Pub Date : 2023-03-10DOI: 10.1080/10511970.2023.2189335
Andrew C. Lee, F. Czerniakowski, Kyle McDermott, Jeremy Reynolds
For undergraduate mathematical modeling courses, a successful semester project can reinforce key learning objectives while enabling creativity and developing critical thinking skills. However, course directors often struggle in developing novel project ideas and balancing the tradeoff between grading burden and project complexity. At the U.S Military Academy, we take an open-ended and discovery-learning approach to the freshman level math modeling project. This article outlines one successful project involving a Zombie Apocalypse scenario along with student responses. To assist the students, we promote flexibility, scaffold the modeling process with in-progress reviews, and train students on how to write concise executive summaries.
{"title":"Discrete Zombie Apocalypse: A Mathematical Modeling Course Project","authors":"Andrew C. Lee, F. Czerniakowski, Kyle McDermott, Jeremy Reynolds","doi":"10.1080/10511970.2023.2189335","DOIUrl":"https://doi.org/10.1080/10511970.2023.2189335","url":null,"abstract":"For undergraduate mathematical modeling courses, a successful semester project can reinforce key learning objectives while enabling creativity and developing critical thinking skills. However, course directors often struggle in developing novel project ideas and balancing the tradeoff between grading burden and project complexity. At the U.S Military Academy, we take an open-ended and discovery-learning approach to the freshman level math modeling project. This article outlines one successful project involving a Zombie Apocalypse scenario along with student responses. To assist the students, we promote flexibility, scaffold the modeling process with in-progress reviews, and train students on how to write concise executive summaries.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"3 1","pages":"841 - 860"},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86643727","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}
Pub Date : 2023-03-10DOI: 10.1080/10511970.2023.2189336
Carl Lutzer
This article presents a simple and natural development of the relationship between the inverse of a nonsingular matrix and the adjugate matrix for use in a first-semester linear algebra class.
本文给出了非奇异矩阵的逆与辅助矩阵之间关系的一个简单而自然的发展，用于第一学期的线性代数课程。
{"title":"The Transpose Begets the Adjugate","authors":"Carl Lutzer","doi":"10.1080/10511970.2023.2189336","DOIUrl":"https://doi.org/10.1080/10511970.2023.2189336","url":null,"abstract":"This article presents a simple and natural development of the relationship between the inverse of a nonsingular matrix and the adjugate matrix for use in a first-semester linear algebra class.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"68 1","pages":"861 - 866"},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76535674","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}
Pub Date : 2023-02-07DOI: 10.1080/10511970.2022.2048929
C. Lo
ABSTRACT Teachers and students had an unusual experience in 2020. Due to the outbreak of the COVID-19 pandemic, regular teaching and learning in schools were suspended in many countries. The prolonged school closure presented unprecedented challenges because all teaching and learning activities had to be converted to a fully online format. This article reports on an attempt to sustain flipped learning using real-time online instruction. A flipped lesson on the cross-disciplinary applications of linear systems (i.e., balancing chemical equations) is presented in detail. Student feedback and the lessons learned from the experience are discussed.
{"title":"How Can Flipped Learning Continue in a Fully Online Environment? Lessons Learned During the COVID-19 Pandemic","authors":"C. Lo","doi":"10.1080/10511970.2022.2048929","DOIUrl":"https://doi.org/10.1080/10511970.2022.2048929","url":null,"abstract":"ABSTRACT Teachers and students had an unusual experience in 2020. Due to the outbreak of the COVID-19 pandemic, regular teaching and learning in schools were suspended in many countries. The prolonged school closure presented unprecedented challenges because all teaching and learning activities had to be converted to a fully online format. This article reports on an attempt to sustain flipped learning using real-time online instruction. A flipped lesson on the cross-disciplinary applications of linear systems (i.e., balancing chemical equations) is presented in detail. Student feedback and the lessons learned from the experience are discussed.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"101 1","pages":"175 - 185"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79485968","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}
Pub Date : 2023-02-01DOI: 10.1080/10511970.2023.2172751
Joanna G. Jauchen, Hannah Klawa, L. Nguyen, Rebecca R. G., E. Sander, P. Seshaiyer, Cigole Thomas
In the fall of 2020, our department at George Mason University integrated graduate learning assistants (GLAs) into our graduate core courses. GLAs are funded graduate students who assist instructors during class, facilitate active learning preliminary exam problem-solving sessions, hold extra office hours, and serve as peer mentors for beginning graduate students. The GLAMS program was designed to support beginning graduate students as they prepared for their preliminary exams. We describe the program and provide details about how it was implemented. We include preliminary student feedback as well as faculty and GLA reflections. To conclude, we outline our plans for programmatic changes moving forward.
