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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]

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 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]

This editorial provides an introduction to the special issue, Infusing active learning into precalculus and calculus courses: Insights and lessons learned from mathematics departments in the process of change. We begin with providing the background for the special issue, including an overview of the current status of active learning in precalculus through calculus, what many of the papers in this issue mean by the term "active learning" (inquiry based mathematics education), and a brief overview of the literature on institutional change. We then offer an overview of each of the three issues, explaining how various papers relate to each other within each issue. We conclude the editorial with some reflections on the institutional changes efforts in light of the COVID-19 pandemic. [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]

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]

Over the past 10 years, the authors of this paper have implemented a series of project-based and inquiry-based learning initiatives in the calculus sequence at our institution. These initiatives took place in a department with an existing strong culture supporting teaching innovation and improvement. In this paper, we describe three initiatives in detail. We describe how in one, a syllabus redesign allowed for more instructor autonomy. In another, we were able to significantly improve student buy-in. We describe key support we received from our department and institutional leadership at each stage, as well as from working in community with each other. Finally, by looking at the long arc of change in our department, we hope to encourage others who are encountering roadblocks. By working in community, we have created an environment where active learning can flourish. [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 will discuss a type of activity that lets the mathematics classroom become a place where students can learn more than mathematical content. Specifically, students can learn interdisciplinary skills in the area of communication (both verbal and non-verbal) and debate skills that are often taught in communication or English classes. This paper discusses activities, which we call TACTivities, that can be added into any mathematics course to make the course more interdisciplinary, merging the arts and the sciences. They are best fit in mathematics courses where skills are to be learned and practiced, but modifications can be made for a variety of mathematics courses. [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]

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The Core Assignment gives the student some initial structure for their first reading of the textbook and is discussed in class. The Conceptual Assignment requires a second, deeper, reading of the textbook, and the instructor uses students' responses to initiate a discussion of the subtleties of the unit. In-class Worksheets and Follow-up Assignments allow for final synthesis of the unit. The staggering of the key components ensures that students engage with each unit of material at least five times throughout the course of a week. All of these key components can be built out of preexisting course materials. This paper, then, provides an accessible way to experiment with flipping an individual lesson, or indeed, one's entire course. [ABSTRACT FROM AUTHOR]

Large lecture halls are a common feature of many undergraduate mathematics programs. However, teaching effectively in a large lecture hall can be challenging. This paper discusses the use of personal whiteboards for students as a way to make large lecture halls a more productive learning environment. I discuss the logistics of using whiteboards, setting up norms, and provide examples of supporting instructional techniques. These techniques are: warmup problems, think-pair-share, group work, and student presentations. To support this exposition, I draw on personal reflections as an instructor and report from a brief student survey on their experiences using the whiteboards. [ABSTRACT FROM AUTHOR]

The typical trigonometry, precalculus, or calculus student might not agree that logarithms are hot stuff, but we drew motivation from chili peppers to help students get a better taste for logarithms. The Scoville scale, which ranges from 0 to 16,000,000, has been the sole quantitative metric to measure the pungency (spiciness) of peppers since its creation in 1912. With justification from the Weber–Fechner Law (perception is the logarithm of stimulus), students were challenged to create a more palatable rating scale for chili peppers. The first author devised a simple but effective 0–10 rating scale for peppers, calling this new rating system the "Ferven scale." While the Weber–Fechner Law has been applied to the senses of touch, sight, and hearing, this paper presents the first known application of this law to the sense of taste. [ABSTRACT FROM AUTHOR]

In this paper, we will describe the experience of the authors in using process-oriented guided inquiry learning (POGIL) in calculus at four institutions across the USA. We will briefly examine how POGIL compares to and fits in with other kinds of inquiry-based learning approaches. In particular, we will first discuss the unique structure of a POGIL activity, which includes a model and a learning cycle of specific types of questions. We then turn to a discussion of the particular characteristics of a classroom implementation of a POGIL activity, including facilitation strategies an instructor might use, the importance of specified student roles in groups, and different ways of reporting out. Finally, we provide some preliminary data on student pass rates in non-POGIL and POGIL calculus classrooms in the participating institutions. Throughout the paper, we use examples from student dialogues as groups were working through POGIL activities developed for Calculus I by the authors. [ABSTRACT FROM AUTHOR]

