Mathematical Curiosity Research Articles

Continuous data assimilation for the 3D and higher-dimensional Navier–Stokes equations with higher-order fractional diffusion

We study the use of the Azouani-Olson-Titi (AOT) continuous data assimilation algorithm to recover solutions of the 3D Navier–Stokes equations modified to have finer-order fractional diffusion. The fractional diffusion case is of particular interest, as it is known to be globally well-posed for sufficiently large diffusion exponent α. In this work, we prove that the assimilation equations are globally well-posed, and we demonstrate that the solutions produced by the AOT algorithm exhibit exponential convergence in time to the reference solution, given a sufficiently high spatial resolution of observations and a sufficiently large nudging parameter. We note that the results hold in arbitrary spatial dimensions d where d≥2, so long as α≥12+d4. Though the cases d>3 are likely only a mathematical curiosity, we include them as they cause no additional difficulty in the proof.

An Analysis of Students’ Mathematical Curiosity in Online Learning Viewed from Academic Level and Gender

Online learning affects students' curiosity, so it is important to develop students' curiosity during the pandemic. The purpose of this study is to describe and analyze students' curiosity about online learning. This study was conducted in the Department of Mathematics Education during the odd semester 2021/2022 with 106 students in three different courses. The research instrument was a mathematical curiosity questionnaire administered to students using the Google Documents application. The data analysis technique used was descriptive analysis. The results showed that the general curiosity of the students is classified as "strong" with a percentage of 75.17%. Academically, students with low, medium and high curiosity are considered strong with percentages of 74.07 percent, 76.5 percent and 75.12 percent. Measured by gender differences, the proportion of male and female students is 76.43 and 77.5 percent. Data analysis showed that in the era of the Covid-19 pandemic, curiosity about learning mathematics does not depend on the academic level of online learning or on gender differences. The effect of the result that the students during the Covid-19 pandemic, mathematical curiosity is still used in online learning and should be improved. This research contributes to the growing body of knowledge on mathematical learning in the digital age and offers practical recommendations for fostering mathematical curiosity in online.

Pengembangan LKPD Matematika dengan Pendekatan Contextual Teaching and Learning Pada Kelas V SD

This research began by finding that students lack mathematical problem-solving, critical thinking, and curiosity skills, due to their difficulty applying mathematical principles in real-world situations. They have difficulty applying what they have learned in real life, thus limiting their ability to solve math difficulties. Learner Worksheets (LKPD) are not designed to allow learners to actively develop their own understanding. The purpose of this study is to develop authentic, practical, and successful LKPD using CTL (Contextual Teaching and Learning) approach to increase students' participation in problem solving in grade V elementary school. This research follows Plomp's development paradigm, which consists of three stages: initial investigation, prototype development, and assessment. The result of this research is a validated, practical, and effective mathematics LKPD with CTL method to be used in grade V elementary school

Playfulness in Mathematics Teaching in the 5th Grade of Elementary School at Tereza Lemos de Oliveira Santos State School in Atalaia do Norte-AM Municipality

The purpose of the present work is to verify if the teaching of mathematics can become interesting for the students of the 5th year of Elementary School, through the playfulness with the use of mathematical games. In this context, mathematical games: contig 60, multiplication domino, division marathon and integer race, emerged as an educational process, with the aim of promoting teaching and learning through play. As a methodology of qualitative documentary approach, a questionnaire was applied to find out the students’ level of learning, right after, there was a class on the contents of addition, subtraction, multiplication and division. As a complement, the games mentioned above were applied. When the questionnaire was applied again, there was a great improvement in the level of learning of the students in this 5th grade class, in relation to the four basic operations of mathematics. Thus, it can be noted that the use of games enabled the construction of students’ knowledge, thus awakening creativity, logical reasoning and their motor skills. Also, through these activities, a greater interest and curiosity in learning mathematics was noticed in the students.

