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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]

Pedagogical training of mathematics graduate students is often disconnected from the actual experience of teaching. Even with the support offered by standard instructor training models, mathematics graduate students find it hard to connect with students, mature pedagogically and contribute meaningfully, especially under the overwhelming conditions of teaching for the first time. In this paper, we discuss features of instructor training that support mathematics graduate students' pedagogical development. Using self-reported experiences of mathematics graduate students who taught in a team teaching model, we single out three features of the model and advocate integrating these features into existing instructor training. [ABSTRACT FROM AUTHOR]

In this article, I will discuss a collective research project that I designed for my History of Mathematics course. My students, who are by and large pre-service teachers, explored online, digital versions of 18th-century British almanacs that contained question-and-answer sections for mathematics. In a multi-stage research process, they explored the primary sources, investigated selected mathematical problems from the almanacs, conducted prosopographies of the contributors to the almanacs, and finally surveyed secondary sources. They then presented their results in pairs to their classmates. Through these presentations, as well as the prosopographies and notes they shared on our online classroom management system, the working pairs of students wrote research papers that placed their findings within the context of the research of the whole class. This collective research project allowed my students to begin focused and purposeful research within the first week of classes. Moreover, this project encouraged them to become highly engaged with their primary sources and enabled them to work as a team. This collective research project framework could be applied to a variety of groups of primary sources from the history of mathematics (such as textbooks and journals), now widely available online, to a variety of mathematics courses. [ABSTRACT FROM PUBLISHER]

Mathematics is not just the queen of the sciences; it permeates through art, commerce, and in fact, every aspect of modern life. However, while we as mathematicians see beauty in the mathematical way of thinking and problem-solving, our students tend to think of mathematics as a set of rules and abstract computations. Our pleasure of doing mathematics usually does not transfer over to our students. In this paper, we describe two liberal arts general education courses which seek to develop a broad appreciation of mathematics for students who may not require any technical mathematics course for their academic major or chosen career path. We present mathematics as it relates to everyday life, with the goal of improving student appreciation of mathematics. [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]

This issue is the first of a specialPRIMUStwo-part issue collecting articles from experienced faculty mentors. We offer it as a valuable resource for faculty leading undergraduate research programs. It is inspired by the “Regional Faculty Workshop on REU Issues” in 2013 and the Joint Mathematics Meeting 2015 Mathematical Association of America’s “Themed Session on Perspectives and Experiences on Mentoring Undergraduate Students in Research.” This issue consists of seven papers focusing on the larger issues involved in creating, running, and sustaining an undergraduate research program in mathematics. [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]

In this paper, we provide a report of preliminary findings of the Morgan State University (MSU) Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) project and its focus on culturally responsive teaching (CRT) as an active learning framework for pre-calculus instruction. The paper concludes with a summary of wins and challenges faced by MSU's Mathematics Department. Lessons learned by MSU SEMINAL will help inform other departments on implementing CRT in a pre-calculus course. [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]

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]

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]

Much has been written about the benefits to be derived by incorporating the history of mathematics into its teaching. Of the various ways to do this, the use of original sources is among the most thrilling for the insights and the challenges it offers for students and instructors alike. In this paper, we describe examples of one particular approach to address these challenges that preserves the thrill of the read. [ABSTRACT FROM PUBLISHER]

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks for our students. Throughout the paper the use of multiple representations (graphical, numerical, symbolic, and narrative) and the distinction between facts, skills, methods, and conceptual understanding is explained and illustrated with examples. Additionally, we present evidence of student learning through excerpts from student journals and exam analysis. [ABSTRACT FROM PUBLISHER]

Mathematics education faculty working in mathematics departments are commonly involved in teaching undergraduate mathematics courses, teaching and supervising postgraduate students of mathematics education, and developing mathematics teachers (pre-service and/or in-service). This paper proposes a new elective course that can be taken by either undergraduate mathematics majors or by graduate teaching assistants pursuing degrees in mathematics and teaching undergraduates themselves. Twenty-eight topics are suggested, and the rationale for each is briefly described. Offering such a course provides different opportunities for students; for example, familiarizing them with effective ways to teach and learn mathematics, which has the potential to improve their effectiveness as tutors within the department. A similar course has been successfully taught to undergraduate students majoring in mathematics at an Iranian university for nearly two decades. [ABSTRACT FROM AUTHOR]

