Mathematical Development Research Articles

“Siapa Pappus of Alexandria?” Analisis Pengetahuan Mahasiswa Prodi Pendidikan Matematika Tentang Pappus of Alexandria

Mathematics is necessary because it has a vital role in civilization. Mathematicians from various nations carried out the development and renewal of mathematics. We must know the mathematicians who played a role in the development and regeneration of mathematics and the theorems they left behind. Pappus of Alexandria is one of the mathematicians who had an essential role in reforming mathematics. Therefore, this research is conducted with the aim that readers can recognize who Pappus of Alexandria is and his findings. The type of research conducted in this writing is qualitative with case study and literature review methods, while the instrument used in this research is an open interview. A literature review was conducted by reviewing articles to obtain Pappus's biography and findings. In contrast, the case study was conducted by selecting ten students as research subjects from the mathematics education program. The results of this study show that there are three categories of students' knowledge about Pappus of Alexandria and his theorems.

Assessing the development of mathematics teachers TPACK through an observation rubric

Assessing the development of mathematics teachers TPACK through an observation rubric

Inovasi Pembelajaran Mapel Matematika Dalam Kurikulum Merdeka Di MIN Kedungwuni

This study aims to explore the effect of innovative mathematics learning in the Merdeka curriculum at MIN Kedungwuni. Using a literature study and interview approach, this research examines the perceptions and experiences of stakeholders, such as teachers, students and parents, related to the implementation of these innovations. The findings of this study are expected to provide insight into the effectiveness of mathematics learning innovations in increasing students' interest, conceptual understanding, critical thinking skills, collaboration, and mathematics achievement. The results of this study can provide a basis for further development in innovative mathematics learning in elementary schools

Application of multiplication method using multiplication board to elementary school students

In order to meet the development of mathematics learning in elementary school children, we find and form media to improve the material to make it easier for students to learn, therefore we create learning media namely "Smart Multiplication Board". which serves to improve teaching methods and facilitate teachers in pedagogy. This research is included in the type of research and development, which is carried out to develop certain products and test the effectiveness of the product. the development example used in this research is the ADDIE development example. Based on the results of observations that have been made during implementation research, students' enthusiasm for using the learning media that has been developed is very good, it can be seen that students are impatient to use learning media. Math Multiplication Smart Board Learning Media on multiplication material is declared feasible to use based on quality assessments from media experts, material experts and learning experts as well as media feasibility from student and teacher responses. The final product of the learning media of the Math Multiplication Smart Board (Panlintarmatika) is a medium that belongs to the type of visual media.

The effect of denaturants on protein thermal stability analyzed through a theoretical model considering multiple binding sites

A novel mathematical development applied to protein ligand binding thermodynamics is proposed, which allows the simulation, and therefore the analysis of the effects of multiple and independent binding sites to the Native and/or Unfolded protein conformations, with different binding constant values. Protein stability is affected when it binds to a small number of high affinity ligands or to a high number of low affinity ligands. Differential scanning calorimetry (DSC) measures released or absorbed energy of thermally induced structural transitions of biomolecules. This paper presents the general theoretical development for the analysis of thermograms of proteins obtained for n-ligands bound to the native protein and m-ligands bound to their unfolded form. In particular, the effect of ligands with low affinity and with a high number of binding sites (n and/or m > 50) is analyzed. If the interaction with the native form of the protein is the one that predominates, they are considered stabilizers and if the binding with the unfolded species predominates, it is expected a destabilizing effect. The formalism presented here can be adapted to fitting routines in order to simultaneously obtain the unfolding energy and ligand binding energy of the protein. The effect of guanidinium chloride on bovine serum albumin thermal stability, was successfully analyzed with the model considering low number of middle affinity binding sites to the native state and a high number of weak binding sites to the unfolded state.

Development of STEAM-Based Mathematics Teaching Materials on Direct and Inverse Proportion to Improve Mathematical Problem-Solving Ability and Self Regulated Learning

