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This paper is a practical how-to guide to help you start using active learning or to have greater success and more fun with it. We categorize active learning techniques as Think, Pair, Share, Composite, Group, Move, or Lead and discuss how to implement activities in each category, along with advice on creating engaging, effective, and equitable learning experiences. We introduce the Active Learning Pedagogy Sequence (ALPS) which orders these categories by difficulty and time for instructors and students. We believe both instructors' teaching skills and students' learning skills develop along the ALPS. [ABSTRACT FROM AUTHOR]

Elementary education makes use of manipulatives in the teaching of fundamental mathematical concepts. As the age of the students progress, mathematics becomes much more abstract and concepts such as the integral become harder for some students to visualize. One approach we have implemented is the use of construction paper as a manipulative. This simple hands-on object can be used to demonstrate the basic properties of integrals to students who struggle greatly with the underlying ideas, especially when they are first encountered. Through the treatment of the integral as something that can be held in the hand and modified with the use of scissors, many of the basic properties of integrals can be demonstrated, as well as the intuition behind the Fundamental Theorem of Calculus. [ABSTRACT FROM PUBLISHER]

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]

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]

Mathematics for liberal arts courses are a staple of most mathematics departments and are often populated with students who have disengaged from mathematics. Inquiry-based learning is a student-centered pedagogical tool for re-engaging students in mathematics. In this paper, we introduce a Special Issue ofPRIMUSon “Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses.” [ABSTRACT FROM PUBLISHER]

This paper discusses the ways in which teacher educators can effectively engage prospective teachers (PTs) in lesson study during mathematics methods courses. Evidence from this work suggests that engagement in lesson study provides PTs with opportunities to strengthen their knowledge about mathematics, students, and pedagogy. More specifically, the results demonstrated that lesson study helped PTs to engage in deep and thoughtful discussions about mathematics, reflect on their teaching, and make effective changes to their lessons that showed noticeable improvements in student learning. Recommendations from this work provide specific methods-course suggestions on the implementation of lesson study as a model for PTs' professional and practitioner development, including strategies and guiding questions that teacher educators can utilize to help deepen PTs' knowledge about mathematics, teaching, and student learning. [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]

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]

Metacognition as a dimension of learning ranks highest in the revised Bloom’s Taxonomy of cognitive tasks. In this paper we illustrate how it can be incorporated into a repeated exercise in the mathematics classroom, through a specific case study in the context of a liberal arts mathematics course. Through the semester, students were asked weekly to evaluate their own progress and review their development in light of their personal goals. We observed positive affective changes (including engagement levels) in the students through the course of the semester. We argue that the weekly metacognitive and self-reflective activities helped students keep their focus on learning deeply and allowed them to remain engaged and motivated through the semester. A brief theoretical discussion is included, and other possible contexts suitable for the described activities are suggested. [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]

The primary goal of this paper is to highlight the possibilities and benefits of incorporating games into college mathematics classrooms. This is illustrated through the personal success of using the board gameThe Resistanceto teach validity and soundness of arguments in a discrete mathematics course. Along the way, we will give some recent history of board games and rationale for incorporating them into classes. [ABSTRACT FROM PUBLISHER]

This paper describes the results of a two-semester-long study of the effects of student-centered instruction on Precalculus courses. We also describe our teaching approaches centering around students, which include a mixture of lectures, student presentations, group work, discussion, and guided investigations. Students were taught with either the traditional, and still dominant, lecture-based, instructor-centered teaching methods, or with the collaborative student-centered methods. We found that the average over all students was higher on quizzes when they were taught with student-centered methods. Moreover, the students in the lower quantiles scored significantly higher than their counterparts in the traditional lecture-based classrooms. This suggests that not only are student-centered approaches more effective than instructor-centered approaches, but that they are particularly helpful to those students who are struggling with Precalculus. [ABSTRACT FROM PUBLISHER]

