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The study focuses on the identification of relationships and/or rules between computational thinking (CT) concepts among the undergraduate students of Applied Informatics due to their attitudes towards mathematics. We analyze three CT concepts -- decomposition, pattern recognition, and algorithmic thinking. We assume that students who have a closer relationship with mathematics, a positive attitude towards mathematics, have better developed CT. We conducted the experiment during the 2022/2023 academic year on the Information Coding and Displaying subject. The results indicate that those students who have no relationship to mathematics, negative attitude towards mathematics, have no problem with decomposition and pattern recognition, but without significant algorithmic thinking. On the other hand, students who have a close relationship with mathematics are also able to decompose or recognize patterns, but moreover they have shown algorithmic thinking. The contribution of the study comprises the identification of relationships and/or patterns of computational thinking concepts among students who have a relationship to mathematics, who cannot assess their relationship to mathematics, as well as among students who have no relationship to mathematics. Our results indicate a different occurrence of computational thinking concepts as well as links and/or relationships between them.

Purpose: Ethnomathematics are used in motifs by the Dayak Ngaju Tribe in Central Kalimantan. The motifs contain some Ethnomathematical objects and concepts for Geometry and values. Therefore, this study aimed to describe the motifs based on mathematical objects and concepts of Geometry and value viewed from ethnomathematics aspects. Methodology: This study used a qualitative approach with an ethnography method. The researchers collected information from documents and books. They conducted in-depth observations and interviews with the subjects regarding the culture of the Dayak Ngaju people who reside downstream of the Kahayan River in Central Kalimantan. The subjects were a Dayak Ngaju craftsman and a priest of the Hindu Kaharingan community. The motifs consist of "tingang," "dandang tingang," "jata," "batang garing," "tanduk muang," "buntut kakupu gajah," "taya" tree and "rambunan tambun." Findings: The motifs contain some mathematical objects and concepts. Mathematical objects are created as circles, "batang garing" and "jata" motifs, and a six-sided shape in the "tanduk muang" motif. The concept is the geometric transformations, namely the axis reflection in the mdandang tingang and tanduk muang motifs the axis reflection in the motifs of "tingang," "batang garing," "tanduk muang" and "taya" tree. The rotation on point (0,0) in the motifs of "buntut kakupu gajah" and "taya" tree, and the translation in the motif of "jata." Significance: The study provides some mathematical objects and concepts in the motifs of the Dayak Ngaju tribe in Central Kalimantan. Students learning those objects and concepts should be related to their culture, namely the motifs, and they should acquire the values in such learning. Ethnomathematics plays an important role among Dayak Ngaju people in understanding mathematics concepts such as Geometry and values.

To fully possess mathematical competence and to understand its relevance, importance and aesthetics, it is essential to be aware of aspects of mathematics not only as a school subject but also as a scientific discipline. In a systematic literature review, the theoretical characterization of compulsory school students' beliefs about mathematics as a discipline is investigated, as well as the empirical tendencies in the nature of their actual beliefs. Furthermore, the valuation of these beliefs is addressed. The 18 included studies demonstrate a clear pattern in applying a dualistic/relativistic spectrum when characterizing and analysing students' beliefs about mathematics as a discipline, with students generally possessing dualistic beliefs, which is in contrast to what is favourable to their learning.

Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students' CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.

The purpose of this research was to explain why many people do not like mathematics and find it difficult because it is difficult to understand or because a teacher they had did not give the appropriate weight. The methodology used in this research was the quantitative method. The sample was collected through electronic questionnaires involving sixty-three (63) participants from pedagogical departments. The following survey shows the main results of the research, more specifically, that negative emotions about mathematics are more prevalent. The three main elements that characterize the successful teaching approach of mathematics at school are the transmission of knowledge by the teacher, the approach of knowledge through play, and the selection of appropriate activities. While the two most appropriate ways of approaching mathematics in kindergarten are through play but also through investigation and discovery by the child based on the participants' answers.

