The Scholarship of Teaching and Learning (SoTL) movement encourages faculty to view teaching 'problems' as invitations to conduct scholarly investigations. In this growing field of inquiry faculty bring their disciplinary knowledge and teaching experience to bear on questions of teaching and learning. They systematically gather evidence to develop and support their conclusions. The results are to be peer reviewed and made public for others to build on. This Notes volume is written expressly for collegiate mathematics faculty who want to know more about conducting scholarly investigations into their teaching and their students' learning. Envisioned and edited by two mathematics faculty, the volume serves as a how-to guide for doing SoTL in mathematics.

Applications of Mathematics in Economics presents an overview of the (qualitative and graphical) methods and perspectives of economists. Its objectives are not intended to teach economics, but rather to give mathematicians a sense of what mathematics is used at the undergraduate level in various parts of economics, and to provide students with the opportunities to apply their mathematics in relevant economics contexts. The volume’s applications span a broad range of mathematical topics and levels of sophistication. Each article consists of self-contained, stand-alone, expository sections whose problems illustrate what mathematics is used, and how, in that subdiscipline of economics. The problems are intended to be richer and more informative about economics than the economics exercises in most mathematics texts. Since each section is self-contained, instructors can readily use the economics background and worked-out solutions to tailor (simplify or embellish) a section’s problems to their students’ needs. Overall, the volume’s 47 sections contain more than 100 multipart problems. Thus, instructors have ample material to select for classroom uses, homework assignments, and enrichment activities.

There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind. In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.

Middle school mathematics teachers occupy a unique place in the mathematical development of students. These teachers need to be proficient in all elementary mathematics topics, together with some secondary mathematics topics. They demand a special kind of preparation that differs from both that of their elementary and secondary colleagues. The Mathematics Education of Teachers (MET) document published by the Conference Board of the Mathematical Sciences set forth criteria for the preparation of mathematics middle school teachers which made it critical that special programs and courses for this group emerge. This collection of articles is in response to the MET document and the result of several gatherings of mathematics educators and mathematicians training middle school teachers. We have chosen the articles that appear in this volume for several purposes: to disseminate various middle school programs structures, to detail methods of teaching specific middle school teachers content courses, and to share materials and resources. While each article describes the unique program or course of its respective institution, each also includes a common core of information to provide some consistency to the volume. In particular, all articles describing middle school programs contain information about the host institution, a history of the program, degree and testing requirements for the program and for state licensure, learning goals and objectives for the program and courses, and any available assessment data. When applicable information is included about particular courses, for example, some articles provide sample activities or syllabi and some have a description of courses in the appendix. Most articles have links to websites containing further information about the program, courses, state requirements, or resources that can be downloaded and used directly.

Are you looking for new ways to engage your students? Classroom voting can be a powerful way to enliven your classroom, by requiring all students to consider a question, discuss it with their peers, and vote on the answer during class. When used in the right way, students engage more deeply with the material, and have fun in the process, while you get valuable feedback when you see how they voted. But what are the best strategies to integrate voting into your lesson plans? How do you teach the full curriculum while including these voting events? How do you find the right questions for your students? This collection includes papers from faculty at institutions across the country, teaching a broad range of courses with classroom voting, including college algebra, precalculus, calculus, statistics, linear algebra, differential equations, and beyond. These faculty share their experiences and explain how they have used classroom voting to engage students, to provoke discussions, and to improve how they teach mathematics. This volume should be of interest to anyone who wants to begin using classroom voting as well as people who are already using it but would like to know what others are doing. While the authors are primarily college-level faculty, many of the papers could also be of interest to high school mathematics teachers.

