Research in Mathematics Education最新文献

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Collaborating with industry to highlight the relevance of mathematics 与工业界合作，突出数学的相关性

Research in Mathematics Education Pub Date : 2023-10-19 DOI: 10.1080/14794802.2023.2263843

Aehsan Haj-Yahya, Aviva Klieger

{"title":"Collaborating with industry to highlight the relevance of mathematics","authors":"Aehsan Haj-Yahya, Aviva Klieger","doi":"10.1080/14794802.2023.2263843","DOIUrl":"https://doi.org/10.1080/14794802.2023.2263843","url":null,"abstract":"ABSTRACTThis study examines whether experiences at industrial facilities help pre-service maths teachers to design authentic mathematical-modelling activities intended for their classroom teaching in high school and how they view the benefits of integrating research and development issues into their instruction. 36 pre-service maths teachers at college in Israel participated the study. The results revealed that the pre-service maths teachers successfully designed authentic activities based on project-based learning that took into account the two cycles of mathematical modelling. The pre-service maths teachers reported that the implementation of the designed activities developed with researchers could serve as a way for them to present their students with a real-life problem that shows them the relevance of mathematics, promotes positive attitudes towards maths, and exposes the students to potential future jobs in the industries. The current study emphasised the use of mathematical modelling as a pathway that links industry and engineering with mathematics education.KEYWORDS: Mathematical modellingrelevance of mathematicsauthentic mathematics task Disclosure statementNo potential conflict of interest was reported by the author(s).Ethical approvalThe authors fulfilled all ethical responsibilities of authors applicable for this journal.Informed consentThe researchers explained the study to the potential participants and told them that they were welcome to take part in the study or to choose not to participate. To protect and respect personal data, pseudonyms are used for the students and this aspect was explained to the students before they started the study.Data availability statementThe data that support the findings of this study are available on request from the corresponding author.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135778951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Collatz dynamics is partitioned by residue class regularly Collatz动力学是按剩余类规则划分的

Research in Mathematics Education Pub Date : 2023-10-19 DOI: 10.1080/27684830.2023.2269657

Wei Ren

{"title":"Collatz dynamics is partitioned by residue class regularly","authors":"Wei Ren","doi":"10.1080/27684830.2023.2269657","DOIUrl":"https://doi.org/10.1080/27684830.2023.2269657","url":null,"abstract":"We propose reduced Collatz conjecture that is equivalent to Collatz conjecture, which states that every positive integer can return to an integer less than it, instead of 1. Reduced Collatz conjecture is easier to explore because certain structures must be presented in reduced dynamics, rather than in original dynamics (as original dynamics is a mixture of original dynamics). Reduced dynamics is a computation sequence from starting integer to the first integer less than it, in terms of “I” that represents (3×+1)/2 and “O” that represents x/2. We formally prove that all positive integers are partitioned into two halves and either present “I” or “O” in next ongoing computation. More specifically, (1) if any positive integer x that is i module 2t (i is an odd integer) is given, then the first t computations (each one is either “I” or “O” corresponding to whether current integer is odd or even) will be identical with that of i. (2) If current integer after t computations (in terms of “I” or “O”) is less than x, then reduced dynamics of x is available. Otherwise, the residue class of x (namely i module 2t) can be partitioned into two halves (namely i module 2t+1 and i+2t module 2t+1), and either half presents “I” or “O” in the intermediately forthcoming (t + 1)-th computation. This discovery will be helpful to the final proof of Collatz conjecture—if the union of residue classes who present reduced dynamics that become larger with the growth of residue module, equals all positive integers asymptotically, then reduced Collatz conjecture (or equivalently, Collatz conjecture) will be true.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"115 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135779844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uniform persistence and backward bifurcation of vertically transmitted vector-borne diseases 垂直传播病媒传播疾病的统一持续性和后向分岔

Research in Mathematics Education Pub Date : 2023-10-18 DOI: 10.1080/27684830.2023.2264581

