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The eight papers making up this special issue on promoting women in mathematics consider the underrepresentation of women in mathematics and the experiences and observations of authors who are immersed in this work. In this editorial, we identify common themes we see across many of these papers, framing our discussion with the "social identity framework of mathematical development" presented in the first paper. This framework consists of three beliefs conducive to the pursuit of mathematics, and we discuss how the authors address each of these beliefs in their work. We also present data to illustrate that the underrepresentation of women in mathematics continues to be an issue, and we hope the papers in this issue will be informative for others who want to lead gender-based initiatives. [ABSTRACT FROM AUTHOR]

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to recognize a continuous function from its graph. To help mitigate this problem, these visuals can be used alongside the definitions in analysis courses, and in calculus courses where the same definitions are used. The content is arranged into a series of pictures accompanied by questions, with suggestions for the instructor on how to guide students in their learning. The design allows students to make their own discoveries and connections. The investigations crescendo to a surprising fact: that almost all continuous functions are differentiable nowhere! [ABSTRACT FROM AUTHOR]

This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women's engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field. [ABSTRACT FROM AUTHOR]

Sonia Kovalevsky Days (SK Days) are nationally-held outreach events that are commonly organized by local chapters of the Association for Women in Mathematics (AWM) to encourage young women to continue their study of mathematics. The AWM Student Chapter at Worcester Polytechnic Institute hosted virtual renditions of SK Day for middle school girls in Spring 2020 and 2021. This paper discusses the implementation of these events, including the virtual program logistics and five interactive online mathematics activities. Participant feedback suggests a successful transition from an in-person to online format of SK Day, with benefits to both the middle school participants and the undergraduate student volunteers. The activities and online resources described in this article have the potential to be utilized in future hybrid outreach events. [ABSTRACT FROM AUTHOR]

The Mathematical Sciences Department at Shenandoah University focused on increasing the participation of women in the mathematics program by fostering a welcoming learning community and promoting double majors. Data from the past decade is presented. During this time, the program saw an increase in women undergraduate mathematics majors from 11% to as high as 71%. This paper describes the initiatives taken to make these changes. [ABSTRACT FROM AUTHOR]

The University of Minnesota Talented Youth Mathematics Program (UMTYMP) is a selective, five-year accelerated mathematics program for students in grades 6–12. During the program, students take college mathematics courses on University of Minnesota campuses, starting with algebra and continuing through logic and proofs, linear algebra, and multivariable calculus. The majority of UMTYMP students come from two demographic groups: White and Asian/Asian American. In 2020, we surveyed UMTYMP students to understand the impact of model minority stereotypes (MMS) on Asian/Asian American students, particularly girls, who are labeled as "gifted" and/or "talented." In this paper, we reveal the preliminary results of this study, discuss their implications, and provide recommendations for addressing the MMS in mathematics programs. [ABSTRACT FROM AUTHOR]

This case study examines how online mathematics homework impacts student learning, attitude, and efficacy in a college Calculus I class. This research is important because it provides data on student perceptions for how to effectively implement online homework. Participants for this study completed homework using a blend of online and paper formats. We use a mixed methods approach to analyze quantitative survey data and qualitative data collected in focus groups and interviews. Our findings indicate students benefited from using a combination of paper homework and online homework. Recommendations are made for how instructors can utilize the benefits of both approaches to support student learning, attitude, and efficacy. [ABSTRACT FROM AUTHOR]

College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods:WeBWorK, an open-source system for web-based homework, or traditional paper-and-pencil homework. We assessed learning for 439 students in 19 college algebra classes at a large public university in the United States. Twelve classes usedWeBWorKand seven had traditional paper-and-pencil homework. Analysis of covariance revealed no significant differences in algebra performance or achievement gain by homework group, ethnicity or gender when statistically controlling for previous mathematics achievement. Results support the conjecture thatWeBWorKis at least as effective as traditionally graded paper-and-pencil homework for students learning college algebra in moderately sized lecture-based classes. [ABSTRACT FROM AUTHOR]

