In this paper, we discuss major issues of mathematics teaching and learning in Nepal. The issues coming from theories such as social and radical constructivism suggest that teachers are not trained to use such approach in teaching mathematics, and there is a lack of teaching aids and materials and technological tools. The issues related to social aspects are gender issues, language issues, social justice issues, and issues related to the achievement gap. The cultural issues are related to the diversity of language and ethnicity. The issues related to political aspects are equity and access, economic status, pedagogical choice, and professional organizations and unions. The issues related to technology include the technological skills, use of technology, and affordance. Finally, we suggest that all the stakeholders should pay attention to resolving these issues by improving the curriculum, training teachers, resourcing the classroom with locally made and new technological tools.

In this paper I describe elements of Game-Based Learning that can be used to support mathematics teaching using games. After creating a game that incorporates the elements described, the game was playtested against a small number of people who answered a questionnaire focusing on user experience, learning motivation and game design. The results are attached separately as well as the analysis. I believe that with further development this game-based approach can be a powerful tool to gamify common learning tools and increase learning motivation and appreciation.

In the study, it was aimed to develop a valid and reliable scale in order to determine the self-efficacy perceptions of classroom teachers in the field of mathematics learning difficulties. In the development process of the scale, the basic resources and the scale development studies in the literature were examined. First, a pool of substances was created. Content validity was ensured by taking the opinions of 21 expert participants in the 24 question areas determined in the item pool. Content validity index was used in content validity. In this analysis, two questions were removed from the scale. Preliminary application was made with 44 participating teachers who are experts in their fields and exploratory factor analysis was started. For exploratory factor analysis, 359 people consisting of classroom teachers in Sakarya province were studied. In the explanatory factor analysis, 5 items were removed from the scale by looking at the factor load. The factor loadings for the 17 items in the scale vary between 0.508 and 0.976. Among the comparative fit indices obtained as a result of confirmatory factor analysis, RMSEA=0.067 and Cmin/DF=1.568 were calculated. The Cronbach alpha reliability coefficient of the measurements is 0.970. The data obtained were analyzed with statistical methods using SPSS 25, AMOS 24 and Microsoft Excel programs. The validity and reliability criteria of the scale developed within the scope of the study were met.

The way in which the human being learns certain complex contents has always been a focus of interest and a challenge for researchers. Given the fact that children's cognitive abilities do not fully develop until a certain age, this topic is particularly important in the young children's learning scope as they do not correctly and easily learn some content of abstract nature, such as contents in math class. This work presents the results of the use of an application called "Mathematics Learning System with Augmented Reality based on Kinect" (SAM-RAK by its acronym in Spanish), which was designed to cover basic topics of mathematics in the Basic General Education level (EGB by its acronym in Span-ish) in Ecuador. The research was carried out under an experimental quantitative approach with 30 children (18 girls and 12 boys), who study in third grade of EGB level, from 2 different educational in-stitutions in Riobamba city. In order to obtain the results that evaluate the developed application, a pre-test and a post-test were applied, which were contrasted with the student’s t-test for paired samples. The statistical evidence suggests that the proposed computer system had a positive effect on children's performance, when it was used as a support tool in the classroom. The system was more effective in low performance children compared to those of high performance. It was also proved that children were motivated and showed positive attitudes when using the proposed System.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

This study presents a designated Flipped Classroom (FC) mathematics environment that utilizes a unique online platform designed for Arab minority students in Israel. It investigates how studying in an FC affects conceptual understanding and motivation to study mathematics among Arab high school students. The study also explores the factors that contribute to effective learning in the FC environment. Participants were 75 Arab high school students in 10th and 11th grade who studied advanced mathematics. Each grade group was randomly divided into two subgroups: an FC group and a traditional classroom group (comparison group). Quantitative questionnaires given before and after the learning program served to measure students’ motivation and conceptual understanding of the derivative and integral topics. Additionally, a random sample of students who studied in the FC group and the teacher who taught all the groups were interviewed. The study describes the positive effect an FC environment has on students' conceptual understanding, particularly for 11th graders. The participants mostly appreciated how the FC resulted in less lecturing in class. The study contributes to the literature about FC among minorities and contributes to national and international efforts being made to reduce the gap in mathematics achievements between minorities and other sectors.