{"title":"GLAMS: Graduate Learning Assistants in Mathematical Sciences","authors":"Joanna G. Jauchen, Hannah Klawa, L. Nguyen, Rebecca R. G., E. Sander, P. Seshaiyer, Cigole Thomas","doi":"10.1080/10511970.2023.2172751","DOIUrl":"https://doi.org/10.1080/10511970.2023.2172751","url":null,"abstract":"In the fall of 2020, our department at George Mason University integrated graduate learning assistants (GLAs) into our graduate core courses. GLAs are funded graduate students who assist instructors during class, facilitate active learning preliminary exam problem-solving sessions, hold extra office hours, and serve as peer mentors for beginning graduate students. The GLAMS program was designed to support beginning graduate students as they prepared for their preliminary exams. We describe the program and provide details about how it was implemented. We include preliminary student feedback as well as faculty and GLA reflections. To conclude, we outline our plans for programmatic changes moving forward.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"73 1","pages":"819 - 840"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87125708","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}
Pub Date : 2023-01-25DOI: 10.1080/10511970.2023.2172750
A. Matchett
This article describes five elementary statistics projects involving the Covid-19 data made available to the public in csv files by the Centers for Disease Control and Prevention. The first project examined data available at the beginning of the covid surge in New York City in spring, 2020, and used the correlation coefficient to estimate the total number of deaths that could be expected as the spike ran its course. The second project is an easy one on the concept of excess deaths and on the mechanics of extracting parts of a data file that answer relevant questions. The data is from a spike in deaths in the particularly bad flu surge in the winter of 2017–2018. The third and fourth projects ask the student to fit a logistic growth curve to observed cumulative numbers of deaths in a spike, like the Covid spikes in New York City and Wisconsin and the nationwide 2017–2018 flu spike. The method is a simple linear regression with transformed variables. The fifth project involves hypothesis testing and judging when a Poisson model might be useful. The paper also documents difficulties and adaptations of the sort familiar to all teachers who have taught during the Covid-19 pandemic.
{"title":"Elementary Statistics Projects Using Covid Data","authors":"A. Matchett","doi":"10.1080/10511970.2023.2172750","DOIUrl":"https://doi.org/10.1080/10511970.2023.2172750","url":null,"abstract":"This article describes five elementary statistics projects involving the Covid-19 data made available to the public in csv files by the Centers for Disease Control and Prevention. The first project examined data available at the beginning of the covid surge in New York City in spring, 2020, and used the correlation coefficient to estimate the total number of deaths that could be expected as the spike ran its course. The second project is an easy one on the concept of excess deaths and on the mechanics of extracting parts of a data file that answer relevant questions. The data is from a spike in deaths in the particularly bad flu surge in the winter of 2017–2018. The third and fourth projects ask the student to fit a logistic growth curve to observed cumulative numbers of deaths in a spike, like the Covid spikes in New York City and Wisconsin and the nationwide 2017–2018 flu spike. The method is a simple linear regression with transformed variables. The fifth project involves hypothesis testing and judging when a Poisson model might be useful. The paper also documents difficulties and adaptations of the sort familiar to all teachers who have taught during the Covid-19 pandemic.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"24 1","pages":"796 - 817"},"PeriodicalIF":0.0,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86597703","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}
Pub Date : 2023-01-18DOI: 10.1080/10511970.2023.2170505
Farzad Radmehr, Khaled Tohidinasab, M. Tavakoli
Traditional lecturing is the dominant method of teaching mathematics in undergraduate mathematical courses in many countries, whereas active student-centered approaches such as inquiry-based learning have been shown in some instances to be more effective. Most teaching resources (inquiry-based tasks) available at the tertiary level are related to calculus, linear algebra, and differential equations courses. In this paper, we focus on using an inquiry-based approach to explore the teaching and learning of vertex coloring, a common topic in graph theory and undergraduate discrete mathematical courses. We designed seven inquiry-based tasks related to vertex coloring to teach vertex coloring in an undergraduate graph theory course to students majoring in mathematics. In sharing these tasks, describing students’ engagement with them, and discussing how these tasks were perceived by the students and lecturer, we hope to promote using inquiry-based tasks in undergraduate discrete mathematical courses.
