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 …

Analysis Of The Meaning Of Continuity And Differentiation: A Study On Graph Problems, Muhammad Ikram, Muhammad Muzaini

Jurnal Riset Pendidikan Matematika

Continuity and differentiability are concepts that students must master to effectively learn and solve problems in a variety of contexts. Thus, this study sought to elicit students' interpretations of the relationship between continuity and differentiability, particularly in graphic problems. Through a qualitative approach, this study involved 195 third-year undergraduate students from various Indonesian universities. Ten of them agreed to an in-depth interview for exploration and clarification. Thematic analysis was conducted to deduce patterns from the responses of participants based on the findings. This study discovered three types of meanings that students construct when they solve problems: 1) physical meaning; 2) …

An Investigation Of Active Learning On Students' Understanding Of Infinite Series Convergence, Zachary Coverstone

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Many students encounter infinite series for the first time as part of their single-variable calculus coursework. As part of this initial engagement with infinite series convergence, students grapple with infinity in ways that they haven't had to before. For instance, the fact that summing infinitely many terms sometimes yields a finite value, but at other times diverges, poses significant conceptual challenges.

I recently designed and implemented a curriculum for second-semester calculus centered in doing problems to help students develop ideas surrounding infinite series convergence, rather than using direct instruction. The unit design was patterned after a workshop at the Park …

Mathematics Mobility In The Middle Grades: Tracking The Odds Of Completing Calculus, Kristian Edosomwan, Jamaal Young, Jemimah Young, Alana Tholen

Middle Grades Review

High school calculus has become indispensable for students seeking a college degree in a STEM field. However, in the present study, we argue that the mathematics opportunities that students seize (when afforded) in middle grades are the key to earning calculus credit in high school. To take calculus in high school, students usually need to take advanced mathematics in middle school to take the prerequisite courses. We analyzed the probability of earning credit in calculus based on a sample of (n =17,765) students and their eighth-grade mathematics courses. Using descriptive statistics and odds ratio effect sizes we found that …

Student Understanding Of The Definite Integral When Solving Calculus Volume Problems, Krista Bresock

Graduate Theses, Dissertations, and Problem Reports

The concept of integration appears in many different scientific fields, and students’ understanding of and ability to use the definite integral in applications is important to success in their STEM (science, technology, engineering, and mathematics) classes. One of the first types of application problems that students encounter is finding the volume of a solid using the definite integral. How students approach these problems and how they use the definite integral to find volumes can have an impact on their future use and understanding of the definite integral.

This study involves a deep and thorough investigation of how ten students understand …

Engaging Students Early By Internationalizing The Undergraduate Calculus Course, Chinenye Ofodile

CODEE Journal

Today's world is global. However, despite increasing numbers and diversity of participants in Study Abroad programs, only 10% of U. S. college students get that experience. There is an ever-growing need for students to become aware of and experience other cultures, to understand why others think and act differently. Internationalization is the conscious effort, begun nearly 40 years ago, to integrate an international, intercultural, and global dimension into the purpose, functions, and delivery of post-secondary education.

Albany State University began a Global Program Initiative in the 1990s. In 2016, we extended into mathematics the curriculum innovations of this program. The …

Analyzing Applied Calculus Student Understanding Of Definite Integrals In Real-Life Applications, Cody Hood

Graduate Theses, Dissertations, and Problem Reports

An individual’s knowledge of definite integrals can range from rote memorization to a strong foundational connection harkening back to its Riemann sum limit definition. In my research, I conducted seven task-based face-to-face interviews with Applied Calculus students. Through the use of real-life examples and guided reinvention, I analyzed ways in which these students, who all initially demonstrated rote memorization, could exhibit a Riemann sum based level of comprehension. This research was conducted in the confines of a student population with definite integral experience, but no formal instruction on limits. My results show that the lack of computational emphasis in class …

Investigating An Approach To Integrating Computational Thinking Into An Undergraduate Calculus Course, Erin Clements

Electronic Thesis and Dissertation Repository

Computational thinking can be conceptualized as patterns of thinking which align with certain fundamental computer science processes. While this algorithmic way of thinking has always been integral to computer science, it has recently gained momentum as a valuable approach to problem solving in a wide variety of contexts. Education researchers highlight the potential of computational thinking to transform, enrich, and revitalize teaching and learning experiences, by providing a systematic framework for analysis and enabling powerful computational tools to be incorporated to further enhance problem-solving activities. Research suggests that in order to maximize the affordances of computational thinking, it should be …

