Developing Critical Thinking in Undergraduate Courses: A Philosophical Approach.

ERIC Educational Resources Information Center

Kalman, Calvin S.

2002-01-01

Examines how 20th century philosophers of science have influenced current physics educational research. Examines the introduction of a study of these philosophers in several courses, including the calculus-based introductory physics course on optics and modern physics. Concludes that students seem to have made a marked improvement in their…

Initial experience with a calculus-based IPLS course at Vanderbilt

NASA Astrophysics Data System (ADS)

Hutson, M. Shane; Rericha, Erin C.

2014-03-01

By implementing research results from the PER community, we have designed a new calculus-based IPLS course and began teaching two sections of this course in Fall 2013, both taught by biological physicists. This course differs from Vanderbilt's other introductory physics offerings in two major ways. First, it seeks to implement PER-based active learning strategies including just-in-time teaching, peer instruction and context-rich problems. The latter are specifically designed within biomedical contexts. Second, the course content has been chosen to closely align with the core competencies delineated in the HHMI-AAMC report Scientific Foundations for Future Physicians. We provide students with a very explicit accounting (in the syllabus) of how this course will contribute to 5 of the 8 SFFP-competencies and 21 of its 37 learning objectives. Throughout the course and associated labs, we make repeated, explicit and hopefully authentic connections between physics and the life sciences. The chosen text reinforces our approach through well-developed biomedical applications of physics concepts. We will report what we've seen work and not work in our first implementation of an IPLS course and detail results regarding student learning and student attitudes towards physics.

Designing for Enhanced Conceptual Understanding in an Online Physics Course

ERIC Educational Resources Information Center

Dunlap, Joanna C.; Furtak, Thomas E.; Tucker, Susan A.

2009-01-01

The calculus-based, introductory physics course is the port of entry for any student interested in pursuing a college degree in the sciences, mathematics, or engineering. There is increasing demand for online delivery options that make the course more widely available, especially those that use best practices in student engagement. However,…

Promoting Metacognition in Introductory Calculus-based Physics Labs

NASA Astrophysics Data System (ADS)

Grennell, Drew; Boudreaux, Andrew

2010-10-01

In the Western Washington University physics department, a project is underway to develop research-based laboratory curriculum for the introductory calculus-based course. Instructional goals not only include supporting students' conceptual understanding and reasoning ability, but also providing students with opportunities to engage in metacognition. For the latter, our approach has been to scaffold reflective thinking with guided questions. Specific instructional strategies include analysis of alternate reasoning presented in fictitious dialogues and comparison of students' initial ideas with their lab group's final, consensus understanding. Assessment of student metacognition includes pre- and post- course data from selected questions on the CLASS survey, analysis of written lab worksheets, and student opinion surveys. CLASS results are similar to a traditional physics course and analysis of lab sheets show that students struggle to engage in a metacognitive process. Future directions include video studies, as well as use of additional written assessments adapted from educational psychology.

The Use of a PDP-11/20 Computer in a Non-Calculus General Physics Course.

ERIC Educational Resources Information Center

Yu, David U. L.

Computer-assisted instruction supplements traditional methods in a non-calculus physics course offered at Seattle Pacific College. Thirty-five science majors enrolled in the first quarter and 32 continued in the second term. The hardware for the course consists of a PDP-11/20 computer and eight teletype terminals; additional peripheral equipment…

Implementing and Assessing Computational Modeling in Introductory Mechanics

ERIC Educational Resources Information Center

Caballero, Marcos D.; Kohlmyer, Matthew A.; Schatz, Michael F.

2012-01-01

Students taking introductory physics are rarely exposed to computational modeling. In a one-semester large lecture introductory calculus-based mechanics course at Georgia Tech, students learned to solve physics problems using the VPython programming environment. During the term, 1357 students in this course solved a suite of 14 computational…

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

ERIC Educational Resources Information Center

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

From "F = ma" to Flying Squirrels: Curricular Change in an Introductory Physics Course

ERIC Educational Resources Information Center

O'Shea, Brian; Terry, Laura; Benenson, Walter

2013-01-01

We present outcomes from curricular changes made to an introductory calculus-based physics course whose audience is primarily life sciences majors, the majority of whom plan to pursue postbaccalaureate studies in medical and scientific fields. During the 2011-2012 academic year, we implemented a Physics of the Life Sciences curriculum centered on…

Comparing the Attitudes of Pre-Health Professional and Engineering Students in Introductory Physics Courses

NASA Astrophysics Data System (ADS)

McKinney, Meghan

2015-04-01

This talk will discuss using the Colorado Learning Attitudes about Science Survey (CLASS) to compare student attitudes towards the study of physics of two different groups. Northern Illinois University has two levels of introductory mechanics courses, one geared towards biology majors and pre-health professionals, and one for engineering and physics majors. The course for pre-health professionals is an algebra based course, while the course for engineering and physics majors is a calculus based course. We've adapted the CLASS into a twenty question survey that measures student attitudes towards the practice of and conceptions about physics. The survey is administered as a pre and post assessment to look at student attitudes before and after their first course in physics.

Problem Solving: Physics Modeling-Based Interactive Engagement

ERIC Educational Resources Information Center

Ornek, Funda

2009-01-01

The purpose of this study was to investigate how modeling-based instruction combined with an interactive-engagement teaching approach promotes students' problem solving abilities. I focused on students in a calculus-based introductory physics course, based on the matter and interactions curriculum of Chabay & Sherwood (2002) at a large state…

Bridging the Gulf between Formal Calculus and Physical Reasoning.

ERIC Educational Resources Information Center

Van Der Meer, A.

1980-01-01

Some ways to link calculus instruction with the mathematical models used in physics courses are presented. The activity of modelling is presented as a major tool in synchronizing physics and mathematics instruction in undergraduate engineering programs. (MP)

Vision and change in introductory physics for the life sciences

NASA Astrophysics Data System (ADS)

Mochrie, S. G. J.

2016-07-01

Since 2010, our physics department has offered a re-imagined calculus-based introductory physics sequence for the life sciences. These courses include a selection of biologically and medically relevant topics that we believe are more meaningful to undergraduate premedical and biological science students than those found in a traditional course. In this paper, we highlight new aspects of the first-semester course, and present a comparison of student evaluations of this course versus a more traditional one. We also present the effect on student perception of the relevance of physics to biology and medicine after having taken this course.

An intermediate-level course on Biological Physics

NASA Astrophysics Data System (ADS)

Nelson, Phil

2004-03-01

I describe both undergraduate and graduate 1-semester courses designed to give a survey of Biological Physics. The courses cover classical as well as recent topics. The undergraduate version requires calculus-based first-year physics as its prerequisite. With this level of assumed background, we can arrive at topics such as molecular motors, manipulation of single molecules, and the propagation of nerve impulses. Students majoring in physics, chemistry, biochemistry, and every engineering major (as well as a few in biology), end up taking this course. The graduate course covers the same material but includes exercises with symbolic mathematics packages and data modeling.

Using Time-on-Task Measurements to Understand Student Performance in a Physics Class: A Four-Year Study

ERIC Educational Resources Information Center

Stewart, John; Stewart, Gay; Taylor, Jennifer

2012-01-01

Student use of out-of-class time was measured for four years in the introductory second-semester calculus-based physics course at the University of Arkansas. Two versions of the course were presented during the time of the measurement. In both versions, the total out-of-class time a student invested in the course explained less than 1% of the…

In Praise of the Catenary

NASA Astrophysics Data System (ADS)

Behroozi, F.

2018-04-01

When a chain hangs loosely from its end points, it takes the familiar form known as the catenary. Power lines, clothes lines, and chain links are familiar examples of the catenary in everyday life. Nevertheless, the subject is conspicuously absent from current introductory physics and calculus courses. Even in upper-level physics and math courses, the catenary equation is usually introduced as an example of hyperbolic functions or discussed as an application of the calculus of variations. We present a new derivation of the catenary equation that is suitable for introductory physics and mathematics courses.

Generalizing a Categorization of Students' Interpretations of Linear Kinematics Graphs

ERIC Educational Resources Information Center

Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul

2016-01-01

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…

Using Computer-Assisted Personalized Assignment System in a Large-Enrollment General Physics

ERIC Educational Resources Information Center

Gok, Tolga

2010-01-01

The on-line tutoring system, LON-CAPA, was implemented in Introductory Calculus-Based Physics-II course at Colorado School of Mines in fall 2008 and spring 2009. In this paper, the features and the case study of the LON-CAPA implementation were described. The performance data obtained from the scores of students enrolled in the course represented…

GRIPs (Group Investigation Problems) for Introductory Physics

NASA Astrophysics Data System (ADS)

Moore, Thomas A.

2006-12-01

GRIPs lie somewhere between homework problems and simple labs: they are open-ended questions that require a mixture of problem-solving skills and hands-on experimentation to solve practical puzzles involving simple physical objects. In this talk, I will describe three GRIPs that I developed for a first-semester introductory calculus-based physics course based on the "Six Ideas That Shaped Physics" text. I will discuss the design of the three GRIPs we used this past fall, our experience in working with students on these problems, and students' response as reported on course evaluations.

Chronicling a successful secondary implementation of Studio Physics

NASA Astrophysics Data System (ADS)

Kohl, Patrick B.; Vincent Kuo, H.

2012-09-01

The Colorado School of Mines (CSM) has taught its first-semester calculus-based introductory physics course (Physics I) using a hybrid lecture/Studio Physics format since the spring of 1997. Starting in the fall of 2007, we have been converting the second semester of our calculus-based introductory physics course (Physics II) to a hybrid lecture/Studio Physics format, beginning from a traditional lecture/lab/recitation course. In this paper, we document the stages of this transformation, highlighting what has worked and what has not, and the challenges and benefits associated with the switch to Studio Physics. A major goal in this study is to develop a method for secondary implementations of Studio physics that keeps the time and resource investments manageable. We describe the history of Studio at CSM and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), exam scores, failure rates, and a variety of qualitative observations. Results suggest that Studio has increased student performance and satisfaction despite an aggressive expansion of class sizes in the past few years. Gains have been concentrated mostly in problem-solving skills and exam performance (as opposed to conceptual survey gains), in contrast to what has sometimes been seen in other studies.

Students' Difficulties with Integration in Electricity

ERIC Educational Resources Information Center

Nguyen, Dong-Hai; Rebello, N. Sanjay

2011-01-01

This study investigates the common difficulties that students in introductory physics experience when solving problems involving integration in the context of electricity. We conducted teaching-learning interviews with 15 students in a second-semester calculus-based introductory physics course on several problems involving integration. We found…

A Transformative Model for Undergraduate Quantitative Biology Education

ERIC Educational Resources Information Center

Usher, David C.; Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The "BIO2010" report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3)…

A "Model" Multivariable Calculus Course.

ERIC Educational Resources Information Center

Beckmann, Charlene E.; Schlicker, Steven J.

1999-01-01

Describes a rich, investigative approach to multivariable calculus. Introduces a project in which students construct physical models of surfaces that represent real-life applications of their choice. The models, along with student-selected datasets, serve as vehicles to study most of the concepts of the course from both continuous and discrete…

Assessing students' conceptual knowledge of electricity and magnetism

NASA Astrophysics Data System (ADS)

McColgan, Michele W.; Finn, Rose A.; Broder, Darren L.; Hassel, George E.

2017-12-01

We present the Electricity and Magnetism Conceptual Assessment (EMCA), a new assessment aligned with second-semester introductory physics courses. Topics covered include electrostatics, electric fields, circuits, magnetism, and induction. We have two motives for writing a new assessment. First, we find other assessments such as the Brief Electricity and Magnetism Assessment and the Conceptual Survey on Electricity and Magnetism not well aligned with the topics and content depth of our courses. We want to test introductory physics content at a level appropriate for our students. Second, we want the assessment to yield scores and gains comparable to the widely used Force Concept Inventory (FCI). After five testing and revision cycles, the assessment was finalized in early 2015 and is available online. We present performance results for a cohort of 225 students at Siena College who were enrolled in our algebra- and calculus-based physics courses during the spring 2015 and 2016 semesters. We provide pretest, post-test, and gain analyses, as well as individual question and whole test statistics to quantify difficulty and reliability. In addition, we compare EMCA and FCI scores and gains, and we find that students' FCI scores are strongly correlated with their performance on the EMCA. Finally, the assessment was piloted in an algebra-based physics course at George Washington University (GWU). We present performance results for a cohort of 130 GWU students and we find that their EMCA scores are comparable to the scores of students in our calculus-based physics course.

Implementing Computer Based Laboratories

NASA Astrophysics Data System (ADS)

Peterson, David

2001-11-01

Physics students at Francis Marion University will complete several required laboratory exercises utilizing computer-based Vernier probes. The simple pendulum, the acceleration due to gravity, simple harmonic motion, radioactive half lives, and radiation inverse square law experiments will be incorporated into calculus-based and algebra-based physics courses. Assessment of student learning and faculty satisfaction will be carried out by surveys and test results. Cost effectiveness and time effectiveness assessments will be presented. Majors in Computational Physics, Health Physics, Engineering, Chemistry, Mathematics and Biology take these courses, and assessments will be categorized by major. To enhance the computer skills of students enrolled in the courses, MAPLE will be used for further analysis of the data acquired during the experiments. Assessment of these enhancement exercises will also be presented.

Understanding Introductory Students' Application of Integrals in Physics from Multiple Perspectives

ERIC Educational Resources Information Center

Hu, Dehui

2013-01-01

Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that…

Studio Physics at the Colorado School of Mines: A model for iterative development and assessment

NASA Astrophysics Data System (ADS)

Kohl, Patrick; Kuo, Vincent

2009-05-01

The Colorado School of Mines (CSM) has taught its first-semester introductory physics course using a hybrid lecture/Studio Physics format for several years. Based on this previous success, over the past 18 months we have converted the second semester of our traditional calculus-based introductory physics course (Physics II) to a Studio Physics format. In this talk, we describe the recent history of the Physics II course and of Studio at Mines, discuss the PER-based improvements that we are implementing, and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), failure rates, and exam scores. We also report on recent attempts to involve students in the department's Senior Design program with our course. Our ultimate goal is to construct one possible model for a practical and successful transition from a lecture course to a Studio (or Studio-like) course.

Math remediation intervention for student success in the algebra-based introductory physics course

NASA Astrophysics Data System (ADS)

Forrest, Rebecca L.; Stokes, Donna W.; Burridge, Andrea B.; Voight, Carol D.

2017-12-01

Pretesting and early intervention measures to identify and remediate at-risk students were implemented in algebra-based introductory physics to help improve student success rates. Pretesting via a math and problem-solving diagnostic exam administered at the beginning of the course was employed to identify at-risk students based on their scores. At-risk students were encouraged to utilize an online math tutorial to increase their chances of passing the course. The tutorial covers the same math topics covered by the diagnostic exam. Results from 643 students enrolled in the course showed that the 61 at-risk students who successfully completed the math tutorial increased their odds of passing the course by roughly 4 times those of the at-risk students who did not. This intervention is easily implemented, short term, and can be administered concurrently with the course. Based on these results, the Department of Physics has implemented the math tutorials in all sections of the introductory algebra as well as the calculus-based physics courses.

Electrons and Positrons--Can Freshmen Get a Charge Out of Physics?

ERIC Educational Resources Information Center

Stevens, J. R.; Winegard, W. C.

1971-01-01

Describes a one semester introductory physics course for physical science students with PSSC and calculus as prerequisites. Course content concentrates on the properties of the electron, positron, andphoton. Summarizes the student evaluation of the course and the laboratory equipment used. (Author/DS)

Modeling Instruction in AP Physics C: Mechanics and Electricity and Magnetism

NASA Astrophysics Data System (ADS)

Belcher, Nathan Tillman

This action research study used data from multiple assessments in Mechanics and Electricity and Magnetism to determine the viability of Modeling Instruction as a pedagogy for students in AP Physics C: Mechanics and Electricity and Magnetism. Modeling Instruction is a guided-inquiry approach to teaching science in which students progress through the Modeling Cycle to develop a fully-constructed model for a scientific concept. AP Physics C: Mechanics and Electricity and Magnetism are calculus-based physics courses, approximately equivalent to first-year calculus-based physics courses at the collegiate level. Using a one-group pretest-posttest design, students were assessed in Mechanics using the Force Concept Inventory, Mechanics Baseline Test, and 2015 AP Physics C: Mechanics Practice Exam. With the same design, students were assessed in Electricity and Magnetism on the Brief Electricity and Magnetism Assessment, Electricity and Magnetism Conceptual Assessment, and 2015 AP Physics C: Electricity and Magnetism Practice Exam. In a one-shot case study design, student scores were collected from the 2017 AP Physics C: Mechanics and Electricity and Magnetism Exams. Students performed moderately well on the assessments in Mechanics and Electricity and Magnetism, demonstrating that Modeling Instruction is a viable pedagogy in AP Physics C: Electricity and Magnetism.

Teaching Integration with Layers and Representations: A Case Study

ERIC Educational Resources Information Center

Von Korff, Joshua; Rebello, N. Sanjay

2012-01-01

We designed a sequence of seven lessons to facilitate learning of integration in a physics context. We implemented this sequence with a single college sophomore, "Amber," who was concurrently enrolled in a first-semester calculus-based introductory physics course which covered topics in mechanics. We outline the philosophy underpinning these…

Vector Knowledge of Beginning Physics Students.

ERIC Educational Resources Information Center

Knight, Randall D.

1995-01-01

Presents the Vector Knowledge Test that was designed to see if beginning physics students possess the minimal basic knowledge of vectors that will allow them to proceed with a study of Newtonian mechanics. Concludes that only one-third of the students in a calculus-based introductory course at California Polytechnic had sufficient vector…

Modeling the Water Balloon Slingshot

NASA Astrophysics Data System (ADS)

Bousquet, Benjamin D.; Figura, Charles C.

2013-01-01

In the introductory physics courses at Wartburg College, we have been working to create a lab experience focused on the scientific process itself rather than verification of physical laws presented in the classroom or textbook. To this end, we have developed a number of open-ended modeling exercises suitable for a variety of learning environments, from non-science major classes to algebra-based and calculus-based introductory physics classes.

Success in introductory college physics: The role of gender, high school preparation, and student learning perceptions

NASA Astrophysics Data System (ADS)

Chen, Jean Chi-Jen

Physics is fundamental for science, engineering, medicine, and for understanding many phenomena encountered in people's daily lives. The purpose of this study was to investigate the relationships between student success in college-level introductory physics courses and various educational and background characteristics. The primary variables of this study were gender, high school mathematics and science preparation, preference and perceptions of learning physics, and performance in introductory physics courses. Demographic characteristics considered were age, student grade level, parents' occupation and level of education, high school senior grade point average, and educational goals. A Survey of Learning Preference and Perceptions was developed to collect the information for this study. A total of 267 subjects enrolled in six introductory physics courses, four algebra-based and two calculus-based, participated in the study conducted during Spring Semester 2002. The findings from the algebra-based physics courses indicated that participant's educational goal, high school senior GPA, father's educational level, mother's educational level, and mother's occupation in the area of science, engineering, or computer technology were positively related to performance while participant age was negatively related. Biology preparation, mathematics preparation, and additional mathematics and science preparation in high school were also positively related to performance. The relationships between the primary variables and performance in calculus-based physics courses were limited to high school senior year GPA and high school physics preparation. Findings from all six courses indicated that participant's educational goal, high school senior GPA, father's educational level, and mother's occupation in the area of science, engineering, or computer technology, high school preparation in mathematics, biology, and the completion of additional mathematics and science courses were positively related to performance. No significant performance differences were found between male and female students. However, there were significant gender differences in physics learning perceptions. Female participants tended to try to understand physics materials and relate the physics problems to real world situations while their male counterparts tended to rely on rote learning and equation application. This study found that participants performed better by trying to understand the physics material and relate physics problems to real world situations. Participants who relied on rote learning did not perform well.

A Calculus-Level Introductory Physics Course with an Astronomy Theme

NASA Astrophysics Data System (ADS)

Amato, Joseph

2011-05-01

Physics from Planet Earth (PPE) is a one-semester, calculus-based introductory course in classical mechanics intended for first year students of physics, chemistry, astronomy and engineering. Most of the core topics in mechanics are included, but many of the examples and applications are drawn from astronomy, space science, and astrophysics. The laws of physics are assigned the task of exploring the heavens - the same task addressed by Newton over 300 years ago at the birth of classical mechanics. How do we know the distance to the Moon, Sun, or other galaxies? How do we know the masses of the Earth, Sun, and other planets and stars, and why do we believe in "missing” mass? As a physics course, PPE concentrates on how we know rather than what we know. Examples and applications include those of historical importance (the Earth-Moon distance, the Earth-Sun distance, Ptolemaic vs. Copernican models, weighing the Earth) as well as those of contemporary interest (Hubble's Law, rocket propulsion, spacecraft gravity boosts, the Roche limit, search for extrasolar planets, orbital mechanics, pulsars, galactic rotation curves). The course has been taught successfully at Colgate for over a decade, using materials that have been developed and refined during the past 15 years. Developers of PPE are eager to enrich the course by identifying other topics in contemporary astronomy that can be adapted for the first year physics audience.

Online Calculus: The Course and Survey Results.

ERIC Educational Resources Information Center

Allen, G. Donald

2001-01-01

Describes the development and implementation of a Web-based calculus course at Texas A & M University. Discusses the course design, layout of content and the contrast with textbook structure, results of course surveys that included student reactions, and how students learn form Web-based materials. (Author/LRW)

Secondary Implementation of Interactive Engagement Teaching Techniques: Choices and Challenges in a Gulf Arab Context

ERIC Educational Resources Information Center

Hitt, G. W.; Isakovic, A. F.; Fawwaz, O.; Bawa'aneh, M. S.; El-Kork, N.; Makkiyil, S.; Qattan, I. A.

2014-01-01

We report on efforts to design the "Collaborative Workshop Physics" (CWP) instructional strategy to deliver the first interactive engagement (IE) physics course at Khalifa University of Science, Technology and Research (KU), United Arab Emirates (UAE). To our knowledge, this work reports the first calculus-based, introductory mechanics…

Assessing the Effectiveness of Studio Physics in Introductory-Level Courses at Georgia State University

NASA Astrophysics Data System (ADS)

Upton, Brianna; Evans, John; Morrow, Cherilynn; Thoms, Brian

2009-11-01

Previous studies have shown that many students have misconceptions about basic concepts in physics. Moreover, it has been concluded that one of the challenges lies in the teaching methodology. To address this, Georgia State University has begun teaching studio algebra-based physics. Although many institutions have implemented studio physics, most have done so in calculus-based sequences. The effectiveness of the studio approach in an algebra-based introductory physics course needs further investigation. A 3-semester study assessing the effectiveness of studio physics in an algebra-based physics sequence has been performed. This study compares the results of student pre- and post-tests using the Force Concept Inventory. Using the results from this assessment tool, we will discuss the effectiveness of the studio approach to teaching physics at GSU.

Professional Development Graduate Courses and a Masters of Arts in Physics Education with Web Based Course Components

NASA Astrophysics Data System (ADS)

Lindgren, Richard; Thornton, Stephen

2010-02-01

Professional development courses offered in physical/Earth science and physics by the Department of Physics are delivered by different venues to accommodate the needs of the K-12 teaching community. The majority of teachers take our courses off-site or through our distance-learning web-based program on the Internet for endorsement or recertification, but with a gradually increasing number enrolling in our 30 credit Masters of Arts in Physics Education degree (MAPE) program. The purpose of the Masters program is to provide increased physics content to those teachers who feel inadequately prepared to teach high school physics. The increase in numbers and success of this program is partly due to the convenience of taking online web-based courses which is made possible by using the latest communication technologies on the high speed internet. There is also a residential component of the MAPE program, which requires the candidates to earn 14 credits of calculus-based core physics in residence in the summer at the University. We have graduated a total of 91 teachers since the program began in 2000. )

Students' Understanding and Application of the Area under the Curve Concept in Physics Problems

ERIC Educational Resources Information Center

Nguyen, Dong-Hai; Rebello, N. Sanjay

2011-01-01

This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving…

"The Age of Newton": An Intensive Physics and Mathematics Course

ERIC Educational Resources Information Center

Calvert, J. B.; And Others

1976-01-01

Describes an intensive course in mathematics (calculus), mechanics, optics, and astronomy directed mainly toward nonscience students. Course format, operation, and student evaluation appear. (Author/CP)

Effects of California community college students' gender, self-efficacy, and attitudes and beliefs toward physics on conceptual understanding of Newtonian mechanics

NASA Astrophysics Data System (ADS)

Said, Asma

Despite the advances made in various fields, women are still considered as minorities in the fields of science and mathematics. There is a gender gap regarding women's participation and achievement in physics. Self-efficacy and attitudes and beliefs toward physics have been identified as predictors of students' performance on conceptual surveys in physics courses. The present study, which used two-way analysis of variance and multiple linear regression analyses at a community college in California, revealed there is no gender gap in achievement between male and female students in physics courses. Furthermore, there is an achievement gap between students who are enrolled in algebra-based and calculus-based physics courses. The findings indicate that attitudes and beliefs scores can be used as predictors of students' performance on conceptual surveys in physics courses. However, scores of self-efficacy cannot be used as predictors of students' performance on conceptual surveys in physics courses.