As calculus instruction moves further from lecture-based instruction toward student-centered pedagogy, support services must align with the changing goals for the course. This paper describes the work of a department as they collectively design and redesign a co-requisite Calculus I course, in an effort to better promote students' academic and social integration into active, student-centered calculus classrooms. We highlight the inclusion of more cognitively demanding and group-worthy tasks, re-negotiation of support for procedures and fundamental concepts, and promotion of collaborative participation. Our discussion is supplemented with reflections from faculty, graduate student instructors, and students. [ABSTRACT FROM AUTHOR]

This article describes the outcomes of a faculty partnership between a math professor and a composition professor to improve the final paper in a research-focused senior capstone math course. Much attention has been paid in recent years to the importance of undergraduate research experiences and how to best create and support such endeavors. However, little space has been dedicated to helping math faculty design and scaffold writing assignments to support their students' development as scholars. We describe how our partnership took place, the changes we made to existing assignments and the creation of new ones, and an assessment of our efforts completed by an interdisciplinary group of faculty and students, which showed marked improvement in the areas of information literacy, critical thinking, and quality of writing. [ABSTRACT FROM AUTHOR]

This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some questions instructors can ask themselves to design novel and engaging activities when constrained to teaching from a particular curriculum. [ABSTRACT FROM AUTHOR]

With this paper, we share an activity for the undergraduate mathematics classroom called The Harp Project that leverages the aesthetic nature of both the mathematical and the musical arts. This project was conceived as a STEAM/PBL project with the added feature that it was carried out in pieces by an entire class. Anecdotal evidence suggests that the uncommonly high level of students' interest and engagement in the experience and the communal feel of their participation can be attributed to this collective quality of the project's design. For this reason, we invite others to consider this curricular experience as it appears viable for supporting efforts to cultivate a broader population of students with an affinity for mathematics. [ABSTRACT FROM AUTHOR]

A project involving data related to socioeconomic indicators was administered in an introductory statistics course. As part of this project, student groups investigated a data set from the United States Department of Agriculture Food and Nutrition Service website with information on recipients of Supplemental Nutrition Assistance Program (SNAP) benefits. Pre/post data from the Miville-Guzman Universality-Diversity Scale (M-GUDS) short form were collected to measure changes in diversity awareness. The survey administered also included demographic information and open-ended questions. Based on study results (n = 48), there was moderate evidence of a change in the diversity of contact subscale of the M-GUDS short form. Written feedback indicated that students demonstrated empathy for individuals with potentially different lived experiences. The focus of this paper is to describe the study results and provide information on the importance of incorporating elements of diversity into curriculum. [ABSTRACT FROM AUTHOR]

This paper reports on a novel corequisite design and implementation for College Algebra at Florida International University. The corequisite course uses online, just-in-time, prerequisite assignments delivered on an open-educational platform. Students get help from near-peer learning assistants inside a math emporium environment. The course remains three credits after the redesign and now supports all students who would otherwise be taking Intermediate Algebra as a prerequisite course. [ABSTRACT FROM AUTHOR]

In this paper, the authors discuss their experiences with ungrading at a small public university in the U.S. and a large public university in Germany. The courses described are Calculus 1 and a content course for pre-service secondary teachers of mathematics. The professors teach differently: one with lecture, the other with inquiry-based learning, and choose to use elements of ungrading in different ways. In one case, the professor lets students self-evaluate their homework, while in the other the professor uses a mix of specifications grading and ungrading for the final grade. We outline and compare our assessment approaches and discuss student performance and feedback. We also present some patterns relating to gender: in both cases, we observed that women students chose lower self-evaluations than men students. We end this paper with a general reflection on our teaching experience and our plans to use ungrading in the future. [ABSTRACT FROM AUTHOR]

This section calls for the submission of papers for occasional special issues of the journal "PRIMUS."

This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an early and integral part in the undergraduate mathematics curriculum. By computation we mean the ability to rapidly and easily program exploratory calculations, and as well display the results with a versatile suite of graphics capabilities. The problems used here, and the philosophy behind them, derive from a MATLAB-based course in computation, programming, and mathematical applications that the author has taught for over 10 years. [ABSTRACT FROM AUTHOR]

The articles discusses the call for submission of papers for the publication Primus' Special Issues, including the requirements and process of selection for the articles that will be published, guest editors like Gavin Larose and Krista Maxson, and the journal's themes.