This research was research and development whose product was in the form of teaching materials based on STEAM (Science, Technology, Engineering, Art, and Mathematics). This research and development aims to analyze the feasibility and readability, as well as test the effectiveness of teaching materials in improving problem-solving abilities and Self Regulated Learning (SRL). The development stages include potentials and problems; data collection; product design; design validation and revision; product trials (readability tests) and revisions; trial implementation and revision; and then the final product. Furthermore, this study used a one-group pretest and posttest design, carried out at MTs Al-Utsmani with 37 class VIID students in the 2022/2023 academic year as respondents. The results of this study indicate that the developed STEAM-based teaching materials have a feasibility level of 92.82% with very feasible criteria; legibility level of 63.22% with easy-to-understand criteria; as well as effectively improve problem-solving abilities and SRL. This effectiveness is indicated by the average mathematical problem-solving abilities of students after using teaching materials is more than or equal to the Minimum Completeness Criteria, the mathematical problem-solving ability of students who achieve Minimum Completeness Criteria after using complete teaching materials in a classical manner with a proportion of at least 75%, Improvement of students' mathematical problem-solving abilities after using teaching materials is in the moderate minimal category, average SRL after using teaching materials are in the minimal moderate SRL categories, SRL that is in the minimal moderate SRL category while after using teaching materials complete in a classical manner with a proportion of at least 75%, improvement of SRL after using teaching materials is in the moderate minimal category.

The Development of STEM-nuanced Mathematics Teaching Materials to Enhance Students’ Mathematical Literacy Ability Through Information and Communication Technology-Assisted Preprospec Learning Model

<p style="text-align:justify">The mathematical literacy ability of Indonesian pupils is still relatively low, as indicated by Indonesia's score of 379 for mathematical literacy in PISA 2018. Paying attention to the learning process such as the teaching materials used in learning, is one of ways to increase mathematical literacy skills. To strengthen students' mathematical literacy skills, it is great for building qualified mathematics teaching materials with the nuances of science, technology, engineering, and mathematics (STEM) which are supported by the information and communication technology (ICT)-assisted Preprospec (Prepare, Problem Solving, Presentation and Conclusion) Learning Model. The research method used in this study is research and development (R&D), with the main reference of 4D-model development by Thiagarajan, whose stages are limited to define, design, and develop. The results showed that the feasibility test on teaching materials obtained the total average percentage of validator I to validator V, respectively, 90.19, 95.45, 93.90, 91.95, and 97.95 with very eligible criteria. It is easy to understand by students with a readability score of ρ = .109 > α = .05 or Cochran's Q = 13.091, and it can improve students' mathematical literacy skills, as evidenced by the Wilcoxon test and a gain normalization result of 485.</p>

Relationship between fine/gross motor skills and language and math development in Colombian Caribbean children: A study in Barranquilla

AbstractLiterature suggests that motor skills are associated with other areas of development or domains, such as language and math, especially at early ages. These results are mainly based on studies developed in medium‐to‐high sociocultural contexts. Thus, this study was conducted in a medium‐to‐low‐income area. The aim was to know the 4–5 years old children's motor development (both fine and gross motor skills), and its relation to language and mathematical development. A total of 219 Colombian Caribbean children (105 boys and 114 girls) aged 4 and 5 years participated in this study. Results revealed higher motor skills among girls, although differences by gender were not notable. Positive and significant correlations were found between motor skills and language and mathematical skills, although most of the correlations were weak or moderate. Also, it was observed that fine motor skills were less related to language or mathematical development in comparison with gross motor skills, especially among boys. These results suggest that among Colombian Caribbean children gross motor skills could have a higher influence on the development and acquisition of some language and mathematical skills in comparison with fine motor skills.

A Theoretical Framework for a Mathematical Cognitive Model for Adaptive Learning Systems.

The emergence of artificial intelligence has made adaptive learning possible, but building an adaptive system requires a comprehensive understanding of students' cognition. The cognitive model provides a crucial theoretical framework to explore students' cognitive attributes, making it vital for learning assessment and adaptive learning. This study investigates 52 experts, including primary and secondary school teachers, mathematics education experts, and graduate students, based on the 16 cognitive attributes in the TIMSS 2015 assessment framework. Through an analysis of their attribute questionnaires, the Interpretive structural modeling (ISM) method is used to construct a five-level mathematical cognitive model. The model is then revised through oral reports and expert interviews, resulting in a final cognitive model ranging from "memorize" to "justify". The cognitive model describes the relationship between different attributes in detail, enabling the development of adaptive systems and aiding in the diagnosis of students' cognitive development and learning paths in mathematics.