STEM education is on demand more than ever as the workforce relies on 21st century skills and STEM disciplines. This paper presents a framework (IMS-TEAM) for integration of mathematics and science with the use of technology and modeling in an authentic context. The activity based on this framework is designed for and implemented with forty-four 8th grade students in Turkey. The study was conducted to investigate the impact of the activity as well as the IMS-TEAM framework. A qualitative methodology was utilized. Data analysis revealed that different components of our conceptual framework fostered the integration of mathematics and science affecting the nature of students' engagement with the activity. Different frameworks are required to be adapted to different environments with the consideration of learners and teachers. Future research investigating the effectiveness of IMS-TEAM framework adapted to different content and disciplines would provide more evidence on the effectiveness of the framework.

The teachers' beliefs in ethnomathematics-based numeracy learning are a crucial element to be able to develop students' numeracy skills. The teachers' beliefs in developing students' numeracy skills through ethnomathematics-based numeracy learning is a teacher's personal view about certain practices that are considered correct, which include four dimensions. The first dimension is the teachers' beliefs about numeracy. The second dimension is teachers' beliefs about the role of ethnomathematics in learning numeracy. The third dimension is teachers' beliefs about ethnomathematics-based numeracy teaching. The fourth dimension is teachers' beliefs about ethnomathematics-based numeracy learning. This study aimed to investigate the characteristics of teachers' beliefs in developing students' numeracy skills through ethnomathematics-based numeracy learning. The teacher's response was acquired through the completion of a questionnaire. The findings indicated that most teachers believed fostering students' numeracy skills could be achieved by implementing ethnomathematics-based numeracy learning inside the semi-realisticmechanistic (SRM) categories. Further analysis reveals that more extended teaching experience may mean something other than that a teacher has a realistically oriented outlook. Teachers with teaching experience of fewer than five years (new teachers) and 5 to 10 years (junior teachers') have a semi-realisticmechanistic (SRM) view. Most teachers with more than 10 to 15 years (semi-senior-teachers) of teaching experience have a dominant realistic (DR) idea. In contrast, teachers with more than 15 years (senior teachers) of teaching experience have a semi-realistic-mechanistic (SRM) view and a dominant realistic (DR) view. Teachers' positive beliefs will likely improve students' numeracy skills in general and based on teaching experience in the dominant realistic (DR) and realistic (R) categories regarding ethnomathematics-based numeracy learning.

The present study examines the first-year engineering students' attitudes towards mathematics, their beliefs and self-efficacy about mathematics, as part of their affective performance, in relation to their mathematical academic performance before and after attending an introductory mathematics course. It aims to contribute on the ongoing discussion about the teaching of mathematics at the level of higher education in engineering programs. First-year engineering students completed a questionnaire and a test after their entrance at the university. Their mathematical performance was examined by using their results at the midterm and the final mathematical mark during AMAT111 course offered at the first semester of their studies. Results indicated that aspects of the affective domain were related with students' performance, while the predominant role belonged to their previous mathematical knowledge and skills (as learning outcome of the high school education), which undoubtedly need further enhancement. The belief about a formalistic perspective of mathematics and the lack of understanding of the implementation of the mathematical concepts on engineering problem solving situations were obstacles for them on recognizing the importance of attending mathematics courses as part of their engineering studies. Discussion concentrates on the following up steps, which have to be done at the level of higher education in order to face the initial difficulties, which have been identified.

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pretest and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students' results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students' disorientation is one of the purposes of history in mathematics education.

The cognitive reflection test (CRT) assesses an individual's capacity to restrain impulsive and intuitive responses and to engage in critical reflection on mathematical problems. The literature indicates that several factors influence students' performance on CRT, including gender, age, and prior knowledge of mathematics. In this study, our objective was to investigate the correlation between CRT scores and students' achievements in both mathematics and physics. We conducted our research with a sample of 150 Italian high school students, and the findings revealed a positive predictive relationship between CRT scores and students' performance in both mathematics and physics. Furthermore, we employed an ordinal logistic regression to evaluate the impact of CRT scores, gender, and school level on students' achievements in mathematics and physics. The results showed that both CRT scores and school level had statistically significant effects on predicting these achievements. In contrast, gender emerged as a statistically significant factor only in predicting students' mathematics achievements.