Increasing evidence supports the use of small group instruction to enhance student learning in undergraduate mathematics. However, effectively enacting such learning methods requires instructors to develop new skills as educators. This paper provides a practical guide for group work in undergraduate mathematics, describing key aspects of group work through the lenses of forming, norming, storming, and performing. I provide vignettes from my own teaching for reference. [ABSTRACT FROM AUTHOR]

This paper summarizes the experiences of two mathematics faculty members who participated in an in-house study abroad program. Descriptions of math courses taught abroad are given, as well as how students were recruited, courses were designed, and the environment was incorporated. Tips for mathematics faculty wanting to offer study abroad are given and impacts on the students are discussed. [ABSTRACT FROM AUTHOR]

Nationwide, many students fail to complete the key mathematics courses that are required for most STEM majors, including Precalculus. This paper describes the rationale, implementation, and impact of the redesign of Precalculus at one regional west coast institution. Prior to the redesign, pass rates in Precalculus were modest (75.8% of all students, calendar years 2009–2014). The redesigned course emphasizes active learning including group work based on conceptual questions and utilizes standards-based grading with a supporting emphasis on growth mindset. In the first three semesters of implementation, 88% of students passed the redesigned course. While the authors focus on the redesign of a Precalculus course, it is our hope that instructors of other core mathematics courses for STEM majors may find information of value in this work. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce partial results from our 3-year NSF funded grant titled "Inverted and Active Learning Pedagogies (IALP) for Student Success." We will present our results comparing student achievement between inverted (flipped) classrooms and traditional lecture formats in statistics classes at Texas Lutheran University. Included are a brief introduction, the study design, data gathering, faculty and students' surveys, and the methodology used for the study. We will share results from instruments that were developed to measure different levels of cognitive understanding across multiple sections of the same introductory statistics classes. We will also examine grades, withdrawals, potential professor effects, student characteristics, class size effects, video saturation, accountability of students for watching videos, and student evaluations of various activities in the classroom. [ABSTRACT FROM AUTHOR]

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions undergoing consolidations or implementing initiatives in core courses. Finally, this work provides proof-of-concept for coordination at a large minority-serving institution. [ABSTRACT FROM AUTHOR]

Faced with students failing to complete Calculus 1 at rates of almost 50%, the Department of Mathematics at Western Michigan University addressed the lack of progression of STEM majors through this gateway course and, thus, through their intended majors. In this case study, we describe the four-year process of redesigning our single variable Calculus 1 course. We coordinated instruction with a changing, highly collaborative instructional team of faculty and graduate students. Conversations among team members have been driving changes in instruction and assessment, and collaborative coordination is helping institutionalize the successful elements of the redesign. At the end of the paper, we describe the major take-aways we have gained as a result of this experience. [ABSTRACT FROM AUTHOR]

In this article, the authors propose a department-level curricular committee structure, called Strand Committees, as a mechanism to facilitate oversight and enact significant change to policies and practices in specific courses. The primary goal of the Strand Committees is improving both student success and instruction while upholding a high degree of shared governance. The focus of this paper is based around three recommendations encapsulating the philosophy of Strand Committees: increasing faculty buy-in for change efforts; capitalizing on the enthusiasm of a few faculty members to serve as change agents; and structuring the committees so participation is open, voluntary, and there is continuity to the work. The authors present the history and context of Strand Committees at a large, recently consolidated public university, highlight examples of successful and beneficial changes resulting from this work, and discuss how Strand Committees may lead to supporting improvements in teaching and learning in undergraduate mathematics. [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]

How can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable, but false, conjectures. [ABSTRACT FROM PUBLISHER]