The idea of cutting out a curve while looking at the direction of cut of the scissors is used to explore concepts related to curves, tangents and derivatives, especially tangent line, concavity and points of inflection, curvature, and a curve as envelope of tangent lines. [ABSTRACT FROM AUTHOR]

This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum cryptography in general. Classroom experiences with individual concepts used in Alkaline support this belief. In addition to cryptography, linear algebra and abstract algebra classes would be good candidates for the use of Alkaline. A few exercises suitable for use in these classes are included. [ABSTRACT FROM AUTHOR]

This editorial introduces the special issue, Resources for Undergraduate Cryptology. We begin by describing possible roles for cryptology in the undergraduate mathematics curriculum together with a brief overview of the subject. We conclude with a brief preview of each paper included in this issue. [ABSTRACT FROM AUTHOR]

The Miller–Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography. [ABSTRACT FROM AUTHOR]

In this paper, I analyze the impact of culture and metaphor on cryptology education. I will compare and contrast the historically grounded metaphors of cryptology-is-warfare and encryption-is-security to a set of counter-metaphors: cryptology-is-privacy and encryption-is-communication. Using this explicit understanding of conceptual metaphor, I present design recommendations and metaphorizing activities for educators building their undergraduate cryptology course. [ABSTRACT FROM AUTHOR]

In this paper, several research topics are presented that provide productive avenues of exploration for students in an undergraduate cryptography course. The topics are intended for a variety of skill levels and interests. In some cases, a student might be inspired to try to solve the proposed problem or write computer code. Other topics might motivate them to learn new mathematics or algorithms, or research a historical event or person. In all cases, a short description of the topic is given along with several references that can be used as a starting point for student research. The author also describes some challenges and recommendations when teaching a course where a project is a main component. [ABSTRACT FROM AUTHOR]

Lesson study, a popular method of professional development in which instructors collaborate to critique and improve a lesson, can be used for curriculum development. This paper describes an implementation of lesson study that went through two iterations across different, related, contexts: an undergraduate mathematics content course for secondary preservice teachers and a professional development session with practicing middle and secondary teachers. We describe the ways in which the lesson study process helped us develop curriculum for advanced undergraduate courses for future teachers and provide our insights into the benefits and challenges of this approach. [ABSTRACT FROM AUTHOR]

Experienced provers employ a host of skills when assessing the validity of a justification, often without names for those skills. This paper offers an introduction to a lens called Toulmin analysis that can help make sense of this process. Then this paper describes both an in-class module to help students learn to apply Toulmin analysis and multiple ways this module can be integrated into courses for mathematics majors and non-majors. Toulmin analysis has helped us bring human dimensions of proving to the surface in our classrooms, and it helps us build stronger and more inclusive entryways for students into mathematical communities. Learning about Toulmin analysis helps our students connect mathematical reasoning to other thinking, supporting transfer in both directions, and it has changed our thinking about the teaching and learning of mathematics even in contexts where we do not devote class time to this model overtly. [ABSTRACT FROM AUTHOR]

In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis of the two approaches. The ultimate goal of the paper is to encourage precalculus instructors teaching either version of logistic growth to consider incorporating our proposed changes in their classes. Sample classroom materials are provided in the supplemental data, along with access to preprogrammed computer spreadsheets for student use and/or classroom demonstrations. [ABSTRACT FROM AUTHOR]

In this work, we discuss the development of descriptive actions that facilitators take in semester-long online professional development geared at supporting instructional change at the undergraduate level. Current work in undergraduate mathematics education includes various large-scale projects aimed to support individuals or departments in reforming their instruction to align with recommendations from professional organizations and existing mathematics education research standards. One research area that has recently grown is the use of online synchronous environments to form collaborations to support the inclusion of student-centered instruction in mathematics. This paper discusses the actions that facilitators take in these collaborative environments and highlights how these actions supported the overall goal of the semester-long online faculty development. [ABSTRACT FROM AUTHOR]

