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…

The purpose of this study was to investigate implementation of an early intervention mastery activity during the first two weeks of college algebra and precalculus courses at a large U.S. public university. Statistical modeling of (N = 935) students' performance in the courses, including a logistic regression model of pass/fail course achievement…

This study explores the question, "What are the school-level characteristics associated with non-white students' access to Calculus courses in the high schools they attend?" This exploration is an extension of an earlier study focused on non-white student access to Algebra II. It will work to expand our understanding of how access to…

The purpose of this study is to determine the factors effected calculus learning outcome of the student. This study was conducted with 176 respondents, which were selected randomly. The data were obtained by questionnaire, and then analyzed by using multiple regressions, and correlation, at level of a = 0.05. The findings showed there is the…

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

Activities for Students appears five times each year in Mathematics Teacher, promoting student-centered activities that teachers can adapt for use in their own classroom. In the course of the activities presented here, students will "look for and make use of structure" by observing algebraic patterns in the power rule and "use…

The ability to categorize problems based upon underlying principles, rather than contexts, is considered a hallmark of expertise in physics problem solving. With inspiration from a classic study by Chi, Feltovich, and Glaser, we compared the categorization of 25 introductory mechanics problems based upon similarity of solution by students in large…

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

Our investigation is concerned with new teachers developing their ability to understand student thinking. We conducted individual interviews with graduate students teaching calculus for the first time, interviewing a representative sample of graduate students before and after their first teaching assignment. The interviews were transcribed and…

In this article, we elaborate methodologies to study the argumentation speech of a teacher involved in argumentative activities. The standard tool of analysis of teachers' argumentation concerning pedagogical matters is Toulmin's model. The theory of argumentation schemes offers an alternative perspective on the analysis of arguments. We propose…

We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…

Interest in understanding mathematics teaching and learning phenomena, and to develop new and effective methodologies to teach Differential Calculus and Linear Algebra led me to look for ways to dialogue between APOS Theory and other mathematics education theories. This enterprise has facilitated a better understanding of them. Bridges between…

We present a case study of how five instructors used gesture when introducing the second derivative test in a first semester calculus class. The second derivative test and optimization naturally evoke hand motions while teaching, making this a fertile ground for studying gesture use in the classroom. Each of the five instructors used a classic…

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

By describing the motion of a charged particle in the well-known nonuniform field of a current-carrying long straight wire, a variety of teaching/learning opportunities are described: 1) Brief review of a standard problem; 2) Vector analysis; 3) Dimensionless variables; 4) Coupled differential equations; 5) Numerical solutions.