This article focuses on the philosophy of creativity and its enhancement through an undergraduate research experience. In this paper we offer suggestions for infusing the undergraduate mathematics and science curriculum with research experiences as a way of fostering creativity in our students. We refer to the termresearchbroadly, offering suggestions to accommodate students from various backgrounds and with different goals. We posit that creativity is a necessary component of scientific thinking, producing students that are motivated, passionate, skilled, adaptable, and responsible. Research experiences at the undergraduate level instill a deep sense of personalized education and learning that can make the entire university experience extremely pleasurable and of lasting value. [ABSTRACT FROM PUBLISHER]

Making connections is one of the most important foundations involved in learning mathematics. Two projects are presented in this article: one involving Newton's Second Law of Motion and the other involving the determination of star numbers, a type of figurate number. The two invoke seemingly different modalities for students at different levels of mathematical maturity, and yet they share a deep academic connection. [ABSTRACT FROM AUTHOR]

Two types of students at our university college were combined with the aim of bringing different knowledge together and in this way improving the learning environment. Based on observations and interviews, the project only partly turned out as expected. In this paper we try to ascertain what went right and what went wrong, explain why, and suggest changes that could be made to improve the scheme. [ABSTRACT FROM AUTHOR]

This article describes key elements for mathematics teachers, through the faculty development process, to increase student engagement and motivation in learning mathematics. It addresses common barriers facing student motivation and achievement in the field of mathematics and provides potential remedies from a faculty development viewpoint to alleviate these barriers. The paper offers practical examples from the authors' own faculty development programs and experiences in teaching mathematics to both foster and grow the intellectual curiosity of students and offers suggestions for successful faculty development programs. [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]

The current work is the first article in a two-paper series exploring the role of explicit learning objectives in undergraduate mathematics instruction. A definition of student-learning objective (SLO) is introduced. We give examples of SLOs for topics from introductory college and university mathematics courses. We list potential advantages of a general program of grounding mathematics instruction in a set of such explicit SLOs. In the second paper in this series, an explicit, step-by-step algorithm for creating sets of student learning objectives will be described and its use illustrated. [ABSTRACT FROM AUTHOR]

Contemporary mathematics education is at a crossroads. It has become exposed to forces, both static and dynamic, that pose a challenge to its traditional place in academia. Mathematics has a long-established status as perhaps the most critical foundation for analytical knowledge. But the manner in which mathematics instructors choose to respond to this challenge may well determine the degree of relevance and importance that traditional mathematical theory eventually commands in newly emerging scientific and technological disciplines. In this paper, we will: (a) identify the forces that are acting on contemporary mathematics instruction; (b) examine some of the historical, social, and psychological underpinnings that have given rise to these forces; (c) enumerate the conditions which mathematics instruction must address if it is to remain a viable discipline; and (d) evaluate the relative success of a case study, addressing the role of mathematics instruction for technical career students, that has been designed to address these conditions. [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 issue ofPRIMUSis a special issue on the topic of service-learning in mathematics. We introduce the topic and special issue with a broad preview of the articles in the issue. [ABSTRACT FROM PUBLISHER]

This article offers some insights into successfully engaging students in research. While most schools encourage undergraduate research, there is little guidance specific to mathematics on how to make it a rewarding experience for both the student and the advisor. With a small support group and a goal-oriented time line, students will be able to point to accomplishments by the end of their unique experience. [ABSTRACT FROM PUBLISHER]

Students rarely use their graded exams to study. An alternative method of grading exams, based on self-reflection, encourages students to use their mistakes as a learning resource. In this grading method, the test is returned with each question simply marked as 'right' or 'wrong.' Students can then go over their exams and resubmit them with separate corrections, where for each wrong question they must identify the error, decide how serious it was, and describe how to fix it. The exam and corrections together are graded, and for each error correctly identified, classified, and fixed, the student gets back half the points lost. I implemented this in two applied calculus classes for non-majors in spring 2006 as well as in a year-long calculus sequence for engineers in 2006-2007. It was very well received, as indicated on the surveys the students filled out after each in-class exam. Most students indicated that, compared to traditionally graded exams, they spent more time going over their exam and felt they learned a lot more from their mistakes. In this article, I discuss the details of the grading method, the logistics involved in administering it, and the results of two years of student surveys assessing its effectiveness. Insofar as this method encourages students to actively learn from their mistakes, it is well worth the time investment on the part of the instructor. [ABSTRACT FROM AUTHOR]