Children’s learning of place value is critical to their future study of mathematics. However, its learning presents a huge challenge for many learners. As result they develop misconceptions and thencommit errors that become an encumbrance to their understanding of place value. It is therefore important to identify these misconceptions and their associated errors early and help children to overcome them. This article reports the findings from literature on what misconceptions learners display in the learning of place value and how they can best be supported to overcome them. The results show that despite the importance of this topic there are limited studies devoted to its research. The dearth of these studies creates a gap in the study of place value.

SLI and SLD constitute two autonomous neurodevelopmental disorders, which frequently cause challenges in the diagnosis process, especially due to their nature, which has caused disagreement among clinicians regarding their recognition as separate or overlapping disorders. The objective of the study was to enlighten the path of valid diagnosis and intervention during adolescence when the two disorders change their manifestation and overlap. 200 Greek adolescents (140 boys and 60 girls), 124 already diagnosed with SLD and 76 diagnosed with SLI, 12-16 years old, participated in the study. All participants were assessed in reading, oral and written language and mathematics (mathematical operations and mathematical reasoning) along with IQ testing. In order to determine statistically significant differences, the chi-square test, independent samples t-test, odd ratios and their 95 per cent confidence intervals were implemented. The results revealed that the SLI group presented significantly greater difficulties than SLD in their overall cognitive-mental profile and in most language and mathematical measurements (number concept, executive-procedural part of solving operations and mathematical reasoning). The similarity of the two groups was mainly detected in their deficient metacognitive, metalinguistic and metamnemonic strategies. The research concludes that SLD adolescents managed to overcome their difficulties to a significant degree, while adolescents with SLI still struggle with many learning areas.

Language is an essential aspect of teaching and learning mathematics. It is necessary for communicating, transmission of concepts and ideas, and formation of meaning of mathematical concepts. In mathematics, besides symbols, which are usually common in different languages, words and expressions are used, which may invoke different concept images to students in various languages. Some words are used in mathematics and in everyday language with different meanings, while others are used only in mathematics or in mathematics and other disciplines in similar but non-identical ways. In Mathematical Analysis, the used vocabulary is gradually enhanced, and the concepts are defined in a more formal way. In the current study, the language used regarding mathematics of change is examined, focusing on rate of change and in relation to misconceptions of students.

The current paper explores the potential interlink between names of individuals in a society and its collective social consciousness, particularly with reference to the pervasive occurrence of the ‘mathematical names’ in the current Hindu society in the Indian subcontinent and beyond. Initially, an attempt is made to put things into mathematical perspective by drawing a quick sketch of some of the stellar achievements of the Indian mathematicians. Under the six broad categories of geometry, trigonometry, numeration, arithmetic, algebra, and mathematics in the Vedic tradition, a concise simple description of these subdivisions is presented, underlining the names of the concepts and terms, sometimes by producing the textual references. Then, upon identification of such mathematical terms, an attempt is made to juxtapose these with the names current in the Indian Hindu society. By employing an extensive dataset of university student names in India and the directories of Facebook and LinkedIn, we produce both qualitative and quantitative evidence of the presence of such names in the Indian subcontinent. Evidently, these names reflect the impressions of the tremendously rich mathematical heritage left by the Hindu stalwart mathematicians. This hypothesis has also been examined by taking surveys of people bearing these mathematical names, as well as by documenting the ‘conscious procedures’ that go behind the naming of a Hindu Indian child. In trying to investigate if such a phenomenon is unique to the Indian tradition, a stark contrast with the ‘names in mathematics’ as prevalent in the European mathematical traditions is presented, as cultural roots of mathematics are explored. Further, we ascribe the presence of these names as the extant remains of the colossal impact of multifarious mathematical traditions existing in India. Interestingly, the present research also brings to the fore, certain unseen facets of the Indian Hindu society as regards the education of mathematics to women – through an indirect exploration of their names. We also show that the pervasive occurrence of these names is not merely the result of semantic chance events, but denotes the richness of the Indian mathematical legacy. Next, we also present cross-cultural comparisons to show the uniqueness of Indian mathematical and scientific traditions that led to the pervasiveness of ‘mathematical names’ in India. Finally, an attempt is made to clarify some subtle points on the associations between mathematics and religion in India and other cultures of the world. It is sincerely hoped that the present study may shed light on the cultural roots of mathematics and may furnish a new dimension in the study of mathematics, culture and civilizations across the world.

