcomes observed. Keyword: Index Card Match, Mathematics Education, Elementary School, Learning Outcomes, Innovative Teaching Methods.

İLKÖĞRETİM MATEMATİK ÖĞRETMENLERİNİN LİSANS EĞİTİMLERİ BAĞLAMINDA MESLEKİ KARİYERLERİNE İLİŞKİN GÖRÜŞLERİ

Bu çalışmanın temel amacı, ilköğretim matematik öğretmenlerinin lisans eğitimleri bağlamında mesleki kariyerlerine ilişkin görüşlerinin alınmasıdır. Bu amaca ulaşmak için çalışma grubunun belirlenmesi, veri toplama kaynakları ve verilerin analizi süreçlerinde nitel yöntem esas alınmıştır. Çalışma grubunda, resmi orta okullarda görev yapan toplam 13 matematik öğretmeni bulunmaktadır. Araştırmada veri toplama aracı olarak dört ayrı form kullanılmıştır. Sonuç olarak matematik öğretmenlerinin lisans eğitimleri bağlamında mesleki yeterliklerine ilişkin görüşleri incelendiğinde öğretmenlik meslek bilgisi ve mesleki doyum anlamında güçlü hissettikleri, bürokrasi, eğitim-öğretim süreci ile sosyo-ekonomik durumlar bağlamında mesleki zorluk yaşadıklarını ifade etmişlerdir. Lisans eğitimlerinin mesleğe hazırlanmada yetersiz olduğunu bu durumu özellikle mesleklerinin ilk yıllarında hissettiklerini belirtmişlerdir. Lisans ders içeriklerinin matematik öğretmenlerinin mesleki yeterliklerini artırabilmesi adına daha çok uygulamaya dönük ve alan eğitimi dersi ağırlıklı olmasını, öğretmenlik uygulaması derslerine sadece dördüncü sınıfta değil ara sınıflarda da yer verilmesi gerektiğini vurgulamışlardır. Araştırma sadece çalışma gurubundaki öğretmen görüşleri ile sınırlıdır. Bu nedenle matematik öğretmenlerinin yetiştirilmesinde görev alan tüm paydaşlarla öğretmenlerin mesleki yeterlikleri üzerine çalışmalar, değişen lisans programların etkililiğine ilişkin boylamsal çalışmalar yapılabilir.

Application of Games-Based Mathematics Learning in the Preschool-Elementary Transition

The results of this study aim to understand the use of Elementary Mathematics Games in Mathematics and Science Learning for PIAUD and PGMI Study Program Students during the PAUD-SD transition period. The research design used a descriptive quantitative approach with data collection techniques through questionnaire distribution. The results of the study found that: 1) Knowledge of Elementary Mathematics Games amounted to 92%; 2) the technique of using Elementary Mathematics Games in lecture activities has increased by 85%; 3) the difficulty faced in the process of using SD Mathematics Games amounted to 80%; 4) the integration technique of SD Mathematics Games is very easy to apply in activities Mathematics and Science Learning in PIAUD and PGMI Study Programs is 90%; 5) The percentage of usefulness in the use of Elementary Mathematics Games in the Mathematics and Science Learning process in the PIAUD and PGMI Study Programs is 95% with a benefit level of 76-100%. Thus, the use of Elementary Mathematics Games can be used in developing material from teaching materials for lecturers, teachers, and students in learning process activities.

Bluefin Trevally Optimizer (BTO): A Metaheuristic Algorithm Using Fuzzy Logic Controller for Feature Selection Problem

Metaheuristic algorithms are increasingly used for feature selection (FS) problems due to their robustness and searchability. This study presents a unique optimization technique called fuzzy bluefin trevally optimizer (BTO). BTO draws its inspiration from bluefin’s cooperative nature and sudden ambush behavior. The trevally will jump out of the water and attack its food in the air or even snag it off the water when it is sufficiently close to it. This study uses mathematical modeling to create an optimization algorithm to replicate dynamic patterns and behaviors. Since parameters play a critical role in optimization, we use the fuzzy concept for dynamic parameter adaptation in fuzzy BTO. By introducing the idea of signature and demonstrating that fuzzy BTO converges to the global optimal point, the mathematical basis for the proposed algorithm is provided. The convergence of fuzzy BTO is proved using the Markov chain property. On benchmark functions (BF), the effectiveness of the suggested strategies is evaluated and compared with other metaheuristic algorithms. Then the proposed algorithms are applied to a fuzzy FS problem. Then they are compared with traditional and recent metaheuristic algorithms on the UCI machine learning repository datasets. Finally, the statistical significance is examined using the Kruskal–Wallis test (KWT).

ASSESSING THE IMPACT OF FLIPPED CLASSROOM ON MATH COMPREHENSION IN PRIMARY SCHOOL STUDENTS

This study aims to evaluate the effectiveness of the Flipped Classroom learning model in improving the understanding of mathematical concepts in elementary school students. Using a quasi-experimental design with a pre-test and post-test nonequivalent control group design, data were collected from 50 sixth graders of an elementary school. The Flipped Classroom model is compared to conventional teaching methods, with students' understanding of mathematical concepts as dependent variables. Results showed significant improvements in both groups, signaling the positive impact of both teaching methods on student understanding. However, no significant differences were observed between the two methods. The study emphasizes the importance of considering a variety of factors, including technology skills, parental support, and cultural context, in choosing the right teaching method. While the Flipped Classroom offers an innovative approach, conventional methods remain relevant in specific contexts. Recommendations for future research include the use of larger samples and considering additional factors that affect learning outcomes. Overall, the research contributes to an understanding of effective teaching practices in basic mathematics education, providing valuable insights for educators and policymakers.

Функция временного отклика — новый метод исследования нейрофизиологических механизмов восприятия речи в экологически валидных условиях

<p style="text-align: justify;">The temporal response function is a new method that allows to investigate the brain mechanisms of perception of natural, naturalistic speech stimuli. In contrast to other methods for studying brain activity (e.g., evoked potentials), the temporal response function does not require the presentation of a large number of uniform stimuli to produce a robust brain response - recordings of narrative speech lasting 10 minutes or more can be used in experimental paradigms, increasing their ecological validity. The temporal response function can be used to study brain mechanisms of online processing of different components of natural speech: acoustic (physical properties of the audio signal such as envelope and spectrogram), phonological (individual phonemes and their combinations), lexical (contextual characteristics of individual words) and semantic (semantic meaning of words), as well as the interaction between these components processing mechanisms. The article presents the history of the method, its advantages in comparison with other methods and limitations, mathematical basis, features of natural speech components extraction, and a brief review of the main studies using this method.</p>