Incorporating Inquiry-Based Learning in the Calculus Sequence: A Most Challenging Endeavour

ERIC Educational Resources Information Center

McLoughlin, M. Padraig M. M.

2009-01-01

A course in the Calculus sequence is arguably the most difficult course in which inquiry-based learning (IBL) can be achieved with any degree of success within the curriculum in part due to: (1) the plethora of majors taking Calculus to which the sequence relates to their majors in what is considered an "applied" manner; and (2) the…

A Lab-Based, Lecture-Free General Physics Course

NASA Astrophysics Data System (ADS)

Schneider, Mark B.

1997-04-01

The past four years have seen the development of a discovery style, lecture-free, lab-based General Physics course at Grinnell College. Similar in spirit to Priscilla Laws' Workshop Physics (P. Laws, Physics Today, Dec. 1991, p. 24.), this course is a calculus- based, two-semester sequence, which is offered in parallel with more conventional lecture sections, allowing students choice of pedagogical styles. This new course is taught without a text, allowing a somewhat atypical ordering of topics and the early inclusion of a modern introduction to quantum and statistical mechanics. A complete set of laboratory materials was developed at Grinnell for this course, with activities considerably different in most cases than Laws' activities. A quick overview of the pedagogical style and topics covered will be given, and then several specific activities will be described in greater detail. The course has been shown to be a popular and viable alternative to the more conventional sections for majors and non-majors; ongoing efforts to assess the course will be described, especially those that make comparisons between this course and more conventional sections.

A Simple Mechanical Experiment on Exponential Growth

ERIC Educational Resources Information Center

McGrew, Ralph

2015-01-01

With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…

Predictors of Grades for Black Americans in a Non-Calculus, Preprofessional Physics Sequence.

ERIC Educational Resources Information Center

Vincent, Harold A.; And Others

Variables to predict grades in a noncalculus, preprofessional college physics course at Xavier University of Louisiana, a historically-black institution, were identified using linear regression. The two-semester, noncalculus physics course emphasizes the application of physics in the health professions. The study population consisted of 123…

Implementing ILDs and Assessment in Small-enrollment, Calculus-based Physics Classes -- Lessons, Observations and Open Questions

NASA Astrophysics Data System (ADS)

Mason-McCaffrey, Deborah

2011-04-01

At Salem State, we offer a Physics minor, but most of our teaching load is support courses for other science majors and a lab sequence which satisfies the University's core education requirement. In three years of using assessments and ILDs in small-enrollment calculus-based Physics classes, there has been a significant implementation learning curve, there are encouraging results, a few cautions, and still some open questions to report. ILDs can be highly effective teaching tools. They do require significant advance preparation as well as a safe environment for student participation. Motivating students to do their best on assessment pre- and post-tests can also be difficult. Strategies for motivating assessment performance, experiments using clickers to encourage participation in ILDs, and modifying and developing home-grown ILDs are discussed.

A transformative model for undergraduate quantitative biology education.

PubMed

Usher, David C; Driscoll, Tobin A; Dhurjati, Prasad; Pelesko, John A; Rossi, Louis F; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions.

A Transformative Model for Undergraduate Quantitative Biology Education

PubMed Central

Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions. PMID:20810949

Tarzan's Dilemma: A Challenging Problem for Introductory Physics Students

ERIC Educational Resources Information Center

Rave, Matthew; Sayers, Marcus

2013-01-01

The following kinematics problem was given to several students as a project in conjunction with a first-semester calculus-based physics course. The students were asked to keep a journal of all their work and were encouraged to keep even their scrap paper. The goal of the project was to expose the students to the process of doing theoretical…

Introductory Physics Gender Gaps: Pre- and Post-Studio Transition

NASA Astrophysics Data System (ADS)

Kohl, Patrick B.; Kuo, H. Vincent

2009-11-01

Prior work has characterized the gender gaps present in college-level introductory physics courses. Such work has also shown that research-based interactive engagement techniques can reduce or eliminate these gender gaps. In this paper, we study the gender gaps (and lack thereof) in the introductory calculus-based electricity and magnetism course at the Colorado School of Mines. We present eight semesters' worth of data, totaling 2577 students, with four semesters preceding a transition to Studio physics, and four following. We examine gender gaps in course grades, DFW (D grade, fail, or withdrawal) rates, and normalized gains on the Conceptual Survey of Electricity and Magnetism (CSEM), and consider factors such as student ACT scores and grades in prior math classes. We find little or no gap in male/female course grades and DFW rates, but substantial gaps in CSEM gains that are reduced somewhat by the transition to Studio physics.

Retention of Differential and Integral Calculus: A Case Study of a University Student in Physical Chemistry

ERIC Educational Resources Information Center

Jukic Matic, Ljerka; Dahl, Bettina

2014-01-01

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly…

Students' Difficulties with Vector Calculus in Electrodynamics

ERIC Educational Resources Information Center

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-01-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

Documenting the conversion from traditional to Studio Physics formats at the Colorado School of Mines: Process and early results

NASA Astrophysics Data System (ADS)

Kohl, Patrick B.; Kuo, H. Vincent; Ruskell, Todd G.

2008-10-01

The Colorado School of Mines (CSM) has taught its first-semester introductory physics course using a hybrid lecture/Studio Physics format for several years. Over the past year we have converted the second semester of our calculus-based introductory physics course (Physics II) to a Studio Physics format, starting from a traditional lecture-based format. In this paper, we document the early stages of this conversion in order to better understand which features succeed and which do not, and in order to develop a model for switching to Studio that keeps the time and resource investment manageable. We describe the recent history of the Physics II course and of Studio at Mines, discuss the PER-based improvements that we are implementing, and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), solicited student comments, failure rates, and exam scores.

Generalizing a categorization of students' interpretations of linear kinematics graphs

NASA Astrophysics Data System (ADS)

Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul

2016-06-01

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.

Preliminary Investigation of Instructor Effects on Gender Gap in Introductory Physics

ERIC Educational Resources Information Center

Kreutzer, Kimberley; Boudreaux, Andrew

2012-01-01

Gender differences in student learning in the introductory, calculus-based electricity and magnetism course were assessed by administering the Conceptual Survey of Electricity and Magnetism pre- and postcourse. As expected, male students outgained females in traditionally taught sections as well as sections that incorporated interactive engagement…

Students' Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin's Symbolic Forms

ERIC Educational Resources Information Center

Becker, Nicole; Towns, Marcy

2012-01-01

Undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. Here we present the findings of a study that examines student understanding of mathematical expressions, including partial derivative expressions, in two undergraduate physical chemistry courses.…

Student Selection of the Textbook for an Introductory Physics Course

ERIC Educational Resources Information Center

Dake, L. S.

2007-01-01

Several years ago I had to select a new textbook for my calculus-based introductory physics class. I subscribe to Just-in-Time Teaching methods,1 which require students to read the book before the material is covered in class. Thus, the readability of the text by the students is critical. However, I did not feel that I was the best judge of this…

Projectile Motion without Calculus

ERIC Educational Resources Information Center

Rizcallah, Joseph A.

2018-01-01

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary…

Teaching Electrostatics and Entropy in Introductory Physics

NASA Astrophysics Data System (ADS)

Reeves, Mark

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology courses is important contribution of the entropy in driving fundamental biological processes towards equilibrium. I will present material developed to teach electrostatic screening in solutions and the function of nerve cells where entropic effects act to counterbalance electrostatic attraction. These ideas are taught in an introductory, calculus-based physics course to biomedical engineers using SCALEUP pedagogy. Results of student mastering of complex problems that cross disciplinary boundaries between biology and physics, as well as the challenges that they face in learning this material will be presented.

Analysis of Newton's Third Law Questions on the Force Concepts Inventory at Georgia State University

NASA Astrophysics Data System (ADS)

Oakley, Christopher; Thoms, Brian

2012-03-01

A major emphasis of the Physics Education Research program at Georgia State University is an effort to assess and improve students' understanding of Newton's Laws concepts. As part of these efforts the Force Concepts Inventory (FCI) has been given to students in both the algebra-based and calculus-based introductory physics sequences. In addition, the algebra-based introductory physics sequence is taught in both a SCALE-UP and a traditional lecture format. The results of the FCI have been analyzed by individual question and also as categorized by content. The analysis indicates that students in both algebra and calculus-based courses are successful at overcoming Aristotelian misconceptions regarding Newton's Third Law (N3) in the context of a stationary system. However, students are less successful on N3 questions involving objects in constant motion or accelerating. Interference between understanding of Newton's Second and Third Laws as well as other possible explanations for lower student performance on N3 questions involving non-stationary objects will be discussed.

Students' difficulties with vector calculus in electrodynamics

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-12-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.

Predicting Performance in a First Engineering Calculus Course: Implications for Interventions

ERIC Educational Resources Information Center

Hieb, Jeffrey L.; Lyle, Keith B.; Ralston, Patricia A. S.; Chariker, Julia

2015-01-01

At the University of Louisville, a large, urban institution in the south-east United States, undergraduate engineering students take their mathematics courses from the school of engineering. In the fall of their freshman year, engineering students take "Engineering Analysis I," a calculus-based engineering analysis course. After the…

Modeling an Outbreak of Anthrax

ERIC Educational Resources Information Center

Sturdivant, Rod; Watts, Krista

2010-01-01

This article presents material that has been used as a classroom activity in a calculus-based probability and statistics course. The application was used in the first few lessons of this course. Students had three previous semesters of math, including calculus (single and multivariable), differential equations, and a course in mathematical…

Reaching Out: The Bachelor of Arts Degree In Physics

NASA Astrophysics Data System (ADS)

Hobson, Art

1996-05-01

Physics degrees are not only for physicists. Our department believes that it would be healthy if attorneys, physicians, journalists, politicians, businesspeople, and others had undergraduate degrees in physics. Thus, we have begun offering a Bachelor of Arts degree in physics, for students who want to study physics as a background for other fields such as law (patents, environmental law), medical school, business (high-tech firms), journalism (science reporting, environmental reporting), music (accoustics, electronic music), and essentially any other profession. The program reaches outward, outside of physics, rather than pointing toward further work in physics. It begins with the algebra-based introductory course rather than the calculus-based course for future physicists and engineers. Two new courses are being created to provide these pre-professional students with broad science literacy and knowledge of physics-related technologies. The program is more flexible and less technical than the traditional Bachelor of Science program, allowing students time for outside electives and professional requirements in other fields.

Effect of Written Presentation on Performance in Introductory Physics

ERIC Educational Resources Information Center

Stewart, John; Ballard, Shawn

2010-01-01

This study examined the written work of students in the introductory calculus-based electricity and magnetism course at the University of Arkansas. The students' solutions to hourly exams were divided into a small set of countable features organized into three major categories, mathematics, language, and graphics. Each category was further divided…

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Martin, Linda

2008-01-01

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

In Praise of the Catenary

ERIC Educational Resources Information Center

Behroozi, F.

2018-01-01

When a chain hangs loosely from its end points, it takes the familiar form known as the catenary. Power lines, clothes lines, and chain links are familiar examples of the catenary in everyday life. Nevertheless, the subject is conspicuously absent from current introductory physics and calculus courses. Even in upper-level physics and math courses,…

Impact of Calculus Reform in a Liberal Arts Calculus Course.

ERIC Educational Resources Information Center

Brosnan, Patricia A.; Ralley, Thomas G.

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

Adapting research-based curricula at Seattle Pacific University: Results on student learning

NASA Astrophysics Data System (ADS)

Close, Eleanor; Vokos, Stamatis; Lindberg, John; Seeley, Lane

2004-05-01

Seattle Pacific University is the recent recipient of a NSF CCLI grant to improve student learning in introductory physics and calculus courses. This talk will outline the goals of this collaborative project and present some initial results on student performance. Results from research-based assessments will be presented as well as specific examples of successes and challenges from mechanics and electricity and magnetism.

The impact of taking a college pre-calculus course on students' college calculus performance

NASA Astrophysics Data System (ADS)

Sonnert, Gerhard; Sadler, Philip M.

2014-11-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.

Role of Mental Representations in Problem Solving: Students' Approaches to Nondirected Tasks

ERIC Educational Resources Information Center

Ibrahim, Bashirah; Rebello, N. Sanjay

2013-01-01

In this paper, we report on a project concerned with the role of cognition during problem solving. We specifically explore the categories of mental representations that students work with during problem solving of different representational task formats. The sample, consisting of 19 engineering students taking a calculus-based physics course,…

Cramster: Friend or Foe?

ERIC Educational Resources Information Center

Grams, Michael

2011-01-01

Recently when teaching a first-semester calculus-based physics course for engineers, I was perplexed by a particular group of students. These individuals were able to solve nearly every homework problem assigned from the end-of-chapter exercises in our textbook, and in some cases were able to do so using methods that we had not covered in class.…

The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance

ERIC Educational Resources Information Center

Sonnert, Gerhard; Sadler, Philip M.

2014-01-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…

Workshop Physics Activity Guide, Module 3: Heat Temperature and Nuclear Radiation, Thermodynamics, Kinetic Theory, Heat Engines, Nuclear Decay, and Random Monitoring (Units 16 - 18 & 28)

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research.

Physics for Scientists and Engineers, 5th edition - Volume 1

NASA Astrophysics Data System (ADS)

Tipler, Paul A.; Mosca, Gene P.

For nearly 30 years, Paul Tipler's Physics for Scientists and Engineers has set the standard in the introductory calculus-based physics course for clarity, accuracy, and precision. In this fifth edition, Paul has recruited Gene Mosca to bring his years of teaching experience to bear on the text, to scrutinize every explanation and example from the perspective of the freshman student. The result is a teaching tool that retains its precision and rigor, but offers struggling students the support they need to solve problems strategically and to gain real understanding of physical concepts.

Developing a magnetism conceptual survey and assessing gender differences in student understanding of magnetism

NASA Astrophysics Data System (ADS)

Li, Jing; Singh, Chandralekha

2012-02-01

We discuss the development of a research-based conceptual multiple-choice survey of magnetism. We also discuss the use of the survey to investigate gender differences in students' difficulties with concepts related to magnetism. We find that while there was no gender difference on the pre-test. However, female students performed significantly worse than male students when the survey was given as a post-test in traditionally taught calculus-based introductory physics courses with similar results in both the regular and honors versions of the course. In the algebra-based courses, the performance of female and male students has no statistical difference on the pre-test or the post-test.

Techniques of Differentiation and Integration, Mathematics (Experimental): 5297.27.

ERIC Educational Resources Information Center

Forrester, Gary B.

This guidebook on minimum course content was designed for students who have mastered the skills and concepts of analytic geometry. It is a short course in the basic techniques of calculus recommended for the student who has need of these skills in other courses such as beginning physics, economics or statistics. The course does not intend to teach…

The Case for Biocalculus: Design, Retention, and Student Performance

PubMed Central

Eaton, Carrie Diaz; Highlander, Hannah Callender

2017-01-01

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus is being actively cut from biology program requirements at many institutions. Here, we present an alternative: a model for learning mathematics that sees the partner disciplines as crucial to student success. We equip faculty with information to engage in dialogue within and between disciplinary departments involved in quantitative education. This includes presenting a process for interdisciplinary development and implementation of biology-oriented Calculus I courses at two institutions with different constituents, goals, and curricular constraints. When life science students enrolled in these redesigned calculus courses are compared with life science students enrolled in traditional calculus courses, students in the redesigned calculus courses learn calculus concepts and skills as well as their traditional course peers; however, the students in the redesigned courses experience more authentic life science applications and are more likely to stay and succeed in the course than their peers who are enrolled in traditional courses. Therefore, these redesigned calculus courses hold promise in helping life science undergraduate students attain Vision and Change recommended competencies. PMID:28450445

Analysis of the Impact of Introductory Physics on Engineering Students at Texas A&M University

NASA Astrophysics Data System (ADS)

Perry, Jonathan; Bassichis, William

Introductory physics forms a major part of the foundational knowledge of engineering majors, independent of discipline and institution. While the content of introductory physics courses is consistent from institution to institution, the manner in which it is taught can vary greatly due to professor, textbook, instructional method, and overall course design. This work attempts to examine variations in student success, as measured by overall academic performance in an engineering major, and matriculation rates, based on the type of introductory physics a student took while enrolled in an engineering degree at Texas A&M University. Specific options for introductory physics at Texas A&M University include two calculus based physics courses, one traditional (UP), and one more mathematically rigorous (DP), transfer credit, and high school (AP or dual) credit. In order to examine the impact of introductory physics on a student's degree progression, data mining analyses are performed on a data set of relatively comprehensive academic records for all students enrolled as an engineering major for a minimum of one academic term. Student data has been collected for years of entering freshman beginning in 1990 and ending in 2010. Correlations will be examined between freshman level courses, including introductory physics, and follow on engineering courses, matriculation rates, and time to graduation.

Investigating and improving introductory physics students’ understanding of electric flux

NASA Astrophysics Data System (ADS)

Li, Jing; Singh, Chandralekha

2018-07-01

A solid grasp of the concept of electric flux is an important pre-requisite for appropriate use of Gauss’s law in solving electrostatics problems. As part of a broader investigation focusing on improving understanding of electrostatics concepts, we investigated the conceptual difficulties of college students in a traditionally taught calculus-based introductory physics course with the concept of electric flux and then the research on student difficulties was used as a guide in the development and evaluation of a research-validated tutorial which strives to help students learn this concept better. During the investigation of difficulties and the design and validation of the guided inquiry-based tutorial, college students in a calculus-based introductory physics course were given written questions to probe the common conceptual difficulties with the electric flux related concepts, and we also interviewed a subset of those students to get an in-depth account of the reasons behind the conceptual difficulties. The guided inquiry-based learning sequences in the tutorial were also iterated several times with instructors who regularly teach these courses. Here we discuss the common student difficulties with the electric flux found in our investigations, and the development and validation of a tutorial that strives to improve student understanding. We analyse how students performed on the pre-test (administered before the electric flux tutorial but after traditional instruction in the electric flux concepts) and on the post-test (administered after students in the tutorial group had engaged with the electric flux related tutorial). The performance of students in all sections of the course was comparable on the pre-test regardless of who taught that section. However, on the post-test, the performance of those in the sections of the course in which students engaged with the tutorial is significantly better that the section in which the tutorial was not used.

Teaching ``The Physics of Energy'' at MIT

NASA Astrophysics Data System (ADS)

Jaffe, Robert

2009-05-01

New physics courses on energy are popping up at colleges and universities across the country. Many require little or no previous physics background, aiming to introduce a broad audience to this complex and critical problem, often augmenting the scientific message with economic and policy discussions. Others are advanced courses, focussing on highly specialized subjects like solar voltaics, nuclear physics, or thermal fluids, for example. About two years ago Washington Taylor and I undertook to develop a course on the ``Physics of Energy'' open to all MIT students who had taken MIT's common core of university level calculus, physics, and chemistry. By avoiding higher level prerequisites, we aimed to attract and make the subject relevant to students in the life sciences, economics, etc. --- as well as physical scientists and engineers --- who want to approach energy issues in a sophisticated and analytical fashion, exploiting their background in calculus, mechanics, and E & M, but without having to take advanced courses in thermodynamics, quantum mechanics, or nuclear physics beforehand. Our object was to interweave teaching the fundamental physics principles at the foundations of energy science with the applications of those principles to energy systems. We envisioned a course that would present the basics of statistical, quantum, and fluid mechanics at a fairly sophisticated level and apply those concepts to the study of energy sources, conversion, transport, losses, storage, conservation, and end use. In the end we developed almost all of the material for the course from scratch. The course debuted this past fall. I will describe what we learned and what general lessons our experience might have for others who contemplate teaching energy physics broadly to a technically sophisticated audience.

“Workshop Astronomy” at Dickinson College

NASA Astrophysics Data System (ADS)

Morgan, Windsor A., Jr.

2006-12-01

Dickinson College, a 2400-student liberal arts college in Carlisle, Pennsylvania, is recognized for the development of Workshop Physics. This innovative, calculus-based introductory course combines physics lectures and laboratories with integrated hands-on, small-group sessions. It allows students to do experiments, so that they will make their own observations and, with the guidance of the professor discover the principles of physics themselves. Since spring 2006, I have been developing an introductory solar-system astronomy course in the “Workshop” format at Dickinson. Students participate in discussions with their classmates and investigate astronomical concepts with computer simulations and guided inquiry. I emphasize “practical” astronomy (such as lunar phases, sky motions, and seasons) and physics concepts (such as density and Doppler shift); thus, my students become familiar with the basics of astronomy before developing a better understanding of the solar system. In my paper, I will discuss class activities and will evaluate their efficacy based on a comparison with traditionally-taught astronomy courses.

Enabling Students to Develop a Scientific Mindset

NASA Astrophysics Data System (ADS)

Kalman, Calvin

2010-02-01

This paper is centered on getting students to understand the nature of science (NOS) by considering historical material in relation to modern philosophers of science. This paper incorporates the methodology of contrasting cases in the calculus-based introductory physics course on optics and modern physics. Students study one philosopher all semester as a group project and report regularly on how their philosopher would view the subject matter of the course. Almost all of the students were able to argue successfully on the final examination about all three philosophers. Students become aware that the same textual material can be viewed in a variety of ways. The answers that students give about the NOS have become clearer at the end of the course.

Integrating Supplementary Application-Based Tutorials in the Multivariable Calculus Course

ERIC Educational Resources Information Center

Verner, I. M.; Aroshas, S.; Berman, A.

2008-01-01

This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible…

On a Calculus-Based Statistics Course for Life Science Students

ERIC Educational Resources Information Center

Watkins, Joseph C.

2010-01-01

The choice of pedagogy in statistics should take advantage of the quantitative capabilities and scientific background of the students. In this article, we propose a model for a statistics course that assumes student competency in calculus and a broadening knowledge in biology. We illustrate our methods and practices through examples from the…

On the Use of History of Mathematics: An Introduction to Galileo's Study of Free Fall Motion

ERIC Educational Resources Information Center

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter

2018-01-01

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

Dissociative conceptual and quantitative problem solving outcomes across interactive engagement and traditional format introductory physics

NASA Astrophysics Data System (ADS)

McDaniel, Mark A.; Stoen, Siera M.; Frey, Regina F.; Markow, Zachary E.; Hynes, K. Mairin; Zhao, Jiuqing; Cahill, Michael J.

2016-12-01

The existing literature indicates that interactive-engagement (IE) based general physics classes improve conceptual learning relative to more traditional lecture-oriented classrooms. Very little research, however, has examined quantitative problem-solving outcomes from IE based relative to traditional lecture-based physics classes. The present study included both pre- and post-course conceptual-learning assessments and a new quantitative physics problem-solving assessment that included three representative conservation of energy problems from a first-semester calculus-based college physics course. Scores for problem translation, plan coherence, solution execution, and evaluation of solution plausibility were extracted for each problem. Over 450 students in three IE-based sections and two traditional lecture sections taught at the same university during the same semester participated. As expected, the IE-based course produced more robust gains on a Force Concept Inventory than did the lecture course. By contrast, when the full sample was considered, gains in quantitative problem solving were significantly greater for lecture than IE-based physics; when students were matched on pre-test scores, there was still no advantage for IE-based physics on gains in quantitative problem solving. Further, the association between performance on the concept inventory and quantitative problem solving was minimal. These results highlight that improved conceptual understanding does not necessarily support improved quantitative physics problem solving, and that the instructional method appears to have less bearing on gains in quantitative problem solving than does the kinds of problems emphasized in the courses and homework and the overlap of these problems to those on the assessment.

A course in tools and procedures for Physics I

NASA Astrophysics Data System (ADS)

Allie, Saalih; Buffler, Andy

1998-07-01

A one-semester course covering the tools, skills, and procedures that are required to engage meaningfully with first-year university physics is described. The course forms part of the Science Foundation Programme at the University of Cape Town which was set up to provide access to a science degree for students who have been educationally disadvantaged, part of the legacy of racial discrimination in South Africa. The course comprises three basic elements: a theoretical component, a laboratory-based experimental component, and a communication skills component. The theory component consists of the various mathematical techniques used in a calculus-based Physics I course, grouped into cognate areas so that each technique is presented immediately in the full range of contexts that will be encountered later on. Part of the theory component involves written explanations of the mathematical formalism. The focus of the communication skills component is on report writing which follows as a natural consequence of the laboratory tasks which have been restructured as problems necessitating an experimental investigation. The implementation of cooperative tutorial groups, which forms an integral part of the learning environment, is also discussed.