We review the processes of goal identification employed in teacher planning. A new type of graphical organizer (Fact-Action- Schema-Transcript or FAST) is introduced and its applications to teacher planning discussed. We describe a pair of algorithms for (a) creating FASTs for undergraduate mathematics and (b) using FASTs to create sets of student learning objectives (SLOs). Application of these algorithms to lesson planning are illustrated with several examples from introductory college mathematics courses. [ABSTRACT FROM AUTHOR]

Math courses graded on homework, tests, and a final examination can result in students putting together enough partial credit to pass the class without gaining a reasonable mastery of the course content. Mastery-based testing can help to address this by allowing the instructor to align course grades with mastery of the learning objectives for the course. This article is a reflection on my experiences implementing mastery-based testing in Discrete Mathematics. I give a brief introduction to the ideas behind mastery-based testing and discuss the construction of two of my mastery tests. The change affected my teaching, helping me to see where students need help understanding the material. Instructor observation and feedback from student evaluations of instruction indicate that student learning was improved with the change. [ABSTRACT FROM AUTHOR]

This study explores the impact of Peer-Assisted Reflection (PAR), a structured active learning strategy that emphasizes peer feedback and reflection, on students' perceptions of mathematical thinking, and of the roles their peers and their instructors play in their learning process. This study also examines the impact of PAR on the students' ability to evaluate mathematical arguments and communicate those evaluations in writing, which has not been specifically measured in prior research on PAR. The findings suggest that the PAR intervention not only increases students' ability to communicate effectively, but also gives them a newfound recognition of the importance of developing communication skills in mathematics. Additionally, students' thinking about mathematics shifts as they come to value the exploration of multiple perspectives in solving math problems. Many students explicitly note their increased appreciation for the role of their peers in the learning process. [ABSTRACT FROM AUTHOR]

Definitions are fundamental to any mathematics classroom. We consider how definitions are presented in textbooks and instructors' lecture notes, and whether students are positioned to gain a full understanding of new terms. Four textbooks, covering precalculus, calculus, and analysis, as well as three professors' Calculus I lecture notes are compared. We find that textbooks often include two versions of definitions, formal and informal, but those definitions differ across texts. Instructors' lecture notes do not usually have more than one version of a definition, and that version may not align with the course textbook, but they do sometimes offer intuitive or visual interpretations. We provide suggestions for being more mindful when deciding how and what definitions to present. [ABSTRACT FROM AUTHOR]

Homework gives students the opportunity to practice new skills in both familiar and unfamiliar situations, and to develop an understanding of related concepts. Although some of these goals can be easily accomplished in online homework, many systems are less useful for handling open-ended questions. Written homework, on the other hand, takes time to grade and delays feedback. To fill the gap left between these approaches in lower-level courses, I supplement online homework with "homework presentations." Students put worked problems up on the board to earn points, and we discuss the problems together. In addition to reducing grading load, homework presentations provide students with feedback at the optimal place in the learning process. [ABSTRACT FROM AUTHOR]

Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that are deemed appropriate for undergraduate students and which foster mathematical habits of mind. These are: generating examples; analyzing reasoning; evaluating mathematical statements; conjecturing and/or generalizing; visualizing; and using definitions. We give rationales for our choices and examples of each type of task suitable for use in an introductory calculus course. [ABSTRACT FROM AUTHOR]

This assessment study examined one potential instructional method for improving student learning in Calculus for majors, flipped learning, in comparison with traditional lecture-based instruction. Results suggest that participation in flipped learning substantially improved growth in achievement over the semester, final exam grades, and final course grades. In contrast, there was no difference between the two groups in terms of students' beliefs about learning mathematics. Additionally presented is a review of the changes made from the first year to the second year of implementing flipped learning, and how these changes are believed to have assisted with the increased impact on student learning. [ABSTRACT FROM AUTHOR]

