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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.

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees, food webs, networks), cellular automata (pattern formation, diffusion limited aggregation), fractals (both measurement and generation of self-similar structures), finite difference equations and deterministic chaos (logistic growth, predator-prey, SIR epidemiology), combinatorics and probability (genetics and evolution), information theory (biodiversity, sequence logos), and Boolean logic (operons) are available to adopt, adapt, and implement. An emphasis has been placed on modules that are freely available, that have been educationally vetted, and that run on a variety of operating systems. Most modules are easy to use, graphically visual, and amenable to modification. In this paper, two different approaches are stressed: (1) "glass box models" that allow students to see equations associated with each cell in a spreadsheet and to modify/extend those models with minimal effort; and (2) agent-based models that emphasize "bottom-up" modeling and that instantiate the power of massively parallel simulation and address the misconceptions of a "centralized mind-set."

Teaching introductory statistics is a service requirement for many mathematics faculty, and the audience is often anxious about the subject and not always excited about the material. Making class fun, relevant, and visually stimulating is key to keeping students engaged in the material and also in promoting student learning. Collecting data from the students, be it demographic information or experimental data, can achieve this, and immediately invites the students to be interested in the data and motivated to answer-related research questions. To facilitate and speed up this process, we developed the free data collection and analysis platform Classroom Stats which is designed to make class more fun and to improve student learning through straightforward visual analysis of the data. In this paper, we will discuss the importance of using student generated data in class and how to use Classroom Stats to make the process easy and efficient.

Local community organizations with data and statistical needs provide beneficial authenticity and context in the classroom. Students can provide creative, broad perspectives to problems and issues relevant to those organizations. This paper describes characteristics of mutually beneficial relationships between classes and community partners. Included is an account of such a partnership with a small liberal arts institution and a non-profit health access resource center in a low income neighborhood in a mid-sized city.

This paper discusses a concept that we call "'m'-tile means," which are the arithmetic mean of data values that break a data set into "m"-1 equal parts. Studying "m"-tile means can engage students' critical thinking skills and demonstrate the concepts underlying commonly used measures of central tendency, and so they are useful for student projects and accessible statistics discussion.

In this paper, we compare and contrast our experiences in using standards-based grading in different courses and across two separate institutions to explore the related tradeoffs and subtleties in designing and implementing such grading systems, guided by innovation diffusion theory. We summarize our individual courses, use Linda Nilson's criteria for evaluating grading systems as a framework for our shared reflections, and present questions for instructors to consider when designing a standards-based grading course. Despite the differences in courses, students, and institutions we had considerable overlap in the challenges we faced and the benefits we experienced.

Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the "Rule-of-Four," initially used in calculus reform efforts, to a "Rule-of-Five" framework for models and modeling that is inclusive of varying disciplinary definitions of each. This unifying framework allows us to both build on strengths that each discipline and its students bring, but also identify gaps in modeling activities practiced by each discipline. We also discuss benefits to student learning and interdisciplinary collaboration.

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills.

As an interdisciplinary team, we set out to create an applied statistics course that would cover the traditional introductory statistics topics in a consistent framework of social justice. The goal was to motivate students to understand and learn math while deepening their understanding of the interplay, at local and global levels, between social and economic issues: for example, crime, victimization, political access, wealth, education, health, gender, and race. This paper describes the process of creating the course, the pedagogical decisions, the intentionality in topic presentation, samples of classwork, and student impressions of the semester-long course.

The purpose of this paper is to present results of a recent study in which students voted on multiple choice questions in mathematics courses of varying levels. Students used clickers to select the best answer among the choices given; in addition, they were also asked whether they were confident in their answer. In this paper we analyze data collected from 192 multiple-choice questions used in five courses (Precalculus, Calculus 1, Differential equations, Linear Algebra, and Real Analysis) by two instructors at two different institutions. We evaluate student votes using four categories: correct and very confident, correct but not very confident, incorrect but not very confident, and incorrect and very confident. We examine and discuss characteristics of some questions from each category. We further assert that access to confidence data of this type will be an effective planning tool for future classroom voting. "Supplementary materials are available for this article. Go to the publisher's online edition of PRIMUS to view the supplementary file."

We discuss an upper division applied statistics course that has been structured to satisfy our college's writing intensive requirements within the mathematics major. In this course, students complete two projects, performing both a statistical survey and a controlled experiment, and then write up their work on each project in a formal paper. After each paper, the students read a group of papers written by their peers and then critique and rank these papers. Next, the students meet in groups, having read the same papers, and together they must form a consensus about their group rankings. Finally, after analyzing and discussing several papers from their peers, the students revise their own papers. (Contains 1 table.)

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.

For some students, using the method of cross sections to find the volume of a solid is difficult to understand because of the abstraction involved. This paper demonstrates a fun way for students to visualize the method of cross sections. Although a fun activity, the paper implicitly conveys the importance of connecting theory and experiment. (Contains 4 figures, 1 table, and 1 footnote.)

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.

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.

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.

The term "flipped" or "inverted" classroom includes a broad range of pedagogical innovations, and has recently received a significant amount of press. Although flipping an entire course might be a more extreme step than most are able to take, we discuss modular ideas for change that can be more easily implemented. This paper offers the perspective of four faculty members at different institutions who have all flipped material in statistics courses that were already highly interactive and activity-based. We share common pitfalls and core ideas that were found among diverse environments.

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.

This paper proposes and discusses how to use an assignment based on "Freakonomics" as a way to foster critical thinking and statistical literacy skills within the classroom.

Understanding the effects of a service-learning component on the classroom culture, socially and academically, brings a novel perspective to designing, executing, and assessing these types of active-learning projects. This paper evaluates the success of a service-learning project from a perspective of social networks by investigating the question: How does a service-learning project affect friendship and academic collaborations in the classroom? We believe that the benefits of service-learning involvement extend beyond helping students' academic success. Especially in a first-year seminar course, building a support system for the incoming student in order to ease the translation to a college setting is beneficial to students and to colleges. Here we use social network analysis tools to analyze relational data where relations are described as friendships or academic collaborations among classmates. Our results show that a group-based service learning project in an introductory level Statistics course has different effects on the evolution of friendship and academic collaboration networks among classmates.

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. (Contains 5 figures.)