The Integration of Biology into Calculus Courses

ERIC Educational Resources Information Center

Comar, Timothy D.

2008-01-01

This article discusses the incorporation of biological content into existing calculus courses without significantly changing the courses. This is exemplified by the common laboratory course taken by students in all first semester calculus courses at Benedictine University. Several biologically oriented projects are implemented in this laboratory…

From F = ma to Flying Squirrels: Curricular Change in an Introductory Physics Course

PubMed Central

O’Shea, Brian; Terry, Laura; Benenson, Walter

2013-01-01

We present outcomes from curricular changes made to an introductory calculus-based physics course whose audience is primarily life sciences majors, the majority of whom plan to pursue postbaccalaureate studies in medical and scientific fields. During the 2011–2012 academic year, we implemented a Physics of the Life Sciences curriculum centered on a draft textbook that takes a novel approach to teaching physics to life sciences majors. In addition, substantial revisions were made to the homework and hands-on components of the course to emphasize the relationship between physics and the life sciences and to help the students learn to apply physical intuition to life sciences–oriented problems. Student learning and attitudinal outcomes were assessed both quantitatively, using standard physics education research instruments, and qualitatively, using student surveys and a series of postsemester interviews. Students experienced high conceptual learning gains, comparable to other active learning–based physics courses. Qualitatively, a substantial fraction of interviewed students reported an increased interest in physics relative to the beginning of the semester. Furthermore, more than half of students self-reported that they could now relate physics topics to their majors and future careers, with interviewed subjects demonstrating a high level of ability to come up with examples of how physics affects living organisms and how it helped them to better understand content presented in courses in their major. PMID:23737630

From F = ma to flying squirrels: curricular change in an introductory physics course.

PubMed

O'Shea, Brian; Terry, Laura; Benenson, Walter

2013-06-01

We present outcomes from curricular changes made to an introductory calculus-based physics course whose audience is primarily life sciences majors, the majority of whom plan to pursue postbaccalaureate studies in medical and scientific fields. During the 2011-2012 academic year, we implemented a Physics of the Life Sciences curriculum centered on a draft textbook that takes a novel approach to teaching physics to life sciences majors. In addition, substantial revisions were made to the homework and hands-on components of the course to emphasize the relationship between physics and the life sciences and to help the students learn to apply physical intuition to life sciences-oriented problems. Student learning and attitudinal outcomes were assessed both quantitatively, using standard physics education research instruments, and qualitatively, using student surveys and a series of postsemester interviews. Students experienced high conceptual learning gains, comparable to other active learning-based physics courses. Qualitatively, a substantial fraction of interviewed students reported an increased interest in physics relative to the beginning of the semester. Furthermore, more than half of students self-reported that they could now relate physics topics to their majors and future careers, with interviewed subjects demonstrating a high level of ability to come up with examples of how physics affects living organisms and how it helped them to better understand content presented in courses in their major.

Beta-Test Data On An Assessment Of Textbook Problem Solving Ability: An Argument For Right/Wrong Grading?

NASA Astrophysics Data System (ADS)

Cummings, Karen; Marx, Jeffrey D.

2010-10-01

We have developed an assessment of students' ability to solve standard textbook style problems and are currently engaged in the validation and revision process. The assessment covers the topics of force and motion, conservation of momentum and conservation of energy at a level consistent with most calculus-based, introductory physics courses. This tool is discussed in more detail in an accompanying paper by Marx and Cummings. [1] Here we present preliminary beta-test data collected at four schools during the 2009/2010 academic year. Data include both pre- and post-instruction results for introductory physics courses as well as results for physics majors in later years. In addition, we present evidence that right/wrong grading may well be a perfectly acceptable grading procedure for a course-level assessment of this type.

Can an Analysis of the Contrast Between pre-Galilean and Newtonian Theoretical Frameworks Help Students Develop a Scientific Mindset

NASA Astrophysics Data System (ADS)

Kalman, Calvin S.; Aulls, Mark W.

This study examines a course in which students use two writing activities and collaborative group activities to examine the conceptual structure of the calculus-based introductory Physics course. Students are presented with two alternative frameworks; pre-Galilean Physics and Newtonian Physics. The idea of the course design is that students would at first view the frameworks almost in a theatrical sense as a view of a drama involving a conflict of actors;Aristotle, Galileo, Newton and others occurring a long time ago. As participants passing through a series of interventions, the students become aware that the frameworks relate concepts from different parts of the course and learn to evaluate the two alternative frameworks. They develop a scientific mindset changing their outlook on the course material from the viewpoint that it consists of a tool kit of assorted practices, classified according to problem type, to the viewpoint that it comprises a connected structure of concepts.

On a Calculus-based Statistics Course for Life Science Students

PubMed Central

2010-01-01

The choice of pedagogy in statistics should take advantage of the quantitative capabilities and scientific background of the students. In this article, we propose a model for a statistics course that assumes student competency in calculus and a broadening knowledge in biology. We illustrate our methods and practices through examples from the curriculum. PMID:20810962

An Inexpensive Toroidal Solenoid for an Investigative Student Lab

NASA Astrophysics Data System (ADS)

Ferstl, Andrew; Broberg, John

2008-09-01

Magnetism and Ampère's law is a common subject in most calculus-based introductory physics courses. Many textbooks offer examples to calculate the magnetic field produced by a symmetric current by using Ampère's law. These examples include the solenoid and the toroidal solenoid (sometimes called a torus; see Fig. 1), which are used in many applications, including the study of plasmas.

Recalling Prerequisite Material in a Calculus II Course to Improve Student Success

ERIC Educational Resources Information Center

Mokry, Jeanette

2016-01-01

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

Bunny hops: using multiplicities of zeroes in calculus for graphing

NASA Astrophysics Data System (ADS)

Miller, David; Deshler, Jessica M.; Hansen, Ryan

2016-07-01

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students' pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.

Who Becomes a Physics Major? A Long-term Longitudinal Study Examining the Roles of Pre-college Beliefs about Physics and Learning Physics, Interest, and Academic Achievement

NASA Astrophysics Data System (ADS)

Perkins, Katherine K.; Gratny, Mindy

2010-10-01

In this paper, we examine the correlation between students' beliefs upon entering college and their likelihood of continuing on to become a physics major. Since 2004, we have collected CLASS survey and self-reported level-of-interest responses from students in the first-term, introductory calculus-based physics course (N>2500). Here, we conduct a retrospective analysis of students' incoming CLASS scores and level of interest, comparing those students who go on to become physics majors with those who do not. We find the incoming CLASS scores and reported interest of these future physics majors to be substantially higher than the class average, indicating that these students enter their first college course already having quite expert-like beliefs. The comparative differences are much smaller for grades, SAT score, and university predicted-GPA.

Computer-Oriented Calculus Courses Using Finite Differences.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

Transforming a fourth year modern optics course using a deliberate practice framework

NASA Astrophysics Data System (ADS)

Jones, David J.; Madison, Kirk W.; Wieman, Carl E.

2015-12-01

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present a study of active learning pedagogies in an upper-division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15% improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier transforms, partial differential equations, and vector calculus), we expect the transformation process could be applied to most upper-division physics courses having a similar mathematical base.

Preliminary investigation of instructor effects on gender gap in introductory physics

NASA Astrophysics Data System (ADS)

Kreutzer, Kimberley; Boudreaux, Andrew

2012-06-01

Gender differences in student learning in the introductory, calculus-based electricity and magnetism course were assessed by administering the Conceptual Survey of Electricity and Magnetism pre- and postcourse. As expected, male students outgained females in traditionally taught sections as well as sections that incorporated interactive engagement (IE) techniques. In two of the IE course sections, however, the gains of female students were comparable to those of male students. Classroom observations of the course sections involved were made over an extended period. In this paper, we characterize the observed instructor-student interactions using a framework from educational psychology referred to as wise schooling. Results suggest that instructor practices affect differential learning, and that wise schooling techniques may constitute an effective strategy for promoting gender equity in the physics classroom.

Active Learning in a Large General Physics Classroom.

NASA Astrophysics Data System (ADS)

Trousil, Rebecca

2008-04-01

In 2004, we launched a new calculus-based, introductory physics sequence at Washington University. Designed as an alternative to our traditional lecture-based sequence, the primary objectives for this new course were to actively engage students in the learning process, to significantly strengthen students' conceptual reasoning skills, to help students develop higher level quantitative problem solving skills necessary for analyzing ``real world'' problems, and to integrate modern physics into the curriculum. This talk will describe our approach, using The Six Ideas That Shaped Physics text by Thomas Moore, to creating an active learning environment in large classes as well as share our perspective on key elements for success and challenges that we face in the large class environment.

Identifying and addressing student difficulties with the ideal gas law

NASA Astrophysics Data System (ADS)

Kautz, Christian Hans

This dissertation reports on an in-depth investigation of student understanding of the ideal gas law. The research and curriculum development were mostly conducted in the context of algebra- and calculus-based introductory physics courses and a sophomore-level thermal physics course. Research methods included individual demonstration interviews and written questions. Student difficulties with the quantities: pressure, volume, temperature, and the number of moles were identified. Data suggest that students' incorrect and incomplete microscopic models about gases contribute to the difficulties they have in answering questions posed in macroscopic terms. In addition, evidence for general reasoning difficulties is presented. These research results have guided the development of curriculum to address the student difficulties that have been identified.

Integrating Mathematics into the Introductory Biology Laboratory Course

ERIC Educational Resources Information Center

White, James D.; Carpenter, Jenna P.

2008-01-01

Louisiana Tech University has an integrated science curriculum for its mathematics, chemistry, physics, computer science, biology-research track and secondary mathematics and science education majors. The curriculum focuses on the calculus sequence and introductory labs in biology, physics, and chemistry. In the introductory biology laboratory…

Designing an Interactive OER Course Development at Athabasca University Based on ODL Principles

ERIC Educational Resources Information Center

Yan, Hongxin; Law, Sandra

2013-01-01

Failure rates in first year calculus courses are high in most post-secondary institutions across North America and other parts of the world. This Inukshuk-funded open education project involved the development of five stand-alone pre-calculus learning modules. The design and revision phases of this project occurred between the fall of 2007 and…

Teaching Special Relativity Without Calculus

NASA Astrophysics Data System (ADS)

Ruby, Lawrence

2009-04-01

I 2007 many AAPT members received a booklet that is the first chapter of a physics textbook available on a CD. This book espouses the new educational philosophy of teaching special relativity as the first item in the topic of mechanics. Traditionally, special relativity is part of one or more modern physics chapters at the end of the text,2 and very often this material is never utilized due to time constraints. From a logical standpoint, special relativity is important in satellite communications and in cosmology, as well as in modern physics applications such as atomic theory and high-energy physics. The purpose of this paper is to show that the new philosophy can be carried out in a noncalculus physics course, by demonstrating that all of the principal results of special relativity theory can be obtained by simple algebra. To accomplish this, we shall propose alternate derivations for two results that are usually obtained with calculus. Textbooks2 typically obtain the equations for time dilation and for length contraction from simple considerations based on Einstein's second postulate.3 We shall start from this point.

Pedagogical approaches, contextual variables, and the development of student self-efficacy in undergraduate physics courses

NASA Astrophysics Data System (ADS)

Fencl, Heidi S.; Scheel, Karen R.

2004-09-01

Self-efficacy, or a person's situation-specific belief that s/he can succeed in a given task, has been successful in a variety of educational studies for predicting behaviors such as perseverance and success (grades), and for understanding which behaviors are attempted or avoided. The focus of this study was to examine if classroom factors such as teaching strategies and classroom climate contribute to students' physics self-efficacy. 121 undergraduates in first semester, calculus-based introductory physics courses completed surveys assessing course experiences, self-efficacy and other outcome variables, and demographic information. Students in sections including a mix of teaching strategies did significantly better than students in the traditional section on outcome variables including self-efficacy. When individual strategies were examined, the strongest relationships were found between cooperative learning strategies and all sources of self-efficacy, and between climate variables and all sources of efficacy.

Learning by doing at the Colorado School of Mines

NASA Astrophysics Data System (ADS)

Furtak, Thomas E.; Ruskell, Todd G.

2013-03-01

With over 260 majors, the undergraduate physics program at CSM is among the largest in the country. An underlying theme in this success is experiential learning, starting with a studio teaching method in the introductory calculus-based physics courses. After their second year students complete a 6-week full-time summer course devoted to hands-on practical knowledge and skills, including machine shop techniques, high-vacuum technology, applied optics, electronic control systems, and computational tools. This precedes a two-semester laboratory sequence that can be taught at an advanced level because of the students' experience. The required capstone senior course is a year-long open-ended challenge in which students partner with members of the faculty to work on authentic research projects, teaming with grad students or post-docs as contributing members to the department's externally funded scholarship. All of these features are important components of our B.S. degree, Engineering Physics, which is officially accredited by ABET.

Assessing the Impacts of a Hybrid ``Flipped'' Approach to University Physics.

NASA Astrophysics Data System (ADS)

Hughes, Chris; Paulson, Scott

2015-03-01

Over the course of several years, the physics faculty at James Madison University has been gradually reforming the introductory calculus-based physics sequence to a hybrid model using a ``flipped classroom'' approach. The content traditionally delivered during lecture was divided into approximately 150 short (5-10 minute) videos. For homework, students are assigned 3-5 videos to watch before each class session. These assignments are combined with in-class activities including gouger problem solving and the tutorials developed by the University of Washington group to provide the students with focused guidance on concepts and skills that students traditionally have left our classes not having mastered. For the fall semester course on mechanics, the Force Concept Inventory (FCI) was used to evaluate student outcomes. For the spring semester course on E&M and optics, the Conceptual Survey of Electricity and Magnetism (CSEM) was used. Student reaction to the course structure was generally positive though there were some complaints in the student evaluations at the end of each semester. However, a positive impact on student outcomes was observed based on the Hake gains on the FCI.

Projectile motion without calculus

NASA Astrophysics Data System (ADS)

Rizcallah, Joseph A.

2018-07-01

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary techniques, which can hardly be assumed of the targeted audience. In the literature, several attempts have been undertaken to avoid calculus altogether and keep the exposition entirely within the realm of algebra and/or geometry. In this paper, we propose yet another non-calculus approach which uses the projectile’s travel times to shed new light on these problems and provide instructors with an alternate method to address them with their students.

Exploring the Relationship between Self-Efficacy and Retention in Introductory Physics

ERIC Educational Resources Information Center

Sawtelle, Vashti; Brewe, Eric; Kramer, Laird H.

2012-01-01

The quantitative results of Sources of Self-Efficacy in Science Courses-Physics (SOSESC-P) are presented as a logistic regression predicting the passing of students in introductory Physics with Calculus I, overall as well as disaggregated by gender. Self-efficacy as a theory to explain human behavior change [Bandura [1977] "Psychological…

Implementing Projects in Calculus on a Large Scale at the University of South Florida

ERIC Educational Resources Information Center

Fox, Gordon A.; Campbell, Scott; Grinshpan, Arcadii; Xu, Xiaoying; Holcomb, John; Bénéteau, Catherine; Lewis, Jennifer E.; Ramachandran, Kandethody

2017-01-01

This paper describes the development of a program of project-based learning in Calculus courses at a large urban research university. In this program, students developed research projects in consultation with a faculty advisor in their major, and supervised by their calculus instructors. Students wrote up their projects in a prescribed format…

Undergraduate Course and Curriculum Development Program and Calculus and the Bridge to Calculus Program: 1993 Awards.

ERIC Educational Resources Information Center

National Science Foundation, Arlington, VA. Div. of Undergraduate Education.

The Undergraduate Course and Curriculum Development Program of the National Science Foundation supports the development of courses in all disciplines to improve the quality of undergraduate courses and curricula in science, mathematics, engineering, and technology. The purpose of the program in Curriculum Development in Mathematics: Calculus and…

Master of Arts in Physics Education (MAPE) Program

NASA Astrophysics Data System (ADS)

Lindgren, Richard A.; Thornton, Stephen T.

2001-11-01

In the past 15 years, the Department of Physics at the University of Virginia in collaboration with the Curry School of Education has supported numerous summer high school physics and physical science teacher enrichment programs through the School of Continuing and Professional Studies. As a result of this accumulated experience in working with teachers, we created the Master of Arts in Physics Education (MAPE) program to address the needs of the high school physics teacher of the present and future. Through distance learning and summer study at UVa, participants earn the 30 hours needed for the Masters degree within 2 1/2 years while maintaining their current teaching position. Summer study includes the calculus based primary physics courses 631, 632, and 633 and associated laboratory courses. Summer physics course assignments and responsibilities do not terminate until late in the fall. Distance learning during the academic year is accomplished via the Internet using WebAssign, chat rooms, email, videotapes, and streamline video. Although recently approved in the spring 2000, 12 teachers have already graduated with the MAPE degree.

Leveraging Prior Calculus Study with Embedded Review

ERIC Educational Resources Information Center

Nikolov, Margaret C.; Withers, Wm. Douglas

2016-01-01

We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…

Effectiveness of Workshop Style Teaching in Students' Learning of Introductory Electricity and Magnetism

NASA Astrophysics Data System (ADS)

Mehta, Nirav; Cheng, Kelvin

2012-10-01

We have developed an interactive workshop-style course for our introductory calculus-based physics sequence at Trinity University. Lecture is limited to approximately 15 min. at the beginning of class, and the remainder of the 50-min. class is devoted to inquiry-based activities and problem solving. So far, lab is done separately and we have not incorporated the lab component into the workshop model. We use the Brief Electricity and Magnetism Assessment (BEMA) to compare learning gains between the workshop and traditional lecture-based course for the Spring 2012 semester. Both the workshop and lecture courses shared the same inquiry-based lab component that involved pre-labs, prediction-observation and post-lab activities. Our BEMA results indicate statistically significant improvement in overall learning gains compared to the traditional course. We compare our workshop BEMA scores both to traditional lecture scores here at Trinity and to those from other institutions.

Gender Differences in Both Force Concept Inventory and Introductory Physics Performance

NASA Astrophysics Data System (ADS)

Docktor, Jennifer; Heller, Kenneth

2008-10-01

We present data from a decade of introductory calculus-based physics courses for science and engineering students at the University of Minnesota taught using cooperative group problem solving. The data include 40 classes with more than 5500 students taught by 22 different professors. The average normalized gain for males is 0.4 for these large classes that emphasized problem solving. Female students made up approximately 20% of these classes. We present relationships between pre and post Force Concept Inventory (FCI) scores, course grades, and final exam scores for females and males. We compare our results with previous studies from Harvard [2] and the University of Colorado [3,4]. Our data show there is a significant gender gap in pre-test FCI scores that persists post-instruction although there is essentially no gender difference in course performance as determined by course grade.

The Case for Biocalculus: Design, Retention, and Student Performance.

PubMed

Eaton, Carrie Diaz; Highlander, Hannah Callender

2017-01-01

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus is being actively cut from biology program requirements at many institutions. Here, we present an alternative: a model for learning mathematics that sees the partner disciplines as crucial to student success. We equip faculty with information to engage in dialogue within and between disciplinary departments involved in quantitative education. This includes presenting a process for interdisciplinary development and implementation of biology-oriented Calculus I courses at two institutions with different constituents, goals, and curricular constraints. When life science students enrolled in these redesigned calculus courses are compared with life science students enrolled in traditional calculus courses, students in the redesigned calculus courses learn calculus concepts and skills as well as their traditional course peers; however, the students in the redesigned courses experience more authentic life science applications and are more likely to stay and succeed in the course than their peers who are enrolled in traditional courses. Therefore, these redesigned calculus courses hold promise in helping life science undergraduate students attain Vision and Change recommended competencies. © 2017 C. D. Eaton and H. C. Highlander. CBE—Life Sciences Education © 2017 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

Design Research on Inquiry-Based Multivariable Calculus: Focusing on Students' Argumentation and Instructional Design

ERIC Educational Resources Information Center

Kwon, Oh Nam; Bae, Younggon; Oh, Kuk Hwan

2015-01-01

In this study, researchers design and implement an inquiry based multivariable calculus course in a university which aims at enhancing students' argumentation in rich mathematical discussions. This research aims to understand the characteristics of students' argumentation in activities involving proof constructions through mathematical…

Preparatory Year Program Courses as Predictors of First Calculus Course Grade

ERIC Educational Resources Information Center

Yushau, B; Omar, M. H

2007-01-01

This study investigates the effect of the preparatory year program courses on the first calculus course (Calculus I) at King Fahd University of Petroleum and Minerals (KFUPM). The data consists of more than 2,000 bilingual Arab university students studying in the English language, tracked over seven semesters. These students represent over 70% of…

Measuring Teacher Immediacy and Communication Competence on Student Achievement in Calculus: A Sequential Explanatory Mixed Method Design

ERIC Educational Resources Information Center

Barclay, Allen C.

2012-01-01

On a national level, data indicate that about 40 percent of students in calculus courses finish with a grade of D or F, drop the course, or withdraw (Reinholz, 2009). This high failure rate has led to research studies investigating the teaching of calculus at the national level (House, 1995). Calculus courses have a history of high failure rates,…

Diversity of Approaches to Problems by Students Enrolled in a Non-Calculus College Physics Course.

ERIC Educational Resources Information Center

Cohen, Anna Foner

This study was undertaken to determine whether hierarchically structured problem situations could be developed and used to identify where individual solutions to problems in elementary physics are interrupted and whether examination of student approaches to problem situations would be useful to physics teaching. A random sample of 26 students…

Using tablets for real-time formative assessment in large-enrollment introductory courses

NASA Astrophysics Data System (ADS)

Ruskell, Todd

2013-04-01

Many large-enrollment introductory physics courses now use personal response devices (clickers) to engage students during class and collect data for real-time formative assessment. However, most systems only allow for multiple-choice or in some cases numeric or simple text answers. A program called inkSurvey allows faculty to ask more open-ended questions and students can submit both text and graphical responses from tablet computers. This provides faculty much greater insight into a student's problem-solving process. In our pilot project standard clickers were used in the first half of a calculus-based physics I course, and in the second half of the semester, tablets and inkSurvey were used to collect formative assessment data. We will report on initial impressions of both the faculty and students regarding the relative utility and effectiveness of each tool.

College Readiness: The Evaluation of Students Participating in the Historically Black College and University Program in Pre-Calculus and the Calculus Sequence

ERIC Educational Resources Information Center

Hall, Angela Renee

2011-01-01

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students

ERIC Educational Resources Information Center

Muzangwa, Jonatan; Chifamba, Peter

2012-01-01

This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…

The Development and Nature of Problem-Solving among First-Semester Calculus Students

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Epperson, James A. Mendoza

2014-01-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

On Flipping the Classroom in Large First Year Calculus Courses

ERIC Educational Resources Information Center

Jungic, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-01-01

Over the course of two years, 2012-2014, we have implemented a "flipping" the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of…

Do evidence-based active-engagement courses reduce the gender gap in introductory physics?

NASA Astrophysics Data System (ADS)

Karim, Nafis I.; Maries, Alexandru; Singh, Chandralekha

2018-03-01

Prior research suggests that using evidence-based pedagogies can not only improve learning for all students, it can also reduce the gender gap. We describe the impact of physics education research-based pedagogical techniques in flipped and active-engagement non-flipped courses on the gender gap observed with validated conceptual surveys. We compare male and female students’ performance in courses which make significant use of evidence-based active-engagement (EBAE) strategies with courses that primarily use lecture-based (LB) instruction. All courses had large enrolment and often had more than 100 students. The analysis of data for validated conceptual surveys presented here includes data from two-semester sequences of algebra-based and calculus-based introductory physics courses. The conceptual surveys used to assess student learning in the first and second semester courses were the force concept inventory and the conceptual survey of electricity and magnetism, respectively. In the research discussed here, the performance of male and female students in EBAE courses at a particular level is compared with LB courses in two situations: (I) the same instructor taught two courses, one of which was an EBAE course and the other an LB course, while the homework, recitations and final exams were kept the same; (II) student performance in all of the EBAE courses taught by different instructors was averaged and compared with LB courses of the same type also averaged over different instructors. In all cases, on conceptual surveys we find that students in courses which make significant use of active-engagement strategies, on average, outperformed students in courses of the same type using primarily lecture-based instruction even though there was no statistically significant difference on the pre-test before instruction. However, the gender gap persisted even in courses using EBAE methods. We also discuss correlations between the performance of male and female students on the validated conceptual surveys and the final exam, which had a heavy weight on quantitative problem solving.