One of the main objectives of international large-scale assessments is to make comparisons between different countries, education policies, education systems, or subgroups. One of the main criteria for making comparisons between different groups is to ensure measurement invariance. The purpose of this study was to test the measurement invariance of the mathematics intrinsic motivation scale across 14 countries. For this purpose, the "students like learning mathematics" scale, which measures intrinsic motivation for mathematics, was included in the TIMSS 2019 cycle. The study sample consisted of a total of 152992 students, 70192 4th grade and 82800 8th grade students from 14 different countries participating in the TIMSS 2019 cycle. Measurement invariance was tested with Multi-Group Confirmatory Factor Analysis (MG-CFA) and Alignment Method. The mathematics intrinsic motivation scale provides only configural invariance according to MG-CFA at the 4th grade level, whereas the scale provides approximate invariance according to the alignment method. At the 8th grade level, the scale provides configural and metric invariance according to MG-CFA, whereas the scale provides approximate invariance according to the alignment method. The results indicate that the mathematics intrinsic motivation scale provides approximate measurement invariance at both grade levels and that comparisons can be made between the scores of the identified countries.

STEM education plays a key role in influencing and orienting students' interests towards STEM fields and careers. This influence is multifaceted, involving not only STEM content and experiences but also teachers, schools, and personal factors. The purpose of this study is to explore the factors impacting the academic performance of 951 tenth grade students in STEM subjects (physics, chemistry, biology, mathematics, and information technologies) who are attending public and private schools in two provinces of Turkey. Using a correlational research model, the study assessed how students' personal characteristics, teacher effectiveness and school characteristics affect achievement in STEM courses. Data were collected using the 'Factors Affecting STEM Achievement Questionnaire (FA-STEM-A)', a 20-item questionnaire divided into three sub-dimensions. Analyses focused on the relationships between student characteristics, teaching quality, school infrastructure and STEM performance. Structural equation modelling revealed that positive student characteristics, especially fondness for STEM subjects and confidence in STEM abilities, moderately increase achievement. In contrast, negative factors attributed to teachers and schools, such as inadequate classroom activities, lack of educator expertise, inadequate technological resources, and large class sizes, hindered student performance. These findings emphasize the important influence of both inherent student qualities and external educational conditions in determining STEM education.

Contribution: Although a limited number of studies have compared textbooks used in introductory science courses (ISCs) and technical engineering courses (TECs), such a study has not been conducted regarding the Laplace transform (LT). The LT is one of the important topics that electrical engineering students learn as part of their undergraduate degree. It is instrumental in both ISCs (e.g., DEs) and TECs (e.g., signal processing (SP)). Background: Textbooks stand as one of the main resources for teaching and learning mathematics. Previous research has highlighted differences in how mathematical concepts are discussed in ISCs and TECs. These disparities might hinder students' opportunities to learn mathematics and identify the importance of mathematics in engineering. Intended Outcomes: The findings have the potential to increase awareness of mathematics and engineering instructors regarding the teaching and learning of the LT in ISCs and TECs. Additionally, it could result in the identification of several suggestions for textbook authors of DEs and SP, ultimately contributing to the improvement of engineering education for (electrical) engineering students. Application Design: This study uses the praxeological analysis rooted in the Anthropological Theory of the Didactic to analyze two textbooks. One is tailored for teaching and learning DEs, while the other addresses teaching and learning SP, a mandatory course for electrical engineering students in many countries. Findings: The findings indicate that there are several differences between the two textbooks, including differences in the purpose/motivation of presenting this topic and the definitions provided for the LT.