Cauchy Theorem, Sylow Theorems, and Orbit-Stabilizer Theorem in Group Theory

With the rapid development of modern mathematics, math researchers have an increasing demand to take the advantage of group theory in the latest field. The group action is one of the essential parts of the group theory. In order to have a better understand of group action, this paper will describe the insight development and logic in it step by step. For this purpose, three essential theorems, which are Cauchy theorem, Sylow theorems, and orbit-stabilizer theorem, are chosen as representative examples. The proof and applications in some fields of modern science of these three theorems are discussed. In the proof, this paper emphasizes that group action can be used conveniently to solve the problem in group theory. In the application, this paper includes as many fields as possible to attach importance to group action. This paper is expected to give the opinion of how the field of group action is established and its far-reaching influence to the modern science.

The History of Fractions and Teaching Insights

The history of mathematics, as the history of mathematical development, is a guide for teaching and has significant implications for contemporary teaching. If teachers can use the resources of the history of mathematical discourse wisely in teaching, they can enable students to experience the wisdom of their predecessors and the charm of mathematical culture in the process of learning new knowledge. As early as around 3000 B.C., human beings began to understand fractions. Since then, the representation of fractions, the application of fractions, and the perspective of understanding fractions have been constantly improved, which have profound implications for the teaching of fractions.

The influence of school culture on teacher development during Covid-19

The COVID-19 pandemic caused teachers and learners to be removed from their school communities, negatively impacting school culture, and limiting teacher professional development (PD). Online PD programmes emerged to meet these needs. This study investigated how schools implemented teacher PD and mechanisms for teaching and learning during the COVID-19 pandemic. It was necessary to understand the complex interplay between school culture and teacher PD, and Wenger's social learning theory was used to prescribe the empirical prescription. This study examined the influence of school culture on Mathematics and Science teacher development during the COVID-19 pandemic. A qualitative approach was used to compare three independent schools in the same Educational Trust in Gauteng. The empirical findings of this study revealed that the COVID-19 pandemic had a significant influence on the school culture, consequently giving rise to explicit professional learning communities (PLCs), which in turn influenced the teachers’ pedagogical repertoires for curriculum delivery during a pandemic. The COVID-19 pandemic highlighted the importance of schools transforming their practices and adapting their school cultures. Results showed that school culture is not static, and individuals had to reflect collectively to develop ideas to transform learning. Schools need to learn from the pandemic, adjust their values, and use their newfound insights and beliefs to work towards a new learning culture. Future research must evaluate unfolding PLC practices, strategies, and implementations during a crisis.

Topos of Noise

This paper focuses on the significance of the concept of noise for cognition and computation. The concept of noise was massively transformed in the twentieth century with the advent of information theory, cybernetics, and computer science, all of which provide formal accounts of information and noise centrally concerned with contingency. We show how the concept has changed from these classical formulations, through developments in mathematics (topology and topos theory), computing (interactive computing and univalent foundations), and cognitive science (predictive processing and cognitive morphodynamics). Ultimately it argues for the central importance of noise not only within a topological conception of cognition and computation, but also in the transcendental-empirical torsion of image schemata and the social interactive elaboration of freedom.

Infinite analytical procedures for the computation of logarithms in works by Benito Bails (1731–1797)

During the Spanish eighteenth century, a process of modernization took place in scientific knowledge, partly driven by the circulation and appropriation of new scientific ideas. In this context, the Spanish mathematician Benito Bails (1731–1797) published his course Elementos de Matemática (Elements of Mathematics) consisting of ten volumes (1779–1799), in which, among other subjects, he presented one of the most complete mathematical developments of logarithmic calculation methods of his time, by using the infinity through infinite series. The aim of our article is to demonstrate how algebraic analytical reasoning enabled Bails to obtain new and more efficient infinite algorithms that converge more quickly in the computation of logarithms in any system. We show how Euler's number ‘e’ is calculated, probably for the first time in Spanish teaching, in an eighteenth century mathematical text. Our analysis concludes that Bails’ course constituted an innovation and provides evidence of its creativity, originality and ingenuity.

Evaluation of the mechanical properties of chopped carbon fibre reinforced polypropylene, polyethylene, polyamide 6, and polyamide 12 composites

In this study, a comparative assessment of the mechanical properties of chopped carbon fibre (CF) reinforced polypropylene (PP), polyethylene (PE), polyamide 6 (PA6), and polyamide 12 (PA12) composites was performed. A variation in the composites was obtained by changing the fibre volume fraction of the composite elements under the same manufacturing method and conditions. After blending reinforcement and matrix materials using the extrusion method, the composite materials were manufactured in the shape of plates with thermoforming. The composites’ tensile and 3-point bending tests were carried out, and the surface morphology of the fractured surfaces was examined by Scanning Electron Microscope (SEM). As the fibre content in all matrices increased, the efficiency of the fibre in the composites decreased. Finally, ANOVA analysis and mathematical model development by the least square optimization method were performed to analyse and fit experimental data. As a result of the ANOVA analysis, it was seen that the matrix type was more effective on the composite than the fibre type. The error of the modelling performed is less than 20% for the tensile and three-point bending tests.