Patterns of Incorrect Responses on the FCI and Course Success

NASA Astrophysics Data System (ADS)

Wells, James; Mokaya, Fridah; Valente, Diego

The Force Concept Inventory (FCI) is often used to measure the effectiveness of instructional pedagogy in introductory physics courses both at the algebra- and calculus-based level. Scores on the FCI are correlated with the performance of students in a class, as measured by their final course grade. We have collected data from several semesters of first-semester introductory mechanics courses at a public 4-year university, taught in large-scale classrooms with pedagogy including elements of Just-in-Time Teaching pedagogy along with active learning course components. The data collected includes pre- and post-test FCI scores, midterm exam grades, and final course grades. We examine whether certain patterns of incorrect answers on the FCI post-test are predictive of course grades, indicating whether certain specific student preconceptions are more detrimental than others to the success of students in an introductory mechanics course. Funding from UConn - College of Liberal Arts and Sciences (CLAS).

Astronomical Simulations Using Visual Python

NASA Astrophysics Data System (ADS)

Cobb, Michael L.

2007-05-01

The Physics and Engineering Physics Department at Southeast Missouri State University has adopted the “Matter and Interactions I Modern Mechanics” text by Chabay and Sherwood for our calculus based introductory physics course. We have fully integrated the use of modeling and simulations by using the Visual Python language also know as VPython. This powerful, high level, object orientated language with full three dimensional, stereo graphics has stimulated both my students and myself to find wider applications for our new found skills. We have successfully modeled gravitational resonances in planetary rings, galaxy collisions, and planetary orbits around binary star systems. This talk will provide a quick overview of VPython and demonstrate the various simulations.

Computer Managed Instruction Homework Modules for Calculus I.

ERIC Educational Resources Information Center

Goodman-Petrushka, Sharon; Roitberg, Yael

This booklet contains 11 modules (290 multiple-choice items) designed for use in the first course of a three-course calculus sequence using the textbook "Calculus with Analytic Geometry" (Dennis G. Zill). In each module, relevant sections of the textbook are identified for users. It can, however, be used in conjunction with any calculus textbook.…

On flipping the classroom in large first year calculus courses

NASA Astrophysics Data System (ADS)

Jungić, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-05-01

Over the course of two years, 2012--2014, we have implemented a 'flipping' the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of both instructors and students.

What physicists should know about finance

NASA Astrophysics Data System (ADS)

Schmidt, Anatoly B.

2005-05-01

There has been growing interest in Econophysics, i.e. analysis and modeling of financial time series using the theoretical Physics concepts (scaling, fractals, chaos). Besides the scientific stimuli, this interest is backed by perception that the financial industry is a viable alternative for those physicists who are not able or are not willing to pursue an academic career. However, the times when any Ph.D. in Physics had a chance to find a job on the Wall Street are gone (if they ever existed). Indeed, not every physicist wields the stochastic calculus, non-normal statistical distributions, and the methods of time series analysis. Moreover, now that many universities offer courses in mathematical finance, the applicants for quantitative positions in finance are expected to know such concepts as option pricing, portfolio management, and risk measurement. Here I describe a synthetic course based on my book [1] that outlines both worlds: Econophysics and Mathematical Finance. The course may be offered as elective for senior undergraduate or graduate Physics majors.

Comparing the efficacy of multimedia modules with traditional textbooks for learning introductory physics content

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Stelzer, Timothy; Gladding, Gary; Mestre, José P.; Brookes, David T.

2009-02-01

We compared the efficacy of multimedia learning modules with traditional textbooks for the first few topics of a calculus-based introductory electricity and magnetism course. Students were randomly assigned to three groups. One group received the multimedia learning module presentations, and the other two received the presentations via written text. All students were then tested on their learning immediately following the presentations as well as 2weeks later. The students receiving the multimedia learning modules performed significantly better on both tests than the students experiencing the text-based presentations.

A Classroom Note on: Modeling Functions with the TI-83/84 Calculator

ERIC Educational Resources Information Center

Lubowsky, Jack

2011-01-01

In Pre-Calculus courses, students are taught the composition and combination of functions to model physical applications. However, when combining two or more functions into a single more complicated one, students may lose sight of the physical picture which they are attempting to model. A block diagram, or flow chart, in which each block…

Energy Experiments for STEM Students

NASA Astrophysics Data System (ADS)

Fanchi, John

2011-03-01

Texas Christian University (TCU) is developing an undergraduate program that prepares students to become engineers with an emphasis in energy systems. One of the courses in the program is a technical overview of traditional energy (coal, oil and gas), nuclear energy, and renewable energy that requires as a pre-requisite two semesters of calculus-based physics. Energy experiments are being developed that will facilitate student involvement and provide hands-on learning opportunities. Students participating in the course will improve their understanding of energy systems; be introduced to outstanding scientific and engineering problems; learn about the role of energy in a global and societal context; and evaluate contemporary issues associated with energy. This talk will present the status of experiments being developed for the technical energy survey course.

Tensor calculus: unlearning vector calculus

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Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-02-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can serve as a bridge for vector calculus into tensor calculus.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

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Kalanov, Temur Z.

2014-03-01

A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.

Leading institutional change: Implementing Studio in physics and beyond

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Kohl, Patrick; Kuo, H. Vincent

2013-04-01

The Colorado School of Mines (CSM) teaches its first-year calculus-based introductory physics courses (Physics I and Physics II) using a hybrid of lecture and Studio physics. This model was first implemented in Physics I in 1997, and was established in Physics II in the fall of 2007. In this talk, we highlight the stages of the transformation from traditional to Studio, highlighting what has worked and what has not, and describing methods for assessment and evaluation. Results suggest that Studio has increased student performance and satisfaction despite an aggressive expansion of class sizes in the past few years. Gains have been concentrated mostly in problem-solving skills and exam performance (as opposed to conceptual survey gains), in contrast to what has sometimes been seen in other studies. Most recently, we as a department have been capitalizing on our successes with Studio physics to take a leadership role in disseminating advanced educational methods throughout CSM, both vertically (into upper division physics courses) and horizontally (into various departments outside of physics). We will briefly describe progress so far.

Hydrology

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Brutsaert, Wilfried

2005-08-01

Water in its different forms has always been a source of wonder, curiosity and practical concern for humans everywhere. Hydrology - An Introduction presents a coherent introduction to the fundamental principles of hydrology, based on the course that Wilfried Brutsaert has taught at Cornell University for the last thirty years. Hydrologic phenomena are dealt with at spatial and temporal scales at which they occur in nature. The physics and mathematics necessary to describe these phenomena are introduced and developed, and readers will require a working knowledge of calculus and basic fluid mechanics. The book will be invaluable as a textbook for entry-level courses in hydrology directed at advanced seniors and graduate students in physical science and engineering. In addition, the book will be more broadly of interest to professional scientists and engineers in hydrology, environmental science, meteorology, agronomy, geology, climatology, oceanology, glaciology and other earth sciences. Emphasis on fundamentals Clarification of the underlying physical processes Applications of fluid mechanics in the natural environment

Tensor Calculus: Unlearning Vector Calculus

ERIC Educational Resources Information Center

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Integrating Precalculus Review with the First Course in Calculus.

ERIC Educational Resources Information Center

Sevilla, Alicia; Somers, Kay

1993-01-01

Describes a course designed by Moravian College, Pennsylvania, to integrate precalculus topics as needed into a first calculus course. The textbook developed for the course covers the concepts of functions, Cartesian coordinates, limits, continuity, infinity, and the derivative. Examples are discussed. (MDH)

Competency-based reforms of the undergraduate biology curriculum: integrating the physical and biological sciences.

PubMed

Thompson, Katerina V; Chmielewski, Jean; Gaines, Michael S; Hrycyna, Christine A; LaCourse, William R

2013-06-01

The National Experiment in Undergraduate Science Education project funded by the Howard Hughes Medical Institute is a direct response to the Scientific Foundations for Future Physicians report, which urged a shift in premedical student preparation from a narrow list of specific course work to a more flexible curriculum that helps students develop broad scientific competencies. A consortium of four universities is working to create, pilot, and assess modular, competency-based curricular units that require students to use higher-order cognitive skills and reason across traditional disciplinary boundaries. Purdue University; the University of Maryland, Baltimore County; and the University of Miami are each developing modules and case studies that integrate the biological, chemical, physical, and mathematical sciences. The University of Maryland, College Park, is leading the effort to create an introductory physics for life sciences course that is reformed in both content and pedagogy. This course has prerequisites of biology, chemistry, and calculus, allowing students to apply strategies from the physical sciences to solving authentic biological problems. A comprehensive assessment plan is examining students' conceptual knowledge of physics, their attitudes toward interdisciplinary approaches, and the development of specific scientific competencies. Teaching modules developed during this initial phase will be tested on multiple partner campuses in preparation for eventual broad dissemination.

Calculus and Success in a Business School

ERIC Educational Resources Information Center

Kim, Dong-gook; Garcia, Fernando; Dey, Ishita

2012-01-01

Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating…

The Basic Principle of Calculus?

ERIC Educational Resources Information Center

Hardy, Michael

2011-01-01

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

Investigating and improving introductory physics students’ understanding of symmetry and Gauss’s law

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Li, Jing; Singh, Chandralekha

2018-01-01

We discuss an investigation of student difficulties with symmetry and Gauss’s law and how the research on students’ difficulties was used as a guide to develop a tutorial related to these topics to help students in the calculus-based introductory physics courses learn these concepts. During the development of the tutorial, we interviewed students individually at various stages of development and administered written tests in the free-response and multiple-choice formats on these concepts to learn about common student difficulties. We also obtained feedback from physics instructors who teach introductory physics courses regularly in which these concepts were covered. The students in several ‘equivalent’ sections worked on the tutorial after traditional lecture-based instruction. We discuss the performance of students on the written pre-test (administered after lecture-based instruction in relevant concepts) and post-test given after students worked on the tutorial. We find that on the pre-test, all sections of the course performed comparably regardless of the instructor. Also, on average, student performance on the post-test after working on the tutorial is significantly better than on the pre-test after lecture-based instruction. We also compare the post-test performance of introductory students in sections of the course in which the tutorial was used versus not used and find that sections in which students engaged with the tutorial outperformed those in which students did not engage with it.

Enhancing Student Writing and Computer Programming with LATEX and MATLAB in Multivariable Calculus

ERIC Educational Resources Information Center

Sullivan, Eric; Melvin, Timothy

2016-01-01

Written communication and computer programming are foundational components of an undergraduate degree in the mathematical sciences. All lower-division mathematics courses at our institution are paired with computer-based writing, coding, and problem-solving activities. In multivariable calculus we utilize MATLAB and LATEX to have students explore…

Maximizing the Range of a Projectile.

ERIC Educational Resources Information Center

Brown, Ronald A.

1992-01-01

Discusses solutions to the problem of maximizing the range of a projectile. Presents three references that solve the problem with and without the use of calculus. Offers a fourth solution suitable for introductory physics courses that relies more on trigonometry and the geometry of the problem. (MDH)

Network Analysis of Students' Use of Representations in Problem Solving

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McPadden, Daryl; Brewe, Eric

2016-03-01

We present the preliminary results of a study on student use of representations in problem solving within the Modeling Instruction - Electricity and Magnetism (MI-E&M) course. Representational competence is a critical skill needed for students to develop a sophisticated understanding of college science topics and to succeed in their science courses. In this study, 70 students from the MI-E&M, calculus-based course were given a survey of 25 physics problem statements both pre- and post- instruction, covering both Newtonian Mechanics and Electricity and Magnetism (E&M). For each problem statement, students were asked which representations they would use in that given situation. We analyze the survey results through network analysis, identifying which representations are linked together in which contexts. We also compare the representation networks for those students who had already taken the first-semester Modeling Instruction Mechanics course and those students who had taken a non-Modeling Mechanics course.

Attendance and Attainment in a Calculus Course

ERIC Educational Resources Information Center

Meulenbroek, Bernard; van den Bogaard, Maartje

2013-01-01

In this paper the relationship between attendance and attainment in a standard calculus course is investigated. Calculus could in principle be studied without attending lectures due to the wealth of material available (in hardcopy and online). However, in this study we will show that the pass rate of students attending classes regularly (>75%…

The Association of Precollege Use of Calculators with Student Performance in College Calculus

ERIC Educational Resources Information Center

Mao, Yi; White, Tyreke; Sadler, Philip M.; Sonnert, Gerhard

2017-01-01

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about…

Commentary on A General Curriculum in Mathematics for Colleges.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

This document constitutes a complete revision of the report of the same name first published in 1965. A new list of basic courses is described, consisting of Calculus I, Calculus II, Elementary Linear Algebra, Multivariable Calculus I, Linear Algebra, and Introductory Modern Algebra. Commentaries outline the content and spirit of these courses in…

What physicists should learn about finance (if they want to)

NASA Astrophysics Data System (ADS)

Schmidt, Anatoly

2006-03-01

There has been growing interest among physicists to Econophysics, i.e. analysis and modeling of financial and economic processes using the concepts of theoretical Physics. There has been also perception that the financial industry is a viable alternative for those physicists who are not able or are not willing to pursue career in their major field. However in our times, the Wall Street expects from applicants for quantitative positions not only the knowledge of the stochastic calculus and the methods of time series analysis but also of such concepts as option pricing, portfolio management, and risk measurement. Here I describe a synthetic course based on my book ``Quantitative Finance for Physicists'' (Elsevier, 2004) that outlines both worlds: Econophysics and Mathematical Finance. This course may be offered as elective for senior undergraduate or graduate Physics majors.

Student Selection of the Textbook for an Introductory Physics Course

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Dake, L. S.

2007-10-01

Several years ago I had to select a new textbook for my calculus-based introductory physics class. I subscribe to Just-in-Time Teaching methods, which require students to read the book before the material is covered in class. Thus, the readability of the text by the students is critical. However, I did not feel that I was the best judge of this factor, so I turned the textbook selection into a class project. The students unanimously chose one textbook, which I have now successfully used for three years. The project was decidedly worthwhile, and I gained considerable insight into what students prefer in a textbook.

Developing and validating a conceptual survey to assess introductory physics students’ understanding of magnetism

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Li, Jing; Singh, Chandralekha

2017-03-01

Development of validated physics surveys on various topics is important for investigating the extent to which students master those concepts after traditional instruction and for assessing innovative curricula and pedagogies that can improve student understanding significantly. Here, we discuss the development and validation of a conceptual multiple-choice survey related to magnetism suitable for introductory physics courses. The survey was developed taking into account common students’ difficulties with magnetism concepts covered in introductory physics courses found in our investigation and the incorrect choices to the multiple-choice questions were designed based upon those common student difficulties. After the development and validation of the survey, it was administered to introductory physics students in various classes in paper-pencil format before and after traditional lecture-based instruction in relevant concepts. We compared the performance of students on the survey in the algebra-based and calculus-based introductory physics courses before and after traditional lecture-based instruction in relevant magnetism concepts. We discuss the common difficulties of introductory physics students with magnetism concepts we found via the survey. We also administered the survey to upper-level undergraduates majoring in physics and PhD students to benchmark the survey and compared their performance with those of traditionally taught introductory physics students for whom the survey is intended. A comparison with the base line data on the validated magnetism survey from traditionally taught introductory physics courses and upper-level undergraduate and PhD students discussed in this paper can help instructors assess the effectiveness of curricula and pedagogies which is especially designed to help students integrate conceptual and quantitative understanding and develop a good grasp of the concepts. In particular, if introductory physics students’ average performance in a class is significantly better than those of students in traditionally taught courses described here (and particularly when it is comparable to that of physics PhD students’ average performance discussed here), the curriculum or pedagogy used in that introductory class can be deemed effective. Moreover, we discuss the use of the survey to investigate gender differences in student performance.

Expectancy violation in physics and mathematics classes in a student-centered classroom

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Alvarado, Carolina; Dominguez, Angeles; Rodriguez, Ruth; Zavala, Genaro

2012-02-01

This report analyzes the results of the implementation at a large private Mexican university of the Pedagogical Expectancy Violation Assessment (PEVA), developed by Gaffney, Gaffney and Beichner [1]. The PEVA was designed to evaluate shifts of the first student's expectations due to the initial orientation and experiences in the classroom. The data was collected at the Student-Centered Learning (ACE) classroom, based on the Student Centered Active Learning Environment for Undergraduate Programs (SCALE-UP) classroom. Three professors participated with their groups during the first semester they implemented their courses in this environment. Participants were enrolled either in a Pre-Calculus, Differential Equations, or Electricity and Magnetism course. The results indicate shifts in students' expectations during the semester and reveals differences in shifts among the different courses.

Research on a Unique Instructional Framework for Elevating Students’ Quantitative Problem Solving Abilities

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Prather, Edward E.; Wallace, Colin Scott

2018-06-01

We present an instructional framework that allowed a first time physics instructor to improve students quantitative problem solving abilities by more than a letter grade over what was achieved by students in an experienced instructor’s course. This instructional framework uses a Think-Pair-Share approach to foster collaborative quantitative problem solving during the lecture portion of a large enrollment introductory calculus-based mechanics course. Through the development of carefully crafted and sequenced TPS questions, we engage students in rich discussions on key problem solving issues that we typically only hear about when a student comes for help during office hours. Current work in the sophomore E&M course illustrates that this framework is generalizable to classes beyond the introductory level and for topics beyond mechanics.

A calculus based on a q-deformed Heisenberg algebra

DOE PAGES

Cerchiai, B. L.; Hinterding, R.; Madore, J.; ...

1999-04-27

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on thismore » derivative differential forms and an exterior differential calculus can be constructed.« less

Injecting Inquiry-Oriented Modules into Calculus

ERIC Educational Resources Information Center

Shelton, Therese

2017-01-01

Implementing inquiry-based modules within a course can be effective and enable instructor experimentation, without completely transforming an entire course. For instructors new to inquiry-based learning (IBL), we state hallmarks of the practice and point out the merits of strong IBL communities. An inquiry-based approach may alleviate some current…

Inquiring Minds Want to Know: Progress Report on SCALE-UP Physics at Penn State Erie

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Hall, Jonathan

2008-03-01

SCALE-UP (Student Centered Activities for Large Enrollment University Programs) is a ``studio'' approach to learning developed by Bob Beichner at North Carolina State University. SCALE-UP was adapted for teaching and learning in the introductory calculus-based mechanics course at Penn State Erie, The Behrend College, starting in Spring 2007. We are presently doing quantitative and qualitative research on using inquiry-based learning with first year college students, in particular how it effects female students and students from groups that are traditionally under-represented in STEM fields. Using field notes of observations of the classes, focus groups, and the collection of quantitative data, the feedback generated by the research is also being used to improve the delivery of the course, and in the planning of adopting SCALE-UP to the second semester course on electromagnetism in the Fall 2008 semester.

An Introductory Calculus-Based Mechanics Investigation

ERIC Educational Resources Information Center

Allen, Bradley

2017-01-01

One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…

Effects of Clicker Use on Calculus Students' Mathematics Anxiety

ERIC Educational Resources Information Center

Batchelor, John

2015-01-01

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

Improving student learning in calculus through applications

NASA Astrophysics Data System (ADS)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

An Active Classroom: The Emerging Scholars Program at West Virginia University

ERIC Educational Resources Information Center

Deshler, Jessica M.; Miller, David; Pascal, Matthew

2016-01-01

In an effort to support the success of minority students and to incorporate inquiry-based learning (IBL) into the calculus sequence of courses at West Virginia University, a modified version of the Emerging Scholars Program (ESP) was implemented in the fall of 2009. Since then, approximately 100 students have taken ESP Calculus I, with many of…

The development and nature of problem-solving among first-semester calculus students

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Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

A useful demonstration of calculus in a physics high school laboratory

NASA Astrophysics Data System (ADS)

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an experiment of a falling magnet in a column of self-induced eddy currents. The presented method combines multiple physics concepts such as 1D kinematics, classical mechanics, electromagnetism and non-trivial mathematics. It offers the opportunity for lateral as well as project-based learning.

Using Case Studies in Calculus-based Physics

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Katz, Debora M.

2006-12-01

Do your students believe that the physics only works in your classroom or laboratory? Or do they see that physics underlies their everyday experience? Case studies in physics help students connect physics principles to their everyday experience. For decades, case studies have been used to teach law, medicine and biology, but they are rarely used in physics. I am working on a calculus-based physics textbook for scientists and engineers. Case studies are woven into each chapter. Stop by and get a case study to test out in your classroom. I would love to get your feedback.

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

NASA Astrophysics Data System (ADS)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

The calculus of differences: Effects of a psychosocial, cultural, and pedagogical intervention in an all women's university calculus class

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Steele, Diana F.; Levin, Amy K.; Blecksmith, Richard; Shahverdian, Jill

2005-10-01

The purpose of this study was to investigate the ways in which a multi-layered women's calculus course influenced the participants' learning of mathematics. This study, conducted in a state university in the Midwestern region of the United States, revealed not only that women in this particular section of calculus were likely to select careers that involved mathematics, but that the focus on peer support, psychosocial issues such as self-confidence, and pedagogy helped the young women overcome gender barriers, as well as barriers of class, poverty, and race. In this article we provide some of the relevant quantitative statistics and relate the stories of two particular women through excerpts from interviews, student artefacts, and participant observation data. We selected these young women because they faced multiple barriers to success in Calculus I and might not have completed the course or taken additional mathematics courses without the support structures that were fundamental to the course.

Factors Shaping Mathematics Lecturers' Service Teaching in Different Departments

ERIC Educational Resources Information Center

Bingolbali, E.; Ozmantar, M. F.

2009-01-01

In this article we focus on university lecturers' approaches to the service teaching and factors that influence their approaches. We present data obtained from the interviews with 19 mathematics and three physics lecturers along with the observations of two mathematics lecturers' calculus courses. The findings show that lecturers' approaches to…

Success in Introductory Calculus: The Role of High School and Pre-Calculus Preparation

ERIC Educational Resources Information Center

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. It is a foundation course for all STEM majors and, if mastered well, should provide students with a positive and successful first-year experience and gateway into more advanced courses. Studies have shown that a…

Development of Curriculum Units as Basic Course for Calculus Provided for Freshmen with Low Academic Achievement

ERIC Educational Resources Information Center

Lue, Yuang-Tswong

2015-01-01

This study was to design, develop, and investigate instructional units for freshmen with low academic achievement to learn before they study calculus. Because the concepts, skills, and theories of function are fundamental for the calculus course but the below average students were not familiar with the basic knowledge and ability in function when…

Identifying student difficulties with basic scientific reasoning skills: An example from control of variables

NASA Astrophysics Data System (ADS)

Boudreaux, Andrew

2006-05-01

Current national and local standards for the science learning of K-12 students emphasize both basic concepts (such as density) and fundamental reasoning skills (such as proportional reasoning, the interpretation of graphs, and the use of control of variables). At Western Washington University (WWU) and the University of Washington (UW), an effort is underway to examine the ability of university students to apply these same concepts and skills. Populations include students in liberal arts physics courses, introductory calculus-based physics courses, and special courses for the preparation of teachers. One focus of the research has been on the idea of control of variables. This topic is studied by students at all levels, from the primary grades, in which the notion of a ``fair test,'' is sometimes used, to university courses. This talk will discuss research tasks in which students are expected to infer from experimental data whether a particular variable influences (i.e., affects) or by itself determines (i.e., predicts) a given result. Student responses will be presented to identify specific difficulties.

Apples vs. Oranges: Comparison of Student Performance in a MOOC vs. a Brick-and-Mortar Class

NASA Astrophysics Data System (ADS)

Dubson, Michael

In the fall of 2013, my colleagues and I taught the calculus-based introductory physics course to 800 tuition-paying students at the University of Colorado at Boulder. At the same time we taught a free massive open online version of the same course (MOOC), through Coursera.com. The initial enrollment in the MOOC was 10,000 students, of whom 255 completed the course. Students in both courses received identical lectures with identical embedded clicker questions, identical homework assignments, and identical timed exams. We present data on participation rates and exam performance for the two groups. We find that the MOOC is like a drug targeted at a very specific population. When it works, it works well, but it works for very few students. This MOOC worked well for older, well-educated students, who already had a good understanding of Newtonian mechanics.

Calculus: The Dynamics of Change. MAA Notes Number 39.

ERIC Educational Resources Information Center

Roberts, A. Wayne, Ed.

This book discusses the calculus reform effort. The first essay captures the basic themes that should characterize a calculus course that is modern in its vision as well as its pedagogy and content. The next section contains essays on the vision of calculus reform: "Visions of Calculus" (Sharon Cutler Ross); "Nonalgebraic Approaches…

Total Quality Management in the Classroom: Applications to University-Level Mathematics.