The Synge G-Method: cosmology, wormholes, firewalls, geometry

Unphysical equations of state result from the unrestricted use of the Synge G-trick of running the Einstein field equations backwards; in particular often this results in ρ+p<0 which implies negative inertial mass density, which does not occur in reality. This is the basis of some unphysical spacetime models including phantom energy in cosmology and traversable wormholes. The slogan ‘ER = EPR’ appears to have no basis in physics and is merely the result of vague and unbridled speculation. Wormholes (the ‘ER’ of the slogan) are a mathematical curiosity of general relativity that have little to no application to a description of our Universe. In contrast quantum correlations (the ‘EPR’ of the slogan) are a fundamental property of quantum mechanics that follows from the principle of superposition and is true regardless of the properties of gravity. The speculative line of thought that led to ‘ER = EPR’ is part of a current vogue for anti-geometrical thinking that runs counter to (and threatens to erase) the great geometrical insights of the global structure program of general relativity.

Some generalisations and extensions of a remarkable geometry puzzle

There is a very interesting mathematical puzzle involving the geometrical configuration in the book Mathematical Curiosities [1, 2] by Alfred Posamentier and Ingmar Lehmann. It is shown in Figure 1.

Developing a Mathematical Curiosity Scale for Adolescents: Validity and Reliability Study

Curiosity offers opportunities for personal growth by instilling a desire to learn, explore, and investigate. Therefore, it is considered essential to encourage curiosity, especially in children and adolescents, for their future lives. Similarly, mathematical curiosity leads the individual to develop in mathematics by directing their desire to learn about mathematics toward discovery. In this context, the study aims to create a scale that provides accurate and reliable measurements that is a valid and reliable Likert-type scale of mathematical curiosity of secondary and high school students. 499 students participated in the exploratory factor analysis, 294 in the confirmatory factor analysis, and 91 in the test-retest analysis. As a result of the exploratory factor analysis, the scale structure with 3 factors and 20 items explains 57.95% of the total variance. The construct validity of the scale was examined through confirmatory factor analysis. The Cronbach alpha reliability coefficient of the scale was found to be 0.903. The reliability coefficients of the sub-dimensions of the scale are .838, .842, and .690, respectively.

The Influence of Creative Problem-Solving Learning Assisted by Ethnomathematics Nuance Modules on Problem-Solving Ability and Curiosity

Mathematics is often perceived as a complex and difficult lesson to solve, thus making students' mathematical problem-solving ability and curiosity low. This study aimed to analyze the influence of learning using the Creative Problem-Solving (CPS) method assisted by ethnomathematics nuance modules on the problem-solving ability and curiosity of class XI students at SMAN 1 Plampang. This research was a type of experimental research using a pre-experimental design with a one-group pretest–post–test design model. The data collection technique used purposive sampling to collect data as a sample of 35 students in class XI MIPA 1 from a total population of 105 students in class MIPA. The determination of the sample is based on the results of the average score in mathematics and discussion with the mathematics teacher. The results of the study showed that the influence of Creative Problem Solving (CPS) learning assisted by ethnomathematics nuance modules had a significant effect on students' problem-solving ability and students' curiosity in geometry transformation material at SMAN 1 Plampang.

Upper secondary school tracking and major choices in higher education: to switch or not to switch.

This study aims to investigate the characteristics of students who switch versus those who do not switch when they transition from upper secondary to higher education. The data from 1338 students randomly selected from 21 HEIs in Cambodia in 2020 found that upper secondary school students are more likely than not to switch academic majors when they enter higher education. The tendency to switch is more common for female students in science-track, most of whom chose non-STEM majors such as business, management, accounting and finance. Probit analysis revealed that the decision to switch is influenced by individual academic performance and interest in science and mathematics at upper secondary school, household's socioeconomic status, higher education institution (HEI)'s location and type. However, students whose like mathematics and physics and who have a higher technology readiness index score and those who were awarded scholarships are less likely to switch from science to non-STEM majors. Teaching approaches that create opportunities for students to engage in practical classroom activities and stimulate their curiosity in science and mathematics should be considered. Efforts to optimise learning experiences should therefore focus on creating a highly interactive teaching-learning environment as a cognitive-activation strategy for promoting students' interest and enjoyment of the subjects they are studying. Scholarship can also be an alternative to address the switching issue.

