Education Commons^™

An Investigation Into Problem Solving In The Calculus Iii Classroom, Joseph Godinez

Honors College

The importance of tertiary education has grown to new heights, especially in the United States. A critical component of successful modern professionals remains the ability to employ problem-solving strategies and techniques. This study seeks to investigate initial problem-solving strategies employed by post-secondary students enrolled in Calculus II when presented with problems common to integral calculus. In- person pair-wise interviews were conducted asking six participants to sort integrals into categories based on the technique they would use to solve it. Participant responses were analyzed using a concept image composed of general and topic-specific symbolic forms, related conceptual images and concept definitions, …

A Collection Of Calculus Lesson Plans: Deriving The 'Why' Behind Derivatives, Kasey Brabec

Honors Theses

The traditional mathematics classroom is led with a focus on procedural understanding, with deep conceptual understanding considered to be unimportant or too difficult to teach within the allotted time. Both levels of understanding are important mathematical competencies, as it is rare for either of them to function well without accessibility to the other. The disparity between conceptual understanding and procedural understanding in the mathematics classroom is no larger than in courses like Calculus. This project is a collection of fifteen lesson plans constructed with an emphasis on conceptual understanding and the connectivity of Calculus. Each lesson plan’s overview contains the …

Transitioning To An Active Learning Environment For Calculus At The University Of Florida, Darryl Chamberlain, Amy Grady, Scott Keeran, Kevin Knudson, Ian Manly, Melissa Shabazz, Corey Stone

Publications

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.

Supporting Student Success And Persistence In Stem With Active Learning Approaches In Emerging Scholars Classrooms, David Miller, Jessica Deshler, Tim Mceldowney, John Stewart, Edgar Fuller, Matt Pascal, Lynnette Michaluk

Faculty & Staff Scholarship

Over the last several decades, Emerging Scholars Programs (ESPs) have incorporated active learning strategies and challenging problems into collegiate mathematics, resulting in students, underrepresented minority (URM) students in particular, earning at least half of a letter grade higher than other students in Calculus. In 2009, West Virginia University (WVU) adapted ESP models for use in Calculus I in an effort to support the success and retention of URM STEM students by embedding group and inquiry-based learning into a designated section of Calculus I. Seats in the class were reserved for URM and first- generation students. We anticipated that supporting students …

Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …

College Of Liberal Arts And Sciences_Covid-19 Course Content, Kristin Vekasi, Frederic Rondeau, Marcella Sorg, Derek Michaud, Ayesha Miller, Kirsten Jacobson, Lillian Herakova, Mark Brewer

College of Liberal Arts and Sciences

List of COVID-19 related course content in the University of Maine's College of Liberal Arts and Sciences during the 2020 Spring Semester. Includes descriptions from:

• Kristin Vekasi, Associate Professor, Political Science for POS 349: Politics of Media and Censorship;
• Frederic Rondeau, Associate Professor, Modern Languages and Classics for Introduction to French Classics Novels of the XX-XXI century;
• Marcella Sorg (Research Professor, Department of Anthropology, Climate Change Institute, and Margaret Chase Smith Policy Center for ANT 260: Forensic Anthropology;
• Derek Michaud, Lecturer, Philosophy; Coordinator of Religious Studies and Judaic Studies for PHI 105: Introduction to Religious Studies and PHI 100: Contemporary …

Attrition In Online And Face-To-Face Calculus And Precalculus Courses: A Comparative Analysis, Sarah Ferguson

STEMPS Faculty Publications

A multitude of online courses are available that provide opportunities for students to meet their higher education needs, goals, and desires in a nontraditional school setting. But, from a content specific perspective, how are students performing in online courses compared to their face-to-face counterparts? This study seeks to examine the attrition rates of online calculus and precalculus students relative to their face-to-face peers in an effort to expand the study of online mathematics pedagogy while providing course-specific data. Several studies have been conducted to explore attrition rates in relation to student demographics, STEM fields, and online course structure, but these …

Life After Calculus: 20 Years Later, Darren B. Glass

Math Faculty Publications

In 1996 Math Horizons interviewed a group of students at the Joint Mathematics Meetings; now, 20 years later, one of those students, Darren Glass, interviews another group of students.

Correlation Between Physics And Calculus Workshop Attendance And University Grades, Caroline Ferguson Ph.D.

Student Success

The Student Learning Centre at the University of Ontario Institute of Technology offers various support services for students enrolled in first year calculus and physics courses; the most widely used of these services are focused workshops. The purpose of this study was to compare student academic performance between those who did and did not attend physics and calculus workshops. Data provided by the Office of Institutional Research and Analysis at UOIT was analyzed using pivot tables in MS Excel. Students enrolled in Physics I and Calculus I were categorized based on their Grade 12 physics and calculus marks, respectively. Students …

Cognitive Load, Cues, And Task Selection In Learning Probability Calculus, Jimmie Leppink, Steven F. Raaijmakers, Fred Paas, Tamara Van Gog, Anique De Bruin, Jeroen Van Merrienboer

Faculty of Social Sciences - Papers (Archive)

Abstract presented at the 8th Cognitive Load Theory Conference, Fort Collins, Colorado, USA, June 15th - 17th, 2015.

