PRIMUSPub Date : 2023-05-15DOI: 10.1080/10511970.2023.2214896
Markus Reitenbach
{"title":"Using Secret Sharing to Store Cryptocurrency","authors":"Markus Reitenbach","doi":"10.1080/10511970.2023.2214896","DOIUrl":"https://doi.org/10.1080/10511970.2023.2214896","url":null,"abstract":"","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"0 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90724515","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}
PRIMUSPub Date : 2023-05-15DOI: 10.1080/10511970.2023.2214893
A. Vanessa Radzimski, B. Pam Sargent, C. Fok-Shuen Leung
{"title":"Time and space to thrive: mathematics graduate students in a team teaching model","authors":"A. Vanessa Radzimski, B. Pam Sargent, C. Fok-Shuen Leung","doi":"10.1080/10511970.2023.2214893","DOIUrl":"https://doi.org/10.1080/10511970.2023.2214893","url":null,"abstract":"","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76261417","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}
PRIMUSPub Date : 2023-05-15DOI: 10.1080/10511970.2023.2214891
F. Yu
{"title":"Promoting Productive Understandings of Rate of Change in Calculus Courses","authors":"F. Yu","doi":"10.1080/10511970.2023.2214891","DOIUrl":"https://doi.org/10.1080/10511970.2023.2214891","url":null,"abstract":"A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on “what is rate of change” can address these issues and better support students in understanding the fundamental ideas of Calculus. This paper provides a short teaching intervention that instructors can utilize to help students build a productive understanding of rate of change that will aid them in understanding derivatives as instantaneous rates of change.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"95 1","pages":"965 - 980"},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75166324","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}
PRIMUSPub Date : 2023-05-15DOI: 10.1080/10511970.2023.2214897
Jennifer L. Nimtz
{"title":"Illustrating Productive and Unproductive Cognitive Interactions in an Online Intermediate Algebra Course","authors":"Jennifer L. Nimtz","doi":"10.1080/10511970.2023.2214897","DOIUrl":"https://doi.org/10.1080/10511970.2023.2214897","url":null,"abstract":"Universities have drawn on an assortment of strategies to address the learning challenges and high attrition rates of developmental mathematics students. One of those strategies has been utilizing computer adaptive instruction (CAI) mathematics software. Reports about the efficacy of CAI vary from glowing to unfavorable. This article presents an instrumental case study, meaning that the purpose is to examine and describe a single case in depth to explain observed phenomena and illustrate a theory [Baxter and Jack 2008. Qualitative case study methodology: Study design and Implementation for novice researchers. The Qualitative Report. 14(4): 544–559]. The phenomena described in this article is productive and unproductive student interactions with a CAI environment. The vignettes in this article illustrate how students, even the same student, can have both productive and unproductive interactions with a CAI system. The vignettes are followed by recommendations for curriculum, instruction, assessment, and further research. Although these recommendations are gathered from observations of student interactions with CAI software in an asynchronous online Intermediate Algebra course, the observations have implications for different modes of instruction (e.g., synchronous online, flipped, hybrid, or face-to-face) that utilize online homework systems.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"706 1","pages":"997 - 1021"},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76898698","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}
PRIMUSPub Date : 2023-03-22DOI: 10.1080/10511970.2023.2193967
Elisa Soosloff, Maryann Huey, Daniel S. Alexander
{"title":"Engaging Students in a Visual and Conceptual Approach to Taylor Series","authors":"Elisa Soosloff, Maryann Huey, Daniel S. Alexander","doi":"10.1080/10511970.2023.2193967","DOIUrl":"https://doi.org/10.1080/10511970.2023.2193967","url":null,"abstract":"In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students’ prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as formulaic, which leads them to focus on procedural aspects. We share our instructional approach, which introduces students to graphs of polynomial functions that resemble transcendental functions. However, students are not told that they are approximating polynomials initially, and through carefully sequenced experiences, students gradually build an intuitive understanding of the Taylor series. With the goal of equipping instructors who wish to embark upon similar journeys, we describe the visual representations employed, the questions we pose to students, students’ typical responses, and important topics for discussion. The activities described engage students in reasoning and sense-making throughout the learning process, which is essential for developing a robust understanding of Taylor series as well as other calculus topics.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"1 1","pages":"981 - 996"},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89673017","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}
PRIMUSPub Date : 2023-03-22DOI: 10.1080/10511970.2023.2193949
Ann Stewart, Jill Tysse