Learning To Promote Students’ Mathematical Curiosity And Creativity

[Background] Discovery learning is a model that guides students to actively learn in finding concepts or knowledge through an inquiry process based on the data or information obtained from experiments or observations. [Objective] The present study examined the implementation of a modification of discovery learning using mind mapping in promoting students’ mathematical curiosity and creativity. [Method] A Classroom Action Research (CAR) design was employed in this study. The participants were 250 students in Middle Indonesian who registered in the academic year of 2020/2021. [Results] The descriptive analysis showed that the students achieved an average score of 44.04 with a standard deviation of 18.716 in pre-CAR, 52.48 with a standard deviation of 22.978 after cycle I, and 76.72 with a standard deviation of 17.097 after cycle II. Based on the students’ mathematical creative thinking scores, 2 (8%) students could perform creative thinking in pre-CAR, 6 (24%) students after cycle I, and 22 (88%) students after cycle II. These figures indicated that the students classically achieved the ability to think creatively in mathematics after cycle II. [Conclusion] It was concluded that the implementation of modified discovery learning and mind mapping could promote students’ mathematical creative thinking ability. The interview results also suggest that the learning model could increase mathematical curiosity of both the low and high achievers.

인공지능(AI) 역량 함양을 위한 고등학교 수학 학습 자료 개발 및 적용에 관한 연구

Objectives The purpose of this study is to develop teaching and learning materials for artificial intelligence(AI) math classes, to confirm the appropriateness of the contents and methods of materials for high school students, and to understand educational effects as math education materials.&#x0D; Methods Teaching and learning materials were developed by selecting a linear regression and Monte Carlo method containing mathematical learning elements of the high school curriculum among machine learning of AI. The developed learning materials were applied to 5 second-year high school students, and based on the results, teaching and learning materials were finally completed.&#x0D; Results As a result of the study, math classes using AI stimulated students' reflective thinking in the learning process and helped them understand math progressively. In addition, it stimulated students' interest and curiosity in mathematics and had a positive effect on improving the affective domain of mathematics.&#x0D; Conclusions The result of this study provides some useful implications to development of teaching and learning materials that can understand AI mathematics using Python programming, and experience internal-external connections. And it is expected to be a useful guide for construction of teaching and learning materials for AI math classes.

How does mathematical modeling competency affect the creativity of middle school students? The roles of curiosity and guided inquiry teaching.

Mathematical modeling has become a crucial competence in mathematics education in many countries and regions due to the increasingly complex real-world problems that students face in the 21st century. Previous research has shown that mathematical modeling contributes to the development of students' creativity, particularly with respect to stimulating and protecting the curiosity of children. However, previous studies have not explored or examined the relationships among middle school students' mathematical modeling competency, curiosity, and creativity based on data drawn from large-scale assessments and have not investigated the influence of teachers' teaching methods in this context. This study used convenience sampling to select 4,531 seventh-grade students from eastern and western, urban and rural areas in China. Online tests and questionnaires were used to measure their mathematical modeling competency, curiosity, creativity and guided inquiry teaching, and a moderated mediation model was used to analyze the effect of mathematical modeling competency on creativity. The results showed the following. (1) There are statistically significant differences between boys and girls in terms of their mathematical modeling competency, curiosity, and creativity. Specifically, boys score significantly higher than girls on these variables. (2) Creativity exhibits a statistically significant positive correlation with mathematical modeling competency, curiosity, and guided inquiry teaching. (3) Curiosity mediates the relationship between mathematical modeling competency and creativity, and guided inquiry teaching moderates the influence of curiosity. In high-level guided inquiry teaching classes, curiosity has a stronger influence on creativity, and it mediates the relationship between mathematical modeling competency and creativity more strongly. This study empirically verified the influence of mathematical modeling competency on creativity and provided a possible way to cultivate children's creativity. Future research should use longitudinal analysis to verify the causal relationship between mathematical modeling competency and creativity and to systematically explore the possible path by which mathematical modeling competency affects creativity.