Contribution: Visual maps that illustrate how mathematics, physics, and electrical engineering classes are connected to each other during the first two years of the electrical engineering curriculum were developed. Key terminology and differences in presentation between fields are discussed. Background: Experience has shown that engineering students struggle when they need to use an approach from their mathematics or physics courses in their first- or second-year engineering courses. In particular, students have difficulty making connections between what they learned in mathematics and physics and how it applies to engineering problems. Improving students' ability to identify the connections between fields could increase student resilience in their engineering coursework. Research Questions: 1) Can visual representations of topic connections between fields across the entry-level engineering curriculum increase student's motivation for learning topics in physics and mathematics and improve their problem solving ability? 2) Are there language barriers or other differences between fields that hinder student learning? Methodology: A multidisciplinary team of faculty members from mathematics, physics, and electrical engineering developed visual representations of the links between the core electrical engineering, physics, and mathematics concepts required to solve problems that students will see in their early electrical engineering coursework. Inconsistencies in terminology or notation were explored and documented. Findings: The developed visual aids, coined systematic approach to problem solving (SAPS) maps, describe a mechanism for linking concepts and skills across the technical courses in the first two years of the electrical engineering curriculum.

To assess the integration of information and communication technologies (ICTs) in teaching and learning, a new construct for ICT competence was developed by the Programme for International Student Assessment (PISA) in 2022. The framework for ICT assessment involves four major dimensions; access to ICT, use of ICT, students' ICT competencies, and subject-related ICT use. In this paper, we analysed this ICT assessment in terms of validity construction of test scores with data from PISA 2018 and investigated ICT competence in relation to the variables of mathematics, science, and reading literacy. The analyses were based on public data from PISA 2018 for Turkey (N = 6890). After removal of univariate and multivariate outliers from the Turkish sample, factor analysis, correlation analysis, and structural equation modelling were performed on 5438 data items. In the study, we confirmed the four-dimensional structure of ICT competence for the Turkish sample. In this study, the construct validity of the PISA 2018 application ICT test was verified using the Turkish sample. The ESCS variable was included as a control variable in the analyses due to its significant impact on the relevant variables. The analysis showed that the mathematical literacy scores of the PISA 2018 Turkish students were positively low affected by the availability of ICT, negatively low affected by the entertainment of ICT, and positively low affected by the interest and perceived competence in ICT, use of ICT for educational purposes at school and outside school, and the use of ICT related to the subject. Considering the ICT variables that affected the PISA 2018 students' science literacy scores; the entertainment of ICT and the interest and perceived competence in ICT significantly low affected the students' use of ICT on the subject. On the other hand, the availability of ICT negative significantly low affect their science literacy scores. While the entertainment of ICT negatively low affected the science literacy scores, interest and perceived competence in ICT and use of ICT for educational purposes at school and outside school positively low affected the students' use of ICT on the subject. Finally, when we look at the ICT variables that low affected the students' reading literacy scores; and use of ICT for educational purposes at school and outside school and the interest and perceived competence in ICT significantly positive low affected the use of ICT on the subject. On the other hand, the availability of ICT negative significantly low affect reading literacy scores. While the entertainment of ICT negatively low affected reading literacy scores; interest and perceived competence in ICT positively low affected the use of ICT on the subject.

Students are encouraged to develop a set of scientific skills and disciplinary practices common across the STEM disciplines. These skills (scientific inquiry, quantitative skills, laboratory and computational skills, communication skills, teamwork/interpersonal skills, interdisciplinary competency) are highlighted as important in discipline-based guiding documents -- biology (Vision and Change in Undergraduate Biology Education: A Call to Action), chemistry (American Chemical Society Guidelines and Evaluation Procedures for Bachelor's Degree Programs), and mathematics (A Common Vision for Undergraduate Mathematical Sciences Programs in 2025) -- for undergraduate teaching of biology, chemistry, and mathematics, and for the professional success of STEM college graduates. To promote interdisciplinary teaching and learning of STEM, we present a comprehensive comparison of the different disciplines' competency statements for undergraduate education. This organization and comparison of commonalities in scientific skills and disciplinary practices can be used by faculty and departments to come together to break down traditional silos, help their students more easily apply learning from one STEM discipline to another, and to create institutional change.