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author’s earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

Students with disabilities are often framed as “the problem” and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. Fifty percent of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with little analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities.

The question does P = NP has confounded mathematicians and computer scientists alike for over 50 years and although there is an almost unanimous agreement that it in fact does not, there still is no absolute proof. In this paper, I attempt to prove to that P does not equal NP.

In this note we consolidate and give a brief description of several recently published results in ring theory having disproof. These results have been published during 2016 to 2021 in the so called non-predatory reputed mathematical journals indexed in the well known database like Scopus. We have considered results on rings in which each element is a sum of two idempotents appeared in Canad. Math. Bull. (2016), weakly tripotent rings appeared in Bull. Korean Math. Soc. (2018) and Rendiconti Sem. Mat. Univ. Pol. Torino (2021), involution t-clean rings appeared in Eur. J. Pure Appl. Math (2022) and strongly 2-nil clean rings with units of order two appeared in Eur. J. Pure Appl. Math (2023).

Background: Bangladeshi students from science, technology, engineering, and mathematics (STEM) often struggle with solving many mathematical problems in different pedagogic contexts. They mostly lack the considerable prior learning or strong basics required to cope with the teaching and learning materials used at the undergraduate levels, which leads many students to take readmissions every year. Objective: This research aims at investigating the factors affecting the success and deficit of university undergraduate mathematics students in Bangladesh. The mixed-method research incorporates quantitative and qualitative data analysis on the students' and teachers’ perspectives regarding the issues. The authors focus more on categorizing the reasons influencing effective mathematics pedagogies than on identifying new or unknown causes. Methodology: This study is outlined in three phases. The phases include i. Exploratory qualitative survey ii. Quantitative triangulation survey, iii. Explanatory semi-structured interviews. Findings: First, the qualitative survey exposes the important factors that highlight the student’s success and failure in mathematics. Next, the quantitative data confirm that there are some similarities and dissimilarities between students’ and teachers’ perceptions. Also, the coefficient correlation analysis shows male students lack consistency and passion for study resulting in poor performances. Conversely, female students emphasize the inability to connect mathematical theories to real-life usages, curriculum loads, and unavailable resources as the reasons for underperformance. Finally, the interview data demonstrate the students attribute their failure to inadequate practices, memorizing habits, poor teaching, low motivation, and external distractions. Also, students acknowledge the necessity of steady practice, clear understanding, regular study, and working strategies for successful mathematics education. Teachers emphasize students’ clear concepts, aptitude, motivation, and curiosity for successful learning. Conclusion: This conclusion proposes a fresh start with the local mathematics pedagogic practices by analyzing teacher-student feedback on the success and failure factors impacted by varied individual and contextual elements. The study offers inclusive feedback on the part of both stakeholders. However, an open discussion or interaction between students and teachers might be needed to enhance mutual trust and understanding between them.

We assume that the current mathematical knowledge K is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any theorem of any mathematician from past or present belongs to K. The set K exists only theoretically. Ignoring K and its subsets, sets exist formally in ZFC theory although their properties can be time-dependent (when they depend on K) or informal. In every branch of mathematics, the set of all knowable truths is the set of all theorems. This set exists independently of K. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivial statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. This and the next sentence justify the article title. For any empirical science, we can identify the current knowledge with that science because truths from the empirical sciences are not necessary truths but working models of truth about particular real phenomena.