Teaching Mathematics to tertiary students can be a challenge to educators, mainly because they must deal with learners' varying levels of readiness. Some of the factors attributing to the variability are learners' perceptions of mathematics, their previous learning experiences, and fear of failure. We implemented a teaching approach to facilitate student ownership through active peer involvement and flexibility with assessments. In this paper, we analyze students' perceptions of learning mathematics when using the new approach for three consecutive semesters. We discuss the results of our study and the factors that helped students overcome their inhibitions and appreciate mathematical concepts. [ABSTRACT FROM AUTHOR]

In the fall of 2009 and in the spring of 2012, supported by the National Institute of General Medical Sciences (NIGMS) in the National Institutes of Health (NIH), we designed a course "Phylogenetic Analysis and Molecular Evolution" (PAME), the first cross-listed course across three different colleges (College of Arts and Sciences, College of Engineering, and College of Agriculture). This course was the first at the author's university. The course will be made available to graduate students and advanced undergraduate students in biology and computer science, and undergraduate student in statistics and mathematics at regional universities and colleges. The graduate students will learn how to gather sequence data, use bioinformatics tools, and analyze biological data using mathematics and statistics throughout the project. In this paper, we propose an online course on PAME facilitated with the statistical software RStudio on Amazon Web Service (AWS). [ABSTRACT FROM AUTHOR]

With knowledge in hand that teaching mathematics through active engagement leads to better learning outcomes for students, the field of mathematics is now tasked with researching effective facilitation of professional development for faculty. Our university embarked on an initial year of active learning professional development for mathematics faculty, implementing and researching a variety of professional development formats. We conjectured that effective faculty professional development, like effective mathematics instruction of students, would engage faculty in active learning experiences. Initial results indicate that effective professional development for faculty is tightly aligned with effective classroom instruction of students. This paper provides a framework of professional development practices for faculty, informed by a subset of mathematics instructional practices. [ABSTRACT FROM AUTHOR]

The percentage of college students receiving unproductive grades in introductory mathematics courses is a concern for post-secondary institutions across the country. Many factors can be targeted as potential explanations for this lack of success, yet none of these issues are more noteworthy than the fact that many students enter college mathematics courses with significant gaps in their fundamental mathematical background. In this paper, the authors discuss a way to implement an online remedial program to help students overcome their deficiencies following a "just-in-time teaching" model. Relevant data are presented supporting a positive outcome. [ABSTRACT FROM AUTHOR]

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A general description of the modules, as well as specifics about two lessons is provided. Student work, including journal entries, surveys, and class assignments, provide evidence that this intentional focus on creativity in mathematics challenged students' conceptions about mathematics, allowed them to reconsider the mathematics familiar to them in new ways, and engaged them in meaningful collaborations. Interviews of instructors revealed that they, too, engaged in creative processes as they planned the course and thought about innovative ways to engage students with mathematics. The course modules have been shared with other faculty teaching the course and will eventually be adapted for use in other mathematics courses, including those for STEM majors. Implications and future avenues for implementation and research are discussed. [ABSTRACT FROM AUTHOR]

Inquiry-based pedagogies have a strong presence in proof-based undergraduate mathematics courses, but can be difficult to implement in courses that are large, procedural, or highly computational. An introductory course in statistics would thus seem an unlikely candidate for an inquiry-based approach, as these courses typically steer well clear of proof, have a list of required topics, and depend critically on computational software. On the other hand, the American Statistical Association (ASA) has long advocated the sort of active and exploratory class design that in many respects parallels traditional inquiry-based learning (IBL). This paper reports on the author’s recent attempt to implement an inquiry-based course in introductory statistics that fuses established IBL techniques with the specific pedagogical recommendations of the ASA. A signature feature of this course is that many of the inquiry-based activities are explicitly tied to computer work in the open source language R. [ABSTRACT FROM PUBLISHER]

This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are situated in the context of the Intermediate Value Theorem, that are designed to promote students' understanding of multiple quantifiers in mathematical statements, as well as outputs and points on graphs of functions in the Cartesian plane. We offer suggestions for instruction and include sample dialogue to illustrate how these tasks may be used in the classroom. [ABSTRACT FROM AUTHOR]

To promote and facilitate the teaching of math modeling throughout the K–16 setting, the Consortium for Mathematics and Its Applications and the Society for Industrial and Applied Mathematics recently published the GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) Report. This paper provides insight into how the GAIMME report can be a valuable asset to undergraduate faculty in terms of better understanding how K–12 students engage in math modeling and how to create a continuum so that college mathematics courses, both pre-existing and perhaps newly developed, can support and further develop those skills. [ABSTRACT FROM AUTHOR]