ERIC Educational Resources Information Center

Williams, Frank

1995-01-01

Describes a Total Quality Management-based system of instruction that is used in a variety of undergraduate mathematics courses. The courses that incorporate this approach include mathematics appreciation, introductory calculus, and advanced applied linear algebra. (DDR)

Determining the relationship between students' scores using traditional homework assignments to those who used assignments on a non-traditional interactive CD with tutor helps

NASA Astrophysics Data System (ADS)

Tinney, Charles Evan

2007-12-01

By using the book "Physics for Scientists and Engineers" by Raymond A. Serway as a guide, CD problem sets for teaching a calculus-based physics course were developed, programmed, and evaluated for homework assignments during the 2003-2004 academic year at Utah State University. These CD sets were used to replace the traditionally handwritten and submitted homework sets. They included a research-based format that guided the students through problem-solving techniques using responseactivated helps and suggestions. The CD contents were designed to help the student improve his/her physics problem-solving skills. The analyzed score results showed a direct correlation between the scores obtained on the homework and the students' time spent per problem, as well as the number of helps used per problem.

Physics faculty beliefs and values about the teaching and learning of problem solving. II. Procedures for measurement and analysis

NASA Astrophysics Data System (ADS)

Henderson, Charles; Yerushalmi, Edit; Kuo, Vince H.; Heller, Kenneth; Heller, Patricia

2007-12-01

To identify and describe the basis upon which instructors make curricular and pedagogical decisions, we have developed an artifact-based interview and an analysis technique based on multilayered concept maps. The policy capturing technique used in the interview asks instructors to make judgments about concrete instructional artifacts similar to those they likely encounter in their teaching environment. The analysis procedure alternatively employs both an a priori systems view analysis and an emergent categorization to construct a multilayered concept map, which is a hierarchically arranged set of concept maps where child maps include more details than parent maps. Although our goal was to develop a model of physics faculty beliefs about the teaching and learning of problem solving in the context of an introductory calculus-based physics course, the techniques described here are applicable to a variety of situations in which instructors make decisions that influence teaching and learning.

How a gender gap in belonging contributes to the gender gap in physics participation

NASA Astrophysics Data System (ADS)

Stout, Jane G.; Ito, Tiffany A.; Finkelstein, Noah D.; Pollock, Steven J.

2013-01-01

A great deal of research indicates that feeling a secure sense of belonging in academic settings is critical to students' achievement. In the current work, we present data collected over multiple semesters of a calculus-based introductory physics class indicating that women feel a lower sense of belonging than men in physics. This finding is important because our data also indicate that having a strong sense of belonging in physics positively predicts the degree to which all students see the value of physics in their daily life (an outcome that predicts motivation and persistence in achievement settings) as well as performance on exams in the course. We identify one potential antecedent of women's relatively lower sense of belonging in physics, namely, negative cultural stereotypes about women's inferior ability in physics compared to men. We then discuss pedagogical strategies that might be employed to enhance women's sense of belonging in physics.

Research as a guide for curriculum development: An example from introductory spectroscopy. II. Addressing student difficulties with atomic emission spectra

NASA Astrophysics Data System (ADS)

Ivanjek, L.; Shaffer, P. S.; McDermott, L. C.; Planinic, M.; Veza, D.

2015-02-01

This is the second of two closely related articles (Paper I and Paper II) that together illustrate how research in physics education has helped guide the design of instruction that has proved effective in improving student understanding of atomic spectroscopy. Most of the more than 1000 students who participated in this four-year investigation were science majors enrolled in the introductory calculus-based physics course at the University of Washington (UW) in Seattle, WA, USA. The others included graduate and undergraduate teaching assistants at UW and physics majors in introductory and advanced physics courses at the University of Zagreb, Zagreb, Croatia. About half of the latter group were preservice high school physics teachers. Paper I describes how several conceptual and reasoning difficulties were identified among university students as they tried to relate a discrete line spectrum to the energy levels of atoms in a light source. This second article (Paper II) illustrates how findings from this research informed the development of a tutorial that led to improvement in student understanding of atomic emission spectra.

Research as a guide for curriculum development: An example from introductory spectroscopy. I. Identifying student difficulties with atomic emission spectra

NASA Astrophysics Data System (ADS)

Ivanjek, L.; Shaffer, P. S.; McDermott, L. C.; Planinic, M.; Veza, D.

2015-01-01

This is the first of two closely related articles (Paper I and Paper II) that together illustrate how research in physics education has helped guide the design of instruction that has proved effective in improving student understanding of atomic spectroscopy. Most of the more than 1000 students who participated in this four-year investigation were science majors enrolled in the introductory calculus-based physics course at the University of Washington (UW) in Seattle, WA, USA. The others included graduate and undergraduate teaching assistants at UW and physics majors in introductory and advanced physics courses at the University of Zagreb, Zagreb, Croatia. About half of the latter group were preservice high school physics teachers. This article (Paper I) describes how several serious conceptual and reasoning difficulties were identified among students as they tried to relate a discrete line spectrum to the energy levels of atoms in a light source. Paper II illustrates how findings from this research informed the development of a tutorial that led to significant improvement in student understanding of atomic emission spectra.

Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?

ERIC Educational Resources Information Center

Gibson, Megan

2013-01-01

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

A First Course in Atmospheric Thermodynamics

NASA Astrophysics Data System (ADS)

Chilson, Phillip

2009-08-01

It is not uncommon to find textbooks that have been written with the intention of catering to a broad spectrum of readers. Often, though not always, the result is a book appropriate for neither advanced nor beginning students. However, Grant Petty had a very specific target audience in mind when he wrote A First Course in Atmospheric Thermodynamics. The book is clearly gauged for atmospheric science and meteorology students who have had introductory courses in physics and calculus but who have not necessarily established a firm foundation in analytic problem solving.

Mathematics preparation for medical school: do all premedical students need calculus?

PubMed

Nusbaum, Neil J

2006-01-01

The premedical student confronts a disparate set of required and recommended courses from the various medical schools to which the student might apply. Students may feel compelled to take courses such as calculus even though most medical schools do not require it and even though it may not be related to either undergraduate academic plans or the core academic needs of the typical future physician. Basic mathematical knowledge--a knowledge of algebra, statistics, and overall numeracy--are each more important for most future physicians than is the traditional calculus course.

Characterizing, modeling, and addressing gender disparities in introductory college physics

NASA Astrophysics Data System (ADS)

Kost-Smith, Lauren Elizabeth

2011-12-01

The underrepresentation and underperformance of females in physics has been well documented and has long concerned policy-makers, educators, and the physics community. In this thesis, we focus on gender disparities in the first- and second-semester introductory, calculus-based physics courses at the University of Colorado. Success in these courses is critical for future study and careers in physics (and other sciences). Using data gathered from roughly 10,000 undergraduate students, we identify and model gender differences in the introductory physics courses in three areas: student performance, retention, and psychological factors. We observe gender differences on several measures in the introductory physics courses: females are less likely to take a high school physics course than males and have lower standardized mathematics test scores; males outscore females on both pre- and post-course conceptual physics surveys and in-class exams; and males have more expert-like attitudes and beliefs about physics than females. These background differences of males and females account for 60% to 70% of the gender gap that we observe on a post-course survey of conceptual physics understanding. In analyzing underlying psychological factors of learning, we find that female students report lower self-confidence related to succeeding in the introductory courses (self-efficacy) and are less likely to report seeing themselves as a "physics person". Students' self-efficacy beliefs are significant predictors of their performance, even when measures of physics and mathematics background are controlled, and account for an additional 10% of the gender gap. Informed by results from these studies, we implemented and tested a psychological, self-affirmation intervention aimed at enhancing female students' performance in Physics 1. Self-affirmation reduced the gender gap in performance on both in-class exams and the post-course conceptual physics survey. Further, the benefit of the self-affirmation was strongest for females who endorsed the stereotype that men do better than women in physics. The findings of this thesis suggest that there are multiple factors that contribute to the underperformance of females in physics. Establishing this model of gender differences is a first step towards increasing females' participation and performance in physics, and can be used to guide future interventions to address the disparities.

Examining issues of underrepresented minority students in introductory physics

NASA Astrophysics Data System (ADS)

Watkins, Jessica Ellen

In this dissertation we examine several issues related to the retention of under-represented minority students in physics and science. In the first section, we show that in calculus-based introductory physics courses, the gender gap on the FCI is diminished through the use of interactive techniques, but in lower-level introductory courses, the gap persists, similar to reports published at other institutions. We find that under-represented racial minorities perform similar to their peers with comparable academic preparation on conceptual surveys, but their average exam grades and course grades are lower. We also examine student persistence in science majors; finding a significant relationship between pedagogy in an introductory physics course and persistence in science. In the second section, we look at student end-of-semester evaluations and find that female students rate interactive teaching methods a full point lower than their male peers. Looking more deeply at student interview data, we find that female students report more social issues related to the discussions in class and both male and female students cite feeling pressure to obtain the correct answer to clicker questions. Finally, we take a look an often-cited claim for gender differences in STEM participation: cognitive differences explain achievement differences in physics. We examine specifically the role of mental rotations in physics achievement and problem-solving, viewing mental rotations as a tool that students can use on physics problems. We first look at student survey results for lower-level introductory students, finding a low, but significant correlation between performance on a mental rotations test and performance in introductory physics courses. In contrast, we did not find a significant relationship for students in the upper-level introductory course. We also examine student problem-solving interviews to investigate the role of mental rotations on introductory problems.

An undergraduate course, and new textbook, on ``Physical Models of Living Systems''

NASA Astrophysics Data System (ADS)

Nelson, Philip

2015-03-01

I'll describe an intermediate-level course on ``Physical Models of Living Systems.'' The only prerequisite is first-year university physics and calculus. The course is a response to rapidly growing interest among undergraduates in several science and engineering departments. Students acquire several research skills that are often not addressed in traditional courses, including: basic modeling skills, probabilistic modeling skills, data analysis methods, computer programming using a general-purpose platform like MATLAB or Python, dynamical systems, particularly feedback control. These basic skills, which are relevant to nearly any field of science or engineering, are presented in the context of case studies from living systems, including: virus dynamics; bacterial genetics and evolution of drug resistance; statistical inference; superresolution microscopy; synthetic biology; naturally evolved cellular circuits. Publication of a new textbook by WH Freeman and Co. is scheduled for December 2014. Supported in part by EF-0928048 and DMR-0832802.

On flipping first-semester calculus: a case study

NASA Astrophysics Data System (ADS)

Petrillo, Joseph

2016-05-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.

A TENTATIVE GUIDE, DIFFERENTIAL AND INTEGRAL CALCULUS.

ERIC Educational Resources Information Center

BRANT, VINCENT; GERARDI, WILLIAM

THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…

Culture Points: Engaging Students outside the Classroom

ERIC Educational Resources Information Center

Fraboni, Michael; Hartshorn, Kevin

2007-01-01

In the typical first-year mathematics course--whether it be calculus or a general education quantitative proficiency course--we struggle to help students see the relevance of mathematics to their own lives. Particularly in a focused course such as calculus, there is a danger that students see mathematics as an isolated subject, with applications…

Examining Student Agency in an Active-Learning Business Calculus Course

ERIC Educational Resources Information Center

Higgins, Abigail L.

2017-01-01

This study explored student agency in an active-learning business calculus course. The lecture-style instructional practices typically used in this course at this institution allow few opportunities for students to interact with their peers, interface with the instructor one-on-one, or do mathematics during class time. Additionally, this course…

A Lesson in Vectors "Plain" and Simple

ERIC Educational Resources Information Center

Bradshaw, David M.

2004-01-01

The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…

An Analysis of Naval Officer Student Academic Performance in the Operations Analysis Curriculum in Relationship to Academic Profile Codes and other Factors.

DTIC Science & Technology

1985-09-01

Code 0 Physics (Calculus-Based) or Physical Science niscioline 0----------------------------------------- lR averaqe...opportunity for fficers with inadequate math- ematical and physical science backgrounds to establish a good math foundation to be able to gualify for a...technical curricu2um [Ref. 5: page 36]. There is also a six week refresher available that is designed to rapidly cover the calculus and physics

An AP Calculus Classroom Amusement Park

ERIC Educational Resources Information Center

Ferguson, Sarah

2016-01-01

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

Physics of the Atmosphere

NASA Astrophysics Data System (ADS)

Caballero, Rodrigo

2014-11-01

With the increasing attention paid to climate change, there is ever-growing interest in atmospheric physics and the processes by which the atmosphere affects Earth's energy balance. This self-contained text, written for advanced undergraduate and graduate students in physics or meteorology, assumes no prior knowledge apart from basic mechanics and calculus and contains material for a complete course. Augmented with worked examples, the text considers all aspects of atmospheric physics except dynamics, including moist thermodynamics, cloud microphysics, atmospheric radiation and remote sensing, and will be an invaluable resource for students and researchers.

Examining related influential factors for dental calculus scaling utilization among people with disabilities in Taiwan, a nationwide population-based study.

PubMed

Lai, Hsien-Tang; Kung, Pei-Tseng; Su, Hsun-Pi; Tsai, Wen-Chen

2014-09-01

Limited studies with large samples have been conducted on the utilization of dental calculus scaling among people with physical or mental disabilities. This study aimed to investigate the utilization of dental calculus scaling among the national disabled population. This study analyzed the utilization of dental calculus scaling among the disabled people, using the nationwide data between 2006 and 2008. Descriptive analysis and logistic regression were performed to analyze related influential factors for dental calculus scaling utilization. The dental calculus scaling utilization rate among people with physical or mental disabilities was 16.39%, and the annual utilization frequency was 0.2 times. Utilization rate was higher among the female and non-aboriginal samples. Utilization rate decreased with increased age and disability severity while utilization rate increased with income, education level, urbanization of residential area and number of chronic illnesses. Related influential factors for dental calculus scaling utilization rate were gender, age, ethnicity (aboriginal or non-aboriginal), education level, urbanization of residence area, income, catastrophic illnesses, chronic illnesses, disability types, and disability severity significantly influenced the dental calculus scaling utilization rate. Copyright © 2014 Elsevier Ltd. All rights reserved.

Scores on the 16 Personality Factor Test and Success in College Calculus 1.

ERIC Educational Resources Information Center

Shaughnessy, Michael F.; And Others

This study explored personality variables measured by the 16 Personality Factor (16PF) test and their relevance to success, as defined by the final course grade, in college calculus courses with 94 students. Two personality variables were significant predictors of success as determined by the final course grade. A Statistical Analysis System…

Shapes of Educational Data in an Online Calculus Course

ERIC Educational Resources Information Center

Caprotti, Olga

2017-01-01

This paper describes investigations in visualizing logpaths of students in an online calculus course held at Florida State University in 2014. The clickstreams making up the logpaths can be used to visualize student progress in the information space of a course as a graph. We consider the graded activities as nodes of the graph, while information…

Space Mathematics, A Resource for Teachers Outlining Supplementary Space-Related Problems in Mathematics.

ERIC Educational Resources Information Center

Reynolds, Thomas D.; And Others

This compilation of 138 problems illustrating applications of high school mathematics to various aspects of space science is intended as a resource from which the teacher may select questions to supplement his regular course. None of the problems require a knowledge of calculus or physics, and solutions are presented along with the problem…

Non-Zero Net Force and Constant Velocity: A Study in Mazur's Peer Instruction

ERIC Educational Resources Information Center

Newburgh, Ronald

2009-01-01

A problem addressed infrequently in beginning physics courses is that of a moving body with changing mass. Elementary texts often have footnotes referring to jet planes and rockets but rarely do they go further. This omission is understandable because calculations with variable mass generally require the tools of calculus. This paper presents a…

Calculus ABCs: A Gateway for Freshman Calculus

ERIC Educational Resources Information Center

Fulton, Scott R.

2003-01-01

This paper describes a gateway testing program designed to ensure that students acquire basic skills in freshman calculus. Students must demonstrate they have mastered standards for "Absolutely Basic Competency"--the Calculus ABCs--in order to pass the course with a grade of C or better. We describe the background, standards, and testing program.…

Putting Differentials Back into Calculus

ERIC Educational Resources Information Center

Dray, Tevian; Manogue, Corrine A.

2010-01-01

We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.

Right tail increasing dependence between scores

NASA Astrophysics Data System (ADS)

Fernández, M.; García, Jesús E.; González-López, V. A.; Romano, N.

2017-07-01

In this paper we investigate the behavior of the conditional probability Prob(U > u|V > v) of two records coming from students of an undergraduate course, where U is the score of calculus I, scaled in [0, 1] and V is the score of physics scaled in [0, 1], the physics subject is part of the admission test of the university. For purposes of comparison, we consider two different undergraduate courses, electrical engineering and mechanical engineering, during nine years, from 2003 to 2011. Through a Bayesian perspective we estimate Prob(U > u|V > v) year by year and course by course. We conclude that U is right tail increasing in V, in both courses and for all the years. Moreover, over these nine years, we observe different ranges of variability for the estimated probabilities of electrical engineering when compared to the estimated probabilities of mechanical engineering.

Toward better physics labs for future biologists

NASA Astrophysics Data System (ADS)

Moore, K.; Giannini, J.; Losert, W.

2014-05-01

We have developed a set of laboratories and hands on activities to accompany a new two-semester interdisciplinary physics course that has been developed and tested in two small test classes at the University of Maryland, College Park (UMD) in 2012-2013. We have designed the laboratories to be taken accompanying a reformed course in the student's second year, with calculus, biology, and chemistry as prerequisites. These prerequisites permit the laboratories to include significant content on physics relevant to cellular scales, from chemical interactions to random motion and charge screening in fluids. We also introduce students to research-grade equipment and modern physics analysis tools in contexts relevant to biology while maintaining the pedagogically valuable open-ended laboratory structure of reformed laboratories. Preliminary student response results from these two classes are discussed.

Effectiveness of different tutorial recitation teaching methods and its implications for TA training

NASA Astrophysics Data System (ADS)

Endorf, Robert

2008-04-01

We present results from a comparative study of student understanding for students who attended recitation classes that used different teaching methods. The purpose of the study was to evaluate which teaching methods would be the most effective for recitation classes associated with large lectures in introductory physics courses. Student volunteers from our introductory calculus-based physics course at the University of Cincinnati attended a special recitation class that was taught using one of four different teaching methods. A total of 272 students were divided into approximately equal groups for each method. Students in each class were taught the same topic, ``Changes in Energy and Momentum,'' from ``Tutorials in Introductory Physics'' by Lillian McDermott, Peter Shaffer and the Physics Education Group at the University of Washington. The different teaching methods varied in the amount of student and teacher engagement. Student understanding was evaluated through pretests and posttests. Our results demonstrate the importance of the instructor's role in teaching recitation classes. The most effective teaching method was for students working in cooperative learning groups with the instructors questioning the groups using Socratic dialogue. In addition, we investigated student preferences of modes of instruction through an open-ended survey. Our results provide guidance and evidence for the teaching methods which should be emphasized in training course instructors.

A Transition Course from Advanced Placement to College Calculus

ERIC Educational Resources Information Center

Lucas, Timothy A.; Spivey, Joseph

2011-01-01

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Assessing Online Homework in First-Semester Calculus

ERIC Educational Resources Information Center

Callahan, Jason T.

2016-01-01

This paper describes and assesses the implementation of online homework in a first-semester calculus course. Comparing sections of the course before implementation to those after, we find statistically significant improvements in retention rates, measures of student engagement, and participation on homework. We do not, however, find statistically…

Getting Limits off the Ground via Sequences

ERIC Educational Resources Information Center

Gass, Frederick

2006-01-01

Most beginning calculus courses spend little or no time on a technical definition of the limit concept. In most of the remaining courses, the definition presented is the traditional epsilon-delta definition. An alternative approach that bases the definition on infinite sequences has occasionally appeared in commercial textbooks but has not yet…

Examining gender differences on FCI performance in algebra and calculus based physics courses

NASA Astrophysics Data System (ADS)

Kreutzer, Kimberley; Boudreaux, Andrew

2009-05-01

The Force Concept Inventory (FCI) has been widely used to asses student understanding of Newtonian principles. Studies have shown a marked difference in the performance of men and women on both pre- and post-tests [1,2] and also indicate that experiential based instruction may lead to a reduction in this gender gap [1,3]. This poster presents FCI data collected at Western Washington University. Initial analysis of gender differences are consistent with those reported nationally. We also discuss factors that may contribute to the differences in performance and propose instructional strategies that are designed to address the gender gap. [4pt] [1] M. Lorenzo, et. al., ``Reducing the gender gap in the physics classroom,'' AJP 74(2), 118-122 (2006) [0pt] [2] J. Docktor and K. Heller, ``Gender Differences in Both Force Concept Inventory and Introductory Physics Performance,'' Proceedings at the 2008 PERC [0pt] [3] S. Pollack, et. al., ``Reducing the gender gap in the physics classroom: How sufficient is interactive engagement?'' PRST-PER 3 (2007)

Conceptual Precalculus: Strengthening Students' Quantitative and Covariational Reasoning

ERIC Educational Resources Information Center

Madison, Bernard L.; Carlson, Marilyn; Oehrtman, Michael; Tallman, Michael

2015-01-01

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…

Calculus Courses' Assessment Data

ERIC Educational Resources Information Center

Pauna, Matti

2017-01-01

In this paper we describe computer-aided assessment methods used in online Calculus courses and the data they produce. The online learning environment collects a lot of time-stamped data about every action a student makes. Assessment data can be harnessed into use as a feedback, predictor, and recommendation facility for students and instructors.…

Use of WIRIS Quizzes in an Online Calculus Course

ERIC Educational Resources Information Center

Calm, Remei; Masià, Ramon; Olivé, Carme; Parés, Núria; Pozo, Francesc; Ripoll, Jordi; Sancho-Vinuesa, Teresa

2017-01-01

Calculus courses often present a large number of difficulties to undergraduate students of scientific studies, especially in engineering degrees. These difficulties are sometimes related to teaching and assessment strategies. In this paper, a teaching innovation experience is presented within the framework of the Universitat Oberta de Catalunya.…

Individual Differences Related to College Students' Course Performance in Calculus II

ERIC Educational Resources Information Center

Hart, Sara A.; Daucourt, Mia; Ganley, Colleen M.

2017-01-01

In this study, we explore student achievement in a semester-long flipped Calculus II course, combining various predictor measures related to student attitudes (math anxiety, math confidence, math interest, math importance) and cognitive skills (spatial skills, approximate number system), as well as student engagement with the online system…

3D CAD: A Plus for STEM Education

ERIC Educational Resources Information Center

Planchard, Marie

2007-01-01

At some point in their education, pre-engineering students will take physics and/or calculus. For many freshmen who aren't certain about their career paths, taking these courses is a litmus test to determine whether they have the aptitude or desire to pursue an engineering degree. Therein lies the challenge for many students in the U.S. Science,…

Impacts of curricular change: Implications from 8 years of data in introductory physics

NASA Astrophysics Data System (ADS)

Pollock, Steven J.; Finkelstein, Noah

2013-01-01

Introductory calculus-based physics classes at the University of Colorado Boulder were significantly transformed beginning in 2004. They now regularly include: interactive engagement using clickers in large lecture settings, Tutorials in Introductory Physics with use of undergraduate Learning Assistants in recitation sections, and a staffed help-room setting where students work on personalized CAPA homework. We compile and summarize conceptual (FMCE and BEMA) pre- and post-data from over 9,000 unique students after 16 semesters of both Physics 1 and 2. Within a single institution with stable pre-test scores, we reproduce results of Hake's 1998 study that demonstrate the positive impacts of interactive engagement on student performance. We link the degree of faculty's use of interactive engagement techniques and their experience levels on student outcomes, and argue for the role of such systematic data collection in sustained course and institutional transformations.

Science 101: How Do We Use Calculus in Science?

ERIC Educational Resources Information Center

Robertson, Bill

2014-01-01

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

An Analysis of College Mathematics Departments' Credit Granting Policies for Students with High School Calculus Experience

ERIC Educational Resources Information Center

Laurent, Theresa A.

2009-01-01

The purpose of this study was to investigate higher education mathematics departments' credit granting policies for students with high school calculus experience. The number of students taking calculus in high school has more than doubled since 1982 (NCES, 2007) and it is estimated that approximately 530,000 students took a calculus course in high…

How Students Use Physics to Reason about Calculus Tasks

ERIC Educational Resources Information Center

Marrongelle, Karen A.