Mastery Learning In Calculus I Affects Student Learning, Grade Improvement, And Professor Exhaustion, Judith Puncochar, Don H. Faust

Conference Presentations

Three Calculus I courses were taught under conditions of either traditional teaching, 2/3 mastery, or full mastery to test four hypotheses. Under conditions of mastery learning on exams, students should attain appropriate higher-level mathematical concepts, achieve more learning of higher-level mathematical concepts, learn higher-level mathematical concepts more quickly, and evaluate mastery learning favorably. Support for all hypotheses occurred only in the 2/3 mastery condition. A shift toward higher grades was attributed to grade improvement, not grade inflation, as determined by six mathematicians with blind review of final exam items. Final exams in mastery learning courses were significantly more …

Students' Perceived Utility Of Precision Taught Calculus, Rebecca-Anne Dibbs, David Glassmeyer, Wafa Yacoub

Faculty Articles

The last decade of calculus research has showed students learn best when lecture is supplemented with thoughtful use of technology and group work; however, educators are given little direction of how they are to balance the already full first semester calculus class. Precision teaching is an instructional model that employs formative assessment to provide information on what topics are understood by students as well as indicate troublesome concepts. With this information, the instructor can adjust class time accordingly by incorporating supplemental activities most beneficial to students. The purpose of this interview study was to explore the perceived utility of precision …

On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.

Instructor Use Of Tablet Pcs In A College Pre-Calculus Course: Implementation & Assessment, Julianna Connelly Stockton, Peter Gregory

Mathematics Faculty Publications

A group of six math instructors used tablet PCs to teach their individual sections of a high enrollment gateway Pre-Calculus course in a diverse urban four-year college. Student performance in the experimental sections were compared to those in 31 other sections in terms of student retention, pass rates, and score on the department-wide standardized final exam. Student performance was higher in Tablet PC sections across all three measures, although in some cases the improvement was not substantial enough to improve students’ overall course grades. Surveys of students and faculty in classes using a Tablet PC reflected overall positive impressions of …

Polynomial Calculus: Rethinking The Role Of Calculus In High Schools, William Crombie, Melva R. Grant

Teaching & Learning Faculty Publications

Access to advanced study in mathematics, in general, and to Calculus, in particular, depends in part on the conceptual architecture of these knowledge domains, and in this paper we outline an alternative architecture. Our general strategy is to separate advanced concepts from the particular advanced techniques used in their definition and exposition. This alternative architecture, thus, affords access to advanced concepts from an elementary standpoint to a larger group of learners than is presently accomplished. In the case of the Calculus we develop the beginning concepts of the Differential and Integral Calculus using only concepts and skills found in secondary …

Teaching Calculus With Wolfram Alpha, Andrew Lang

College of Science and Engineering Faculty Research and Scholarship

This article describes the benefits and drawbacks of using Wolfram|Alpha as the platform for teaching calculus concepts in the lab setting. It is a result of our experiences designing and creating an entirely new set of labs using Wolfram|Alpha. We present the reasoning behind our transition from using a standard computer algebra system (CAS) to Wolfram|Alpha in our differential and integral calculus labs, together with the positive results from our experience. We also discuss the current limitations of Wolfram|Alpha, including a discussion on why we still use a CAS for our multivariate calculus labs.

A Closer Look At The Crease Length Problem, Sean F. Ellermeyer

Faculty Articles

An optimization problem that appears as an exercise in most modern calculus textbooks is the crease length problem. Here, Ellermeyer provides a solution of the general crease length problem in which all possible foldings of a corner to the opposite edge are taken into account. One of his findings will be that the minimum crease length is never produced by a Case 2 fold and hence that the general crease length problem always yields a different minimum than the constrained problem that is treated in the textbooks. He discovers a criterion that determines which foldings must be performed in order …

Mathematics Placement Test: Helping Students Succeed, Norma Rueda, Carole Sokolowski

Mathematics Faculty Publications

A study was conducted at Merrimack College in Massachusetts to compare the grades of students who took the recommended course as determined by their mathematics placement exam score and those who did not follow this recommendation. The goal was to decide whether the mathematics placement exam used at Merrimack College was effective in placing students in the appropriate mathematics class. During five years, first-year students who took a mathematics course in the fall semester were categorized into four groups: those who took the recommended course, those who took an easier course than recommended, those who took a course more difficult …

Project-Based Freshmen Engineering Courses In Civil Engineering Technology, Vernon W. Lewis Jr., Carol L. Considine

Engineering Technology Faculty Publications

Old Dominion University (ODU) has developed two fundamental courses for freshmen engineering students. The first course introduces the fundamentals of the practice of engineering including innovation, creativity, design and manufacturing, commercialization, teaming skills, environmental impact, and ethics. The second course is an exploration of engineering and engineering technology disciplines with an emphasis on projects. The purpose of these courses is to engage the students in the application of engineering early in their course of study with the hope that their interest will be reinforced and the likelihood of their being retained as students will increase. The courses are divided into …