Many students experience mathematics as a neutral entity, without understanding its impact on social justice and equity. Students must understand that mathematics and statistics are powerful tools for creating social change, and that students themselves are capable to enact positive social change through their mathematical abilities. In this paper, we discuss how we have integrated both service learning and mathematical consulting into a single course to promote civic engagement by mathematics majors through professional applications. We outline methods to engage with community partners to create consulting projects for students while integrating discussions of professionalism, practice, ethics, and social justice into the classroom. We provide qualitative evidence that the integration of service learning and consulting empowers mathematics students to make a difference by doing social justice with mathematics. [ABSTRACT FROM AUTHOR]

This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the benefit of themselves and their peers. The intervention appears to have incentivized students to engage with and learn mathematics contents in an effective way, and it also helped the mathematics teacher to reflect on, adapt, and develop his teaching strategies. To conclude, it would seem that both students and teachers in mathematics have much to gain from giving students opportunities to develop their own voice in learning contexts otherwise relying on books and lectures. [ABSTRACT FROM AUTHOR]

A growing body of mathematics education research points to the importance of fostering students’ mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative assessment tool, theCreativity-in-Progress Rubric(CPR)on Proving. This tool is developed to help students evaluate their own proving process, as well as provide instructors insight into students’ self-evaluation and process. In this paper, we provide a brief description of the CPR on Proving and explain its implementation in two courses at different institutions. Additionally, we share several students’ usages of the CPR and provide some practical implementation suggestions. [ABSTRACT FROM PUBLISHER]

Many mathematics departments have instituted transition-to-proof courses for second semester sophomores to help them learn how to construct proofs and to prepare them for proof-based courses, such as abstract algebra and real analysis. We have developed a way of getting students, who often stare at a blank piece of paper not knowing what to do, to start writing proofs. This is the technique of writing proof frameworks, which is based on the logical structure of the statements of the theorems and associated definitions. Also, in order to unpack the conclusion and know what is to be proved, students need definitions to become “operable.” [ABSTRACT FROM PUBLISHER]

Researchers have demonstrated that required, sustained professional development programs play an important role in developing instructors who are more student-focused, but financial constraints, time limitations, and lack of buy-in by faculty and/or administrators often serve as barriers to offering such programs. This special issue showcases several professional development programs situated in mathematics departments that aim to develop the teaching capacity of early-career instructors, primarily focusing on graduate students. Graduate teaching assistants (GTAs) who support other instructors and graduate student instructors (GSIs) are a vital part of the instructional workforce in many mathematics departments. Research programs alone of course do not prepare mathematics graduate students for the teaching that they will do during their programs or potentially after they graduate. We present below some of the findings of research on graduate students as instructors, and an overview of the articles in this issue that focus on how departments are addressing a lack of a variety of resources through their professional development programs. [ABSTRACT FROM AUTHOR]

Facebook provides businesses and organizations with copious data that describe how users are interacting with their page. This data affords an excellent opportunity to turn introductory statistics students into consultants to analyze the Facebook data using descriptive and inferential statistics. This paper details a semester-long project that partners student groups with local businesses and organizations and serves as a platform to work on articulating technical statistics to a non-expert audience. [ABSTRACT FROM PUBLISHER]

This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one that they themselves can justify. This experiment was conducted in the Discrete Mathematical Structures course; as it contains several subtopics, each of which uses a discrete set of elements with specific conditions. The textbook does not mention how those conditions are effectively put to use, and often uses the natural numbers as the default domain. Students are required to identify in their journals the exact properties that the elements need to have, justify how they are being put to use, and in ambitious cases attempt to sharpen them if possible. This activity can be adapted to different contexts and is not specific to the topic of Discrete Mathematical Structures. [ABSTRACT FROM PUBLISHER]

Undergraduate research occurs in a variety of mathematical fields and in diverse settings, but all mentors of undergraduates face a number of common considerations. This article is a brief guide to help faculty with various levels of previous mentoring experience lead students in research projects. In particular, we discuss the issues of picking appropriate research problems, recruiting students, setting expectations, moving research forward, and helping students to communicate their work. [ABSTRACT FROM AUTHOR]

Mentoring undergraduate students in research is both rewarding and challenging. In this paper we present how we established a summer Research Experience for Undergraduates (REU) program in the mathematical sciences at Michigan State University. A goal of our REU is to include students who are at an early stage of their study of mathematics. We share our experiences in recruiting students, designing research projects, and mentoring our participants. We discuss the challenges we faced and the solutions we found while working with a diverse group of undergraduate students from across the nation. [ABSTRACT FROM AUTHOR]