Counting the stars: advancing mathematical activity in a scripting journey

ABSTRACT Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers’ mathematical development. In this study, we demonstrate the potential of a novel method of data collection, the scripting journey, as an avenue for describing mathematical activity that takes place during an investigation. Participants, comprised of prospective and practicing teachers, explored the concept of a star polygon and wrote a scripting journey based on their deliberations, ideas, and conclusions. We analyzed their submissions using the construct of advancing mathematical activity, which allowed us to explore the examples of symbolizing, defining, algorithmatizing, and theoremizing that appeared within participants’ scripting journeys.

A Transient-Based Analysis of a Leak in a Junction of a Series Pipe System: Mathematical Development and Numerical Modeling

In this paper, a numerical model is proposed to simulate the effect of a leak occurring at a pipe junction. The developed model, based on the method of characteristics, considers both hydraulic singularities, the leak and the junction, as superposed boundary conditions located in the same section. Obtained results representing the temporal evolution of pressure signals have allowed for locating the leak through the separation of its effect from that of the junction. For testing purposes, the transient was created by a sudden closure of a downstream valve in a reservoir-two series pipe-valve system. The novel proposed approach has proven its usefulness on locating and sizing the leak through detailed test cases. In sizing the leak, better accuracy is obtained when using the maximum pressure head reached by the incident wave before encountering the leaky junction instead of that of the transmitted wave through the leak. On the other hand, for the localization of the leak, rather than looking for an equivalent characteristic period of the two-pipe system, it was shown that the characteristic period of the pipe connected to the reservoir, once incorporated into the localization formula, leads to precise results with minimal uncertainty. For the piping system, two cases of configuration, viz. expansion and shrinkage (narrowing), were tested. In general, using the proposed approach, the maximum uncertainty values for the sizing and localization of a leak in the junction are 0.1513% and 1.09%, respectively. Additionally, the friction effect on the localization and sizing of the leak at the junction was investigated to conclude that the friction does not significantly affect the precision of the numerically obtained results for the sizing and localization of the leak at the junction.

The Privilege of Art

The Privilege of Art

Mathematical Model Development for Schizophrenia Risk Prediction Based on Assessment of Polymorphic Alleles Carriage in 13 Genetic Loci Affecting Pterin Metabolism

Real-time PCR was used to analyze the carriage of alleles in 13 genetic loci that affect pterin metabolism in 116 patients with schizophrenia and 62 healthy volunteers. To analyze the accuracy of predicting the risk of schizophrenia, we used the binary logistic regression method with the assessment of the contribution of all studied loci. Results: A mathematical model was developed that makes it possible to predict the risk of schizophrenia manifestation in a carrier of the combination of genotypes MTHFD1 1958CC/MTRR 66GG with a probability of 90.6%, MTHFD1 1958CC/MTRR66AG with a probability of 81.9%. The use of this model is expedient in routine psychiatric practice among individuals at high risk of schizophrenia manifestation after replication in other samples and obtaining a larger volume of observations.

Study of barley yellow dwarf virus: dynamics of aphid-plant interaction

Physics continues to be an inexhaustible source of problems that have inspired the theoretical development of mathematics, particularly in the development of the theory of dynamical systems that have their origin in the physics of the 15th century, with the beginning of differential calculus by Newton and Leibniz; differential equations are an appropriate tool for research in different areas of knowledge. Our objective is to show an example of how we can use dynamical systems in a problem framed in forestry and agricultural systems, ecology, and epidemiology. This work is inspired by one of the essential primary crops in the energy intake of the human diet, wheat; as it turns out, the productivity of this food can be affected by several biotic stresses, including viral diseases and their associated vectors. Among the viral infections is the barley yellow dwarf virus, which causes 11% to 33% yield losses in wheat fields; the virus moves through the agricultural landscape via different aphid species (vectors). The main problem is that aphids prefer colonizing plants with the virus, causing rapid growth of infected plants and substantially decreasing crop productivity; therefore, we propose to study the dynamics of aphid-plant interaction, in which the impact of aphid preference for infected plants is determined, and we obtained as a result that a key parameter is the quantity and quality of food consumed by aphids.