Nicole Engelke Infante

West Virginia University | WVU · Department of Mathematics

We analyzed video data of five instructors teaching the Mean Value Theorem (MVT) in a first-semester calculus course as part of a broader project investigating how active learning strategies were being implemented and supported in calculus courses. We sought to identify the ways examples of functions that did or did not satisfy the conclusion of MV...

In calculus, related rates problems are some of the most difficult for students to master. This is due in part to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elides import...

In this paper, we present an exploratory study on the important but under-researched area in undergraduate mathematics education: How do mathematics professors assign points to the proofs that their students submit? We interviewed nine mathematicians while they assigned points to three student-generated proofs from a transition-to-proof course. We...

The chapter sketches some of the landscape of current research in undergraduate mathematics education and offers useful information for present and future faculty members. Six research projects related to the teaching and learning of post-secondary mathematics are summarized. Approaches in the research reported here include individual interviews, c...

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus stu...

WeBWorK CLASS combines the best features of online homework and digital whiteboards to create a system that provides instructors with information on students’ problem solving processes, as well as their final answer. Utilizing tools which can sort students according to correct and incorrect homework and quiz answers and can display students’ soluti...

Model analysis is a quantitative research method used in physics education research to analyze and interpret the meaning of students' incorrect responses on a well-designed research-based multiple-choice test. We have adapted this method to study students' understanding of function composition when functions are represented graphical. Model analysi...

Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional problem-s...

This study explored first-semester calculus students' understanding of tangent lines as well as how students used tangent lines within the context of Newton's method. Task-based interviews were conducted with twelve first-semester calculus students who were asked to verbally describe a tangent line, sketch tangent lines for multiple curves, and use...

In a new approach, rate problems—the bane of students—can connect to higher-level concepts.

The Great Gorilla Jump (see appendix) is an activity that was designed by the authors to introduce students to the topic of the Riemann sum within the familiar context of position, velocity, and acceleration. Prior to the implementation of the gorilla activity, the students had worked with several examples of finding the velocity of an object given...

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These incl...

Related rates problems in first semester calculus are a source of difficulty for many students. These problems require students to be able to visualize the problem situation and attend to the nature of the changing quantities. I have developed a sequence of teaching activities that employs a computer program designed to foster the students' explora...

Related rates problems are a source of difficulty for many calculus students. There has been little research on the role of the mental model when solving these problems. Three first semester calculus students participated in a teaching experiment focused on solving related rates problems. The results of this teaching experiment were analyzed using...

Typescript. A thesis presented to the Honors Coordinator and Committee. Thesis (Honors)--University of Nebraska at Omaha, 1996. Includes bibliographical references.