Math Girls $ \mathbb {R} $ R ock! is a year-long, two-tiered mathematics mentoring program that prepares female undergraduate mentors to facilitate high school girls' engagement in challenging mathematics concepts through a dynamic after-school program. In this article, we describe the distinct educational component of this program in which female faculty members mentor female undergraduate mathematics and mathematics education students in researching and developing the content to be presented at the high schools. In addition, we discuss some of the feedback collected from program participants about various aspects of this program relating to the involvement of the undergraduate students. In conclusion, we share advice for those interested in starting and running similar outreach programs. [ABSTRACT FROM AUTHOR]

Since its founding in 2013, the Kutztown University Association for Women in Mathematics student chapter has built a supportive community of women students and faculty on campus and beyond. This article aims to share our successful experiences with the broader community by presenting our pre- and mid-pandemic AWM activities including Mathematics Day for Girls, Women's Empowerment Day, Beyond Pink-Collar Jobs, and our Kutztown University AWM Virtual Lecture Series. Feedback from past and current participants of our AWM student chapter is also included. [ABSTRACT FROM AUTHOR]

The inverted classroom allows more in-class time for inquiry-based learning and for working through more advanced problem-solving activities than does the traditional lecture class. The skills acquired in this learning environment offer benefits far beyond the statistics classroom. This paper discusses four ways that can make the inverted classroom successful in an Introductory Statistics class: how to motivate students to prepare for each class, how to move the teaching of technology out of the classroom, how to balance student classwork, and how to create a mindset for learning. [ABSTRACT FROM PUBLISHER]

Over the last 10 years faculty members in the Department of Mathematical Sciences at the United States Air Force Academy have incorporated individual oral exams into mathematics courses. We have experimented with various approaches, shared results and ideas with other department members, and refined our techniques. We have found that this alternative assessment gives the instructor considerable insight into students’ understanding, and, in general, students value the opportunity to demonstrate their abilities via this kind of assessment. In this paper, we provide suggestions on successfully administering oral exams and offer evidence supporting their use in mathematics courses. [ABSTRACT FROM PUBLISHER]

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the type of writing assigned in my mathematical modeling course. Where the assignments are unusual, they are thoroughly described and I share my experiences on what worked well and what was not as successful. Where the assignments are more traditional, I offer an analysis of problems and pitfalls in teaching writing. Formal project reports for the class teach students how to write scientific articles. Unusual reflective assignments help students integrate their learning and apply it in new contexts. [ABSTRACT FROM PUBLISHER]

As an often recommended but under-utilized pedagogical strategy, writing in mathematics has many benefits for students. However, creating and grading worthwhile writing projects can be more time-consuming than utilizing more traditional forms of assessment. This paper provides a concrete example of a writing project prompt, questions, directions, and rubric which can be utilized in any of a Calculus, Differential Equations, or Mathematical Modeling course. The authors provide strategies for reducing the writing project workload by reusing a well-formulated project prompt to address varying levels of mathematical content. Strategies and author comments about lessons learned while implementing the projects are included. [ABSTRACT FROM PUBLISHER]

In many post-secondary, introductory mathematics courses failure and withdrawal rates are reaching as high as 50% and average GPA is steadily decreasing. This is a problem that has been witnessed across the globe. With widespread reforms taking place in K-12 mathematics education, many innovative teaching strategies have been created, implemented, and analyzed in an attempt to increase the conceptual knowledge of mathematics students at all levels. However, most of these strategies are not appropriate for large, lecture-style classrooms as are usually seen in large universities. This paper outlines some teaching and assessment strategies that have been modified to accommodate the needs and restrictions of such classrooms. [ABSTRACT FROM PUBLISHER]

Differences in definitions of limit and continuity of functions as treated in courses on calculus and in rigorous undergraduate analysis yield contradictory outcomes and unexpected language. There are results about limits in calculus that are false by the definitions of analysis, functions not continuous by one definition and continuous by another, and continuous functions with discontinuities. This paper uncovers these issues and resolves them in five guided classroom discoveries ideal for students in a first course in real analysis, an honors calculus course, or a course on transitions to higher-level mathematical thinking. The conclusion provides definitions consistent with analysis in a setting for the general student of calculus. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

To be successful, junior faculty must properly manage their time in the face of expanding responsibilities. One such responsibility is supervising undergraduate research projects. Student research projects (either single or multi-student) can be undertaken as a full-time summer experience, or as a part-time academic year commitment. With many potential undergraduate research formats, and with different types of students, junior faculty may find challenges in forming their research group, establishing a structure that promotes student productivity, picking an appropriate project, or in effectively mentoring their students. This article draws from the authors’ experiences to help junior faculty navigate these complexities so that all parties reap the benefits of undergraduate research in interdisciplinary mathematical disciplines. [ABSTRACT FROM AUTHOR]

