International Journal of Mathematical Education in Science and Technology最新文献_第10页

Using graph-colouring to organise multi-version assessments 使用图形着色来组织多版本评估

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-13 DOI: 10.1080/0020739x.2023.2255592

Jonathan Hoseana, Andy Leonardo Louismono, Oriza Stepanus

{"title":"Using graph-colouring to organise multi-version assessments","authors":"Jonathan Hoseana, Andy Leonardo Louismono, Oriza Stepanus","doi":"10.1080/0020739x.2023.2255592","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2255592","url":null,"abstract":"AbstractWe describe and evaluate a method to mitigate unwanted student collaborations in assessments, which we recently implemented in a second-year undergraduate mathematics module. The method requires a list of specific pairs of students to be prevented from collaborating, which we constructed based on the results of previous assessments. We converted the list into an undirected graph – in which vertices represent students and adjacent vertices represent pairs of students to be prevented from collaborating – and determined a proper colouring of this graph. Subsequently, we designed multi-version assessments, the number and the distribution of the versions being as prescribed by the proper colouring. To assess this method's effectiveness, we conducted an anonymous survey collecting the students' opinions. The results showed that the method indeed reduced collaborations, and that it did so more significantly in the case of quizzes than take-home assignments.Keywords: Academic dishonestygraphproper colouringmulti-version assessment AcknowledgmentsThe authors thank the module lecturers Iwan Sugiarto, Ari Waworoentoe, and Evelyn Waworoentoe, who took part in creating a supportive environment for the activities reported in this note.Disclosure statementNo potential conflict of interest was reported by the authors.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784328","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 susceptible–infected–recovered model as a tool to motivate and teach differential equations: an analytic approach 易感-感染-恢复模型作为激励和教授微分方程的工具:一种分析方法

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-13 DOI: 10.1080/0020739x.2023.2249898

Minchul Kang

{"title":"The susceptible–infected–recovered model as a tool to motivate and teach differential equations: an analytic approach","authors":"Minchul Kang","doi":"10.1080/0020739x.2023.2249898","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2249898","url":null,"abstract":"AbstractSince the introduction by Kermack and McKendrick in 1927, the Susceptible–Infected–Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious diseases including recent COVID-19 breakouts, which stimulates the advance in mathematical epidemiology theory significantly. Some of the mathematical ideas and techniques developed are also relevant to motivate teaching various topics in differential equations by connecting students' life experiences with current pandemics to meaningful classroom learning activities. Here, various pedagogically relevant topics from the SIR model are provided for undergraduate differential equation class, which includes (1) compartmental modelling and mass action kinetic modelling, (2) conservation rule and model reduction, (3) introduction to phase plane by removing time variable to derive trajectory equations, (4) transformation of equations to equivalent forms, (5) transformation of second-order system to second-order ODE, (6) deriving an analytic solution to the SIR equation by solving Bernoulli's equation, (7) deriving an analytic solution to the SIR equation from trajectory equations and (8) deriving an analytic solution to the SIR equation from exponential substitutions.Keywords: SIR modelundergraduateeducationdifferential equationsanalytic solutionsMathematics Subject Classifications: 97M1097M60 Disclosure statementNo potential conflict of interest was reported by the author.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783778","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

Designing example-generating tasks for a technology-rich mathematical environment 为技术丰富的数学环境设计示例生成任务

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-13 DOI: 10.1080/0020739x.2023.2255188

Maria Fahlgren, Mats Brunström

{"title":"Designing example-generating tasks for a technology-rich mathematical environment","authors":"Maria Fahlgren, Mats Brunström","doi":"10.1080/0020739x.2023.2255188","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2255188","url":null,"abstract":"This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students’ mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined use of a dynamic mathematics software environment and a computer-aided assessment system. In example-generating tasks, students are asked to generate examples that fulfil certain conditions. Based on data in terms of examples generated by 491 first-year engineering students, taking a first course in calculus, the paper examines patterns of student response to three example-generating tasks. As a theoretical lens, the notions of dimensions of possible variation and associated ranges of permissible change are used. In light of the observed patterns, the paper provides some guiding principles for designing example-generating tasks and associated formative feedback to foster students’ mathematical understanding by enriching their example spaces. For example, this paper illustrates occasions where it might be instructive to start by asking for two examples, followed by adapted feedback before requesting a third example.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784506","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

Using mathematical modelling to provide students with a contextual learning experience of differential equations 利用数学建模为学生提供微分方程的情境学习经验

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-11 DOI: 10.1080/0020739x.2023.2244472

Kerri Spooner

引用次数: 0

Bringing back the people in modelling epidemics 把人们带回到流行病模型中

IF 0.9

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-06 DOI: 10.1080/0020739x.2023.2249466

Shophika Vaithyanathasarma, France Caron, Geneviève Bistodeau-Gagnon, Jacques Bélair

引用次数: 0

Modeling a building during an earthquake to demonstrate resonance 在地震期间对建筑物进行建模以演示共振

IF 0.9

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-06 DOI: 10.1080/0020739x.2023.2247408

Tracy Weyand

引用次数: 0

Epidemic modeling using differential equations with implementation in R 基于微分方程的流行病建模及其在R中的实现

IF 0.9

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-06 DOI: 10.1080/0020739x.2023.2249902

Liang Kong

引用次数: 0

Using physical simulations to motivate the use of differential equations in models of disease spread 利用物理模拟来激发疾病传播模型中微分方程的使用

IF 0.9

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-04 DOI: 10.1080/0020739x.2023.2244494

Elizabeth G. Arnold, Elizabeth A. Burroughs, Owen Burroughs, M. Carlson

引用次数: 0

Functional modelling with study and research paths: a theoretical proposal 具有学习和研究路径的函数建模：一个理论建议

IF 0.9

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-04 DOI: 10.1080/0020739x.2023.2246976

Ismael Cabero, Carl Winsløw

引用次数: 0

Modelling tank drainage using a simple apparatus 用简易装置模拟水箱排水

IF 0.9

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-04 DOI: 10.1080/0020739x.2023.2249472

Michael A. Rother

引用次数: 0