Physical Sciences and Mathematics Commons^™

Oer Book Review For Calculus - Openstax Calculus, Jing Hu

Open Educational Resources Publications

This OER textbook review provides a comprehensive evaluation of the "Calculus" textbook series published by OpenStax. The reviewer, Jing Hu, an adjunct lecturer at Bentley University, highlights the textbook's strengths, including its thorough coverage of essential calculus topics, accurate and well-established mathematical principles, practical relevance, and user-friendly design. The open-access nature of the resource is seen as a significant advantage, contributing to its long-term utility and accessibility for both students and educators. Overall, the review concludes that the OpenStax Calculus textbook is a high-quality, comprehensive, and freely available resource that effectively supports the learning and teaching of calculus.

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, …

Wicked Problems And The Invention Of Calculus, Ernesto Diaz

Natural Sciences and Mathematics | Faculty Scholarship

Since the 1980s, wicked problems have represented a category of challenges that defy clear description, cannot be addressed with existing models or theories, and resist experimentation in trying to solve them. This class of problems existed before they were identified and have been unsuccessfully addressed with Thomas Kuhn’s model of scientific discovery, an expectation that requires the identification of a new object and the development of its correct interpretation. This paper proposes an alternative view of scientific discovery using the invention of Calculus as a case study that describes a successful process addressing wicked-like problems from a philosophical perspective, develops …

Broadening Views Of Mathematical Creativity: Inclusion Of The Undergraduate Student Perspective, Emily Cilli-Turner, V. Rani Satyam, Miloš Savić, Gail Tang, Houssein El Turkey, Gulden Karakok

Mathematics: Faculty Scholarship

Numerous conceptions of creativity exist in the literature; yet these are commonly based on the perspectives of professional mathematicians. Including students’ perspectives in creativity is crucial not only for a more robust picture of what it means to be creative but also to combat damaging dominant narratives about who can be creative. We examined calculus students’ views of mathematical creativity, a group not often considered in the creativity literature, to broaden future considerations of creativity. Interviews with N=55 calculus students across various institutions were conducted. Results show six emergent wide-ranging themes of these students’ creativity views: actions and attitudes, application, …

Resources For Supporting Mathematics And Data Science Instructors During Covid-19, Eduardo C. Balreira, C. Hawthorne, G. Stadnyk, Z. Teymuroglu, M. Torres, J. R. Wares

Mathematics Faculty Research

In late May of 2020, a few months after the raging COVID-19 pandemic forced university faculty to quickly switch to online teaching, the Associated Colleges of the South (ACS) released a call for grant applications to support working groups "to help faculty within our consortium who will be teaching during the pandemic (e.g., from hybrid courses with some remote/online components to fully remote/online courses; socially distanced face-to-face courses)." We replied to this call and the ACS awarded the six of us (from four ACS schools) a Summer Rapid Response Grant in early June. The grant funded our efforts to create …

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 …

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.

Being Active In Research Makes A Person A Better Teacher And Even Helps When Working For A Company, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At first glance, it looks like being active in research is not necessarily related to a person's success in being a teacher or being a productive company employee -- moreover, it looks like research distracts from other tasks. Somewhat surprisingly, however, in practice, the best teachers and the best employees are actually the ones who are active in research. In this paper, we provide an explanation for this seemingly counter-intuitive phenomenon.

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 …

Class Notes And Worksheets For Calculus: Early Transcendentals, Bikash Das, Hashim Saber

Mathematics Ancillary Materials

This set of Calculus 1 Lecture Notes and Worksheets was created under a Round Thirteen Mini-Grant for Ancillary Materials Creation and Revision. These materials were created to supplement the Lyrix version of Calculus: Early Transcendentals (https://lyryx.com/calculus-early-transcendentals/).

Topics covered include:

• Limits;
• Derivatives;
• Differentiation;
• Differentials;
• Integrals and Integration.

Webwork Problems For Openstax Calculus Volume I, Scott Kersey, Stephen Carden

Mathematics Ancillary Materials

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Calculus Volume I. They were created through a Round Eight Textbook Transformation Grant.

How To Calculate Π: Machin's Inverse Tangents, A Mini-Primary Source Project For Calculus Ii Students, Dominic Klyve

Mathematics Faculty Scholarship

Almost every mathematical culture through history seems to have proved, trusted, or suspected that the area of a circle is a fixed constant times the square of its radius. It is maybe not surprising, then, that the last two millennia have seen a seemingly endless array of attempts to calculate this constant (today usually called π" role="presentation">π) with increasing precision.

The Derivatives Of The Sine And Cosine Functions: A Mini_Primary Source Project For Calculus I Students, Dominic Klyve

Mathematics Faculty Scholarship

This curricular modular guides students through a method of calculating the derivative of the sine and cosine functions using differentials. It is based on one primary source: Leonhard Euler's Institutiones calculi differentialis (Foundations of Differential Calculus) [2], published in 1755.

06: Reciprocal Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ReciprocalFunctions.nb asks the user to input a function. The notebook will graph the original function and its reciprocal.

10: Roots Of Unity, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RootsOfUnity.nb offers some solutions to x⁶ -1=0 and then graphs and labels the complex roots of unity up through x⁸ -1=0 .

07: Tan Animation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

TanAnimation.nb is a nice little animation to illustrate similar triangles to show why the graph of y = tan(x) looks the way it does.

08: Sine Transformations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SineTransformations.nb allows you to use sliders to see the effects of parameters on the amplitude, period, phase shift, and vertical shift.

13: Polar Reciprocal, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarReciprocal.nb first shows a transformation of the circle r = 3 into the circle r = 3sin (theta). Second, it shows the original and reciprocal graphs through the animation. Interesting stuff!

03: Poly Basics 2, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics2.nb looks for patterns in polynomial graphs with three different factors when each factor is raised to various powers.

15: Koch Snowflakes, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

KochSnowflakes.nb contains several animations that show several steps of graphical iteration for Koch Snowflakes and several other patterns.

16: Sequences And Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.

04: Domain And Range, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DomainAndRange.nb allows you to graph various types of functions and shows the domain and/or range along the appropriate axis.

12: Polar Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarPath.nb allows the user to input any polar function and use a slider to see how the path is created. That is, it will allow the user to see the order in which the petals or loops are created.

11: Parametric Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.

09: Solving Trig Equations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SolvingTrigEquations.nb develops the idea of solving trigonometric equations with special angles by looking at a sequence of problems. The student is asked to think about solutions and to do more problems along the way.

14: Polar Vs Rectangular Animation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarVsRectangularAnimation.nb allows the user to input a polar function and then relates the graphs of r = ƒ(theta) and y = ƒ(x).

02: Poly Basics 1, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics1.nb deals with the graphs of polynomial functions of higher degrees. In this notebook, each factor is linear.

01: Quadratic Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

QuadraticFunctions.nb examines the path of the vertex of quadratic polynomial graphs as each parameter a, b, and c changes.

02: Derivative Approximation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DerivativeApproximation.nb contains two sections. Both allow the user to input a function and an x-window and to vary the center point. Then the value of h may be changed. The first section will show a symmetric approximation while the second shows a one-sided approximation.