Recent Developments on Introducing a Historical Dimension in Mathematics Education consists of 24 papers (coming from 13 countries worldwide). The volume aims to constitute an all-embracing outcome of recent activities within the HPM Group (International Study Group on the Relations Between History and Pedagogy of Mathematics). We believe these articles will move the field forward and provide faculty with many new ideas for incorporating the history of mathematics into their teaching at various levels of education. The book is organized into four parts. The first deals with theoretical ideas for integrating the history of mathematics into mathematics education. The second part contains research studies on the use of the history of mathematics in the teaching of numerous mathematics topics at several levels of education. The third part concentrates on how history can be used with prospective and current teachers of mathematics. We also include a special fourth part containing three purely historical papers based on invited talks at the HPM meeting of 2008. Two of these articles provide an overview of the development of mathematics in the Americas, while the third is a study of the astronomical origins of trigonometry.

Mathematical Time Capsules offers teachers historical modules for immediate use in the mathematics classroom. Readers will find articles and activities from mathematics history that enhance the learning of topics covered in the undergraduate or secondary mathematics curricula. Each capsule presents at least one topic or a historical thread that can be used throughout a course. The capsules were written by experienced practitioners to provide teachers with historical background and classroom activities designed for immediate use in the classroom, along with further references and resources on the chapter subject.

The Beauty of Fractals includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject. Each essay is self-contained and expository. Moreover, each of the essays is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that are not regularly in textbooks on fractals.

The Moore Method: A Pathway to Learner-Centered Instruction offers a practical overview of the method as practiced by the four co-authors, serving as both a 'how to' manual for implementing the method and an answer to the question, 'what is the Moore method?'. Moore is well known as creator of The Moore Method (no textbooks, no lectures, no conferring) in which there is a current and growing revival of interest and modified application under inquiry-based learning projects. Beginning with Moore's Method as practiced by Moore himself, the authors proceed to present their own broader definitions of the method before addressing specific details and mechanics of their individual implementations. Each chapter consists of four essays, one by each author, introduced with the commonality of the authors' writings. Topics include the culture the authors strive to establish in the classroom, their grading methods, the development of materials and typical days in the classroom. Appendices include sample tests, sample notes, and diaries of individual courses. With more than 130 references supporting the themes of the book the work provides ample additional reading supporting the transition to learner-centered methods of instruction.

A resource for discrete mathematics teachers at all levels. Resources for Teaching Discrete Mathematics presents nineteen classroom tested projects complete with student handouts, solutions, and notes to the instructor. Topics range from a first day activity that motivates proofs to applications of discrete mathematics to chemistry, biology, and data storage. Other projects provide: supplementary material on classic topics such as the towers of Hanoi and the Josephus problem, how to use a calculator to explore various course topics, how to employ Cuisenaire rods to examine the Fibonacci numbers and other sequences, and how you can use plastic pipes to create a geodesic dome. The book contains eleven history modules that allow students to explore topics in their original context. Sources range from eleventh century Chinese figures that prompted Leibniz to write on binary arithmetic, to a 1959 article on automata theory. Excerpts include: Pascal's 'Treatise on the Arithmetical Triangle,' Hamilton's 'Account of the Icosian Game,' and Cantor's (translated) 'Contributions to the Founding of the Theory of Transfinite Numbers.' Five articles complete the book. Three address extensions of standard discrete mathematics content: an exploration of historical counting problems with attention to discovering formulas, a discussion of how computers store graphs, and a survey connecting the principle of inclusion-exclusion to Möbius inversion. Finally, there are two articles on pedagogy specifically related to discrete mathematics courses: a summary of adapting a group discovery method to larger classes, and a discussion of using logic in encouraging students to construct proofs.

The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any mathematics department or any individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem solving abilities, and students' understanding of fundamental ideas such as variable, and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice.

This volume is a compilation of articles from researchers and educators who use the history of mathematics to facilitate active learning in the classroom. The contributions range from simple devices such as the rectangular protractor that can be made in a geometry classroom, to elaborate models of descriptive geometry that can be used as a major project in a college mathematics course. Other chapters contain detailed descriptions on how to build and use historical models in the high school or collegiate mathematics classroom. Some of the items included in this volume are: sundials, planimeters, Napier's Bones, linkages, cycloid clock, a labyrinth, and an apparatus that demonstrates the brachistocrone in the classroom. Whether replicas of historical devices or models are used to represent a topic from the history of mathematics, using models of a historical nature allows students to combine three important areas of their education: mathematics and mathematical reasoning; mechanical and spatial reasoning and manipulation; and evaluation of historical versus contemporary mathematical techniques.