2004-01-01

The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her "paradigmatic physical" context and begins to address…

An investigation of student thinking regarding calorimetry, entropy, and the second law of thermodynamics

NASA Astrophysics Data System (ADS)

Christensen, Warren Michael

This thesis constitutes an investigation into student understanding of concepts in thermal physics in an introductory calculus-based university physics course. Nearly 90% of students enrolled in the course had previous exposure to thermodynamics concepts in chemistry and/or high-school physics courses. The two major thrusts of this work are (1) an exploration of student approaches to solving calorimetry problems involving two substances with differing specific heats, and (2) a careful probing of student ideas regarding certain aspects of entropy and the second law of thermodynamics. We present extensive free-response, interview, and multiple-choice data regarding students' ideas, collected both before and after instruction from a diverse set of course semesters and instructors. For topics in calorimetry, we found via interviews that students frequently get confused by, or tend to overlook, the detailed proportional reasoning or algebraic procedures that could lead to correct solutions. Instead, students often proceed with semi-intuitive reasoning that at times may be productive, but more often leads to inconsistencies and non-uniform conceptual understanding. Our investigation of student thinking regarding entropy suggests that prior to instruction, students have consistent and distinct patterns of incorrect or incomplete responses that often persist despite deliberate and focused efforts by the instructor. With modified instruction based on research-based materials, significant learning gains were observed on certain key concepts, e.g., that the entropy of the universe increases for all non-ideal processes. The methodology for our work is described, the data are discussed and analyzed, and a description is given of goals for future work in this area.

A new course and textbook on Physical Models of Living Systems, for science and engineering undergraduates

NASA Astrophysics Data System (ADS)

Nelson, Philip

2015-03-01

I'll describe an intermediate-level course on ``Physical Models of Living Systems.'' The only prerequisite is first-year university physics and calculus. The course is a response to rapidly growing interest among undergraduates in a broad range of science and engineering majors. Students acquire several research skills that are often not addressed in traditional courses: Basic modeling skills Probabilistic modeling skills Data analysis methods Computer programming using a general-purpose platform like MATLAB or Python Dynamical systems, particularly feedback control. These basic skills, which are relevant to nearly any field of science or engineering, are presented in the context of case studies from living systems, including: Virus dynamics Bacterial genetics and evolution of drug resistance Statistical inference Superresolution microscopy Synthetic biology Naturally evolved cellular circuits. Work supported by NSF Grants EF-0928048 and DMR-0832802.

Examining students' views about validity of experiments: From introductory to Ph.D. students

NASA Astrophysics Data System (ADS)

Hu, Dehui; Zwickl, Benjamin M.

2018-06-01

We investigated physics students' epistemological views on measurements and validity of experimental results. The roles of experiments in physics have been underemphasized in previous research on students' personal epistemology, and there is a need for a broader view of personal epistemology that incorporates experiments. An epistemological framework incorporating the structure, methodology, and validity of scientific knowledge guided the development of an open-ended survey. The survey was administered to students in algebra-based and calculus-based introductory physics courses, upper-division physics labs, and physics Ph.D. students. Within our sample, we identified several differences in students' ideas about validity and uncertainty in measurement. The majority of introductory students justified the validity of results through agreement with theory or with results from others. Alternatively, Ph.D. students frequently justified the validity of results based on the quality of the experimental process and repeatability of results. When asked about the role of uncertainty analysis, introductory students tended to focus on the representational roles (e.g., describing imperfections, data variability, and human mistakes). However, advanced students focused on the inferential roles of uncertainty analysis (e.g., quantifying reliability, making comparisons, and guiding refinements). The findings suggest that lab courses could emphasize a variety of approaches to establish validity, such as by valuing documentation of the experimental process when evaluating the quality of student work. In order to emphasize the role of uncertainty in an authentic way, labs could provide opportunities to iterate, make repeated comparisons, and make decisions based on those comparisons.

Productive and ineffective efforts: how student effort in high school mathematics relates to college calculus success

NASA Astrophysics Data System (ADS)

Barnett, M. D.; Sonnert, G.; Sadler, P. M.

2014-10-01

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the commonly expected benefits, the latter is associated with negative consequences. Time spent reading the course text in US high schools was negatively related to college calculus performance. Daily study time, however, was found to be either a productive or an ineffective effort, depending on the level of high school mathematics course and the student's performance in it.

Is classical mechanics a prerequisite for learning physics of the 20th century?

NASA Astrophysics Data System (ADS)

Walwema, Godfrey B.; French, Debbie A.; Verley, Jim D.; Burrows, Andrea C.

2016-11-01

Physics of the 20th century has contributed significantly to modern technology, and yet many physics students are never availed the opportunity to study it as part of the curriculum. One of the possible reasons why it is not taught in high school and introductory physics courses could be because curriculum designers believe that students need a solid background in classical mechanics and calculus in order to study physics of the 20th century such as the photoelectric effect, special and general relativity, the uncertainty principle, etc. This presumption may not be justifiable or valid. The authors of this paper contend that teaching physics of the 20th century aids students in relating physics to modern technology and the real world, making studying physics exciting. In this study, the authors correlated scores for matched questions in the Mechanics Baseline Test and a physics of the 20th century test in order to examine the trend of the scores. The participants included undergraduate students attending an introductory algebra-based physics course with no intention of taking physics at a higher level. The analysis of the scores showed no significant correlation for any of the matched pairs of questions. The purpose of this article is to recommend that even without a solid background in classical mechanics, teachers can introduce physics of the 20th century to their students for increased interest.

Identifying the elements of physics courses that impact student learning: Curriculum, instructor, peers, and assessment

NASA Astrophysics Data System (ADS)

West, Emily Lincoln Ashbaugh

Prior research across hundreds for introductory physics courses has demonstrated that traditional physics instruction does not generally lead to students learning physics concepts in a meaningful way, but that interactive-engagement physics courses do sometimes promote a great deal more student learning. In this work I analyze a reform effort in a large-enrollment, introductory, physics course. I find that evaluating a curriculum in isolation from other influences, such as the instructor implementation and the student population, is problematical. Instead, I propose a model of classroom culture identifying the curriculum, instructor, and student peer group as key components to creating a learning environment. Assessment, a key influence of classroom culture, is considered a product of the instructor/curriculum interaction. All three aspects of the classroom culture have the potential to influence student learning outcomes. I analyze the implementation of two different reformed physics series in terms of classroom culture. In a calculus-based course, I evaluate a new reform-based curriculum for the first and third quarters of instruction. In the first quarter, mechanics, I find that having an instructor teach in alignment with the philosophy of the reformed curriculum is essential, with students of only certain section instructors having improved outcomes over traditional instruction on measures of conceptual understanding. In the electromagnetism quarter of instruction, student outcomes for all reformed sections are higher than those from traditional sections in spite of variations in instructor implementation. The vast range of instructor-student interactions within such a reformed course are analyzed in an observational study, finding that some types of interactions are characteristic of particular instructors, regardless of the content studied that day. An analysis of assessment proposes an alternative grading method that is superior to the traditional grading practices, which are inadequate to consistently evaluate certain classes of test items. Those taking part in curriculum design or research in the context of physics classrooms must be aware that variations in instructor implementation, the student population, and assessment practices all have tremendous potential to influence student learning outcomes.

Motivation, Volition and Belief Change Strategies to Improve Mathematics Learning

ERIC Educational Resources Information Center

Kim, C.; Keller, J. M.

2010-01-01

The purpose of this study was to investigate the effects of motivation, volition and belief change strategies, implemented with personal and group email messages, on students' attitudes, study habits and achievement in a calculus course for non-mathematics majors. Eighty four undergraduates enrolled in a calculus course received emails over a…

A Study of Creative Reasoning Opportunities in Assessments in Undergraduate Calculus Courses

ERIC Educational Resources Information Center

Mac an Bhaird, Ciarán; Nolan, Brien C.; O'Shea, Ann; Pfeiffer, Kirsten

2017-01-01

In this article we present the findings of a research study which investigated the opportunities for creative reasoning (CR) made available to first year undergraduate students in assessments. We compared three first year calculus courses across two Irish universities using Lithner's framework. This framework sets apart imitative reasoning (IR)…

Struggles and Successes Implementing Classroom Communication Technology in a College Pre-Calculus Course

ERIC Educational Resources Information Center

Case, Erin; Pape, Stephen

2013-01-01

This case study documents the struggles and successes encountered by a pre-calculus teacher while using Classroom Connectivity Technology (CCT) daily in her community college mathematics course. CCT refers to a wireless communication system that connects a teacher's computer with an individual student's handheld calculator and has been associated…

Hands-On Calculus

ERIC Educational Resources Information Center

Sutherland, Melissa

2006-01-01

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

Assessment of student knowledge of the weak and strong nuclear forces

NASA Astrophysics Data System (ADS)

Shakya, Pramila

The purpose of this study was to determine if the use of active-learning activities to teach weak force and strong force to students enrolled in various courses at The University of Southern Mississippi, Hattiesburg campus and Gulf Park campus at different class times would increase their knowledge. There were eighty-six students that took part in this study. The study was conducted in the lab classes of an introductory astronomy survey course (AST 111), an introductory algebra-based physics course (PHY 112), and an introductory calculus-based physics course (PHY 202) during fall semester, 2014. Each class was randomly assigned as active-learning or direct instruction. A pretest followed by lecture was administered to all groups. The active-learning group performed four activities whereas the direct group watched a video irrelevant to the lesson. At the end of the lesson, the same post-test was given to all groups. Various statistical methods were used to analyze the differences in mean pretest and posttest scores. Overall, results show that the mean posttest scores were higher than the mean pretest scores. Findings support the use of active-learning activities work to the small number of students or the equal number of students in a group. The mean posttest scores of the direct instruction classes were higher than those of the active-learning groups.

The Physics Learning Center at the University of Wisconsin-Madison

NASA Astrophysics Data System (ADS)

Nossal, S. M.; Watson, L. E.; Hooper, E.; Huesmann, A.; Schenker, B.; Timbie, P.; Rzchowski, M.

2013-03-01

The Physics Learning Center at the University of Wisconsin-Madison provides academic support and small-group supplemental instruction to students studying introductory algebra-based and calculus-based physics. These classes are gateway courses for majors in the biological and physical sciences, pre-health fields, engineering, and secondary science education. The Physics Learning Center offers supplemental instruction groups twice weekly where students can discuss concepts and practice with problem-solving techniques. The Center also provides students with access on-line resources that stress conceptual understanding, and to exam review sessions. Participants in our program include returning adults, people from historically underrepresented racial/ethnic groups, students from families in lower-income circumstances, students in the first generation of their family to attend college, transfer students, veterans, and people with disabilities, all of whom might feel isolated in their large introductory course and thus have a more difficult time finding study partners. We also work with students potentially at-risk for having academic difficulty (due to factors academic probation, weak math background, low first exam score, or no high school physics). A second mission of the Physics Learning Center is to provide teacher training and leadership experience for undergraduate Peer Mentor Tutors. These Peer Tutors lead the majority of the weekly group sessions in close supervision by PLC staff members. We will describe our work to support students in the Physics Learning Center, including our teacher-training program for our undergraduate Peer Mentor Tutors

A Cross-National Study of Calculus

ERIC Educational Resources Information Center

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-01-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…

Calculus Instructors' Responses to Prior Knowledge Errors

ERIC Educational Resources Information Center

Talley, Jana Renee

2009-01-01

This study investigates the responses to prior knowledge errors that Calculus I instructors make when assessing students. Prior knowledge is operationalized as any skill or understanding that a student needs to successfully navigate through a Calculus I course. A two part qualitative study consisting of student exams and instructor interviews was…

Aspects of Calculus for Preservice Teachers

ERIC Educational Resources Information Center

Fothergill, Lee

2011-01-01

The purpose of this study was to compare the perspectives of faculty members who had experience teaching undergraduate calculus and preservice teachers who had recently completed student teaching in regards to a first semester undergraduate calculus course. An online survey was created and sent to recent student teachers and college mathematics…

DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

ERIC Educational Resources Information Center

BRANT, VINCENT; GERARDI, WILLIAM

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Student Achievement in College Calculus, Louisiana State University 1967-1968.

ERIC Educational Resources Information Center

Scannicchio, Thomas Henry

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

Expanding the FCI to Eevaluate Conceptual Mastery of Energy, Momentum, and Rotational Dynamics

NASA Astrophysics Data System (ADS)

Chediak, Alex; Hay, Katrina

2010-03-01

Normalized gain on the Force Concept Inventory (FCI) has deservedly become a widely accepted assessment tool to evaluate conceptual mastery in a high school, college, or university-level mechanics course. Left out of this assessment, however, are important physics concepts typically presented in the same course. Conservation of energy and momentum as well as rotational motion receive scant (if any) coverage on the FCI (or, for that matter, the Mechanics Baseline Test). Yet these concepts are foundational for popular majors such as mechanical engineering, where high failure rates are often a concern. A revised assessment tool is presented, one that incorporates the strengths of the FCI (and preserves the straightforward multiple choice format), but assesses these other mechanics-related concepts. Ten additional questions are included, inspired in part by material from the Physics Education Group at the University of Washington and in part by the authors' own experiences with common student misperceptions. The questions are given as pre- and post tests at the authors' institutions, California Baptist University and Pacific Lutheran University, in both calculus-based and algebra-based mechanics courses, exploring breadth of applicability for our findings. We present normalized gain data for the traditional thirty FCI questions and for our ten additional questions.

Reducing gender differences in performance in introductory college physics through values affirmation

NASA Astrophysics Data System (ADS)

Kost-Smith, Lauren

2011-04-01

Despite males and females being equally represented at the college level in several STEM disciplines (including biology, chemistry and mathematics), females continue to be under-represented in physics. Our research documents and addresses this participation gender gap in the introductory, calculus-based physics courses at the University of Colorado. We characterize gender differences in performance, psychological factors (including attitudes and beliefs) and retention that exist in Physics 1 and 2 [L. E. Kost, et al., Phys. Rev. ST Phys. Educ. Res. 5, 010101 (2009); L. E. Kost-Smith, et al., Phys. Rev. ST Phys. Educ. Res. 6, 020112 (2010)]. We find that the gender differences in performance can largely be accounted for by measurable differences in the physics and mathematics backgrounds and incoming attitudes and beliefs of males and females. But these background factors do not completely account for the gender gaps. We hypothesize, based on gender differences in responses to survey questions about students' sense of physics identity and confidence levels, that identity threat (the fear of confirming a negative characterization about one's identity) is playing a role in our courses. Working with researchers in psychology, we implemented an intervention where students either wrote about their most important values or not, twice at the beginning of the course [A. Miyake, et al., Science, 330, 1234 (2010)]. This ``values affirmation'' activity reduced the male-female performance difference substantially and elevated women's modal grades from the C to B range. Benefits were strongest for women who tended to endorse the stereotype that men do better than women in physics. This brief psychological intervention may be a promising way to address the gender gap in science performance.

Increasing Student Success in Large Survey Science Courses via Supplemental Instruction in Learning Centers

NASA Astrophysics Data System (ADS)

Hooper, Eric Jon; Nossal, S.; Watson, L.; Timbie, P.

2010-05-01

Large introductory astronomy and physics survey courses can be very challenging and stressful. The University of Wisconsin-Madison Physics Learning Center (PLC) reaches about 10 percent of the students in four introductory physics courses, algebra and calculus based versions of both classical mechanics and electromagnetism. Participants include those potentially most vulnerable to experiencing isolation and hence to having difficulty finding study partners as well as students struggling with the course. They receive specially written tutorials, conceptual summaries, and practice problems; exam reviews; and most importantly, membership in small groups of 3 - 8 students which meet twice per week in a hybrid of traditional teaching and tutoring. Almost all students who regularly participate in the PLC earn at least a "C,” with many earning higher grades. The PLC works closely with other campus programs which seek to increase the participation and enhance the success of underrepresented minorities, first generation college students, and students from lower-income circumstances; and it is well received by students, departmental faculty, and University administration. The PLC staff includes physics education specialists and research scientists with a passion for education. However, the bulk of the teaching is conducted by undergraduates who are majoring in physics, astronomy, mathematics, engineering, and secondary science teaching (many have multiple majors). The staff train these enthusiastic students, denoted Peer Mentor Tutors (PMTs) in general pedagogy and mentoring strategies, as well as the specifics of teaching the physics covered in the course. The PMTs are among the best undergraduates at the university. While currently there is no UW-Madison learning center for astronomy courses, establishing one is a possible future direction. The introductory astronomy courses cater to non-science majors and consequently are less quantitative. However, the basic structure of small groups focusing on fundamental understanding taught mostly by dedicated undergraduates should transfer well.

Impact of Course Policy Changes on Calculus I DFW Rates

ERIC Educational Resources Information Center

Norton, Paran; Bridges, William; High, Karen

2018-01-01

This paper examines the impact of departmental policy changes on the trend in DFW proportions for introductory calculus at a large research university, where DFW denotes the proportion of students receiving a grade of D, F, or withdrawing from the course. We defined three distinct policy periods: Traditional (2002-2005), Active Learning (SCALE-UP)…

The Use of Mathematical Modeling in an Interdisciplinary Setting.

ERIC Educational Resources Information Center

Harshbarger, Ronald J.; Upshaw, Jane

The University of South Carolina at Hilton Head offers a major in Hotel, Restaurant, and Tourism Administration (HRTA). Many students in the HRTA major take both the HRTA Tourism course and a business calculus course. An interdisciplinary research project was designed in an effort to interest these students in the power of calculus as a…

The Effect of Attending Tutoring on Course Grades in Calculus I

ERIC Educational Resources Information Center

Rickard, Brian; Mills, Melissa

2018-01-01

Tutoring centres are common in universities in the United States, but there are few published studies that statistically examine the effects of tutoring on student success. This study utilizes multiple regression analysis to model the effect of tutoring attendance on final course grades in Calculus I. Our model predicted that every three visits to…

AN ADVANCED PLACEMENT COURSE IN ANALYTIC GEOMETRY AND CALCULUS (MATHEMATICS XV X AP).

ERIC Educational Resources Information Center

DEROLF, JOHN J.; MIENTKA, WALTER E.

THIS TEXT ON ANALYTIC GEOMETRY AND CALCULUS IS A CORRESPONDENCE COURSE DESIGNED FOR ADVANCED PLACEMENT OF HIGH SCHOOL STUDENTS IN COLLEGE. EACH OF THE 21 LESSONS INCLUDES READING ASSIGNMENTS AND LISTS OF PROBLEMS TO BE WORKED. IN ADDITION, SUPPLEMENTARY EXPLANATIONS AND COMMENTS ARE INCLUDED THAT (1) PROVIDE ILLUSTRATIVE EXAMPLES OF CONCEPTS AND…

Innovative Interactive Lecture Demonstrations Using Wireless Force Sensors and Accelerometers for Introductory Physics Courses

NASA Astrophysics Data System (ADS)

Yoder, G.; Cook, J.

2010-12-01

Interactive lecture demonstrations1-6 (ILDs) are a powerful tool designed to help instructors bring state-of-the-art teaching pedagogies into the college-level introductory physics classroom. ILDs have been shown to improve students' conceptual understanding, and many examples have been created and published by Sokoloff and Thornton.6 We have used the new technology of Vernier's Wireless Dynamics Sensor System (WDSS)7 to develop three new ILDs for the first-semester introductory physics (calculus-based or algebra-based) classroom. These three are the Force Board, to demonstrate the vector nature of forces, addition of vectors, and the first condition of equilibrium; the Torque Board, to demonstrate torque and the second condition for equilibrium; and the Circular Motion Board, to discover the nature of the acceleration an object exhibiting uniform circular motion. With the WDSS, all three of these ILDs are easy to set up and use in any classroom or laboratory situation, and allow more instructors to utilize the technique of interactive lecture demonstrations.

Hands-on-Entropy, Energy Balance with Biological Relevance

NASA Astrophysics Data System (ADS)

Reeves, Mark

2015-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is important contribution of the entropy in driving fundamental biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy). This has enabled students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce complex biological processes and structures in order model them mathematically to account for both deterministic and probabilistic processes. The students test these models in simulations and in laboratory experiments that are biologically relevant such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront random forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

Evaluating the Use of Learning Objects for Improving Calculus Readiness

ERIC Educational Resources Information Center

Kay, Robin; Kletskin, Ilona

2010-01-01

Pre-calculus concepts such as working with functions and solving equations are essential for students to explore limits, rates of change, and integrals. Yet many students have a weak understanding of these key concepts which impedes performance in their first year university Calculus course. A series of online learning objects was developed to…

An Exploration of Definition and Procedural Fluency in Integral Calculus

ERIC Educational Resources Information Center

Grundmeier, Todd A.; Hansen, Jennifer; Sousa, Emily

2006-01-01

A survey was administered to calculus students who had previously been exposed to a course on integral calculus. The purpose of the survey was to explore students' understanding of the definition of a definite integral, their abilities to evaluate definite integrals, and their graphical interpretations of definite integrals. The analysis of…

Calculus Challenges: An Active Learning Approach

ERIC Educational Resources Information Center

Crawford, Pam; Moseley, Daniel; Nancarrow, Mike; Ward, Erika

2018-01-01

One of the greatest challenges facing students new to calculus is the ability to persevere in the face of failure. Whether the student is choosing an integration technique or a series test, calculus is often the first course in mathematics where the path to the solution is not prescribed in an algorithmic way. At Jacksonville University we…

Student Created Calculus Movies Using Computers and the TI-92.

ERIC Educational Resources Information Center

Sher, Lawrence; Wilkinson, Patricia

The Mathematics Department at Borough of Manhattan Community College (BMCC) (New York) has been actively involved since 1988 in a serious and successful program to improve instruction, understanding, and retention for women and minority students in calculus courses. One result of this work has been students creating calculus animations using…

Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles

ERIC Educational Resources Information Center

Thomas, Matthew

2013-01-01

This dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the…

Interactive, Collaborative, Electronic Learning Logs in the Physics Classroom

NASA Astrophysics Data System (ADS)

Gosling, Chris

2006-12-01

I describe my experiences using Hickman's Interactive Collaborative Electronic Learning Logs teaching HS Physics. ICE Learning Logs are written in student groups to answer questions posed by the instructor, who then in turn responds to each group’s entry before the next class. These logs were used with non-physics majors in both algebra and calculus-based introductory physics courses, and also at the high school level. I found ICE Learning Logs were found to be a clear improvement over traditional student journals. Excerpts from group entries will be presented to demonstrate the group identities that formed as well as the utility of the journals to probe for conceptual understanding. In addition, the ICE Learning Logs served as an excellent resource for students to review before exams and also to examine for critical moments to reflect on in formal essays. Hickman, P. (2000). Assessing student understanding with interactive-electronic-collaborative learning logs. ENC Focus, 7(2), 24-27. Sponsored by the National Science Foundation DUE0302097 and SUNY-Buffalo State Physics

Student Blogging about Physics

NASA Astrophysics Data System (ADS)

Daniels, Karen E.

2010-09-01

In traditional introductory physics classes, there is often limited opportunity for students to contribute their own ideas, interests, and experiences as they engage with the subject matter. This situation is exacerbated in university lecture-format classes, where students may not feel comfortable speaking during class. In the last few years, Internet blogs have become a decentralized format for diarists, independent journalists, and opinion makers to both post entries and allow commentary from their readers. Below, I will describe some techniques for using student blogging about physics to engage students from two different classroom environments: a calculus-based introductory mechanics class for scientists and engineers, and an honors seminar for first-year students. These assignments required them to make their own connections between classroom knowledge and situations where it might find applications. A second goal of including blogging in the introductory physics course was to induce students to write about the physics content of the class in a more substantive way than was previously part of the class.

Toward Better Physics Labs for Future Biologists

NASA Astrophysics Data System (ADS)

Giannini, John; Moore, Kim; Losert, Wolfgang

2014-03-01

We have developed a set of laboratories and hands on activities to accompany a new two-semester interdisciplinary physics course that has been successfully developed and tested in two small test classes of students at the University of Maryland, College Park (UMD) in 2012-2013, and is currently being used on a wider scale. We have designed the laboratories to be taken accompanying a reformed course in the student's second year, with calculus, biology, and chemistry as prerequisites. This permits the laboratories to include significant content on physics relevant to cellular scales, from chemical interactions to random motion and charge screening in fluids. One major focus of the laboratories is to introduce the students to research-grade equipment and modern physics analysis tools in contexts relevant to biology, while maintaining the pedagogically valuable open-ended laboratory structure of reformed laboratories. Lab development procedures along with some preliminary student results from these two small test classes are discussed.

Suggested Courseware for the Non-Calculus Physics Student: Simple Harmonic Motion, Wave Motion, and Sound.

ERIC Educational Resources Information Center

Grable-Wallace, Lisa; And Others

1989-01-01

Evaluates 5 courseware packages covering the topics of simple harmonic motion, 7 packages for wave motion, and 10 packages for sound. Discusses the price range, sub-topics, program type, interaction, time, calculus required, graphics, and comments of each courseware. Selects several packages based on the criteria. (YP)

The Effects of Implementing Recitation Activities on Success Rates in a College Calculus Course

ERIC Educational Resources Information Center

Watt, Jeffrey X.; Feldhaus, Charles R.; Sorge, Brandon H.; Fore, Grant A.; Gavrin, Andrew D.; Marrs, Kathleen A.