This article proposes that in addition to training teams of students to succeed in the Mathematical Contest in Modeling, the contest and the preparation for competition can be successfully used as a framework to teach an auxiliary skill set to undergraduate STEM majors through workshop-style modules. The skills emphasized are collaboration across disciplines to creatively approach a problem, scientific writing, and the visual display of quantitative information. These skills are highly valued in industry and graduate study, yet are not always explicitly taught in a traditional undergraduate curriculum. The contest experience gives students a realistic appreciation for collaborative science work. Moreover, the active learning aspect of the preparation is broadly linked with student success in STEM, particularly for traditionally underrepresented STEM students. [ABSTRACT FROM AUTHOR]

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and investigations which can be used with their future middle school classes. Their study of calculus gives them a broader understanding of the formulae developed in the investigations. [ABSTRACT FROM AUTHOR]

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or four, beginning in class and finishing outside of class. In this paper, we explore examples of homework questions that promote abstract thought and the details necessary to implement this system in a calculus class. We discuss the ways in which group assignments invalidate solutions found online and ease the grading burden for the instructor. We mention possible pitfalls of this approach as well as ways in which to avoid them. Finally, we discuss student attitudes and feedback on this particular method of homework. [ABSTRACT FROM AUTHOR]

Escape rooms are an increasingly popular puzzle game, and educators have started implementing them in classrooms. This paper will describe the motivations and implementation of escape-room-like puzzles in an undergraduate cryptography course, including how the open-source mathematics software system SageMath is used. In addition, there is a discussion about generalizations of the activity to other courses. [ABSTRACT FROM AUTHOR]

This paper describes an active learning idea that I have used in my applied statistics class as a first lesson in correlation and regression. Students propel spitballs from various standing distances from the target and use the recorded data to determine if the spitball accuracy is associated with standing distance and review the algebra of lines (slope and intercept) and learn about the meaning of correlation. At the end of the activity, students listed positive aspects of the experiment and things to be improved. [ABSTRACT FROM PUBLISHER]

In this editorial, we provide an introduction to the special issue on Inquiry-Based Learning in First and Second Year Courses. We also discuss the essential features of inquiry-based learning and provide a brief overview of the literature and evidence for its effectiveness. [ABSTRACT FROM PUBLISHER]

This article describes the author's experience designing and implementing an inquiry-based learning (IBL) pedagogical approach to an upper-division undergraduate cryptology course. The author shares the course goals and how the IBL style supports their achievement. The article concludes with sample activities – in-class exercises that touch on one-time pad, the Birthday Problem, the Meet-in-the-Middle attack, and Diffie–Hellman key exchange protocol, and a programing assignment on the Vigenère cipher. [ABSTRACT FROM AUTHOR]

The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation developed to help illustrate the Central Limit Theorem. Students use the computer mouse to hand draw a population of arbitrary shape and then watch as the sampling distribution grows with each sample selected. A simple assessment tool is also given to check students’ understanding of this crucial concept. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15–20 minutes of videos before class. We discuss a portion of an in-class activity and a writing project used in the course. The results after one semester are that the students in this model did marginally better than students in the traditional lecture sections on common final exam questions. [ABSTRACT FROM PUBLISHER]

The flipped classroom model of teaching can be an ideal venue for turning a traditional classroom into an engaging, inquiry-based learning (IBL) environment. In this paper, we discuss how two instructors at different universities made their classrooms come to life by moving the acquisition of basic course concepts outside the classroom and using class time for active problem-based learning. Results from student surveys are presented to relate student perceptions of the flipped/IBL classroom model. [ABSTRACT FROM PUBLISHER]

This paper describes the linear algebra class I taught during Spring 2014 semester at Adelphi University. I discuss the details of how I flipped the class and incorporated elements of inquiry-based learning as well as the reasoning behind specific decisions I made. I give feedback from the students on the success of the course and provide my own reflections of the semester. Examples of some of the materials used are provided in the Appendix. [ABSTRACT FROM PUBLISHER]

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught without clickers. The purpose of the study is to determine what relationship, if any, exists between clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course. [ABSTRACT FROM PUBLISHER]