Incorporating substantial sustainable development issues into teaching and learning is the ultimate task of Education for Sustainable Development (ESD). The purpose of our study is to identify the confused students who have failed to master the skill(s) given by the tutors as a homework using Intelligent Tutoring System (ITS). We have focused ASSISTments, an ITS in this study and scrutinized the skill-builder data using machine learning techniques and methods. We used seven candidate models that include: Naïve Bayes (NB), Generalized Linear Model (GLM), Logistic Regression (LR), Deep Learning (DL), Decision Tree (DT), Random Forest (RF), and Gradient Boosted Trees (XGBoost). We trained, validated and tested learning algorithms, performed stratified cross-validation and measured the performance of the models through various performance metrics i.e., ROC (Receiver Operating Characteristic), Accuracy, Precision, Recall, F-Measure, Sensitivity & Specificity. We found GLM, DT & RF are high accuracies achieving classifiers. However, other perceptions such as detection of unexplored features that might be related to the forecasting of outputs can also boost the accuracy of the prediction model. Through machine learning methods, we identified the group of students which were confused attempting the homework exercise and can help students foster their knowledge, and talent to play a vital role in environmental development.

The National Examination in Indonesia has been abolished since 2020. Hence, the Indonesian junior high schools makes its final examination items for the 9th-grade, and from the results, the school determines students' graduation. The final examination has an important role and significant value in making decisions about students' graduation. Therefore, this study is aimed to analyze the Online Final Examination items in one of the public junior high schools in Bandung. The sample was 234 students in grade 9 using their mathematics examination tests, comprising 20 multiple-choice items with 4 options, while the data processing used Winsteps software with the Rasch modeling technique. Subsequently, the Rasch model results showed an acceptable person separation statistic of 1.54 and sufficient person reliability at 0.74. The item separation statistics was in a good category at 4.59, while the item reliability at 0.95 was excellent. Although four online final examination items were in the fit category, 16 were good and capable of dividing students according to their abilities. The result also provided very detailed data about the quality of the items and the ability of each grade 9 student. Since each test item is included in the fit category, this study contributes information on preparing and analyzing the Online Final Examination to teachers..

Steganography is the branch of cryptology that deals with concealing information inside another information. it’s prefer over cryptography as it hides a message inside another innocent looking message, while cryptography shows scrambled message that might arouse attention of an attacker, however the challenges in steganography is the modification of carrier that causes some abnormalities which is detectable and often the methods are not optimize. This paper presents a novel approach in cryptography and steganography, which utilizes mathematical concept of bits combination to optimize time of transmission using sets of multiple transmitter, and receiver’s addresses where each abstractly represents a bits combination without itself modified. In addition, the paper introduces a concept of dynamical clockwise and anti-clockwise rotation of bits combination over addresses after every transmission to reinforce resistivity against steganalysis.

The generation and maintenance of membrane potential is considered a fundamental element of the cellular machinery. They are based on elements of physics and chemistry. Mathematics is used to validate the equations and evaluate the results. However, this computation process can lead to a misunderstanding of the phenomena involved or to the masking of crucial events. It is even possible that the calculation no longer corresponds to the hypothesis considered. Membrane theory is no exception to these trivial considerations, which are essential for normal theory validation.

: Predicting long-term student learning is a critical task for teachers and for educational data mining. However, most of the models do not consider two typical situations in real-life classrooms. The first is that teachers develop their own questions for formative assessment. Therefore, there are a huge number of possible questions, each of which is answered by only a few students. Second, formative assessment often involved open-ended questions that students answer in writing. These types of questions in formative assessment are highly valuable. However, analyzing the responses automatically can be a complex process. In this paper, we address these two challenges. We analyzed 621,575 answers to closed-ended questions and 16,618 answers to open-ended questions by 464 fourth-graders from 24 low-SES schools. We constructed a classifier to detect incoherent responses to open-ended mathematics questions. We then used it in a model to predict scores on an end-of-year national standardized test. We found that despite answering 36.4 times fewer open-ended questions than closed questions, including features of the students’ open responses in our model improved our prediction of their end-of-year test scores. To the best of our knowledge, this is the first time that a predictor of end-of-year test scores has been improved by using automatically detected features of answers to open-ended questions on formative assessments.

