International Journal of Mathematical Education in Science and Technology最新文献_第5页

Modelling labs for a course on differential equations 微分方程课程的建模实验

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-14 DOI: 10.1080/0020739x.2023.2251480

Ala' J. Alnaser, Justin Hoffmeier

{"title":"Modelling labs for a course on differential equations","authors":"Ala' J. Alnaser, Justin Hoffmeier","doi":"10.1080/0020739x.2023.2251480","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2251480","url":null,"abstract":"AbstractDifferential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential. However, students often struggle to create and understand these models in the course. The purpose of this article is to share and examine a scaffolded sequence of labs implemented at regular intervals throughout a semester intended to train students in construction and analysis of mathematical models using differential equations. In these labs students learn basic principles of modelling that better prepare them for many of the high-quality modelling projects already available in differential equations. The course in which these activities were developed is taught using the SIMIODE text, Differential Equations: A Toolbox for Modelling the World, by Kurt Bryan. The labs are split into two components, with the first completed during class time and the second as out of class assignments. Furthermore, the course was re-organised to allow for the time needed to introduce the labs in class. We include classroom materials for labs, analysis, results on student perceptions and pedagogical recommendations.Keywords: Ordinary differential equationsmodellinglabspedagogyMathematics Subject Classification: 97M10 AcknowledgmentsWe would like to thank Alexandra Desaulniers for tirelessly working to support the creation and review of the labs. In addition, we thank Kurt Bryan for creating a textbook and many helpful resources to help us teach modelling in our differential equations course.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":"29 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":"134911928","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

A set theory analysis of the relationship between active learning and equitable and inclusive teaching 主动学习与公平包容教学关系的集合论分析

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-13 DOI: 10.1080/0020739x.2023.2255183

Amy Been Bennett, Karina Uhing, Molly Williams, Nancy Kress

{"title":"A set theory analysis of the relationship between active learning and equitable and inclusive teaching","authors":"Amy Been Bennett, Karina Uhing, Molly Williams, Nancy Kress","doi":"10.1080/0020739x.2023.2255183","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2255183","url":null,"abstract":"AbstractAlthough research on active learning suggests strong connections to equitable and inclusive teaching, few studies have explored the relationship between the two concepts. In this qualitative study, we examined how 13 participants in an equity-focused workshop described the relationship between active learning, and equitable and inclusive teaching. We used set theory as an analytic tool to categorise their descriptions. We found that all participants saw active learning, and equitable and inclusive teaching as related. The two relationships that were most strongly supported by participants’ statements were that active learning, and equitable and inclusive teaching are related yet independent sets, or that equitable and inclusive teaching is a subset of active learning. We discuss implications of these findings and pose questions for further exploration.KEYWORDS: Active learningequitable and inclusive teachingset theoryundergraduate mathematics AcknowledgmentsData were collected through an NSF-funded project (#1624639, #1624643 - SEMINAL). We would like to thank SEMINAL for designing the larger project from which these data were collected. All conclusions and opinions in this paper are from the authors and do not represent the opinions of the National Science Foundation.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThis work was supported by National Science Foundation [grant number 1624639, 1624643].","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783516","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

Cooling the perfect cup with Laplace 用拉普拉斯冷却完美的杯子

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-09-13 DOI: 10.1080/0020739x.2023.2250337

R. C. Harwood

{"title":"Cooling the perfect cup with Laplace","authors":"R. C. Harwood","doi":"10.1080/0020739x.2023.2250337","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2250337","url":null,"abstract":"AbstractAfter waiting in a long line for your favourite cup of coffee, you finally sit down with your mug and find that the coffee is still scalding hot! How long do you need to wait before you can enjoy it? Once it cools enough, how much time do you have to enjoy it? Are there ways to speed up the process? These questions motivate the presented modelling scenario about tracking the temperature of a cup of coffee as it cools. Students are put in the role of an inquisitive coffee enthusiast who does their due diligence in preventing burns and carefully experimenting on their coffee so that they, and others to come, can enjoy that perfect cup. They identify their assumptions and interventions before developing model differential equations for each case, which force discontinuities on the derivative and even on the solution itself. Being familiar with basic Laplace transforms and learning key properties of the unit step and unit impulse functions, they solve these differential equations and compare the interval of time when the coffee will be at its peak level of enjoyment. This paper includes an implementation guide, grading rubric, example solutions, and example assessment questions.Keywords: Newtonlaw of coolingLaplace transformmodellingtemperaturecoffeeMathematics Subject Classifications: 00-0101-0134-0134A25 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":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784187","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 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":"349 1","pages":"0"},"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":"89 1","pages":"0"},"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":"362 1","pages":"0"},"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