Learning With Ethnomathematics Based Open Ended Approach Improves Creative Thinking Ability, Curiosity Character

Think more creatively and innovatively in dealing with problems and sites will not be possessed without extensive knowledge. This is one of the demands on all students to be able to think more creatively. the character of curiosity to be observed. The character of curiosity that will be instilled so that students have a strong self-curiosity, strength, and do not give up easily. Curiosity needs to be instilled in students through a fun approach so that students do not feel bored. Here, teachers as educators must be more creative in finding ideas to choose the right approach in developing students' curiosity. Many teachers are found using an expository model, where the teacher explains the material, provides examples and practice questions so that students are trained to do questions such as mechanics or machines. In addition, the assessment carried out emphasizes more on the final assessment and pays less attention to the process, so that mathematics learning is less meaningful; Prioritizing memorization over understanding. The purpose of this study is to examine whether learning with an Ethnomathematics-based Open Ended approach can improve students' creative thinking ability and curiosity in mathematics. Based on the above problems, an appropriate learning approach is needed that can bridge these problems, namely learning with an Ethnomathematics-based Open Ended Learning approach, where students are given the flexibility to answer their abilities to find and develop their own knowledge. The steps begin with the awarding of a problem sourced from culture and end with analyzing and evaluating the problem-solving process. Thus, learning with an Open Ended Learning approach based on Ethnomathematics, will have a very high contribution to students' mathematical creative thinking ability and the character of students' curiosity in mathematics learning.

Learning With Ethnomathematics Based Open Ended Approach Improves Creative Thinking Ability, Curiosity Character

Think more creatively and innovatively in dealing with problems and sites will not be possessed without extensive knowledge. This is one of the demands on all students to be able to think more creatively. the character of curiosity to be observed. The character of curiosity that will be instilled so that students have a strong self-curiosity, strength, and do not give up easily. Curiosity needs to be instilled in students through a fun approach so that students do not feel bored. Here, teachers as educators must be more creative in finding ideas to choose the right approach in developing students' curiosity. Many teachers are found using an expository model, where the teacher explains the material, provides examples and practice questions so that students are trained to do questions such as mechanics or machines. In addition, the assessment carried out emphasizes more on the final assessment and pays less attention to the process, so that mathematics learning is less meaningful; Prioritizing memorization over understanding. The purpose of this study is to examine whether learning with an Ethnomathematics-based Open Ended approach can improve students' creative thinking ability and curiosity in mathematics. Based on the above problems, an appropriate learning approach is needed that can bridge these problems, namely learning with an Ethnomathematics-based Open Ended Learning approach, where students are given the flexibility to answer their abilities to find and develop their own knowledge. The steps begin with the awarding of a problem sourced from culture and end with analyzing and evaluating the problem-solving process. Thus, learning with an Open Ended Learning approach based on Ethnomathematics, will have a very high contribution to students' mathematical creative thinking ability and the character of students' curiosity in mathematics learning.

Emerging diversity in a population of evolving intransitive dice.

Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for coevolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a set of evolving agents that interact competitively in a closed system, in which both the dynamics of mutations and competitive advantage emerge directly from interpreting a genome as the sides of a die. The model demonstrates sympatric speciation where new species evolve from existing ones while in contact with the entire ecosystem. Allowing free mutations both in the genomes and the mutation rates, we find, in contrast to hierarchical models of fitness, the emergence of a metastable state of finite mutation rate and diversity.

KEMAMPUAN DISPOSISI MATEMATIS MAHASISWA STKIP MUHAMMADIYAH ACEH BARAT DAYA

The purpose of this study was to determine the ability of students' mathematical disposition at one of the college in Aceh Barat Daya district. This research is descriptive quantitative, the data collection technique used was a mathematical disposition questionnaire. The research subjects are 21 students of mathematics education program, the results of the research show that for the indicator of confidence in learning mathematics, 67.1 is less in the category, the indicator of flexibility in doing math work is 76.7 medium category, indicator is persistent and tenacious in doing math tasks 75.0 medium category, indicator has curiosity in learning mathematics 83.5 moderate category, indicator reflects on the way of thinking and performance on oneself in learning mathematics 77.8 medium category, indicator appreciating math application 74.4 medium category, and indicator appreciating the role of mathematician 85 high category. Suggestions in this study are expected in the process of learning mathematics to give enthusiasm and motivation to students to learn mathematics by using various methods that are interesting and show usefulness in learning mathematics and increase confidence in learning mathematics.