An approach to estimating the objective function value of minimization maximum lateness problem is proposed. It is shown how to use transformed instances to define a new continuous objective function. After that, using this new objective function, the approach itself is formulated. We calculate the objective function value for some polynomially solvable transformed instances and use them as interpolation nodes to estimate the objective function of the initial instance. What is more, two new polynomial cases, that are easy to use in the approach, are proposed. In the end of the paper numeric experiments are described and their results are provided.

This dissertation is a rigorous study of ecology and macrocellular biology as a subfield of abstract algebra. We begin with the creation of an axiomatic paradigm, then move onto constructing a universal genetic code of biology. We use this to define increasingly complex algebraic structures (ecosystem, evolving populations, etc.). We prove a variety of theorems regarding to the members of the previous mathematical constructs, notably the following three: 1. There is one unique phenotypic representation of each organism. For example, if you subdivide any piece of genetic code into its phenotypic components, then two identical organisms have identical decomposed DNA 2. There are a finite number of indivisible phenotypic traits. 3. The three sophioid-definitions are equivalent: (a) dynamical evolutionary enlargement of the medial temporal lobe and frontal lobe, (b) reliance upon intelligence, (c) the existence of an intellectually- or socially-hierarchical society. Much has yet to be done on this work, but as a first draft, it stands as a jumping point for future exploits; I am working on an entirely revised second draft.

Development of early math skills is linked to future success in mathematics and other academics. Educational videogames have been shown to promote academic achievement; however, few rigorous studies have evaluated the use of educational videogames in supporting math development, especially in early primary education. In the current study, an open-label randomized controlled trial was conducted involving 134 first grade students to determine, using standardized assessments, the impact of the educational mathematics tablet-based videogame, Knowledge Battle, on math scores and self-competency. Overall, Knowledge Battle did improve math skills in participants who played the game. Among those with lower pre-game math skills, the Knowledge Battle group’s mean math score increased more than the control group’s mean math score (9.7 vs. 6.0; p=0.02). There was no association between perceived sense of self-competency and total math score (p=0.8141). However, players who had a higher sense of self-competency were more likely to enjoy playing the game. In conclusion, our findings suggest that Knowledge Battle was an acceptable and enjoyable educational mathematical videogame for first grade students, and may be most impactful for those with low math skills.

Science evolves over a gentle arc spanning centuries, with scientists building upon and extending the hypotheses and discoveries of their forebears when nurturing their own work from ideation to crystallization and finally implementation. However, evidence suggests several limitations of our modern academic pursuits including major inertia and epistemological biases to implement even major advancements. For instance, the transformative uncertainty principles of quantum mechanics are yet to be satisfactorily integrated in modern analyses and publications, even almost a century after Heisenberg received the Nobel prize for these. Another example is ever expanding reliance on mathematics to validate the hypotheses of Physics, and undermine the opinions to the contrary. In addition, modern science limits itself to the era post fifteenth century and hastily rejects premodern achievements despite glaring examples. This reluctance and inertia to capitalize on existing knowledge is a challenge that imperils our intellectual pursuits. A salient facet of science is "the willingness to admit ignorance". Only on this foundational principle can science meaningfully evolve. It is time we take a step back to evaluate widely accepted and foundational premises of modern science and institute structured processes to implement the treasure trove of knowledge amassed by our predecessors. This essay highlights some of the opportunities that can and should be availed capitalizing upon the recent developments of computational and analytical capabilities along with artificial intelligence.

Iyer Markoulakis Helmholtz Hamiltonian mechanics formalisms mathematically modeled physics with vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields. Here, Helmholtz metrics have been gaged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields out of the mechanical fields from Helmholtz Hamiltonian mechanics. This ansatz general gaging helps to properly isolate field effects – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gage metrics, having the power to analyze dark energy superluminal phase, dark matter luminal phase, and light matter subluminal phase. Interpreting particle physics gage matrix pointing to Dirac seas electrons, monopoles with positrons, electron-positron annihilation leading to energy production, relativistic energy generating matter, and both monopoles – vacuum and compressed out of vortex Helmholtz decomposition fields have been interpolated. Quantum ASTROPHYSICS gage metrix posits superluminal profile of signals velocity generating electron-positron chain like “curdling” action that is consistent with physics literature reporting nature electron photon observed oscillatory fields configurations. This helps proposing creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon. These aspects will explain receding or fast expanding universe with dark matter in terms of flavor metrics versus gage associating metrics flavor. Additional interpretations of virtual gravitational dipoles that have gravitational charge of opposite signs, reported per physics literature at Planck dimensions, that may originate at the center of supermassive blackhole. On the other hands, vacuum monopoles occur probably at infinity with cosmos extent.