The Effect Of Self-Reflection On Relative Student Success In Undergraduate Calculus 1, Kevin Shryock

Graduate Research Theses & Dissertations

This thesis examines the effect of completion and self-reflection credit on multiple aspects of undergraduate student success in Calculus 1. Specifically, this study assessed the validity of a plug-and-play classroom framework utilizing a combination of a holistic rubric and corresponding worksheets to direct students’ attention towards their conceptual understanding of material and written work, all while removing the pressure of performance grades on all but four summative assessments. By comparing students’ relative performance on these summative assessments, as well as students’ responses on regular surveys, this study found that students who chose to forego performance grades in favor of completion …

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 …

Using Active Learning Strategies In Calculus To Improve Student Learning And Influence Mathematics Department Cultural Change, Melissa A. Dagley, Michele Gill, Erin Saitta, Brian Moore, Jacquelyn Chini, Xin Li

Proceedings of the Interdisciplinary STEM Teaching and Learning Conference (2017-2019)

An interdisciplinary team of physics, education, math and chemistry faculty developed MATH-GAINS (Growing as Adaptive INstructors) creating an ecosystem where mathematics faculty persistently and sustainably apply active learning strategies in their teaching of calculus courses. As a result of implementation, MATH-GAI NS proposed to positively affect the wide-spread adaptation of active learning strategies by department faculty as well as student learning, retention and graduation of over 900 students annually. The objective of this paper is to provide details on how the project was conceived and implemented; instruments, research methodologies and active learning strategies used; and examples of faculty projects and …

Launch-Explore-Summarize In High School Calculus, Nate Mattis

Honors Theses

Current research on high school calculus instruction indicates that students often possess a procedural knowledge of differentiation and integration as opposed to a conceptual knowledge (Orton, 1983; Ferrini-Mundy & Graham, 1994). Given the prominence of traditional lecture and textbook-based calculus classes in the United States, students are not always given the opportunity to expand their conceptual knowledge of essential calculus concepts. This project introduces calculus students to a more active and communal method of teaching: Launch-Explore-Summarize (LES) (CMP, n.d.). This methodology places students at the center of their learning and emphasizes inquiry-based thinking during a class. Specifically, two LES lessons …

The Calculus War: The Ultimate Clash Of Genius, Walker Briles Bussey-Spencer

Chancellor’s Honors Program Projects

No abstract provided.

Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace

Numeracy

The importance of mathematics to biology is illustrated by search data from Google Scholar. I argue that a pedagogical approach based on student research projects is likely to improve retention and foster critical thinking about mathematical modeling, as well as reinforce quantitative reasoning and the appreciation of calculus as a tool. The usual features of a course (e.g., the instructor, assessment, text, etc.) are shown to have very different purposes in a research-based course.

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 …

Formative Assessment And Its Influence On Classroom Community In Biocalculus, Rebecca A. Dibbs, Daniel Rios, Brian Christopher

The Qualitative Report

Most of the attrition from STEM majors occurs between the first two semesters of calculus, and prospective life science majors are one of the groups with the highest attrition rate. One of the largest factors for students that persist in STEM major beyond the first semester of calculus was a sense of community and a perceived connection with their instructor. Since building a sense of community is one of the stated purposes of formative assessment, we investigated how instructor and student perceptions of the purpose of formative assessment contributed to the formation of classroom community in a calculus for life …

Using Pre-Calculus And Calculus Student Work To Examine Student Problem Solving Abilities In Online And Face-To-Face Mathematics Courses, Sarah Catherine Ferguson

Teaching & Learning Theses & Dissertations

This study compares the outcomes of student learning between two pairs of courses. Each pair of courses consists of an online section and a face-to-face section. One pair of courses focuses on pre-calculus content while the second pair focuses on calculus content. Both pairs of courses are taught by the same instructor using the same course appropriate materials. Participants for this study include 9 online and 14 face-to-face pre-calculus students and 14 online and 23 face-to-face calculus students from an urban community college in the southeastern portion of the U.S. Written responses from the subjects to a collection of problems …

Mathematics Discourse And Its Relationship To The Development Of Collective And Individual Student Knowledge In The Context Of Limits, Patterson Rogers

Legacy Theses & Dissertations (2009 - 2024)

Observing a group discussion, it is not possible to infer an individual student’s understanding from the dialogue. When students discuss, they share their individual ideas to develop a collective understanding which in turn informs students’ individual understanding. Clarifying the relationship between collective and individual understanding provides insight into how individuals construct mathematical thinking. This study presented an embedded case study to answer three questions regarding the role discourse plays in student development of mathematical knowledge: (1) how individual students construct mathematical knowledge through discourse, (2) the nature of discourse which supports the development of mathematical knowledge, and (3) the relationship …

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.