Kbenesh W. Blayneh

{"title":"Uniform persistence and backward bifurcation of vertically transmitted vector-borne diseases","authors":"Kbenesh W. Blayneh","doi":"10.1080/27684830.2023.2264581","DOIUrl":"https://doi.org/10.1080/27684830.2023.2264581","url":null,"abstract":"Vertical transmissions of vector-borne diseases such as dengue virus, malaria, West Nile virus and Rift Valley fever are among challenging factors in disease control. In this paper, we used a system of differential equations to study the impacts of vertical transmission (in the vector) and horizontal (vector-to-host) transmissions cycle on the uniform persistence of a vertically transmitted disease. This is given analytically when the secondary reproduction number is greater than unity. Additional numerical results indicate that vertical transmission rates raise the epidemic level. However, we provide analytical results to reveal that vertical transmission of the disease in vectors alone without horizontal transmission, could not make the disease endemic. Furthermore, by transforming the system of differential equations to a nonlinear eigenvalue equation, the existence of a backward bifurcation is established. The directions of bifurcation is forward when the disease-induced death rate of hosts is reduced below a threshold. It is shown that the bifurcation is backward when the disease-induced death rate in the host is above a critical value. Additionally, increased disease transmission parameters also contribute to backward bifurcation. Numerical results are also provided to highlight that, depending on the initial conditions, the disease could be persistent even when the secondary reproduction number is less than unity.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

O-Fuzzy ideals in distributive lattices 分配格中的模糊理想

Research in Mathematics Education Pub Date : 2023-10-17 DOI: 10.1080/27684830.2023.2266902

Wondwosen Zemene Norahun

引用次数: 0

BSRLM day conference proceedings BSRLM日会议记录

Research in Mathematics Education Pub Date : 2023-10-17 DOI: 10.1080/14794802.2023.2260356

Taro Fujita

引用次数: 0

Helping Students Become Powerful Mathematical Thinkers. Case Studies of Teaching for Robust Understanding“ Helping Students Become Powerful Mathematical Thinkers. Case Studies of Teaching for Robust Understanding ” by Alan Schoenfeld, Heather Fink, and Sandra Zuñiga-Ruiz, with Siqi Huang, Xinyu Wei, and Brantina Chirinda, New York/London, Routledge, 2023, 255 pp., ISBN: 978-1-03-244168-9“ Mathematics Teaching on Target. A Guide to Teaching for Robust Understanding at All Grade Levels… 帮助学生成为强大的数学思想家。“稳健理解教学案例研究”帮助学生成为强大的数学思考者。《稳健理解教学案例研究》，作者:Alan Schoenfeld、Heather Fink和Sandra Zuñiga-Ruiz，与黄思琪、韦新宇和Brantina Chirinda合著，纽约/伦敦，Routledge出版社，2023年，255页，ISBN: 978-1-03-244168-9。在所有年级培养强健理解能力的教学指南

Research in Mathematics Education Pub Date : 2023-10-12 DOI: 10.1080/14794802.2023.2261410

Esther Brunner

{"title":"Helping Students Become Powerful Mathematical Thinkers. Case Studies of Teaching for Robust Understanding“ Helping Students Become Powerful Mathematical Thinkers. Case Studies of Teaching for Robust Understanding ” by Alan Schoenfeld, Heather Fink, and Sandra Zuñiga-Ruiz, with Siqi Huang, Xinyu Wei, and Brantina Chirinda, New York/London, Routledge, 2023, 255 pp., ISBN: 978-1-03-244168-9“ Mathematics Teaching on Target. A Guide to Teaching for Robust Understanding at All Grade Levels…","authors":"Esther Brunner","doi":"10.1080/14794802.2023.2261410","DOIUrl":"https://doi.org/10.1080/14794802.2023.2261410","url":null,"abstract":"Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsEsther BrunnerEsther Brunner is a Professor of Mathematics Education at the Thurgau University of Teacher Education in Kreuzlingen in Switzerland, where she directs the Mathematics Department. Her research aims to understand mathematics teaching processes, the quality of mathematics instructions from a content-specific perspective, mathematical reasoning and proof, and early mathematics education. She combines her research with a reference to practice and makes results usable for schools.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136013541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0

Some results on fuzzy ℓ-ideals and fuzzy ℓ-filters in ℓ-group 关于fuzzy -理想和fuzzy -滤波器的一些结果