The objective of this work is to present the results of an investigation on the technological, pedagogical and content knowledge evidenced by mathematics teachers in the second-level of initial training (preservice) at the Universidad Nacional, from the TPACK model perspective, on the subject of functions. The research has a qualitative approach with an interpretive hermeneutical stance. A sample of 27 teachers in training who were enrolled in courses related to the three base domains of the TPACK model (pedagogical, technological and content of quadratic function) during the first semester (I cycle) of 2020 was used. A theoretical inquiry was carried out that allowed the creation of an instrument that made possible the description of the participants’ knowledge based on this model focused on the topic of quadratic function. The results show that participants possess instrumental dominance over the basic forms of knowledge underlying the model. It is concluded that, although participants have already experimented in courses related to these forms of knowledge, there is insufficient evidence to ascertain that their current knowledge would allow them to integrate technologies as a didactic resource within the teaching of the subject of quadratic function.

Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for his claim is insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is adequate framework for elaboration of the measurement problem. It considers signals to be stochastic processes, whether they correspond to variables or distribution densities. Signal processing like that utilizes statistical properties to perform its tasks, which is the definition of statistical signal processing. A hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has generalized to an open system by the use of duality in frame theory.

This qualitative study explores the implementation and conformation process of digital devices in teaching and learning before, during, and after the COVID-19 pandemic in Nepal. Using Rogers' Diffusion of Innovation Theory as a framework, the study examines the adoption and adaptation of digital devices by in-service secondary mathematics teachers (n=62) and their perceptions and preferences towards instructional modality. The findings suggest that despite the increased reliance on digital devices during the pandemic, there is a less likelihood of using them in face-to-face classrooms in developing countries like Nepal. The adoption of online learning has not yet reached the confirmation stage, even after the onset of the COVID-19 pandemic. Prior to the pandemic, online learning was not widely implemented or confirmed by teachers in developing countries societies. The study also provides important insights into the challenges and opportunities of using digital devices in post-COVID-19 classrooms, and its implications for policymakers and educators in Nepal.

The switching game Lights Out and its variants were studied extensively as recreational mathematics problems. The game board of the ordinary Lights Out is a rectangular grid of lights, where each light is either on or off. By clicking a light, the clicked light and its adjacent rectilinear neighbors are toggled. Given an arbitrary initial configuration of lights, the final mission is to “solve” this game by switching off all the lights. Most studies on Lights Out and its variants focused on the solvability of given games or the number of solvable games, but when the game is viewed in a coding-theoretical perspective, more interesting questions with special meanings in coding theory will naturally pop up, such as finding the minimal number of lit lights among all solvable games except the solved game, or finding the minimal number of lit lights that the player can achieve from a given unsolvable game, etc. However, these problems are usually hard to be solved in general in terms of algorithmic complexity. This study considers a natural extension of the Lights Out game, which enlarges the toggle pattern in a way that all the lights in the same row and those in the same column of the clicked light are toggled. This variant of Lights Out is a two-state version of a switching game called Alien Tiles. In this paper, we investigate the properties of the two-state Alien Tiles, and discuss several coding-theoretical problems about this game. Then, we apply this game as an error correction code and investigate its optimality. We also give a brief overview on algorithmic complexity and coding theory for readers who are not familiar with these topics. The purpose of this paper is to propose ways of playing switching games in a think-outside-the-box manner, which benefit the recreational mathematics community.