Texas A&M University-Commerce has implemented supplemental instruction (SI) for Calculus since the fall of 2013. A direct display of the ABC rates from fall 2005 to spring 2021 only presents fluctuation from semester to semester, and one can hardly deduce that the ABC rates are increasing. In this paper, the "moving average" technique is used to reveal the effectiveness of SI in improving the percentage of students earning a grade of A, B, or C (ABC rates) in Calculus. Our longitudinal data under the "moving average" also shows that the SI implementation increased the ABC rates of major ethnic groups. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Mastery-based testing is an assessment scheme that encourages students to learn from their mistakes and develop an understanding of material before moving on. For an entry-level course with large enrollment like College Algebra, this could allow some students to move at an appropriate pace for themselves. This paper outlines the changes made to make College Algebra at the University of Florida an asynchronous mastery-based course for the 500+ students who take the course per year and concludes with a series of lessons learned from the endeavor. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we study how well SAT scores, high school GPA, and undergraduate precalculus grades relate to undergraduate calculus grades at a 4-year private nonprofit university that does not have a placement exam. In addition, we compare the success in calculus of two groups of students, both of whom require two semesters to pass calculus. The first group takes calculus twice (failing the first attempt) and the second group takes precalculus followed by calculus. [ABSTRACT FROM AUTHOR]

In the spring of 2018, the Pomona College mathematics department hosted a community seminar on identity, culture, and power in the discipline and education of mathematics. The seminar was free and open to all students, faculty, and staff of the college. In this paper, I describe the specifics of the seminar, what types of issues we discussed, what a typical seminar session looked like, and what we all gained from experience. Similar community seminars might support mathematics departments and faculty in their own endeavors to create inclusive and healthy mathematical communities. [ABSTRACT FROM AUTHOR]

As part of a departmental reform project, a large University converted a "Precalculus College Mathematics" lecture-based course for 97 students into an active learning flipped classroom for first-year engineering students. The curriculum was designed specifically to provide applications of pre-calculus in various engineering subjects. This paper outlines the course evolution, design features, ongoing adjustments made to the course, and quantitative data from the common examination and course evaluations to support the instructional design. The paper concludes with a reflection on which aspects of the learning environment helped facilitate successful learning and guidance for future implementations of a large-scale flipped undergraduate mathematics classroom. [ABSTRACT FROM AUTHOR]

This paper presents ideas for constructing mathematics homework assignments based on lessons from the cognitive science of learning and memory. In particular, we focus on two popular techniques from the field: spaced practice and mixed practice. The paper describes the techniques and supporting research, and then discusses various straightforward ways to incorporate them into mathematics instruction via homework assignments. The ideas presented can be applied at virtually any level of instruction and may be of interest to educators looking to implement research-based practices from cognitive science. [ABSTRACT FROM AUTHOR]

In this paper, I share an activity that reinforces students' understanding of translations, reflections, and rotations via body movement. As a result of this activity, students gain a different perspective compared to previous explorations on paper, communicate mathematics, and visualize transformations as rigid motions on the plane. Furthermore, the combination of sensation and perception helped some students assess whether their work was correct. [ABSTRACT FROM AUTHOR]

In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be used to interpret or inform classroom discourses by applying the framework to a selected transcript from a student-centered mathematics project called the Catwalk problem. We summarize how an awareness of students' forming mathematical identities can be used positively in the undergraduate classroom to help educators support students to form productive mathematical identities. [ABSTRACT FROM AUTHOR]

In this paper, we assess the pedagogical approaches we employ in our US-based undergraduate mathematics courses during the COVID-19 pandemic. Our goal is to share anecdotal evidence on the use of math journals, oral exams, and learning portfolios in the synchronous online mathematics classroom. We reflect on our experience using artifacts of student materials, feedback, and dialogues. [ABSTRACT FROM AUTHOR]