2014-01-01

Over a period of six years, three different types of recitation sessions were implemented into the large enrollment section of a college calculus course. During the fall semesters, the results on the departmental final examination, the DFW rates, and the one-year retention rates of students as STEM majors were examined by the type of recitation…

The Effects of Computer Algebra System on Undergraduate Students' Spatial Visualization Skills in a Calculus Course

ERIC Educational Resources Information Center

Karakus, Fatih; Aydin, Bünyamin

2017-01-01

This study aimed at determining the effects of using a computer algebra system (CAS) on undergraduate students' spatial visualization skills in a calculus course. This study used an experimental design. The "one group pretest-posttest design" was the research model. The participants were 41 sophomore students (26 female and 15 male)…

To Flip or Not to Flip? An Exploratory Study Comparing Student Performance in Calculus I

ERIC Educational Resources Information Center

Schroeder, Larissa B.; McGivney-Burelle, Jean; Xue, Fei

2015-01-01

The purpose of this exploratory, mixed-methods study was to compare student performance in flipped and non-flipped sections of Calculus I. The study also examined students' perceptions of the flipping pedagogy. Students in the flipped courses reported spending, on average, an additional 1-2 hours per week outside of class on course content.…

The Impact of Implementing Web Homework in Second-Semester Calculus

ERIC Educational Resources Information Center

LaRose, P. Gavin

2010-01-01

In this study we examine the introduction of on-line homework to a Calculus II course as a replacement for ungraded pencil-and-paper homework assignments. We consider how this had an impact on students' performance in the course, on student behavior in completing the assigned work, and on student attitudes toward it. We find that students working…

Students' Perceptions of Institutional Practices: The Case of Limits of Functions in College Level Calculus Courses

ERIC Educational Resources Information Center

Hardy, Nadia

2009-01-01

This paper presents a study of instructors' and students' perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I modeled these perceptions using a theoretical framework that combines elements of the Anthropological Theory of the Didactic, developed…

Instructor Use of Tablet PCs in a College Pre-Calculus Course: Implementation & Assessment

ERIC Educational Resources Information Center

Connelly Stockton, Julianna; Gregory, Peter

2012-01-01

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…

Using a Three-Step Method in a Calculus Class: Extending the Worked Example

ERIC Educational Resources Information Center

Miller, David

2010-01-01

This article discusses a three-step method that was used in a college calculus course. The three-step method was developed to help students understand the course material and transition to be more independent learners. In addition, the method helped students to transfer concepts from short-term to long-term memory while lowering cognitive load.…

A Mathematics Entrance Exam for General (Non-Majors) Physics

ERIC Educational Resources Information Center

Chediak, Alex

2010-01-01

In a previous issue of "The Physics Teacher", John Hubisz explained how a mathematics background check has been used at three different colleges to determine the appropriate physics sequence for incoming students. Based on their performance, students are placed into either calculus-based physics (CBP), algebra-trig physics (ATP), or a year of…

Calculus for a New Century: A Pump, Not a Filter. Papers Presented at a Colloquium (Washington, D.C., October 28-29, 1987). MAA Notes Number 8.

ERIC Educational Resources Information Center

Steen, Lynn Arthur, Ed.

This document, intended as a resource for calculus reform, contains 75 separate contributions, comprising a very diverse set of opinions about the shape of calculus for a new century. The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory,…

Studies in Mathematics, Volume XV. Calculus and Science.

ERIC Educational Resources Information Center

Twersky, Victor

This book is designed to illustrate how one general method of calculus is used in many different sciences and how different methods of calculus have furthered the development of essentially one field of science. The material is written so that it could serve as a math-science supplement for many courses. Chapters included are: (1) Introduction;…

Improving Student Learning of Calculus Topics via Modified Just-in-Time Teaching Methods

ERIC Educational Resources Information Center

Natarajan, Rekha; Bennett, Andrew

2014-01-01

Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…

Calculus: A Computer Oriented Presentation, Part 1 [and] Part 2.

ERIC Educational Resources Information Center

Stenberg, Warren; Walker, Robert J.

Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on…

Disappearing renal calculus.

PubMed

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-04-10

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging.

Tablet PC: A Preliminary Report on a Tool for Teaching Calculus

ERIC Educational Resources Information Center

Gorgievski, Nicholas; Stroud, Robert; Truxaw, Mary; DeFranco, Thomas

2005-01-01

This study examined students' perceptions of the Tablet PC as an instructional tool for teaching Calculus. A thirteen item survey was developed by the researchers and administered to 103 students in an introductory Calculus course at a large university in the Northeast of the United States. The purpose of this survey was to collect data regarding…

Resequencing Skills and Concepts in Applied Calculus Using the Computer as a Tool.

ERIC Educational Resources Information Center

Heid, M. Kathleen

1988-01-01

During the first 12 weeks of an applied calculus course, two classes of college students studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Three weeks were spent on skill development. Students showed better understanding of concepts and performed almost as well on routine skills.…

Students Targeting Engineering and Physical Science (STEPS) at California State University Northridge (CSUN):Activities and Outcomes 2011-2016

NASA Astrophysics Data System (ADS)

Cadavid, A. C.; Pedone, V. A.; Horn, W.; Rich, H.

2016-12-01

The specific goal of STEPS at CSUN is to increase the number bachelor's degrees in STEM majors, particularly those in engineering, computer science, mathematics and the physical sciences. Prior to STEPS, only 33% of first-time freshmen in these majors graduated from CSUN within 6-7 years. We employ two main strategies: 1) fostering success in lower-division mathematics for freshmen and sophomores, 2) Summer Interdisciplinary Team Experience (SITE) for students transitioning to junior level courses. To improve success in mathematics, we have advanced initial placements in the foundational mathematics sequence by one or two semesters through improvements in the placement test (6-7% improvement) and have increased the first-time pass rate in foundational math courses through mandatory supplementary laboratories for at-risk students. Students who successfully complete the supplemental laboratories pass the lecture class at a higher rate than the total population of at-risk students (65% compared to 61%). Both approaches have been institutionalized. SITE targets students entering their junior years in a 3-week interdisciplinary team project that highlights problem solving and hands-on activities. Survey results of the 233 participants show that SITE: 1) maintained or increased desire to earn a STEM degree, 2) increased positive attitudes toward team-based problem solving, 3) increased understanding in how they will use their major in a career, and 4) increased interest in faculty-mentored research and industry internships. Our 5-year program is nearing completion and shows success in meeting our goal. We have measured a 9% point increase in the pass rate of Calculus I for post-STEPS cohorts compared to pre-STEPS cohorts. Failure to pass Calculus is a leading cause in non-completion of the majors targeted by STEPS. We have analyzed the graduation rates of two pre-STEPS cohorts that have had over 6 years to graduate. Both have a graduate rate of 28%. We expect that the 9% point increase in calculus passers will lead to a comparable increase in graduation rate, resulting in a 37% graduation rate for the post-STEPS cohorts.

Catwalk: First-Semester Calculus.

ERIC Educational Resources Information Center

Speiser, Bob; Walter, Chuck

1994-01-01

Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)

Does interactive instruction in introductory physics impact long-term outcomes for students?

NASA Astrophysics Data System (ADS)

Gordon, Vernita

Early college classroom experiences contribute greatly to students leaving STEM majors. Peer instruction is a research-based pedagogy in which students, in small groups in the classroom, discuss concepts and work short problems. A single study at Harvard found that taking peer-instruction introductory physics also increases persistence in science majors. To what degree, if at all, peer instruction helps retention and performance for STEM majors at large public institutions (like University of Texas, Austin) is not known. Here I describe the results of a retrospective pilot study comparing outcomes for students who took different sections of the same calculus-based introductory mechanics course in Fall 2012 and Fall 2014. Compared with traditional lecture sections, peer-instruction sections had a 50% lower drop rate, a 40% / 55% higher rate of enrollment in the 2nd/ 3rd courses in the sequence, and, for the Fall 2012 cohort, a 74% / 165% higher rate of graduating from UT Austin / the UT Austin College of Natural Sciences by Fall 2015. I will discuss weaknesses of this retrospective pilot study and present plans for an intentionally-designed study to be implemented beginning Fall 2017.

Developing the Fundamental Theorem of Calculus. Applications of Calculus to Work, Area, and Distance Problems. [and] Atmospheric Pressure in Relation to Height and Temperature. Applications of Calculus to Atmospheric Pressure. [and] The Gradient and Some of Its Applications. Applications of Multivariate Calculus to Physics. [and] Kepler's Laws and the Inverse Square Law. Applications of Calculus to Physics. UMAP Units 323, 426, 431, 473.

ERIC Educational Resources Information Center

Lindstrom, Peter A.; And Others

This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…

Evolution of Student Knowledge in a Traditional Introductory Classroom

NASA Astrophysics Data System (ADS)

Sayre, Eleanor C.; Heckler, Andrew F.

2008-10-01

In the physics education research community, a common format for evaluation is pre- and post-tests. In this study, we collect student test data many times throughout a course, allowing for the measurement of the changes of student knowledge with a time resolution on the order of a few days. The data cover the first two quarters (mechanics, E&M) of a calculus-based introductory sequence populated primarily by first- and second-year engineering majors. To avoid the possibility of test-retest effects, separate and quasi-random subpopulations of students are evaluated every week of the quarter on a variety of tasks. Unsurprisingly for a traditional introductory course, there is little change on many conceptual questions. However, the data suggest that some student ideas peak and decay rapidly during a quarter, a pattern consistent with memory research yet unmeasurable by pre-/post-testing.

Characterizing the Fundamental Intellectual Steps Required in the Solution of Conceptual Problems

NASA Astrophysics Data System (ADS)

Stewart, John

2010-02-01

At some level, the performance of a science class must depend on what is taught, the information content of the materials and assignments of the course. The introductory calculus-based electricity and magnetism class at the University of Arkansas is examined using a catalog of the basic reasoning steps involved in the solution of problems assigned in the class. This catalog was developed by sampling popular physics textbooks for conceptual problems. The solution to each conceptual problem was decomposed into its fundamental reasoning steps. These fundamental steps are, then, used to quantify the distribution of conceptual content within the course. Using this characterization technique, an exceptionally detailed picture of the information flow and structure of the class can be produced. The intellectual structure of published conceptual inventories is compared with the information presented in the class and the dependence of conceptual performance on the details of coverage extracted. )

A Useful Demonstration of Calculus in a Physics High School Laboratory

ERIC Educational Resources Information Center

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an…

Learning physical biology via modeling and simulation: A new course and textbook for science and engineering undergraduates

NASA Astrophysics Data System (ADS)

Nelson, Philip

To a large extent, undergraduate physical-science curricula remain firmly rooted in pencil-and-paper calculation, despite the fact that most research is done with computers. To a large extent, undergraduate life-science curricula remain firmly rooted in descriptive approaches, despite the fact that much current research involves quantitative modeling. Not only does our pedagogy not reflect current reality; it also creates a spurious barrier between the fields, reinforcing the narrow silos that prevent students from connecting them. I'll describe an intermediate-level course on ``Physical Models of Living Systems.'' The prerequisite is first-year university physics and calculus. The course is a response to rapidly growing interest among undergraduates in a broad range of science and engineering majors. Students acquire several research skills that are often not addressed in traditional undergraduate courses: •Basic modeling skills; •Probabilistic modeling skills; •Data analysis methods; •Computer programming using a general-purpose platform like MATLAB or Python; •Pulling datasets from the Web for analysis; •Data visualization; •Dynamical systems, particularly feedback control. Partially supported by the NSF under Grants EF-0928048 and DMR-0832802.

Effectiveness of different tutorial recitation teaching methods and its implications for TA training

NASA Astrophysics Data System (ADS)

Koenig, Kathleen M.; Endorf, Robert J.; Braun, Gregory A.

2007-06-01

We present results from a comparative study of student understanding for students who attended recitation classes that used different teaching methods. Student volunteers from our introductory calculus-based physics course attended a special recitation class that was taught using one of four different teaching methods. A total of 272 students were divided into approximately equal groups for each method. Students in each class were taught the same topic, “Changes in Energy and Momentum,” from Tutorials in Introductory Physics. The different teaching methods varied in the amount of student and teacher engagement. Student understanding was evaluated through pre- and post-tests. Our results demonstrate the importance of the instructor’s role in teaching recitation classes. The most effective teaching method was for students working in cooperative learning groups with the instructors questioning the groups using Socratic dialogue. In addition, we investigated student preferences for modes of instruction through an open-ended survey. Our results provide guidance and evidence for the teaching methods that should be emphasized in training course instructors.

An empirical study of the effect of granting multiple tries for online homework

NASA Astrophysics Data System (ADS)

Kortemeyer, Gerd

2015-07-01

When deploying online homework in physics courses, an important consideration is how many tries learners should be allowed to solve numerical free-response problems. While on the one hand, this number should be large enough to allow learners mastery of concepts and avoid copying, on the other hand, granting too many allowed tries encourages counter-productive behavior. We investigate data from an introductory calculus-based physics course that allowed different numbers of tries in different semesters. It turns out that the probabilities for successfully completing or abandoning problems during a particular try are independent of the number of tries already made, which indicates that students do not learn from their earlier tries. We also find that the probability for successfully completing a problem during a particular try decreases with the number of allowed tries, likely due to increased carelessness or guessing, while the probability to give up on a problem after a particular try is largely independent of the number of allowed tries. These findings lead to a mathematical model for learner usage of multiple tries, which predicts an optimum number of five allowed tries.

Disappearing renal calculus

PubMed Central

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-01-01

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging. PMID:23580676

Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

ERIC Educational Resources Information Center

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-01-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

Techniques of Water-Resources Investigations of the United States Geological Survey. Book 3, Applications of Hydraulics. Chapter B2, Introduction to Ground-Water Hydraulics: Programed Text for Self-Instruction.

ERIC Educational Resources Information Center

Bennett, Gordon D.

This programmed text of self-instruction is one of a series of manuals on techniques describing procedures for planning and executing specialized work in water-resources investigations. It has been prepared on the assumption that the reader has completed standard courses in calculus and college physics and is presented in eight parts. Part I…

Motivating Calculus-Based Kinematics Instruction with Super Mario Bros

NASA Astrophysics Data System (ADS)

Nordine, Jeffrey C.

2011-09-01

High-quality physics instruction is contextualized, motivates students to learn, and represents the discipline as a way of investigating the world rather than as a collection of facts and equations. Inquiry-oriented pedagogy, such as problem-based instruction, holds great promise for both teaching physics content and representing the process of doing real science.2 A challenge for physics teachers is to find instructional contexts that are meaningful, accessible, and motivating for students. Today's students are spending a growing fraction of their lives interacting with virtual environments, and these environments—physically realistic or not—can provide valuable contexts for physics explorations3-5 and lead to thoughtful discussions about decisions that programmers make when designing virtual environments. In this article, I describe a problem-based approach to calculus-based kinematics instruction that contextualizes students' learning within the Super Mario Bros. video game—a game that is more than 20 years old, but still remarkably popular with today's high school and college students.

The relationship between selected standardized test scores and performance in advanced placement math and science exams: Analyzing the differential effectiveness of scores for course identification and placement

NASA Astrophysics Data System (ADS)

Urbina, Josue N.

There is a national need to increase the STEM-related workforce. Among factors leading towards STEM careers include the number of advanced high school mathematics and science courses students complete. Florida's enrollment patterns in STEM-related Advanced Placement (AP) courses, however, reveal that only a small percentage of students enroll into these classes. Therefore, screening tools are needed to find more students for these courses, who are academically ready, yet have not been identified. The purpose of this study was to investigate the extent to which scores from a national standardized test, Preliminary Scholastic Assessment Test/ National Merit Qualifying Test (PSAT/NMSQT), in conjunction with and compared to a state-mandated standardized test, Florida Comprehensive Assessment Test (FCAT), are related to selected AP exam performance in Seminole County Public Schools. An ex post facto correlational study was conducted using 6,189 student records from the 2010 - 2012 academic years. Multiple regression analyses using simultaneous Full Model testing showed differential moderate to strong relationships between scores in eight of the nine AP courses (i.e., Biology, Environmental Science, Chemistry, Physics B, Physics C Electrical, Physics C Mechanical, Statistics, Calculus AB and BC) examined. For example, the significant unique contribution to overall variance in AP scores was a linear combination of PSAT Math (M), Critical Reading (CR) and FCAT Reading (R) for Biology and Environmental Science. Moderate relationships for Chemistry included a linear combination of PSAT M, W (Writing) and FCAT M; a combination of FCAT M and PSAT M was most significantly associated with Calculus AB performance. These findings have implications for both research and practice. FCAT scores, in conjunction with PSAT scores, can potentially be used for specific STEM-related AP courses, as part of a systematic approach towards AP course identification and placement. For courses with moderate to strong relationships, validation studies and development of expectancy tables, which estimate the probability of successful performance on these AP exams, are recommended. Also, findings established a need to examine other related research issues including, but not limited to, extensive longitudinal studies and analyses of other available or prospective standardized test scores.

Workshop Physics Activity Guide, Module 4: Electricity and Magnetism

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research. The Workshop Physics Activity Guide is supported by an Instructor's Website that: (1) describes the history and philosophy of the Workshop Physics Project; (2) provides advice on how to integrate the Guide into a variety of educational settings; (3) provides information on computer tools (hardware and software) and apparatus; and (4) includes suggested homework assignments for each unit. Log on to the Workshop Physics Project website at http://physics.dickinson.edu/ Workshop Physics is a component of the Physics Suite--a collection of materials created by a group of educational reformers known as the Activity Based Physics Group. The Physics Suite contains a broad array of curricular materials that are based on physics education research, including:

Understanding Physics, by Cummings, Laws, Redish and Cooney (an introductory textbook based on the best-selling text by Halliday/Resnick/Walker) RealTime Physics Laboratory Modules Physics by Inquiry (intended for use in a workshop setting) Interactive Lecture Demonstration Tutorials in Introductory Physics Activity Based Tutorials (designed primarily for use in recitations)

• The Role of Mothers' Communication in Promoting Motivation for Math and Science Course-Taking in High School.

  PubMed

  Hyde, Janet S; Canning, Elizabeth A; Rozek, Christopher S; Clarke, Emily; Hulleman, Chris S; Harackiewicz, Judith M

  2017-03-01

  In the context of concerns about American youths' failure to take advanced math and science (MS) courses in high school, we examined mothers' communication with their adolescent about taking MS courses. At ninth grade, U.S. mothers (n = 130) were interviewed about their responses to hypothetical questions from their adolescent about the usefulness of algebra, geometry, calculus, biology, chemistry, and physics. Responses were coded for elaboration and making personal connections to the adolescent. The number of science, technology, engineering, and mathematics courses taken in 12th grade was obtained from school records. Mothers' use of personal connections predicted adolescents' MS interest and utility value, as well as actual MS course-taking. Parents can play an important role in motivating their adolescent to take MS courses. © 2016 The Authors. Journal of Research on Adolescence © 2016 Society for Research on Adolescence.

• Task Design for Students' Work with Basic Theory in Analysis: The Cases of Multidimensional Differentiability and Curve Integrals

  ERIC Educational Resources Information Center

  Gravesen, Katrine Frovin; Grønbaek, Niels; Winsløw, Carl

  2017-01-01

  We investigate the challenges students face in the transition from calculus courses, focusing on methods related to the analysis of real valued functions given in closed form, to more advanced courses on analysis where focus is on theoretical structure, including proof. We do so based on task design aiming for a number of generic potentials for…

• Using Student-Made Games to Learn Mathematics

  ERIC Educational Resources Information Center

  Gallegos, Irene; Flores, Alfinio

  2010-01-01

  First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

• Assessment of Peer-Led Team Learning in Calculus I: A Five-Year Study

  ERIC Educational Resources Information Center

  Merkel, John Conrad; Brania, Abdelkrim

  2015-01-01

  This five-year study of the peer-led team learning (PLTL) paradigm examined its implementation in a Calculus I course at an all-male HBCU institution. For this study we set up a strong control group and measured the effect of PLTL in the teaching and learning of Calculus I through two points of measure: retention and success rates and learning…

• What Is Old Is New Again: A Systemic Approach to the Challenges of Calculus Instruction

  ERIC Educational Resources Information Center

  Carreon, Fernando; DeBacker, Stephen; Kessenich, Paul; Kubena, Angela; LaRose, P. Gavin

  2018-01-01

  In the abstract for "Calculus for a New Century: A Pump, Not a Filter," Lynn Steen wrote: "The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory, yet disagree about new content emphases. They agree that the neglect of…

• A Mean-Based Approach for Teaching the Concept of Integration

  ERIC Educational Resources Information Center

  Zazkis, Dov; Rasmussen, Chris; Shen, Samuel P.

  2014-01-01

  The Riemann sum definition of integration is ubiquitous in college calculus courses. This, however, is not the only possible way to define an integral. Here, we present an alternative mean-based definition of integration. We conjecture that this definition is more accessible to students. In support of this proposition we first present a…

• Students' Critical Thinking Ability: Description Based on Academic Level and Gender

  ERIC Educational Resources Information Center

  Zetriuslita, Hj.; Ariawan, Rezi; Nufus, Hayatun

  2016-01-01

  This research aims to describe students' critical thinking ability based on the level academic and gender. The populations of this study were 132 students participating in five classes of Calculus course. The research data obtained through technical tests and interview techniques. This study found that the high level of capability, both male…

• Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

  ERIC Educational Resources Information Center

  Helmreich, James E.; Krog, K. Peter

  2018-01-01

  We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

• Problems with the rush toward advanced physics in high schools

  NASA Astrophysics Data System (ADS)

  Gollub, Jerry

  2003-04-01

  The Advanced Placement (AP) Program has a major impact on the physics experience of many high school students. It affects admission to college, course choices and performance in college, and subsequent career decisions. A study committee of the National Research Council published a review of these programs in 2002, and concluded that while the program has many positive features, important problems need to be addressed. [1] The programs are not currently consistent with what we have learned about student learning from cognitive research. Students are often poorly prepared for AP courses, because of lack of coordination within schools. The Physics AP-B (non-calculus) program is too broad to allow most high school students to achieve an adequate level of conceptual understanding. Participation by minority students in these programs is far below that of other students. The AP exams need to be re-evaluated to insure that they actually measure conceptual understanding and complex reasoning. The AP exams are sometimes used inappropriately to rate teachers or schools. College and high school courses are poorly coordinated, with the result that students often take an introductory physics survey as many as three times. Policies on college credit for AP courses differ widely. These problems cannot be fixed by the College Board alone. [1] Jerry P. Gollub and Robin Spital, "Advanced Physics in the High Schools", Physics Today, May 2002.

• Resolution of localized chronic periodontitis associated with longstanding calculus deposits.

  PubMed

  Lai, Pin-Chuang; Walters, John D

  2014-01-01

  This report, which is based on nonstandardized serial radiographs obtained over a period of 15 years, documents a case of localized chronic periodontitis associated with progressive deposition of calculus on the distal aspect of a mandibular second molar. The site was treated by scaling and root planing, followed by a course of adjunctive systemic azithromycin. Treatment yielded favorable reductions in probing depth and clinical inflammation, leaving only few isolated sites with pockets no deeper than 4 mm. Two years after completion of active treatment, there was radiographic evidence of increased bone density distal to the second molar.

• Evaluating and redesigning teaching learning sequences at the introductory physics level

  NASA Astrophysics Data System (ADS)

  Guisasola, Jenaro; Zuza, Kristina; Ametller, Jaume; Gutierrez-Berraondo, José

  2017-12-01

  In this paper we put forward a proposal for the design and evaluation of teaching and learning sequences in upper secondary school and university. We will connect our proposal with relevant contributions on the design of teaching sequences, ground it on the design-based research methodology, and discuss how teaching and learning sequences designed according to our proposal relate to learning progressions. An iterative methodology for evaluating and redesigning the teaching and learning sequence (TLS) is presented. The proposed assessment strategy focuses on three aspects: (a) evaluation of the activities of the TLS, (b) evaluation of learning achieved by students in relation to the intended objectives, and (c) a document for gathering the difficulties found when implementing the TLS to serve as a guide to teachers. Discussion of this guide with external teachers provides feedback used for the TLS redesign. The context of our implementation and evaluation is an innovative calculus-based physics course for first-year engineering and science degree students at the University of the Basque Country.

• Cramster: Friend or Foe?