In this article, we discuss Micro Assignment Guided Inquiry and Collaboration (MAGIC), an active learning method that draws on the merits of inquiry-based learning in STEM courses. We describe the use of Micro Assignments (MAs) consisting of a series of short, instructive guiding questions that scaffold the course material. Students work through these questions and present solutions to the class. The instructor facilitates learning as well as collaboration among the students during face-to-face interactions, providing the Guided Inquiry and Collaboration (GIC). We present a qualitative discussion about this active learning approach that achieves some of the documented benefits, such as deep student engagement with the material and familiarity with communicating arguments. This method also helps students develop the skills they need as they move from lower- to upper-level courses, such as collaborating, active reading, and breaking down involved assignments and problems into manageable steps. Through GIC and use of the MAs, the instructor guides students to become more abstract thinkers who desire evidence, evaluate arguments, and no longer follow step-by-step formulas but rather produce logical thought processes.

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

Mentorship has been widely recognized as an effective means to promote student learning and engagement in undergraduate research experiences. However, little work exists for understanding different mentors perceived approaches to mentorship, including mentorship of students from backgrounds and educational trajectories not well represented in science, technology, engineering, and mathematics (STEM). Transfer students, in particular, face unique trajectories in their pursuit of research opportunities, yet few studies investigate how mentors describe their approaches to supporting these students. Using semistructured interviews, this study examines how mentors approach mentoring students from diverse backgrounds as research trainees, with an emphasis on transfer students. First, using phenomenography as an analytical approach, we identified four categories describing variations in how mentors reflected upon or accounted for the transfer student identity in their approaches. We find that research mentors vary in their understanding and exposure to the transfer student identity and may have preconceived notions of the transfer student experience. Second, we present vignettes to illustrate how mentors approaches to the transfer student identity may relate or diverge from their general approaches to mentoring students from different backgrounds and identities. The emerging findings have implications for developing effective mentorship strategies and training mentors to support transfer students.

Authoring of help content within educational technologies is labor intensive, requiring many iterations of content creation, refining, and proofreading. In this paper, we conduct an efficacy evaluation of ChatGPT-generated help using a 3 x 4 study design (N = 274) to compare the learning gains of ChatGPT to human tutor-authored help across four mathematics problem subject areas. Participants are randomly assigned to one of three hint conditions (control, human tutor, or ChatGPT) paired with one of four randomly assigned subject areas (Elementary Algebra, Intermediate Algebra, College Algebra, or Statistics). We find that only the ChatGPT condition produces statistically significant learning gains compared to a no-help control, with no statistically significant differences in gains or time-on-task observed between learners receiving ChatGPT vs human tutor help. Notably, ChatGPT-generated help failed quality checks on 32% of problems. This was, however, reducible to nearly 0% for algebra problems and 13% for statistics problems after applying self-consistency, a hallucination mitigation technique for Large Language Models.

Fostering equity in undergraduate science, technology, engineering, and mathematics (STEM) programs can be accomplished by incorporating learner-centered pedagogies, resulting in the closing of opportunity gaps (defined here as the difference in grades earned by minoritized and non-minoritized students). We assessed STEM courses that exhibit small and large opportunity gaps at a minority-serving, research-intensive university, and evaluated the degree to which their syllabi are learner-centered, according to a previously validated rubric. We specifically chose syllabi as they are often the first interaction students have with a course, establish expectations for course policies and practices, and serve as a proxy for the course environment. We found STEM courses with more learner-centered syllabi had smaller opportunity gaps. The syllabus rubric factor that most correlated with smaller gaps was Power and Control, which reflects Students Role, Outside Resources, and Syllabus Focus. This work highlights the importance of course syllabi as a tool for instructors to create more inclusive classroom environments.