{"title":"A Short Summer Research Experience for Secondary Education Mathematics Majors at a Small Liberal Arts College","authors":"Ann Stewart, Jill Tysse","doi":"10.1080/10511970.2023.2193949","DOIUrl":"https://doi.org/10.1080/10511970.2023.2193949","url":null,"abstract":"One of the best ways for STEM students to understand the methods and thought process of their discipline is through participation in an undergraduate research project. However, mathematics secondary education students at Hood College are historically less likely to self-select for these types of supplemental experiences than traditional mathematics majors. Hood’s Noyce STEM Teacher Education Partnership (NSTEP) sought to address this by designing a shortened summer research experience specifically for secondary education students in mathematics. The Summer Research Experience in Mathematical Modeling (SREM2) was a 4-week summer research project that provided this opportunity at a small college. Here we describe the benefits of such an experience and present the design of our program and its outcomes.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"97 1","pages":"889 - 900"},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86022451","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}
PRIMUSPub Date : 2023-03-22DOI: 10.1080/10511970.2023.2193963
Martin E. Malandro
{"title":"Ask Your Students Research-Like Questions: Examples from Calculus II","authors":"Martin E. Malandro","doi":"10.1080/10511970.2023.2193963","DOIUrl":"https://doi.org/10.1080/10511970.2023.2193963","url":null,"abstract":"I introduce a teaching method that involves asking students to answer investigative, research-like questions, and I detail my experience with this method in Calculus II in Fall 2019 and Fall 2020. This method is applicable to a range of undergraduate courses and can be used in both face-to-face and online settings. I give several examples of research-like questions and student responses, I detail some of the benefits and potential pitfalls with this method, and I include in the appendix a complete list of research-like questions asked during the Fall 2020 semester.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"23 1","pages":"916 - 937"},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90455879","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}
PRIMUSPub Date : 2023-03-22DOI: 10.1080/10511970.2023.2193951
Katherine S. Ritchey, S. Patterson, B. Patterson, Nathan Ritchey
{"title":"Wordle as a Teaching Tool","authors":"Katherine S. Ritchey, S. Patterson, B. Patterson, Nathan Ritchey","doi":"10.1080/10511970.2023.2193951","DOIUrl":"https://doi.org/10.1080/10511970.2023.2193951","url":null,"abstract":"Wordle, a game in which a player has six chances to find a five-letter word, has become quite popular. In this paper, we present four activities that are based on Wordle and are designed to help students advance their knowledge and skill of a particular concept. Some of the activities could be used for beginning students and some activities could be used for more advanced students. The activities are designed to promote mathematical engagement and interest and can be used individually, or collectively, to fit the specific needs of the intended audience. The first two activities enhance students' knowledge of combinatorics and probability when letter words are chosen at random. In another activity, individual and pairs of letter counts from the list of possible Wordle words are presented in graphical format. More advanced students can replicate these graphs using a computer program, while other students can simply use the graphs that are included. In the fourth activity, students have the opportunity to play Wordle and develop strategies to minimize the number of steps required to solve a particular puzzle. Classroom experience is included and student responses to the activities are presented.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"73 1","pages":"901 - 915"},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91270557","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}
PRIMUSPub Date : 2023-03-16DOI: 10.1080/10511970.2022.2048931
Feryâl Alayont, Gizem Karaali, Lerna Pehlivan
{"title":"Analysis of Calculus Textbook Problems via Bloom's Taxonomy","authors":"Feryâl Alayont, Gizem Karaali, Lerna Pehlivan","doi":"10.1080/10511970.2022.2048931","DOIUrl":"https://doi.org/10.1080/10511970.2022.2048931","url":null,"abstract":"In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within the framework of Bloom's Taxonomy. We provide examples of the types of problems assigned to each of the six categories in this taxonomy and share some of the deliberations that led us to these assignments. Finally, we discuss the implications of our results for teaching calculus courses. We believe that our analysis will help calculus instructors be more cognizant of the cognitive demand of problems when assigning them for homework and, as a result, help them to appropriately support, assess, and enhance their students' understanding of the topics.","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"44 1","pages":"203 - 218"},"PeriodicalIF":0.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84614313","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}
PRIMUSPub Date : 2023-03-10DOI: 10.1080/10511970.2023.2189337
Ulrich A Hoensch
{"title":"Smudge Attack or: How to Secure Your Dirty Keypad","authors":"Ulrich A Hoensch","doi":"10.1080/10511970.2023.2189337","DOIUrl":"https://doi.org/10.1080/10511970.2023.2189337","url":null,"abstract":"","PeriodicalId":39375,"journal":{"name":"PRIMUS","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87522996","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}