: The performance of the students in academics depends on many different factors. One of these factors is the economic status of their families. Education in public schools, though it is free, some parents cannot afford to send their children to school due to financial constraints. Education as a free is every individual's right in society, but it becomes a privilege because of a lack of financial support. This research work is a comparative study of students' or learners' performance in mathematics among students from working and non-working. This research article's ultimate objective is to investigate and compare a significant difference in their performance in the subject mathematics. The research methodology utilizes a t-test to analyze and synthesize primary data sources collected via interview and academic records, and diverse literature on the study area. However, the research findings revealed no significant difference in the two groups (the working and non-working group of learners). Therefore, it is recommended that secondary schools should be provided with adequate books and facilities and faculty school interventions and programs and promote the usage of SIM or Strategic Intervention Materials for learning and memory enhancement among learners.

Molenaar’s manifesto on psychology as idiographic science brought the N = 1 times series perspective firmly to the attention of developmental scientists. The rich intraindividual variation in complex developmental processes requires the study of these processes at the level of the individual. Yet, the idiographic approach is all but easy in practical research. One major limitation is the collection of short interval times series of high quality data on developmental processes. In this paper we present a novel measurement approach to this problem. We developed an online practice and monitoring system which is now used by thousands of Dutch primary school children on a daily or weekly basis, providing a new window on cognitive development. We will introduce the origin of this new instrument, called Math Garden, explain its setup, and present and discuss ways to analyze children’s individual developmental pathways.

Bounded number theory says that number is not infinite; that is, the number is limited. To come to a conclusion about limited number, one needs to understand the meaning of math and varying spaces, so one needs to understand that math and spaces interact. A matemática tem a função de descrever com precisão o mundo, onde os números representam elementos ou fatos que racionalmente elementos ou fatos pertencem ao espaço, e os espaços têm propriedades que os diferenciem de outros espaços; portanto, não há nenhum elemento ou fato infinito devido a diferenças nas propriedades dos espaços não permite o elemento ou fato em todos os espaços.

Anomaly detection in equipment processes plays an important role in the oil and gas sector. Algorithms for detecting anomalies in measured data are best understood in computer science and mathematics. Therefore, a possible transfer of knowledge from the latter knowledge area to the former can play a significant role. This paper addresses such a task by analyzing bibliometric data of Computer Science and Mathematics papers published in MDPI journals and publications found on the SPE search platform. It is shown that the main algorithms both extensively studied in MDPI publications and found in SPE publications and reflecting the anomaly detection problem are Random Forest, Support Vector Machine, Long-term Memory Method and Recurrent Neural Network. The main advantages and disadvantages of these methods are briefly described. Examples of classical, highly cited publications describing the work of these algorithms are given. Examples of papers describing their application in the oil and gas industry are given. The sections of SPE disciplines with the largest number of publications using the above algorithms that are frequently used for anomaly detection are presented.

It is known from ancient Egyptian mathematical papyri that the Egyptians were able to calculate the area of a circle with great accuracy. How they found the formula for this calculation was still unknown. Here it is shown how the unknown ancient Egyptian mathematician found a method for calculating the area of a circle and the ratio of a circle’s circumference to diameter.

In this work, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced bilattice of four vertices. We use the logarithmic function of the Shannon entropy H_(s) to construct the paraconsistent equations and thus adapt a probabilistic model for representations in quantum physics. Through analyses of the interlaced bilattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, quantum entanglement, wave functions, and equations that determine the energy levels of the layers of an atom. At the end of this article, we use the hydrogen atom as a basis of the representation of the PAL2v model, where the values of the energy levels in six orbital layers are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.

This work is devoted to the construction and study of commutative gates for a two-qubit quantum system. Using four-dimensional algebra developed by the Kazakh mathematician Abenov M.M. all groups of commutative gates have been constructed, and among all states of a two-qubit quantum system, unitary states with which a specific gate is connected have been identified. An explicit type of gate is described that transfers a quantum system from one unitary state to another unitary state. The proposed approach opens up new possibilities for the design of quantum algorithms not only for two-qubit quantum systems, but also for $n$-qubit quantum systems.