Investigation of Primary Teacher Candidates' Curiosity in Mathematics in Terms of Various Variables

Curiosity is essential to scientific discovery and innovation, and more universally, it is a natural and unavoidable characteristic of children. It is shown as a process in which efforts are made to fill the knowledge gap. It is an important element of learning and it increases math achievement. This research reveals the level of curiosity in candidate primary mathematics teachers and discusses the precautions to be taken through various variables. A descriptive survey model was used in this study. This research was carried out during the 2022–2023 academic year. The study group of the research consists of 262 candidate primary school teachers studying at state universities located in the south of Turkey. In the research, "Mathematical Curiosity Scale for Classroom Teachers and Teacher Candidates" and "Personal Information Form" were used as data collection tools. In the study, primary school teacher candidates' gender, type of the high school they graduated from, positive and negative experiences about mathematics throughout their education life, and their level of mathematics curiosity and liking mathematics teachers were examined. According to the research results, primary school teacher candidates have a high level of curiosity about mathematics. Besides, sex generally does not affect curiosity in mathematics. Candidate primary school teachers who have negative experience with mathematics are less curious about mathematics. Primary school teacher candidates who like mathematics teachers are more curious about mathematics.

EFEKTIVITAS MODEL PEMBELAJARAN PROBLEM BASED LEARNING DITINJAU DARI KEMAMPUAN LITERASI MATEMATIKA DAN RASA INGIN TAHU PESERTA DIDIK DI SEKOLAH DASAR

The transition of learning from the COVID-19 pandemic to the new normal phase at this time provides many changes that occur and must be made. In the aspect of education, it is necessary to redevelop students' abilities, namely mathematical literacy and curiosity, and in learning it is necessary to apply problem-based learning models because problem-based learning (PBL) models make students the center of learning. The research was carried out at SDN 001 North Samarinda Class IV A where this research was an experimental study with the method of 1) One-Shot Case Study, to obtain data on students' mathematical literacy abilities and 2) One-Group Pretest-Posttest Design, to obtain data on curiosity. know students. Based on the results of the research, 1) learning with problem-based learning models is effective in terms of students' mathematical literacy abilities and 2)) learning with problem-based learning models is effective in terms of students' curiosity.

Post-quantum steering is a stronger-than-quantum resource for information processing

We present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing – remote state preparation. In addition, we show that the phenomenon of post-quantum steering is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyond quantum theory, hence making its study fundamentally relevant. We show these results by formulating a new compositional general probabilistic theory – which we call Witworld – with strong post-quantum features, which proves to be a intuitive and useful tool for exploring steering and its applications beyond the quantum realm.

Mathematical Disposition Scheme of Elementary School Students based on Adversity Quotient (AQ)

This research is motivated by the lack of public awareness of the importance of affective aspects in the world of education, especially mathematics. In mathematics, a positive attitude towards mathematics which includes self-confidence, flexibility, persistence, curiosity and appreciation of the role of mathematics is called a mathematical disposition. One of the internal factors that influence the mathematical disposition is Advesity Quotient (AQ) which has three levels, namely climber, camper and quitter. The purpose of this study is describe the mathematical disposition of students with AQ climbers, campers and quitters. The approach used in this research is qualitative with descriptive type. The instrument used is an aq questionnaire which is used to classify students' aq levels and an observation sheet which is used to determine students' mathematical dispositions. The research subjects were fifth grade students in the Mataram City area. The conclusions of this research are (1) Subjects with AQ climber have a mathematical disposition score of 90% can show all indicators of students' mathematical disposition, namely self-confidence, flexibility, persistence, curiosity and appreciation of the role of mathematics. (2) Subjects with AQ camper have a score of 57.5% mathematical disposition can show three indicators of students' mathematical disposition, namely self-confidence, curiosity and appreciation of the role of mathematics. (3) Subjects with AQ quitter have a mathematical disposition score of 41.5% that does not show a mathematical disposition at all.