Students sometimes struggle with visualizing the three-dimensional solids encountered in certain integral problems in a calculus class. We present a project in which students create solids of revolution with clay on a pottery wheel and estimate the volumes of these objects using Riemann sums. In addition to giving students an opportunity for tactile learning, this project focuses students’ attention on concepts relating to (i) functions that have no algebraic formula; (ii) notation and construction of Riemann sums; and (iii) error estimation. We will describe our project design, implementation, and suggested adaptations. [ABSTRACT FROM PUBLISHER]

The Euclidean Discus Toss is an active and tactile learning activity that models the extended Euclidean algorithm with a frisbee relay. The extended Euclidean algorithm involves both iterative and recursive programming and is regularly taught throughout the mathematics and computer science curricula. The Euclidean Discus Toss invites students to toss and catch frisbees in a collaborative and hands-on effort designed to sharpen modular arithmetic skills, enhance familiarity with iterative and recursive algorithms, and strengthen classroom community. The activity is fun, low-stakes, and can be customized to meet a variety of pedagogical objectives. [ABSTRACT FROM AUTHOR]

Two years ago I implemented a basic outline of each class for my students to take notes on for Calculus II at the United States Military Academy. The outline provided students with a shell of the class material for each day of class. Their job was to fill in the shell as we went through the material. The outlines provided students an easy method to organize their own notes exactly how I organized the class. Space was provided to fill in pertinent definitions, label figures, or drawings that I provided, and to work step-by-step examples that I planned to go over in the class. The reason behind this approach was to help the student follow the flow of the class without having to think about what they should write down and what they should not write down. The things I wanted them to write down were on the outlines. Essentially the outlines represented the minimum material each student needed to take away from each class. Further, I chose difficult problems to include in the outline that were not in the text for students to work on their own. After executing this style of teaching for three semesters the following paper discusses my experience implementing this technique. [ABSTRACT FROM AUTHOR]

In this paper, I will discuss two related activities that I have developed for use in a college geometry course directed at pre-service secondary and elementary school teachers. These activities ask students to develop geometry on pool tables and on cones. The two activities are closely related, and both ask students to relate computer models with physical models. The pool table activity was developed as a lead in for the cone project, which is by far the most successful project that I have used for getting pre-service teachers actively engaged with the full cycle of exploring a new space, making conjectures about it, and then coming up with explanations for and proofs of the conjectures. [ABSTRACT FROM AUTHOR]

We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible approaches, each with their own advantages and disadvantages. Because these open-ended problems lacked the normal cues that tell students how to get started, they were very effective at revealing student misconceptions, and illuminating weaknesses in their understanding. Further, they were very effective at challenging the strongest students, without leaving the weaker students behind. All students were required to write up their work on each project into a formal paper. This not only taught the valuable skill of mathematical writing, but was also an important step in teaching more organized thinking skills. Over the course of the semester, the students developed impressive abilities at dealing with these sorts of realistic problems. The students became more systematic in their explorations, and more aware of the different methods that they were forced to choose from at each stage in the project. [ABSTRACT FROM AUTHOR]

The reform movement, with its bold and innovative approaches that focus on student-centered learning, has been able to uncover the richness in undergraduate mathematics. The most outstanding pedagogical practices take into account the environment in which learning occurs as well as the background of the student body. Mathematics educators should be aware that what count as the finest practices are institution dependent. This paper reports on three such pedagogical practices, with cooperative learning at their core, that have worked with remarkable success and could be adopted at different institutions. Formatted Interactive Lecture Leaves highlight the need for active learning by creating an interactive learning environment. Student Projects showcase the relevancy of mathematics by making connections to the diverse majors prevalent in our classrooms. The Program for Excellence in Mathematics, based on collaborative learning, challenges motivated students to strive for excellence. Details of these pedagogical practices as well as appropriate evidence of success are presented. [ABSTRACT FROM AUTHOR]

In the fall of 2020, our department at George Mason University integrated graduate learning assistants (GLAs) into our graduate core courses. GLAs are funded graduate students who assist instructors during class, facilitate active learning preliminary exam problem-solving sessions, hold extra office hours, and serve as peer mentors for beginning graduate students. The GLAMS program was designed to support beginning graduate students as they prepared for their preliminary exams. We describe the program and provide details about how it was implemented. We include preliminary student feedback as well as faculty and GLA reflections. To conclude, we outline our plans for programmatic changes moving forward. [ABSTRACT FROM AUTHOR]