We describe a case study of a problem-solving section, using the “Harkness” discussion method, of an honors multivariable calculus course. Students in the problem-solving section had equivalent outcomes on exams, reported higher ratings in self-assessments of skills, and took more math classes in the following year, compared with students in the lecture-based sections. [ABSTRACT FROM AUTHOR]

The Georgia College mathematics department has reimagined its major requirements to integrate meaningful undergraduate research experiences. We have developed and implemented a multi-year action plan to transform our major. In this article we discuss how the department has developed and implemented a year-long research experience as a capstone requirement. We address how we gained faculty and student buy-in, built a curriculum to support the experience, and developed assessment and evaluation tools. We conclude with a discussion of challenges and next steps in the program. [ABSTRACT FROM PUBLISHER]

Implementing inquiry-based modules within a course can be effective and enable instructor experimentation, without completely transforming an entire course. For instructors new to inquiry-based learning (IBL), we state hallmarks of the practice and point out the merits of strong IBL communities. An inquiry-based approach may alleviate some current common issues in Calculus I. We present two activities and evidence of their effectiveness and adaptability, and describe their POGIL style of guided inquiry learning that raises awareness of the learning process. We share the experience of a “traditionally-oriented” faculty member transitioning to a more student-centered pedagogy, reflecting on advantages of using a combination of pedagogical styles. [ABSTRACT FROM PUBLISHER]

In this article, I present a collection of puzzles appropriate for use in a variety of undergraduate courses, along with suggestions for relevant discussion. Logic puzzles and riddles have long been sources of amusement for mathematicians and the general public alike. I describe the use of puzzles in a classroom setting, and argue for their use as a basis for discussion of the nature of mathematics, for development of problem-solving skills and confidence, and as a means of engaging students from a broad range of mathematical backgrounds. I suggest a consistent use of puzzles in a low-pressure setting as a possible means of fostering inquiry and a positive learning mindset among students. [ABSTRACT FROM PUBLISHER]

Online homework systems, which deliver homework assignments to students and provide real-time feedback on their responses, have the potential to increase student learning in college mathematics classes. However, current research on their effectiveness is inconclusive, with some studies showing gains in student achievement, whereas others report only that the systems “do no harm.” Our own experience has convinced us that online homework systems can increase student engagement and achievement, especially in lower-level classes, such as statistics, precalculus, and calculus. Successfully integrating online homework systems into face-to-face mathematics classes requires instructors to confront several issues, including the differing natures of online homework and in-class assessments such as tests. We explore these issues, and offer guidelines gleaned from our experience, which can help instructors and students maximize the benefits offered by these systems to improve student learning. [ABSTRACT FROM PUBLISHER]

The author has taught an inquiry-based liberal arts mathematics class using the text “The Heart of Mathematics: An Invitation to Effective Thinking” by Edward B. Burger and Michael Starbird a total of 20 times since Spring 2001. The students in this class have almost all been in non-technical majors and many started the semester with negative or ambivalent attitudes toward mathematics based on their prior experiences. The author has gathered responses from students in this class that illustrate significant changes in their attitudes towards mathematics during the course. In particular, the responses gathered at the end of the semester are often eloquent about understanding the great ideas of mathematics that students confronted in this course and about seeing many more and varied connections between mathematics and the “real world” than they had previously realized existed. [ABSTRACT FROM PUBLISHER]

This article presents a problem-based approach that prepares students for future learning in the classroom. In this approach, students complete problem-based activities before coming to class to familiarize themselves with the topics to be covered. After the discussion on how the use of these activities relate to the learning and transfer theories, the structure of the activities is described in detail. Specific examples in a variety of topics are provided. Student perceptions of these activities based on anonymous course evaluations are also included. [ABSTRACT FROM PUBLISHER]

Over the past decade there has been a dramatic increase in undergraduate research activities at colleges and universities nationwide. However, this comes at a time when budgets are being tightened and some institutions do not have the resources to pursue new initiatives. In this article we present some ideas for obtaining funding and support for building an undergraduate research program in mathematics. [ABSTRACT FROM PUBLISHER]