{"title":"Teaching and Learning of Vertex Coloring Using an Inquiry-Based Approach","authors":"Farzad Radmehr, Khaled Tohidinasab, M. Tavakoli","doi":"10.1080/10511970.2023.2170505","DOIUrl":"https://doi.org/10.1080/10511970.2023.2170505","url":null,"abstract":"Traditional lecturing is the dominant method of teaching mathematics in undergraduate mathematical courses in many countries, whereas active student-centered approaches such as inquiry-based learning have been shown in some instances to be more effective. Most teaching resources (inquiry-based tasks) available at the tertiary level are related to calculus, linear algebra, and differential equations courses. In this paper, we focus on using an inquiry-based approach to explore the teaching and learning of vertex coloring, a common topic in graph theory and undergraduate discrete mathematical courses. We designed seven inquiry-based tasks related to vertex coloring to teach vertex coloring in an undergraduate graph theory course to students majoring in mathematics. In sharing these tasks, describing students’ engagement with them, and discussing how these tasks were perceived by the students and lecturer, we hope to promote using inquiry-based tasks in undergraduate discrete mathematical courses.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"28 1","pages":"780 - 795"},"PeriodicalIF":0.0,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88030782","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}
Pub Date : 2023-01-18DOI: 10.1080/10511970.2023.2167250
Kirk Weller, Anil Venkatesh, E. Militzer
We present a model for professional development of instructional faculty. Though initially conceived for accreditation compliance as a credentialing process for adjunct faculty, this project led to increases in participants’ collaboration on lesson design, investment in curricular decisions, and adoption of active learning methods. In this paper, we identify five barriers that initially impeded these outcomes: Time, Isolation, Connection Between Content and Pedagogy, Change, and Risk-Taking. Through extensive coding of discussion board posts and participant interviews, we show that participants initially encountered these barriers but largely overcame them by the end of the project.
{"title":"Overcoming Barriers to Adjunct Engagement: A Community-First Approach to Professional Development","authors":"Kirk Weller, Anil Venkatesh, E. Militzer","doi":"10.1080/10511970.2023.2167250","DOIUrl":"https://doi.org/10.1080/10511970.2023.2167250","url":null,"abstract":"We present a model for professional development of instructional faculty. Though initially conceived for accreditation compliance as a credentialing process for adjunct faculty, this project led to increases in participants’ collaboration on lesson design, investment in curricular decisions, and adoption of active learning methods. In this paper, we identify five barriers that initially impeded these outcomes: Time, Isolation, Connection Between Content and Pedagogy, Change, and Risk-Taking. Through extensive coding of discussion board posts and participant interviews, we show that participants initially encountered these barriers but largely overcame them by the end of the project.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"83 1","pages":"729 - 743"},"PeriodicalIF":0.0,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81449956","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}
Pub Date : 2023-01-12DOI: 10.1080/10511970.2023.2167252
Matthew Phillips, Kayla Robb, B. Shipman
In an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and investigate non-standard questions. The ideas are arranged as a series of questions for students to explore, with expositions to the instructor on how to guide them in looking for answers. The investigations culminate in a satisfying outcome: that partition topologies are the same as unique factorization topologies, those that satisfy our topological version of the Fundamental Theorem of Arithmetic.
{"title":"Topological Explorations on the Fundamental Theorem of Arithmetic","authors":"Matthew Phillips, Kayla Robb, B. Shipman","doi":"10.1080/10511970.2023.2167252","DOIUrl":"https://doi.org/10.1080/10511970.2023.2167252","url":null,"abstract":"In an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and investigate non-standard questions. The ideas are arranged as a series of questions for students to explore, with expositions to the instructor on how to guide them in looking for answers. The investigations culminate in a satisfying outcome: that partition topologies are the same as unique factorization topologies, those that satisfy our topological version of the Fundamental Theorem of Arithmetic.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"9 1","pages":"759 - 779"},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78281713","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}
Pub Date : 2023-01-10DOI: 10.1080/10511970.2023.2167249
Andrea Arnold
{"title":"Virtual Sonia Kovalevsky Day Mathematics Outreach Events for Middle School Girls","authors":"Andrea Arnold","doi":"10.1080/10511970.2023.2167249","DOIUrl":"https://doi.org/10.1080/10511970.2023.2167249","url":null,"abstract":"","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82011791","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}
Pub Date : 2023-01-10DOI: 10.1080/10511970.2023.2167248
Lyn McQuaid, Vanessa G. Maybruck, Yun Lu
{"title":"Building community: One AWM chapter’s tale of programmatic outreach","authors":"Lyn McQuaid, Vanessa G. Maybruck, Yun Lu","doi":"10.1080/10511970.2023.2167248","DOIUrl":"https://doi.org/10.1080/10511970.2023.2167248","url":null,"abstract":"","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"125 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78655031","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}
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