Abstract: The flipped classroom approach was implemented across three semesters of a College Algebra course. This paper is part of a larger design and development research study and focuses on student percep...

Abstract: This paper reports on a research project that investigated the effects of a flipped instructional approach on student attitudes and achievement in a lower division university-level Finite Mathematics course. The project employed a mixed-methods design that included content exams, an attitude survey, open-ended student responses, observations, and instructor insights. Findings indicate that “flipping” allows instructors to repurpose class time for more student-centered interaction and problem solving, has positive effects on student attitudes toward mathematics, but has no significant impact on student learning over a more traditional approach. Discussion of implications focuses on factors that may influence the effectiveness of a flipped methodological approach.

Abstract: Recent studies have highlighted the positive effects on learning and retention rates that active learning brings to the classroom. A flipped classroom is a type of active learning where transmission of content occurs outside of the classroom environment and problem solving and learning activities become the focus of classroom time. This article reports on results of a study conducted in flipped and non-flipped Introductory Statistics classroom environments measuring student achievement in both classrooms on traditional assessments as well as measuring student attitudes toward the flipped classroom environment.

Abstract: 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: At Binghamton, Calculus 1 is taught to over 1000 students each fall in sections of about 30–40 students, with graduate student instructors teaching most sections. Despite having small classrooms instead of lecture halls, the satisfaction and performance of students has historically been poor. We had hoped to improve student success by changing how we teach and not by lowering our standards. In the fall of 2013, the Binghamton University Department of Mathematical Sciences undertook an experiment in flipped teaching with calculus 1 in which we compared a flipped model to our traditional lecture model. Overall, our quantitative analysis found moderate benefits to flipping over traditional methods for all groups studied. Informally, while student opinion varied, instructors largely were quite positive, finding that their students were more engaged and that instructors were able to give students more individualized attention.

Abstract: 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.

Abstract: In this paper I will share my experience with flipping a math content course for pre-service elementary teachers. The flipped class format involves students receiving instruction outside the classroom through readings and/or video lectures and working on “homework” inside the classroom. I will share strategies for creating lessons for my students to view outside of class, the structure of the in-class sessions, reflections on student learning, and comments from students.

Abstract: This paper describes one instructor’s experiences during a year of flipping four calculus classes. The first exploration attempts to understand student expectations of a math class and their preference towards a flipped classroom. The second examines success of students from a flipped classroom, and the last investigates relationships with student success and learning style and between personality and classroom style preference. The intent of the paper is to share experiences and provide advice for those who are considering flipping.

Abstract: College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: WeBWorK, an open-source system for web-based homework, or traditional paper-and-pencil homework. We assessed learning for 439 students in 19 college algebra classes at a large public university in the United States. Twelve classes used WeBWorK and seven had traditional paper-and-pencil homework. Analysis of covariance revealed no significant differences in algebra performance or achievement gain by homework group, ethnicity or gender when statistically controlling for previous mathematics achievement. Results support the conjecture that WeBWorK is at least as effective as traditionally graded paper-and-pencil homework for students learning college algebra in moderately sized lecture-based classes.

Abstract: The purpose of this exploratory, mixed-methods study was to compare student performance in flipped and non-flipped sections of Calculus I. The study also examined students’ perceptions of the flipping pedagogy. Students in the flipped courses reported spending, on average, an additional 1–2 hours per week outside of class on course content. Students enrolled in the flipped sections also performed better than students from the non-flipped sections on the common final exam. A follow-up examination of Calculus II grades revealed a statistically significant difference in course grades between these two groups of students.

Abstract: Introduction to the Flipped Classroom Krista Maxson Ph.D.; Professor & Chair, Mathematical Sciences How does the flipped classroom work? Dr. Maxson examines resources and issues in undergraduate classes that are flipped. She includes particular issues departmental chairs face with flipped classrooms, and she answers common questions about how to flip a class as well as the benefits and drawbacks of flipping a classroom.

Abstract: Flipped classrooms and inquiry-based learning (IBL) have each become popular in their own right, leading to a natural question: Why not combine these two great ideas? Although flipping a class usually involves students reading or watching videos before class, and IBL focuses on allowing and encouraging students to develop material on their own, both styles emphasize active learning and critical thinking through activities such as group work and presentations while minimizing lectures. In this article, I discuss ways that the two teaching styles can complement each other and be implemented concurrently, with some examples from my flipped calculus II course. Throughout this discussion the focus remains on ways to keep students engaged and how to instill deep content knowledge.

Abstract: Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside of class. No statistical difference was found in test scores of the students, though qualitative data indicated potential problems with implementing the flipped pedagogy. Specifically, many students had negative opinions of the flipped model, and attitudes toward math in general tended to decline, comparatively, for students in the flipped class.