We detail our experience running an annual four-day workshop at the University of Minnesota, called the Mathematics Project at Minnesota (MPM). The workshop is for undergraduates who come from groups underrepresented in mathematics and aims to increase the participation and success of such groups in the mathematics major at the University. In this paper, we explain how MPM is organized, discuss its objectives, and highlight some of the sessions that we feel are emblematic of the program's success. The paper concludes with an analysis of achievements and obstacles in the programs' first three years. [ABSTRACT FROM AUTHOR]

In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the opportunity for students to develop rate of change equations for themselves. In this paper, we highlight an open-ended single salty tank task that provides the foundation for more complicated salty tank models that we also detail herein. Furthermore, we discuss instructional implementation techniques that instructors can use in their classes to meet their specific learning goals. [ABSTRACT FROM AUTHOR]

There are many perceived benefits to undergraduate student research; however, students may not have a full understanding of the research process prior to engaging in a project. In this paper, we analyze the impact of an undergraduate research workshop on students' understanding of academic research as well as the impact on their self-efficacy for conducting research through an analysis of the 2018 and 2019 Intercollegiate Biomathematics Alliance Cross-Institutional Research Experience (CURE) workshops. Students were asked to complete a survey at the start and end of the three-day workshop, which included both Likert-type scale questions as well as free response questions addressing their understanding of research and effective collaboration in conducting research, their perceived role in conducting research, and their perception of their own skills specific to biomathematics research. We observed improved self-efficacy in specific research skills where students had not already indicated a high level of self-efficacy prior to the workshop. Additionally, student responses indicated a shift in perception of research from solving a particular problem to contributing to a field by discovering or creating new knowledge. Other shifts in student perceptions are discussed in the paper as well as recommendations for the workshop organizers. [ABSTRACT FROM AUTHOR]

This paper introduces a course design for a post-Calculus undergraduate course on mathematical modeling for the life sciences. The course includes differential equations, discrete, and cellular automata approaches (among others) to modeling questions in the life sciences, as well as a variety of biological topics. The course focuses on model set-up and revision for these different scenarios and approaches as well as contemporary science approaches. Changes in student ranking of biology and math as well as student feedback are included. This paper may be of interest to any faculty member designing or revising a similar course or inserting modules on these topics into any related course. [ABSTRACT FROM AUTHOR]

We now know how best to teach our students – student-centered learning. Yet many of us face challenges when trying to design courses that are student-centered. In this paper, we present our experience with a Web 2.0 technology, VoiceThread, that has helped us address some of the challenges we have encountered when designing student-centered classrooms. We share our VoiceThread activities, and we discuss how mathematics educators and mathematicians can continue studying how to effectively use VoiceThread in face-to-face, blended, and online math courses. [ABSTRACT FROM AUTHOR]

Homework completion and self-regulatory ability have both been extensively studied to examine their impact on learning achievement. Moreover, the reciprocal nature of how these two qualities affect one another is also an area of research. While evidence shows that voluntary completion of assigned homework predicts self-regulation in students, a natural question is whether this can be facilitated with mandatory homework assignments. Research to this extent has been tentative: results are often positive, but issues with experimental design preclude strong conclusions or repeatability of the experiment. This paper aims to quantify the effect of mandatory homework assignments on learning achievement at the tertiary level while improving on the experimental design of existing research. [ABSTRACT FROM AUTHOR]

Student retention is a priority in universities, as drop-out rates among university students within 12 months of starting continue to rise, according to UK figures released by the Higher Education Statistics Agency (HESA) (, accessed February 2022), and with approximately a quarter of freshmen not enrolling for a second year in the US (NSC Research Centre. 2020. Persistence and Retention. Snapshot report. , accessed 1 June 2021). The transition to university, and in particular to a mathematics degree, is a challenging period for many students. Several methods to support HE students through this initial stage have been developed across the years, mostly designed in and for academic settings. This paper will describe an innovative approach, beyond the traditional classroom, which involves a three-day residential course tailored specifically to support the transition of mathematics students into HE, examining its implementation into the BSc Mathematics and MMath degree programs and its effectiveness with first-year Mathematics students at the University of Central Lancashire. The results provide an evaluation of this intervention over four years, showing the positive impact on attainment, together with increased student participation and engagement. [ABSTRACT FROM AUTHOR]