In this paper, we first investigate the regularity of finite energy solutions to the following Wolff type integral system: { u (x) = R 1 (x) W β , γ (v p u r) (x) , u (x) > 0 , x ∈ R N , v (x) = R 2 (x) W β , γ (u q v s) (x) , v (x) > 0 , x ∈ R N , where γ > 1 , β > 0 , β γ < N , W β , γ is the Wolff potential, R 1 , R 2 are double bounded functions in R N and p , q > max ⁡ { 1 , γ − 1 } , r , s ≥ 0 with p − s ≥ q − r > − γ + 1. We exploit the regularity lifting lemma to obtain the optimal integrability, boundedness and decaying property of finite energy solutions to the system. Secondly, we establish sharp pointwise estimates of positive finite energy solutions to the p -Laplacian and k -Hessian systems related to the above integral system, by using the previous regularity results, the interior Hölder estimates of solutions for the corresponding differential systems and a doubling lemma of Poláčik, Quittner and Souplet (Duke Math. J.,2007). These extend Vétois's decay results (Indiana Univ. Math. J.,2019) on the positive solutions of Laplacian systems to the p -Laplacian and k -Hessian cases. We remark that our methods do not need Harnack type inequalities and it can be applied to deal with the solutions without radial structures. As far as we know, this is the first attempt to derive sharp decay estimates for possibly non-radial solutions involving k -Hessian operators. We also obtain some decay estimates of the gradients at infinity. [ABSTRACT FROM AUTHOR]

We show that a compact representation of either a semisimple Lie group or a totally disconnected group has a filtration with irreducible subquotients of finite multiplicity. In the Lie group case we show the stronger assertion, that it has an orthogonal decomposition into summands of finite lengths. This generalises and simplifies a number of more special spectral theorems in Deitmar and Monheim (Math Z 284(3–4):1199–1210, 2016, https://doi.org/10.1007/s00209-016-1695-9), Müller (Int Math Res Not 9(2):2068–2109, 2011), Venkov (in: Proceedings of the Steklov Institute of Mathematics, no. 4(153), ix+163 pp. (1983), 1982). We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms. We finally show that the space of cusp forms is complemented by the space of Eisenstein series. [ABSTRACT FROM AUTHOR]

Let (G/\Gamma,R_a) be an ergodic k-step nilsystem for k\geq 2. We adapt an argument of Parry [Topology 9 (1970), pp. 217–224] to show that L^2(G/\Gamma) decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multiplicity. In particular, we generalize a result previously established by Host–Kra–Maass [J. Anal. Math. 124 (2014), pp. 261–295] for 2-step nilsystems and a result by Stepin [Uspehi Mat. Nauk 24 (1969), pp. 241–242] for nilsystems G/\Gamma with connected, simply connected G. [ABSTRACT FROM AUTHOR]

Motivated by the many roles that hook lengths play in mathematics, we study the distribution of the number of t-hooks in the partitions of n. We prove that the limiting distribution is normal with mean \[ \mu _t(n)\sim \frac {\sqrt {6n}}{\pi }-\frac {t}{2} \] and variance \[ \sigma _t^2(n)\sim \frac {(\pi ^2-6)\sqrt {6n}}{2\pi ^3}. \] Furthermore, we prove that the distribution of the number of hook lengths that are multiples of a fixed t\geq 4 in partitions of n converge to a shifted Gamma distribution with parameter k=(t-1)/2 and scale \theta =\sqrt {2/(t-1)}. [ABSTRACT FROM AUTHOR]

Financial forecasting involves predicting the future financial states and performance of companies and investors. Recent technological advancements have demonstrated that machine learning-based models can outperform traditional financial forecasting techniques. In particular, hybrid approaches that integrate diverse methods to leverage their strengths have yielded superior results in financial prediction. This study introduces a novel hybrid model, entitled EMD-TI-LSTM, consisting of empirical mode decomposition (EMD), technical indicators (TI), and long short-term memory (LSTM). The proposed model delivered more accurate predictions than those generated by the conventional LSTM approach on the same well-known financial datasets, achieving average enhancements of 39.56%, 36.86%, and 39.90% based on the MAPE, RMSE, and MAE metrics, respectively. Furthermore, the results show that the proposed model has a lower average MAPE rate of 42.91% compared to its state-of-the-art counterparts. These findings highlight the potential of hybrid models and mathematical innovations to advance the field of financial forecasting. [ABSTRACT FROM AUTHOR]

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ -Fibonacci statistical convergence, strong Δ -Fibonacci summability, and Δ -Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers. [ABSTRACT FROM AUTHOR]