A teoria diz que o número interage com os espaços com base no significado da matemática, desta forma é possível obter conhecimento numérico. A teoria mostra a possibilidade de usar espaços relacionados entre si para explicar as razões pelas quais dois números pares formam um par, dois números ímpares formam um par, um número par e um ímpar formam um número ímpar, três números ímpares formam um número ímpar, três números pares formam um número ímpar. um par, um ímpar e dois pares formam um ímpar, dois ímpares e um par formam um par.

This article objectively assesses, the hypothesis of the streamline's shape theory and its formulated equation. The deduction of proof uses algebra rather than first-order partial differential equations to address the specific hypothesis of "Streamline's shape theory" from the fundamental perspective of applied mathematics and scientifically derives mathematical relations of the axioms and corollaries in the field of fluid dynamics. The algebraic methods employed provide progressively more distinct and precise solutions compared to first-order partial differential equations. The foremost objective of this work is to evaluate if the formulations of the streamline's shape theory can have solutions for inviscid-incompressible and viscid-compressible flows of Newtonian fluids and to identify their nature. Secondly, to understand how the topology of the body and the free-stream conditions affect these solutions with due regards to the shape and size of the body interacting with the fluid flow. Finally, to explore the possibility of this theory to develop a CFD solver for streamline simulation to reduce the experimentation in the analysis of flow-structure interactions of Newtonian fluids and also to identify its scope of applications and limitations.

This paper presents a novel approach to demonstrate the Collatz Conjecture, an unsolved problem in mathematics stating that all positive integers will eventually converge to 1 when subjected to a recursive sequence of operations. We introduce Algebraic Inverse Trees (AITs), innovative data structures that characterize relationships within the Collatz sequence by tracing inverse transformations back to the origin. Leveraging properties unveiled through this inverted representation, including absence of non-trivial cycles and guaranteed convergence of paths, we construct a topological framework to formally prove that all trajectories invariably lead to 1 under the Collatz iterative process. This modern technique provides not only the machinery to manifest a rigorous proof, but also grants intuitive insights into the deep complexity of this notorious yet elementary conjecture.

The usage of Quantum Similarity through the equation Z = {∀θ ∈ Z → ∃s ∈ S ∧ ∃t ∈ T : θ = (s, t)}, represents a way to analyze the way communication works in our DNA. Being able to create the object set reference for z being (s, t) in our DNA strands, we are able to set logical tags and representations of our DNA in a completely computational form. This will allow us to have a better understanding of the sequences that happen in our DNA. With this approach, we can also utilize mathematical formulas such as the Euler–Mascheroni constant, regression analysis, and computational proofs to answer important questions on Quantum biology, Quantum similarity, and Theoretical Physics.

Several problems of radiative transfer are yet unsolved because of the difficulties of the calculations involved in them, especially if the intervening shapes are geometrically complex. The main goal of our investigation in this domain is to convert the formulas that were previously derived, into a graphical interface based on the projected solid-angle principle. Such procedure is now feasible by virtue of several widely diffused programs for Algorithms Aided Design (AAD). Accuracy and reliability of the process is controlled by means of the analytical software DianaX developed at an earlier stage by the authors. With this new approach the often cumbersome procedure of lighting and thermal exchange calculations can be simplified and made available for the neophyte, with the undeniable advantage of reduced computer time.

Solving Linear equations with large number of variable contains many computations to be performed either iteratively or recursively. Thus it consumes more time when implemented in a sequential manner. There are many ways to solve the linear equations such as Gaussian elimination, Cholesky factorization, LU factorization, QR factorization. But even these methods when implemented on a sequential platform yield slower results as compared to a parallel platform where the time consumption is reduced considerably due to concurrent execution of instructions. The above mentioned linear equation solving methods can be implemented on the parallel platform using the direct approaches such as pipelining or 1D and 2D Partitioning approach. Vedic mathematics is a very ancient approach for solving mathematical problems. These Vedic mathematical approaches are well known for quicker and faster computation of mathematical problems. Vedic Mathematics provides a very different outlook towards the approach of solving linear Equation on parallel platform. It could be considered as a better approach for reducing space consumption and minimizing the number of algebraic operations involved in solving linear equation. In future Vedic Mathematics might serve as a viable solution for solving linear equation on parallel platform.