This book deals with issues involved in setting up and running a program which allows undergraduate students to work on problems from real world sources. A number of practitioners share their experiences with the reader. How are such programs set up and what resources are required? How are clients found? What problems are suitable for students to work on? What difficulties can be anticipated and how can they be resolved? What benefits does the client derive from the students' work and what do the students get out of such projects? These issues and others like them are explored in a number of different academic environments. It is the contention of this book that students develop an appreciation of mathematics and its usefulness by engaging in programs such as those described here. Furthermore it is possible to develop such programs for a variety of student audiences over a wide spectrum of colleges and universities. A chapter is devoted to relevant materials available from the Consortium for Mathematics and its Applications (COMAP). Lists of student projects and examples of their work are provided. There is also a discussion of the pros and cons of consultancy projects by representatives of industry familiar with such project.

Each year, over 1,000,000 students take college-level courses below calculus such as pre-calculus, college algebra and others that fulfill general education requirements. Most college algebra courses, and certainly all pre-calculus courses, were originally intended to prepare students for calculus. Most are still offered in this spirit, even though only a small percentage of students has any intention of taking calculus. The MAA'S goal has been to refocus the courses below calculus to provide better mathematical experiences for all students. This initiative involves a greater emphasis on conceptual understanding with a de-emphasis on rote manipulation. The use of realistic applications, math modeling and data analysis that reflect the way mathematics is used in other disciplines is encouraged, along with active learning approaches (including group work, exploratory activities and projects). The initiative emphasizes communication skills: reading, writing, presenting and listening. The appropriate use of technology to enhance conceptual understanding, visualization, and inquiry enables students to tackle real-world problems. The 49 papers in this volume discuss various aspects of this issue. The major themes include: new visions for introductory collegiate mathematics, transition from high school to college, needs of other disciplines, research on student learning, implementation issues, and ideas and projects that work.

Current Practices in Quantitative Literacy present a wide sampling of efforts being made on campuses across the country to achieve our common goal of having a quantitatively literate citizenry. Colleges and universities have grappled with complicated issues in order to define quantitative literacy within their own communities and to implement appropriate curriculum. It is clear that any quantitative literacy program must be responsive to the local conditions of an institution including its mission, its student clientele, its history and its resources.

From Calculus to Computers is a resource for undergraduate teachers that provide ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader. Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Among the topics included are: projects with significant historical content successfully used in a numerical analysis course; a discussion of the role of probability in undergraduate statistics courses; integration of the history of mathematics in undergraduate geometry instruction, to include non-Euclidean geometries; the evolution of mathematics education and teacher preparation over the past two centuries; the use of a seminal paper by Cayley to motivate student learning in an abstract algebra course; the integration of the history of logic and programming into computer science courses; ideas on how to implement history into any class and how to develop history of mathematics courses.

This book describes innovative approaches that have been used successfully by a variety of instructors in the undergraduate mathematics courses that follow calculus. These approaches are designed to make upper division mathematics courses more interesting, more attractive, and more beneficial to our students. The authors of the articles in this volume show how this can be done while still teaching mathematics courses. These approaches range from various classroom techniques to novel presentations of material to discussing topics not normally encountered in the typical mathematics curriculum.

Every year thousands of new mathematics instructors and teaching assistants begin their teaching careers, and, scores of experienced faculty seek ways to explore the new teaching possibilities offered by technological and pedagogical innovations. There is a great need for tools to train college mathematics instructors in both basic teaching skills and innovative methodologies. Learning to Teach and Teaching to Learn is a self-contained and extensive resource that addresses this need. It describes training and mentoring activities that have been successfully used in a variety of settings. with a wide range of new instructors, including graduate student teaching assistants, undergraduate tutors, graders and lab assistants, as well as postdoctoral, adjunct, part-time and new regular-rank faculty. It addresses a variety of teaching issues including cooperative learning, technology, and assessment.