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- Limits (6)
- A Simple Introduction to Rates (5)
- Differential Equations (4)
- Integrals (4)
- More on Derivatives (3)
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- All Graduate Plan B and other Reports, Spring 1920 to Spring 2023 (1)
- Boise State University Theses and Dissertations (1)
- Chancellor’s Honors Program Projects (1)
- Electronic Theses, Projects, and Dissertations (1)
- Graduate Student Portfolios, Professional Papers, and Capstone Projects (1)
- Graduate Theses, Dissertations, and Problem Reports (1)
- Journal of Educational Research and Practice (1)
- Milne Open Textbooks (1)
- Numeracy (1)
- Open Educational Resources (1)
- Pursue: Undergraduate Research Journal (1)
- Rose-Hulman Undergraduate Mathematics Journal (1)
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Articles 1 - 30 of 34
Full-Text Articles in Other Mathematics
Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers
Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers
Milne Open Textbooks
Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
Rose-Hulman Undergraduate Mathematics Journal
We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.
Performance In Calculus Ii For Students In Clear Calculus: A Causal Comparative Study, Ty Mckinney, Rebecca Dibbs
Performance In Calculus Ii For Students In Clear Calculus: A Causal Comparative Study, Ty Mckinney, Rebecca Dibbs
Pursue: Undergraduate Research Journal
Calculus is one of the greatest intellectual achievements of the world and is the main gateway for students that are heading into the fields that will power the economy of the 21st century. However, over 25% of students fail U.S. calculus courses each year and end up changing majors. It is important for educators and researchers to try to improve student success and find ways to increase STEM major retention. The purpose of this study was to compare the performance between students that are in traditional and non-traditional calculus II courses based on their preparation in either traditional or non-traditional …
Spatial Training And Calculus Ability: Investigating Impacts On Student Performance And Cognitive Style, Lindsay J. Mccunn, Emily Cilli-Turner
Spatial Training And Calculus Ability: Investigating Impacts On Student Performance And Cognitive Style, Lindsay J. Mccunn, Emily Cilli-Turner
Journal of Educational Research and Practice
Undergraduate calculus is a foundational mathematics sequence that previews the sophistication students will need to succeed in higher-level courses. However, students often struggle with concepts in calculus because they are more abstract and visual than those in other foundational mathematics courses. Additionally, women continue to be underrepresented in the STEM fields. This study builds on previous work indicating a malleability in spatial ability by testing whether improvement occurs in students’ spatial and mathematics ability after implementing spatial training in calculus courses. The researchers also measured associations between spatial training and self-reported cognitive style. While spatial training did not significantly improve …
Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber
Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber
Graduate Student Portfolios, Professional Papers, and Capstone Projects
Over the course of a year, I investigated reformative approaches to the teaching of calculus. My research revealed the substantial findings of two educators, Michael Oehrtman and Pat Thompson, and inspired me to design a course based upon two key ideas, covariation and approximation metaphors. Over a period of six weeks, I taught a course tailored around these ideas and documented student responses to both classroom activities and quizzes. Responses were organized intonarratives, covariation, rates of change, limits, and delta notation. Covariation with respect to rates of change was found to be incredibly complex, and students would often see it …
Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, Ty Stockham
Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, Ty Stockham
Electronic Theses, Projects, and Dissertations
This study investigates the effects of implementing a remediation program in a high school Advanced Placement Calculus AB course on student class grades and success in passing the AP Calculus AB exam.
A voluntary remediation program was designed to help students understand the key concepts and big ideas in beginning Calculus. Over a period of eight years the program was put into practice and data on student participation and achievement was collected. Students who participated in this program were given individualized recitation activities targeting their specific misunderstandings, and then given an opportunity to retest on chapter exams that they had …
Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn Mccarty
Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn Mccarty
Graduate Theses, Dissertations, and Problem Reports
The differential is a symbol that is common in first- and second-year calculus. It is perhaps expected that a common mathematical symbol would be interpreted universally. However, recent literature that addresses student interpretations of differentials, usually in the context of definite integration, suggests that this is not the case, and that many interpretations are possible. Reviews of textbooks showed that there was not a lot of discussion about differentials, and what interpretations there were depended upon the context in which the differentials were presented. This dissertation explores some of these issues. Since students may not have the experience necessary to …
The Calculus War: The Ultimate Clash Of Genius, Walker Briles Bussey-Spencer
The Calculus War: The Ultimate Clash Of Genius, Walker Briles Bussey-Spencer
Chancellor’s Honors Program Projects
No abstract provided.
Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton
Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton
Numeracy
This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added …
1. Coffee, Ruth Dover
3: Drugs And De's, Ruth Dover
3: Drugs And De's, Ruth Dover
Differential Equations
Making a connection between discrete recursion and differential equations.
2. Population, Ruth Dover
2. Population, Ruth Dover
Differential Equations
Introduction to logistic population growth.
4. Dragging Along, Ruth Dover
1. Measuring Speed, Ruth Dover
2. Intro To Concavity, Ruth Dover
2. Intro To Concavity, Ruth Dover
More on Derivatives
Looking at changes in ƒ’ to understand concavity.
3. Derivatives Of Exponential Functions, Ruth Dover
3. Derivatives Of Exponential Functions, Ruth Dover
More on Derivatives
Exploring the derivative of exponential functions.
Limits3, Ruth Dover
More Limits, Ruth Dover
Limits2, Ruth Dover
Limits2, Ruth Dover
Limits
More on limits, both algebraic and graphical, including one-sided limits.
Limits5, Ruth Dover
Limits1, Ruth Dover
Limits4, Ruth Dover
Rate Of Change 1, Ruth Dover
Rate Of Change 4, Ruth Dover
Rate Of Change 3, Ruth Dover
Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover
Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover
A Simple Introduction to Rates
Before beginning this section of handouts, students will be introduced to a variety of vocabulary words often associated with calculus. These words will be used in an intuitive sense only and will not have been formally defined. Vocabulary should include graphical terms such as continuous, increasing, decreasing, maximum and minimum points, concave up, concave down, and point of inflection. In addition, discussion of the concept of "rate of change" should begin. It should be mentioned that many quantities change – population, cost, and temperature, to name just a few. All that is specifically required at this point can be related …
Rate Of Change 2, Ruth Dover
Approximations 1, Ruth Dover
Approximations 4, Ruth Dover
Approximations 3, Ruth Dover
Approximations 3, Ruth Dover
Integrals
Understanding Riemann sum approximations, including technology.