Abstract: This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses what students thought of the course based on surveys and course evaluations. It also compares results on a similar final exam to those of a control group.

Abstract: This study investigates the effects of applying an inverted classroom model in a second-semester calculus course at a large regional university in the southwest during the Spring of 2013. The sample consisted of four class sections with the same instructor, with a total of 173 students; two class sections were in the experimental group, whereas the other two sections served as a control group. In the experimental sections, students watched video lectures of the course content outside of class, and class time was dedicated to solving problems associated with the content. Learning gains and academic differences between the two groups were investigated by analyzing exam scores and homework grades. In addition a survey (Motivated Strategies for Learning Questionnaire) was used to measure the students’ motivational orientations and their use of various learning strategies. Results showed there was a significant difference between the two groups on conceptual portions of some exams, where the control gr...

Abstract: This quantitative research compares five sections of College Algebra using flipped classroom methods with six sections using the traditional lecture/homework structure and its effect on student achievement as measured through a common final exam. Common final exam scores were the dependent variables. Instructors of flipped sections who had previous classroom experience with inquiry-based and cooperative learning methods had sections with statistically significant higher common final exam scores.

Abstract: In this article we describe a partially flipped Introductory Linear Algebra course developed by three faculty members at two different universities. We give motivation for our partially flipped design and describe our implementation in detail. Two main features of our course design are team-developed preview videos and related in-class activities. We share quantitative data and qualitative lessons learned related to our project.

Abstract: This paper contains a description of my experiences flipping undergraduate mathematics and statistics courses for the first time with some advice for any fellow novice flippers. This paper discusses ways to start small and build up to a completely flipped class over the span of a few terms with advice on what technology to use including software and hardware.

Abstract: In this article, we share a model of flipped instruction that allowed us to gain a window into our students’ mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be used to design experiences that help students make sense of mathematics during class sessions.

Abstract: Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate a classroom focused on mathematical discourse. The paper brings this discourse alive through classroom vignettes and explores various teacher moves and their impacts. The mathematical theme of the classroom investigations, Maypole dance patterns, stems from the learning guide “Discovering the Art of Mathematics: Dance.” Both authors are part of the NSF-funded project “Discovering the Art of Mathematics,” which provides IBL materials for mathematics for liberal arts courses, see www.artofmathematics.org.

Abstract: A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test results were reasonably consistent with the ACT Math benchmark score of 22 for college readiness. Analysis of ACT Math scores, basic algebra scores, calculus readiness scores, and course grades indicated that basic algebra scores are reasonable predictors of grades in College Algebra, whether traditional or modeling-based.

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

Abstract: Inquiry-based learning is a topic of growing interest in the mathematical community. Much of the focus has been on using these methods in calculus and higher-level classes. This article describes the design and implementation of a set of inquiry-based learning activities in a Math for Liberal Arts course at a small, private, Catholic college. Activity design, student responses, class management, and student and instructor attitudes are discussed.

Abstract: The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course content via a writing or research experience. Here we discuss methods of preparing students for a research/writing experience, the critical thinking involved in completing the project, and the basic assessment of student work.

Abstract: 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 of PRIMUS on “Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses.”

Abstract: This article discusses a cost-effective approach to flipping the calculus classroom. In particular, the emphasis is on low-cost choices, both monetarily and with regards to faculty time, that make the daunting task of flipping a course manageable for a single instructor. Student feedback and overall impressions are also presented.

Abstract: In order to strengthen departmental collegiality and improve teaching, our mathematics department instituted a Teaching Polygon. Building on the faculty development idea of Teaching Squares, each member of our department visited one class taught by every other department member in a round-robin fashion during the school year. The visits were followed by structured reflection and conversations about our observations. We found that being in each other’s classrooms strengthened our sense of community as a department, re-energized our enthusiasm for teaching, and encouraged us to reflect on ways to improve our own teaching.

Abstract: Our goal with this paper is three-fold. We want to increase awareness of inquiry-based learning by presenting the strategy we use to develop and implement lessons and activities. We describe our approach to structuring lessons in mathematics in a way that engages the students by using language and constructs with which they are familiar from other non-science classes. Finally, we include samples from an exploration of celtic knots that we think works well to engage students in the inquiry process, making use of these ideas.

Abstract: This article describes a developmental math course design that uses flipped instruction and self-paced learning. The design was created and taught at Metropolitan State University, where most students are returning adult students with little preparation in mathematics. The author argues that this design suits the students well: the learning outcome is better than traditional classes and student satisfaction is high. This article contains three parts: a description of the procedures of the course, learning outcomes with comparison to traditional classes, and analysis and outlooks for future development.