This article presents several activities suitable for a transition to proofs course. In addition, this article surveys literature in support of active learning in the transition to proofs course and discusses how these activities have been successfully implemented in one such course. [ABSTRACT FROM AUTHOR]

The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom model, there are two lecture days and two discovery-based discussion days each week. Discussions center around group activities that build intuition for abstract concepts while avoiding excessive technical machinery. Teaching this course presents some unique challenges, as much of the content typically appears in a second course in abstract algebra, yet the students exhibit a wide range of mathematical preparation. [ABSTRACT FROM AUTHOR]

Teachers and students had an unusual experience in 2020. Due to the outbreak of the COVID-19 pandemic, regular teaching and learning in schools were suspended in many countries. The prolonged school closure presented unprecedented challenges because all teaching and learning activities had to be converted to a fully online format. This article reports on an attempt to sustain flipped learning using real-time online instruction. A flipped lesson on the cross-disciplinary applications of linear systems (i.e., balancing chemical equations) is presented in detail. Student feedback and the lessons learned from the experience are discussed. [ABSTRACT FROM AUTHOR]

We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google Cardboard compatible viewer. Example uses for math, physics, chemistry, and other STEM fields are presented, including a project-based assignment for calculus courses at The Ohio State University. The platform enables students, educators, and researchers to create stereoscopic VR visualizations on multiple platforms without needing to learn a complete VR development system. [ABSTRACT FROM AUTHOR]

Collegiate mathematics instructors are moving away from traditional lecture-based teaching practices to accommodate the pedagogies that support more active student learning. As part of the movement, groupwork has been increasingly implemented. At the same time, mathematics classrooms have become increasingly diverse and also in the distribution of students' primary languages. In this report, we examine two students' experiences with groupwork in a collegiate mathematics course. What commonly binds these two students is that they each found themselves to be the only member of their respective groups who uses a different primary language from the other group members. After presenting the experiences, we provide instructional implications for group formation in linguistically heterogeneous classrooms. [ABSTRACT FROM AUTHOR]

In this study, we use Class Preparation Worksheets (CPWs) as pre-class reading assignments for a Calculus I course. We describe the implementation and data collection as well as a qualitative and quantitative analysis. Then, we discuss the implications for student engagement with course materials, a student-and-instructor feedback loop, impacts on student attitudes, and changes in student use of tutoring centers. Overall, the CPWs promoted increased communication and more meaningful class interactions. In particular, students frequently used CPWs to provide status updates to the instructor, including positive and negative emotions as well as student assessments of difficulty. [ABSTRACT FROM AUTHOR]

Graphs about Us (GaU) is an activity for building classroom community within mathematics classrooms. Through the creation and analysis of graphical representations of data about the students' lives in and out of school, this activity aims to allow each student to feel seen and validated in the class, create shared knowledge of students' experiences, and to identify and challenge dominant narratives that may be unproductive for learning mathematics. By situating this activity within a mathematical context, GaU promotes students' learning about each other and about mathematics. This article describes three phases of the GaU activity, connects the activity with these goals for building classroom community, and discusses challenges that have arisen when using GaU with students. [ABSTRACT FROM AUTHOR]

According to the MAA Instructional Practices Guide, deep learning requires student engagement with content both inside and outside the classroom. Hence, mathematics instructors must work to engage students in the learning experience. Higher education research often equates engaged learning and active learning, but what does engaged learning mean to our students? In this study, we asked calculus 1 students at a private, liberal arts university to reflect on their perceptions of engagement in the course in hopes of determining if our students agree that active learning is engaged learning. Students completed an end-of-semester survey in which they gave their own definitions of engaged learning and identified classroom practices that they found engaging. We found that our students' perceptions and definitions of engagement varied greatly and many of our students did not see active learning as engaged learning, which indicates a need to better motivate active learning strategies in the classroom. [ABSTRACT FROM AUTHOR]