The article deals with the shortage of STEM teachers in Germany and its impact on the education system and the economy. It is pointed out that well-trained teachers are essential for high-quality teaching and equal opportunities in the education system. The shortage of teachers in STEM disciplines (mathematics, computer science, natural sciences, technology) is already leading to a massive loss of teaching hours and a decline in student performance. Industry, science, and research heavily rely on well-trained STEM professionals. The article suggests measures to counteract the teacher shortage, such as involving external learning partners, targeted recruitment of career changers and lateral entrants, and increased use of digital teaching and learning methods. It is recommended to create spaces for individual learning in teacher training and to promote research and project-based learning in STEM subjects. It is emphasized that schools should be designed in a contemporary and modern way to make the teaching profession more attractive. [Extracted from the article]

Students are encouraged to develop a set of scientific skills and disciplinary practices common across the STEM disciplines. These skills (scientific inquiry, quantitative skills, laboratory and computational skills, communication skills, teamwork/interpersonal skills, interdisciplinary competency) are highlighted as important in discipline-based guiding documents—biology (Vision and Change in Undergraduate Biology Education: A Call to Action), chemistry (American Chemical Society Guidelines and Evaluation Procedures for Bachelor's Degree Programs), and mathematics (A Common Vision for Undergraduate Mathematical Sciences Programs in 2025)—for undergraduate teaching of biology, chemistry, and mathematics, and for the professional success of STEM college graduates. To promote interdisciplinary teaching and learning of STEM, we present a comprehensive comparison of the different disciplines' competency statements for undergraduate education. This organization and comparison of commonalities in scientific skills and disciplinary practices can be used by faculty and departments to come together to break down traditional silos, help their students more easily apply learning from one STEM discipline to another, and to create institutional change. [ABSTRACT FROM AUTHOR]

Using learning objectives to guide course design is often considered an educational best practice, but little research exists that explores how students use them over time and across courses. We surveyed students on their use and perceived value of learning objectives as the semester progressed across four science, technology, engineering, and mathematics (STEM) disciplines, examined students' ability to match exam questions with learning objectives, and analyzed how their course performance related to these qualities. We also gathered instructors' information on their implementation of learning objectives in these courses. We identified distinct disciplinary differences both in students' use and perceived benefit of learning objectives and in instructors' implementation of them. Students in less quantitatively focused courses, i.e., biology and organic chemistry, reported valuing and using learning objectives more than students in more quantitatively focused math and physics courses. Students' ability to match learning objectives with exam questions, however, positively correlated with exam score and final course grade in all our study courses. Our results have implications for considering disciplinary practices for use of learning objectives as instructors design and implement courses, educational researchers plan studies, and assessment specialists formulate institutional assessment plans. [ABSTRACT FROM AUTHOR]

Based on the geometric background of Sombor index and motivating by the higher order connectivity index and the Sombor index, we introduce the path-coordinate of a path in a graph and a degree-point in a higher dimensional coordinate system, and define the higher order Sombor index of a graph. We first consider mathematical properties of the higher order Sombor index, show that the higher order connectivity index of a starlike tree is completely determined by its branches and that starlike trees with a given maximum degree which have the same higher order Sombor indices are isomorphic. Then, we determine the extremal values of the second order Sombor index for all trees with n vertices and characterize the corresponding extremal trees. Finally, the chemical importance of the second order Sombor index is investigated and it is shown that the new index is useful in predicting physicochemical properties with high accuracy compared to some well-established indices. [ABSTRACT FROM AUTHOR]

We study (1 + 2u + 2v)-constacyclic code over a semi-local ring S = Z4 + uZ4 + vZ4 with the condition u² = 3u, v² = 3v, and uv = vu = 0, we show that (1+2u+2v)-constacyclic code over S is equivalent to quasi-cyclic code over Z4 by using two new Gray maps from S to Z4. Also, for odd length n we have defined a generating set for constacyclic codes over S. Finally, we obtained some examples which are new to the data base [Database of Z4 codes [online], http://Z4 Codes.info(Accessed March 2, 2020)]. [ABSTRACT FROM AUTHOR]