As an extension to various sponsored summer undergraduate research programs, academic year research for undergraduate students is becoming popular. Mathematics faculty around the country are getting involved with this type of research and administrators are encouraging this effort. Since 2007, we have been conducting academic year research at Lamar University. This study describes our academic year research program and some of its benefits. [ABSTRACT FROM PUBLISHER]

The Mathematical and Theoretical Biology Institute (MTBI) is a successful summer research experience for undergraduates, with a strong record of mentoring Ph.D. graduates, particularly, underrepresented minority students. However, the MTBI program was designed for education in research, not for research in education, and the mechanisms of the students’ success has never been adequately studied. This article begins the process of studying MTBI from an educational theory perspective by examining the MTBI community model from the perspective of four researchers: Piaget, Vygotsky, Bandura, and the MTBI students themselves. [ABSTRACT FROM PUBLISHER]

There is a growing interest in the use of hands-on learning activities in undergraduate mathematics classrooms, as evidenced by over 70 well-attended talks during MAA Special Sessions on tactile learning activities at the 2012 and 2013 Joint Mathematics Meetings. This article introduces a special issue ofPRIMUSdedicated to hands-on learning activities, giving an overview of the pedagogical foundations as well as a short overview of the included articles which cover activities ranging from precalculus to upper level mathematics courses. [ABSTRACT FROM PUBLISHER]

This article describes the author's pedagogical transformation from “traditional” lecture-based instruction to Inquiry Based Learning (IBL) instruction of an introductory proofs class for sophomore mathematics majors. The story of the course overhaul follows from inception, through implementation, and ultimately to reflection. Quantitative and qualitative data suggest that the author's shift to IBL in this course was a change for the better. [ABSTRACT FROM PUBLISHER]

Most instructors desire to create a learning environment conducive to deep learning. However, in courses where grades are based upon the accumulation of points, students may focus on collecting points rather than on learning and achieving the course objectives. We discuss an alternative points-free course design based on the development of clear learning objectives, practical descriptions of grades based on these objectives, and open discussions with students about their progress relative to the objectives. [ABSTRACT FROM PUBLISHER]

The purpose of this article is to provide a deeper understanding of the natural rhythm of a typical semester, as observed in students' reflections in journals kept during the semester. Our analysis of students' writings rendered a breakdown of the semester into four distinct periods that were independent of the particular semester or section the students were attending. These periods were characterized by changes in the emotional state of students, which affected their learning. This article includes descriptions of the different periods in the students' own words, as well as suggestions for teaching practices aimed at improving student-learning outcomes based on our findings. [ABSTRACT FROM PUBLISHER]

This article suggests an activity, called the ε-strip activity, as an instructional method for conceptualization of the rigorous definition of the limit of a sequence via visualization. The article also describes the learning objectives of each instructional step of the activity, and then provides detailed instructional methods to guide students to reach the learning objectives. [ABSTRACT FROM AUTHOR]

We consider two different algebra topics that can be taught in a typical college class. With each topic, we demonstrate how a teacher can delve deeper using a computer algebra system. [ABSTRACT FROM AUTHOR]

To help students understand the real-world applications of calculus, our calculus students all take part in a lab. This is not another "computer lab" but a lab where the students perform experiments and then collect and analyze the data. The students are able to verify for themselves many of physical claims that are left as theory in most calculus courses. We describe our lab, the experiments and what the students actually do while in lab. We discuss some of the difficulties of such a lab as well as some simplifications that would be possible for a similar lab elsewhere. [ABSTRACT FROM AUTHOR]

The practice of students going to the boards to work problems has been a tradition in undergraduate education for over two hundred years. A study was conducted to determine what instructional techniques enabled students to better learn fundamental concepts in mathematics. This study identifies board work as a highly effective instructional technique for developing a student's ability to succeed on a standardized exam covering basic algebra, geometry, and trigonometry skills. This study offers insight into student motivation, and it suggests that board work improves student performance and learning. [ABSTRACT FROM AUTHOR]

In teaching a course without a textbook, we introduce a project in which students develop their own text. Details of the project, student reactions, benefits to students, and more are discussed. [ABSTRACT FROM AUTHOR]