Calculus Students' Reasoning About Slope And Derivative As Rates Of Change, Jennifer G. Tyne

Electronic Theses and Dissertations

Students’ low success rates in college calculus courses are a factor that leads to high attrition rates from science, technology, engineering and mathematics (STEM) degree programs. To help reach our nation’s goal of one million additional STEM majors in the next decade, we must address the conceptual difficulties of our students. Studies have shown that students have difficulty with the concepts of slope and derivative, especially in cases when students are asked to utilize these concepts in real-life contexts.

For this study, written surveys were collected from 69 differential (first semester) calculus students. Follow-up clinical interviews were performed on 13 …

Calculus Problems, Joshua N. Cooper

Journal of Humanistic Mathematics

No abstract provided.

A Truly Beautiful Theorem: Demonstrating The Magnificence Of The Fundamental Theorem Of Calculus, Dan Mcquillan, Darlene M. Olsen

Journal of Humanistic Mathematics

In standard treatments of calculus, the Fundamental Theorem of Calculus is often presented as a computational method to evaluate definite integrals, with such powerful utility that one is tempted to overlook its beauty. To improve students' appreciation for the first part of the Fundamental Theorem of Calculus, we suggest a few classroom examples focusing on the accumulation function, to be introduced early and often throughout an introductory calculus course. These examples are small enough that they would not necessarily result in changes to a typical course schedule; yet we believe their contribution to student understanding can be significant. Furthermore, such …

Parts Of The Whole: Teaching Quantitative Reasoning In An Exponential Decay Model, Dorothy Wallace

Numeracy

The simple calculus example of exponential decay can be an excellent vehicle for teaching quantitative reasoning in calculus or differential equations. Insect maturation provides a rich context for thinking about the meaning of the rate constant for exponential decay, which is derived in the context of a system at equilibrium but is generally measured using a single cohort of individuals.

How Calculus Students At Successful Programs Talk About Their Instructors, Annie Bergman, Dana Kirin, Ben Wallek

Student Research Symposium

Over the past decade, numerous reports point to the need for national efforts to increase the number of students pursuing and professionals with degrees in science, technology, engineering, and mathematics (STEM) fields (see for example NSB, 2007; PCAST, 2012; Thomasian, 2011). According to the PCAST report (2012) increasing the retention rate of the students who enter college intending to major in a STEM field has the potential to significantly decrease the gap between the number of STEM degrees produced and the projected number of STEM degrees needed to sustain the United States position in the global market. While there are …

The Effects Of Metacognitive Writing On Student Achievement In Advanced Placement Calculus, Lindsay M. O'Neal

Education Dissertations

Grounded in metacognitive theory (Flavell, 1976) and historical foundations that reach back as far as the writings of Plato (1973), the last few decades have seen an increase in research regarding the impact of metacognitive practice on student learning, often through the use of reflective writing. Studies have focused on a range of aspects, from how to measure metacognition to the effect metacognitive practice has on the academic achievement of students in a variety of subject areas. Specifically with regard to mathematics, researchers have studied the impact of reflective strategies on primary, secondary, and university level students.

The purpose of …

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz

Lori Beth Ziegelmeier

No abstract provided.

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz

Chad M. Topaz

No abstract provided.

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Donna L. Sundre

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students. Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

Student Application Of The Fundamental Theorem Of Calculus With Graphical Representations In Mathematics And Physics, Rabindra R. Bajracharya

Electronic Theses and Dissertations

One mathematical concept frequently applied in physics is the Fundamental Theorem of Calculus (FTC). Mathematics education research on student understanding of the FTC indicates student difficulties with the FTC. Similarly, a few studies in physics education have implicitly indicated student difficulties with various facets of the FTC, such as with the definite integral and the area under the curve representation, in physics contexts. There has been no research on how students apply the FTC in graphically-based physics questions.

This study investigated student understanding of the FTC and its application to graphically-based problems. Our interest spans several aspects of the FTC: …