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities from multiple courses in the program, we offer general principles of instruction for supporting mathematical inquiry at all grade levels. We contend that an awareness and application of the multiple facets of mathematical knowledge for teaching can be critical to supporting mathematical inquiry across the K-16 spectrum. [ABSTRACT FROM PUBLISHER]

Evidence shows that to improve student persistence in mathematics, we must change our course design to encourage students to have a growth mindset. By using standards-based grading, students earn grades based on their actual learning, so they are motivated to persist with difficult topics until they achieve understanding. Mastery-based testing has the potential to reduce test anxiety, improve students' confidence in their mathematical ability, reduce grading workload for faculty, and improve content retention. [ABSTRACT FROM AUTHOR]

Retaining mathematics majors is a pressing concern in many departments. We examined the pass rates of students across our mathematics major and then analyzed student persistence between math courses along with the underlying data collection required to make these analyses. We found that mathematics majors leaving the major after successfully completing a mathematics course is a huge issue and particularly prevalent among female and Hispanic students. Finally, we consider why this lack of persistence might exist and possible avenues to assist students in continuing a mathematics major. [ABSTRACT FROM AUTHOR]

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes (ALARMs) or to difficulty with the calculus material. The experiment found that over 65% of all students sacrificed at least one-third of a letter grade specifically to ALARMs, while nearly 20% sacrificed two-thirds of a letter grade. [ABSTRACT FROM AUTHOR]

We describe a small-group, model-building activity designed to lead students to conjecture the number, and some of the nature, of polytopes in four-dimensional space. We build models of regular polyhedra in three dimensions with the goal of understanding why there are only five of them, and then use them to make predictions about regular polytopes in four dimensions. [ABSTRACT FROM PUBLISHER]

Developmental mathematics is often a barrier to student progress and success in college. As a result and for this reason, this research study describes the redesign of a developmental mathematics course at a U.S. East Coast university to decrease the amount of time it takes for students to complete their developmental requirement and increase the success rate of students who move on to college-level mathematics. It also describes the motivation for the redesign and the implementation process. An analysis of quantitative data relating to student performance provides insight into how the course redesign presents opportunities and challenges for student progress and learning. The redesign demonstrated a high percentage of students passing the course over three years and has contributed to a high retention rate for developmental mathematics students. Recommendations for colleges and universities are included. [ABSTRACT FROM AUTHOR]

There is growing awareness of the need for mathematics and computing to quantitatively understand the complex dynamics and feedbacks in the life sciences. Although several institutions and research groups are conducting pioneering multidisciplinary research, communication and education across fields remain a bottleneck. The opportunity is ripe for using education research-supported mechanisms of cross-disciplinary training at the intersection of mathematics, computation, and biology. This case study uses the computational apprenticeship theoretical framework to describe the efforts of a computational biology lab to rapidly prototype, test, and refine a mentorship infrastructure for undergraduate research experiences. We describe the challenges, benefits, and lessons learned, as well as the utility of the computational apprenticeship framework in supporting computational/math students learning and contributing to biology, and biologists in learning computational methods. We also explore implications for undergraduate classroom instruction and cross-disciplinary scientific communication. [ABSTRACT FROM AUTHOR]

It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. Slopes is a mobile application designed to visualize solutions to differential equations and support active learning in the classroom. We implemented group activities using Slopes into an ordinary differential equations class, conducted observations and focus groups, and examined final poster projects to determine the benefits of the app. We found that students used Slopes to visualize solutions, aid in discussion and cooperation, and demonstrate understanding of differential equations concepts. [ABSTRACT FROM AUTHOR]

Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks connect three topics ubiquitous to such courses: logic, proof techniques, and sets. In particular, we were motivated by recent research showing that focusing on sets is propitious to novice students' ability to reason about logic and construct valid arguments. Our objectives were to (1) analyze examples of how these connections were made in relation to what is known about student thinking and learning in TTP courses and also to (2) identify situations in these texts in which there are opportunities for such connections to be made that could benefit students' learning. We focus on how logic was used to explain ideas related to sets and proof techniques, and how sets were used to explain ideas in the other domains. In addition to providing examples from our textbook sample illustrating instances in which connections were (or potentially could be made), we suggest several key recommendations TTP instructors can leverage in their unit(s) on sets. [ABSTRACT FROM AUTHOR]