Research in Mathematics Education Pub Date : 2023-09-27 DOI: 10.1080/27684830.2023.2259687

Taye Sisay Tadesse, Kishore Parimi Radhakrishna, Melesse Mulugeta Habte

{"title":"Some results on fuzzy ℓ-ideals and fuzzy ℓ-filters in ℓ-group","authors":"Taye Sisay Tadesse, Kishore Parimi Radhakrishna, Melesse Mulugeta Habte","doi":"10.1080/27684830.2023.2259687","DOIUrl":"https://doi.org/10.1080/27684830.2023.2259687","url":null,"abstract":"In this paper, we study the concept of fuzzy ℓ-ideals and fuzzy ℓ-filters of an ordered group. We provide several characterizations for fuzzy ℓ-ideals and fuzzy ℓ-filters in different perspective. We observe that for any fuzzy convex sub ℓ-group we can find a fuzzy ℓ-ideal and a fuzzy ℓ-filter containing it. Finally, for any fuzzy convex sub ℓ-group can be expressed as the intersection of some fuzzy ℓ-ideals and fuzzy ℓ-filters containing it.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135538860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0

The join problem of subnormal L -subgroups of an L -group L -群的次正规L -子群的连接问题

Research in Mathematics Education Pub Date : 2023-09-24 DOI: 10.1080/27684830.2023.2259178

I. Jahan, N. Ajmal

{"title":"The join problem of subnormal L -subgroups of an L -group","authors":"I. Jahan, N. Ajmal","doi":"10.1080/27684830.2023.2259178","DOIUrl":"https://doi.org/10.1080/27684830.2023.2259178","url":null,"abstract":"","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135924317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0

γ -fuzzy filters and space of γ -- fuzzy filters in P-algebra p -代数中的γ -模糊滤波器和γ -模糊滤波器的空间

Research in Mathematics Education Pub Date : 2023-09-21 DOI: 10.1080/27684830.2023.2258591

Wondwosen Zemene Norahun, Teferi Getachew Alemayehu

{"title":"γ -fuzzy filters and space of γ -- fuzzy filters in P-algebra","authors":"Wondwosen Zemene Norahun, Teferi Getachew Alemayehu","doi":"10.1080/27684830.2023.2258591","DOIUrl":"https://doi.org/10.1080/27684830.2023.2258591","url":null,"abstract":"In this paper, we introduce the concept of γ−fuzzy filters in a pseudo-complemented distributive lattices. We study the special class of fuzzy filters called γ−fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of boosters. We observe that every γ−fuzzy filters is the intersection of all prime γ−fuzzy filters containing it. We also topologize the set of all prime γ−fuzzy filters of a pseudo-completed distributive lattice. Properties of the space also studied. We show that there is a one to one correspondence between the class of γ−fuzzy filters and the lattice of all open sets in Pγ. It is proved that the space Pγ is a T0 space.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0

Sums of Powers and Harmonic Numbers: A new approach 幂和与调和数:一种新方法

Research in Mathematics Education Pub Date : 2023-09-14 DOI: 10.1080/27684830.2023.2230705

Carlos Morton Barrera

{"title":"Sums of Powers and Harmonic Numbers: A new approach","authors":"Carlos Morton Barrera","doi":"10.1080/27684830.2023.2230705","DOIUrl":"https://doi.org/10.1080/27684830.2023.2230705","url":null,"abstract":"There have been derivations for the Sums of Powers published since the sixteenth century. All techniques have used recursive processes, producing the following formula in the series. I present a new method that calculates the Sums of Powers and Harmonic Numbers. Starting with a novel relationship between Pascal’s Numbers and Stirling’s Numbers of the First Kind, the Sums of Powers is developed. This formula, published previously using a different methodology, is in terms of Pascal Numbers multiplied by constant coefficients. However, a further step is introduced. A recursive relationship is discovered among the coefficients of these formulae. A double sigma master formula is developed, allowing one to calculate all formulae for Sums of Powers without needing Bernoulli Numbers. Finally, from the Sums of Powers master formula, I derive a formula to calculate the Bernoulli Numbers. I further develop a summation formula for the Harmonic Numbers using the same relationships.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134911503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0

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