  NASA Astrophysics Data System (ADS)

  Grams, Michael

  2011-04-01

  Recently when teaching a first-semester calculus-based physics course for engineers, I was perplexed by a particular group of students. These individuals were able to solve nearly every homework problem assigned from the end-of-chapter exercises in our textbook, and in some cases were able to do so using methods that we had not covered in class. However, they were unable to explain the steps in their solutions and when given similar problems on exams they performed very poorly. I became suspicious that these students were submitting homework solutions that were not their own, and a quick Internet search confirmed my fears. These students had been plagiarizing their homework assignments from a website called Cramster (www.cramster.com). In this article I would like to discuss the website, what some of my previous students and fellow educators think about it, and also consider whether or not Cramster could be useful in helping students learn physics.

• Communicating physics and the design of textbooks

  NASA Astrophysics Data System (ADS)

  Barojas, J.; Trigueros, M.

  1991-05-01

  The cognitive domains of a communication scheme for learning physics are related to a framework based on epistemology, and the planning of an introductory calculus textbook in classical mechanics is shown as an example of application.

• The Physics Learning Program at the University of Wisconsin-Madison

  NASA Astrophysics Data System (ADS)

  Nossal, S. M.; Watson, L.; Huesmann, A.; Jacob, A.; Fretz, J.; Clarke, M.

  2006-05-01

  The Physics Learning Program at the University of Wisconsin-Madison provides a supportive learning environment for students studying physics. We pair staff and upper level physics and secondary science education majors in small study groups with students studying introductory physics. Approximately 33-50% of our students are from racial and ethnic groups underrepresented in the sciences. In addition, students participating in our program include others who may be feeling isolated such as first-generation college students, returning adults, students with disabilities, international students, and students from small rural schools; as well as students with weak math and physics preparation and/or who are struggling with the course. The Physics Learning Program is run in conjunction with similar programs for chemistry and biochemistry. During the past year with a move to a new building we obtained a dedicated space for the Physics Learning Program, facilitating students to form their own study groups. We also began a pilot program for students in the calculus-based physics sequence. We will discuss these additions, as well as recruitment, pedagogy, teacher training, and mentoring practices that we use with the aim of creating an inclusive learning environment.

The effect of attending tutoring on course grades in Calculus I

NASA Astrophysics Data System (ADS)

Rickard, Brian; Mills, Melissa

2018-04-01

Tutoring centres are common in universities in the United States, but there are few published studies that statistically examine the effects of tutoring on student success. This study utilizes multiple regression analysis to model the effect of tutoring attendance on final course grades in Calculus I. Our model predicted that every three visits to the tutoring centre is correlated with an increase of a students' course grade by one per cent, after controlling for prior academic ability. We also found that for lower-achieving students, attending tutoring had a greater impact on final grades.

Challenges in assessing college students' conception of duality: the case of infinity

NASA Astrophysics Data System (ADS)

Babarinsa-Ochiedike, Grace Olutayo

Interpreting students' views of infinity posits a challenge for researchers due to the dynamic nature of the conception. There is diversity and variation among students' process-object perceptions. The fluctuations between students' views however reveal an undeveloped duality conception. This study examined college students' conception of duality in understanding and representing infinity with the intent to design strategies that could guide researchers in categorizing students' views of infinity into different levels. Data for the study were collected from N=238 college students enrolled in Calculus sequence courses (Pre-Calculus, Calculus I through Calculus III) at one of the southwestern universities in the U.S. using self-report questionnaires and semi-structured individual task-based interviews. Data was triangulated using multiple measures analyzed by three independent experts using self-designed coding sheets to assess students' externalization of the duality conception of infinity. Results of this study reveal that college students' experiences in traditional Calculus sequence courses are not supportive of the development of duality conception. On the contrary, it strengthens the singularity perspective on fundamental ideas of mathematics such as infinity. The study also found that coding and assessing college students' conception of duality is a challenging and complex process due to the dynamic nature of the conception that is task-dependent and context-dependent. Practical significance of the study is that it helps to recognize misconceptions and starts addressing them so students will have a more comprehensive view of fundamental mathematical ideas as they progress through the Calculus coursework sequence. The developed duality concept development framework called Action-Process-Object-Duality (APOD) adapted from the APOS theory could guide educators and researchers as they engage in assessing students' conception of duality. The results of this study could serve as a facilitating instrument to further analyze cognitive obstacles in college students' understanding of the infinity concept.

Workshop Physics Activity Guide, Module 2: Mechanics II, Momentum, Energy, Rotational and Harmonic Motion, and Chaos (Units 8 - 15)

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research. The Workshop Physics Activity Guide is supported by an Instructor's Website that: (1) describes the history and philosophy of the Workshop Physics Project; (2) provides advice on how to integrate the Guide into a variety of educational settings; (3) provides information on computer tools (hardware and software) and apparatus; and (4) includes suggested homework assignments for each unit. Log on to the Workshop Physics Project website at http://physics.dickinson.edu/ Workshop Physics is a component of the Physics Suite--a collection of materials created by a group of educational reformers known as the Activity Based Physics Group. The Physics Suite contains a broad array of curricular materials that are based on physics education research, including:

Understanding Physics, by Cummings, Laws, Redish and Cooney (an introductory textbook based on the best-selling text by Halliday/Resnick/Walker) RealTime Physics Laboratory Modules Physics by Inquiry (intended for use in a workshop setting) Interactive Lecture Demonstration Tutorials in Introductory Physics Activity Based Tutorials (designed primarily for use in recitations)

• The Legendre transform in geometric calculus

  NASA Astrophysics Data System (ADS)

  McClellan, Gene E.

  2013-10-01

  This paper explores the extension of the Legendre transform from scalar calculus to geometric calculus. In physics, the Legendre transform provides a change of variables to express equations of motion or other physical relationships in terms of the most convenient dynamical quantities for a given experimental or theoretical analysis. In classical mechanics and in field theory, the Legendre transform generates the Hamiltonian function of a system from the Lagrangian function or vice versa. In thermodynamics, the Legendre transform allows thermodynamic relationships to be written in terms of alternative sets of independent variables. In this paper, we review the properties of the Legendre transform in scalar calculus and show how an analogous transformation with similar properties may be constructed in geometric calculus.

• Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

  ERIC Educational Resources Information Center

  Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

  2016-01-01

  The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

• Using assessments to investigate and compare the nature of learning in undergraduate science courses.

  PubMed

  Momsen, Jennifer; Offerdahl, Erika; Kryjevskaia, Mila; Montplaisir, Lisa; Anderson, Elizabeth; Grosz, Nate

  2013-06-01

  Assessments and student expectations can drive learning: students selectively study and learn the content and skills they believe critical to passing an exam in a given subject. Evaluating the nature of assessments in undergraduate science education can, therefore, provide substantial insight into student learning. We characterized and compared the cognitive skills routinely assessed by introductory biology and calculus-based physics sequences, using the cognitive domain of Bloom's taxonomy of educational objectives. Our results indicate that both introductory sequences overwhelmingly assess lower-order cognitive skills (e.g., knowledge recall, algorithmic problem solving), but the distribution of items across cognitive skill levels differs between introductory biology and physics, which reflects and may even reinforce student perceptions typical of those courses: biology is memorization, and physics is solving problems. We also probed the relationship between level of difficulty of exam questions, as measured by student performance and cognitive skill level as measured by Bloom's taxonomy. Our analyses of both disciplines do not indicate the presence of a strong relationship. Thus, regardless of discipline, more cognitively demanding tasks do not necessarily equate to increased difficulty. We recognize the limitations associated with this approach; however, we believe this research underscores the utility of evaluating the nature of our assessments.

• Using Assessments to Investigate and Compare the Nature of Learning in Undergraduate Science Courses

  PubMed Central

  Momsen, Jennifer; Offerdahl, Erika; Kryjevskaia, Mila; Montplaisir, Lisa; Anderson, Elizabeth; Grosz, Nate

  2013-01-01

  Assessments and student expectations can drive learning: students selectively study and learn the content and skills they believe critical to passing an exam in a given subject. Evaluating the nature of assessments in undergraduate science education can, therefore, provide substantial insight into student learning. We characterized and compared the cognitive skills routinely assessed by introductory biology and calculus-based physics sequences, using the cognitive domain of Bloom's taxonomy of educational objectives. Our results indicate that both introductory sequences overwhelmingly assess lower-order cognitive skills (e.g., knowledge recall, algorithmic problem solving), but the distribution of items across cognitive skill levels differs between introductory biology and physics, which reflects and may even reinforce student perceptions typical of those courses: biology is memorization, and physics is solving problems. We also probed the relationship between level of difficulty of exam questions, as measured by student performance and cognitive skill level as measured by Bloom's taxonomy. Our analyses of both disciplines do not indicate the presence of a strong relationship. Thus, regardless of discipline, more cognitively demanding tasks do not necessarily equate to increased difficulty. We recognize the limitations associated with this approach; however, we believe this research underscores the utility of evaluating the nature of our assessments. PMID:23737631

• Evaluating learning and teaching using the Force Concept Inventory

  NASA Astrophysics Data System (ADS)

  Zitzewitz, Paul

  1997-04-01

  Teaching methods used in the calculus-based mechanics course for engineers and scientists (P150) at the University of Michigan-Dearborn were markedly changed in September, 1996. Lectures emphasize active learning with Mazur's ConcepTests, Sokoloff's Interactive Demonstrations, and Van Heuvelen's ALPS Kit worksheets. Students solve context-rich problems using Van Heuvelen's multiple representation format in cooperative groups in discussion sections. Labs were changed to use MBL emphasizing concepts and Experiment Problems to learn lab-based problem solving. Pre- and post-testing of 400 students with the Force Concept Inventory has demonstrated considerable success. The average increase in score has been 35-45methods as defined by Hake. The methods and results will be discussed. Detailed analyses of the FCI results will look at success in teaching specific concepts and the effect of student preparation in mathematics and high school physics.

• Secondary implementation of interactive engagement teaching techniques: Choices and challenges in a Gulf Arab context

  NASA Astrophysics Data System (ADS)

  Hitt, G. W.; Isakovic, A. F.; Fawwaz, O.; Bawa'aneh, M. S.; El-Kork, N.; Makkiyil, S.; Qattan, I. A.

  2014-12-01

  We report on efforts to design the "Collaborative Workshop Physics" (CWP) instructional strategy to deliver the first interactive engagement (IE) physics course at Khalifa University of Science, Technology and Research (KU), United Arab Emirates (UAE). To our knowledge, this work reports the first calculus-based, introductory mechanics course on the Arabian Peninsula using physics education research (PER)-based instruction. A brief history and present context of general university and STEM teaching in the UAE is given. We present this secondary implementation (SI) as a case study of a novel context and use it to determine if PER-based instruction can be successfully implemented far from the cultural context of the primary developer and, if so, how might such SIs differ from SIs within the United States (U.S.) in terms of criteria for and risks to their success. With these questions in view, a prereform baseline comprised of Maryland Physics Expectations in Physics survey, Force Concept Inventory (FCI), course exam grades, and English language proficiency data are used to design a hybrid implementation of Cooperative Group Problem Solving. We find that for students with high English proficiency, normalized gain on FCI improves substantially, from ⟨g⟩=0.16±0.10 prereform to ⟨g⟩=0.47±0.08 in the CWP pilot (standard errors), indicating a successful SI. However, we also find evidence that normalized gains on FCI are strongly modulated by language proficiency and discuss likely causes. Regardless of language ability, problem-solving skill is also substantially improved and course drop-fail-withdrawal rates are cut from 50% to 24%. In particular, we find evidence in postreform student interviews that prior classroom experiences, and not broader cultural expectations about education, are the more significant cause of expectations that are at odds with the classroom norms of well-functioning PER-based instruction. We present this result as evidence that PER-based innovations can be implemented across great changes in cultural context, provided that the method is thoughtfully adapted in anticipation of context and culture-specific student expectations. This case study should be valuable for future reforms at KU, the broader Gulf region, and other institutions facing similar challenges involving SI of PER-based instruction outside the U.S.

• Active Learning in a Math for Liberal Arts Classroom

  ERIC Educational Resources Information Center

  Lenz, Laurie

  2015-01-01

  Inquiry-based learning is a topic of growing interest in the mathematical community. Much of the focus has been on using these methods in calculus and higher-level classes. This article describes the design and implementation of a set of inquiry-based learning activities in a Math for Liberal Arts course at a small, private, Catholic college.…

• Building an Understanding of Functions: A Series of Activities for Pre-Calculus

  ERIC Educational Resources Information Center

  Carducci, Olivia M.

  2008-01-01

  Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.

• Teaching Calculus Students How to Study.

  ERIC Educational Resources Information Center

  Boelkins, Matthew R.; Pfaff, Thomas J.

  1998-01-01

  Addresses the problem of poor study habits in calculus students and presents techniques to teach students how to study consistently and effectively. Concludes that many students greatly appreciate the added structure, work harder than in previous courses, and witness newfound success as a consequence. (Author/ASK)

• Primary Vaginal Calculus in a Woman with Disability: Case Report and Literature Review.

  PubMed

  Castellan, Pietro; Nicolai, Michele; De Francesco, Piergustavo; Di Tizio, Luciano; Castellucci, Roberto; Bada, Maida; Marchioni, Michele; Cindolo, Luca; Schips, Luigi

  2017-01-01

  Background: Vaginal stones are rare and often unknown entities. Most urologists may never see a case in their careers. Case Presentation: We present the case of a 34-year-old bedridden Caucasian woman with mental and physical disabilities who presented with a large primary vaginal calculus, which, surprisingly, had remained undiagnosed until the patient suffered a right renal colic caused by a ureteral stone. The vagina was completely filled and a digital examination was not possible. For this reason, the stone was removed using surgical pliers with some maneuvering. A vesicovaginal fistula was excluded, as well as foreign bodies or other nidi of infection. After, urethral lithotripsy was performed as planned. The postoperative course and follow-up were uneventful. Conclusion: Although vaginal calculi are extremely rare in literature, their differential diagnosis should be considered in women with incontinence and associated disabilities, paraplegia, or prolonged immobilization in recumbent position.

• The Quantitative Preparation of Future Geoscience Graduate Students

  NASA Astrophysics Data System (ADS)

  Manduca, C. A.; Hancock, G. S.

  2006-12-01

  Modern geoscience is a highly quantitative science. In February, a small group of faculty and graduate students from across the country met to discuss the quantitative preparation of geoscience majors for graduate school. The group included ten faculty supervising graduate students in quantitative areas spanning the earth, atmosphere, and ocean sciences; five current graduate students in these areas; and five faculty teaching undergraduate students in the spectrum of institutions preparing students for graduate work. Discussion focused in four key ares: Are incoming graduate students adequately prepared for the quantitative aspects of graduate geoscience programs? What are the essential quantitative skills are that are required for success in graduate school? What are perceived as the important courses to prepare students for the quantitative aspects of graduate school? What programs/resources would be valuable in helping faculty/departments improve the quantitative preparation of students? The participants concluded that strengthening the quantitative preparation of undergraduate geoscience majors would increase their opportunities in graduate school. While specifics differed amongst disciplines, a special importance was placed on developing the ability to use quantitative skills to solve geoscience problems. This requires the ability to pose problems so they can be addressed quantitatively, understand the relationship between quantitative concepts and physical representations, visualize mathematics, test the reasonableness of quantitative results, creatively move forward from existing models/techniques/approaches, and move between quantitative and verbal descriptions. A list of important quantitative competencies desirable in incoming graduate students includes mechanical skills in basic mathematics, functions, multi-variate analysis, statistics and calculus, as well as skills in logical analysis and the ability to learn independently in quantitative ways. Calculus, calculus-based physics, chemistry, statistics, programming and linear algebra were viewed as important course preparation for a successful graduate experience. A set of recommendations for departments and for new community resources includes ideas for infusing quantitative reasoning throughout the undergraduate experience and mechanisms for learning from successful experiments in both geoscience and mathematics. A full list of participants, summaries of the meeting discussion and recommendations are available at http://serc.carleton.edu/quantskills/winter06/index.html. These documents, crafted by a small but diverse group can serve as a starting point for broader community discussion of the quantitative preparation of future geoscience graduate students.

• a Speculative Study on Negative-Dimensional Potential and Wave Problems by Implicit Calculus Modeling Approach

  NASA Astrophysics Data System (ADS)

  Chen, Wen; Wang, Fajie

  Based on the implicit calculus equation modeling approach, this paper proposes a speculative concept of the potential and wave operators on negative dimensionality. Unlike the standard partial differential equation (PDE) modeling, the implicit calculus modeling approach does not require the explicit expression of the PDE governing equation. Instead the fundamental solution of physical problem is used to implicitly define the differential operator and to implement simulation in conjunction with the appropriate boundary conditions. In this study, we conjecture an extension of the fundamental solution of the standard Laplace and Helmholtz equations to negative dimensionality. And then by using the singular boundary method, a recent boundary discretization technique, we investigate the potential and wave problems using the fundamental solution on negative dimensionality. Numerical experiments reveal that the physics behaviors on negative dimensionality may differ on positive dimensionality. This speculative study might open an unexplored territory in research.

• Flipping Freshman Mathematics

  ERIC Educational Resources Information Center

  Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen

  2015-01-01

  Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…

• Mathematics for the New Millennium

  ERIC Educational Resources Information Center

  Gordon, Sheldon P.

  2004-01-01

  Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…

• An Investigation of Factors Affecting the Degree of Naïve Impetus Theory Application

  NASA Astrophysics Data System (ADS)

  Liu, Xiufeng; MacIsaac, Dan

  2005-03-01

  This study investigates factors affecting the degree of novice physics students' application of the naïve impetus theory. Six hundred and fourteen first-year university engineering physics students answered the Force Concept Inventory as a pre-test for their calculus-based course. We examined the degree to which students consistently applied the naïve impetus theory across different items. We used a 2-way repeated measures ANOVA and linear regression to analyze data coded from incorrect student responses. It was found that there were statistically significant main effects for item familiarity and item requirement for explanation vs. prediction on the measured degree of impetus theory application. Student course grades had no significant effect on impetus theory application. When faced with items that were unfamiliar and predictive, students appeared to rely on non-theoretical, knowledge-in-pieces reasoning. Reasoning characteristic of naïve theories was more frequently applied when students were completing familiar problem tasks that required explanation. When considering all the above factors simultaneously, we found that the degree of naïve impetus theory application by students is attributable to variables in the following order: familiarity, prediction, and explanation.

• Learner-Centered Teaching and Improving Learning by Writing Down the Statement of Problems in an Introductory Physics Course

  NASA Astrophysics Data System (ADS)

  Aurora, Tarlok

  2005-04-01

  In a calculus-based introductory physics course, students were assigned to write the statements of word problems (along with the accompanying diagrams if any), analyze these, identify important concepts/equations and try to solve these end-of- chapter homework problems. They were required to bring to class their written assignment until the chapter was completed in lecture. These were quickly checked at the beginning of the class. In addition, re-doing selected solved examples in the textbook were assigned as homework. Where possible, students were asked to look for similarities between the solved-examples and the end-of-the-chapter problems, or occasionally these were brought to the students' attention. It was observed that many students were able to solve several of the solved-examples on the test even though the instructor had not solved these in class. This was seen as an improvement over the previous years. It made the students more responsible for their learning. Another benefit was that it alleviated the problems previously created by many students not bringing the textbooks to class. It allowed more time for problem solving/discussions in class.

• Mathematics Placement at the University of Illinois

  ERIC Educational Resources Information Center

  Ahlgren Reddy, Alison; Harper, Marc

  2013-01-01

  Data from the ALEKS-based placement program at the University of Illinois is presented visually in several ways. The placement exam (an ALEKS assessment) contains precise item-specific information and the data show many interesting properties of the student populations of the placement courses, which include Precalculus, Calculus, and Business…

How to Teach Hicksian Compensation and Duality Using a Spreadsheet Optimizer

ERIC Educational Resources Information Center

Ghosh, Satyajit; Ghosh, Sarah

2007-01-01

Principle of duality and numerical calculation of income and substitution effects under Hicksian Compensation are often left out of intermediate microeconomics courses because they require a rigorous calculus based analysis. But these topics are critically important for understanding consumer behavior. In this paper we use excel solver--a…

Visualizing Volume to Help Students Understand the Disk Method on Calculus Integral Course

NASA Astrophysics Data System (ADS)

Tasman, F.; Ahmad, D.

2018-04-01

Many research shown that students have difficulty in understanding the concepts of integral calculus. Therefore this research is interested in designing a classroom activity integrated with design research method to assist students in understanding the integrals concept especially in calculating the volume of rotary objects using disc method. In order to support student development in understanding integral concepts, this research tries to use realistic mathematical approach by integrating geogebra software. First year university student who takes a calculus course (approximately 30 people) was chosen to implement the classroom activity that has been designed. The results of retrospective analysis show that visualizing volume of rotary objects using geogebra software can assist the student in understanding the disc method as one way of calculating the volume of a rotary object.

Fractional kinetics of compartmental systems: first approach with use digraph-based method

NASA Astrophysics Data System (ADS)

Markowski, Konrad Andrzej

2017-08-01

In the last two decades, integral and differential calculus of a fractional order has become a subject of great interest in different areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned in 1695 by Leibniz and L'Hospital. The first definition of the fractional derivative was introduced by Liouville and Riemann at the end of the 19th century. Fractional calculus was found to be a very useful tool for modelling the behaviour of many materials and systems. In this paper fractional calculus was applied to pharmacokinetic compartmental model. For introduced model determine all possible quasi-positive realisation based on one-dimensional digraph theory. The proposed method was discussed and illustrated in detail with some numerical examples.

The Negative Sign and Exponential Expressions: Unveiling Students' Persistent Errors and Misconceptions

ERIC Educational Resources Information Center

Cangelosi, Richard; Madrid, Silvia; Cooper, Sandra; Olson, Jo; Hartter, Beverly

2013-01-01

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential…

A Graphical Introduction to the Derivative

ERIC Educational Resources Information Center

Samuels, Jason

2017-01-01

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

Using Matlab in a Multivariable Calculus Course.

ERIC Educational Resources Information Center

Schlatter, Mark D.

The benefits of high-level mathematics packages such as Matlab include both a computer algebra system and the ability to provide students with concrete visual examples. This paper discusses how both capabilities of Matlab were used in a multivariate calculus class. Graphical user interfaces which display three-dimensional surfaces, contour plots,…

Self-Paced Calculus: A Case Study.

ERIC Educational Resources Information Center

Johnson, Guy, Jr.; Pascarella, Ernest T.

Increasingly higher education is confronted with the task of educating a population of students whose entry aptitudes and skills have grown more heterogeneous. Perhaps nowhere is this diversity of abilities more apparent, and at the same time more difficult to deal with, than in courses in introductory calculus. This paper outlines an experimental…

Writing-to-Learn Activities to Provoke Deeper Learning in Calculus

ERIC Educational Resources Information Center

Jaafar, Reem

2016-01-01

For students with little experience in mathematical thinking and conceptualization, writing-to-learn activities (WTL) can be particularly effective in promoting discovery and understanding. For community college students embarking on a first calculus course in particular, writing activities can help facilitate the transition from an "apply…

The Pendulum and the Calculus.

ERIC Educational Resources Information Center

Sworder, Steven C.

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

Flipping the Calculus Classroom: A Cost-Effective Approach

ERIC Educational Resources Information Center

Young, Andrea

2015-01-01

This article discusses a cost-effective approach to flipping the calculus classroom. In particular, the emphasis is on low-cost choices, both monetarily and with regards to faculty time, that make the daunting task of flipping a course manageable for a single instructor. Student feedback and overall impressions are also presented.

Formalization of the Integral Calculus in the PVS Theorem Prover

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

2004-01-01

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

Motivating Calculus-Based Kinematics Instruction with Super Mario Bros

ERIC Educational Resources Information Center

Nordine, Jeffrey C.

2011-01-01

High-quality physics instruction is contextualized, motivates students to learn, and represents the discipline as a way of investigating the world rather than as a collection of facts and equations. Inquiry-oriented pedagogy, such as problem-based instruction, holds great promise for both teaching physics content and representing the process of…

A quantitative analysis of the relationship between an online homework system and student achievement in pre-calculus

NASA Astrophysics Data System (ADS)

Babaali, Parisa; Gonzalez, Lidia

2015-07-01

Supporting student success in entry-level mathematics courses at the undergraduate level has and continues to be a challenge. Recently we have seen an increased reliance on technological supports including software to supplement more traditional in-class instruction. In this paper, we explore the effects on student performance of the use of a computer software program to supplement instruction in an entry-level mathematics course at the undergraduate level, specifically, a pre-calculus course. Relying on data from multiple sections of the course over various semesters, we compare student performance in those classes utilizing the software against those in which it was not used. Quantitative analysis of the data then leads us to conclusions about the effectiveness of the software as well as recommendations for future iterations of the course and others like it.

Physical Chemistry for the Chemical and Biological Sciences (by Raymond Chang)

NASA Astrophysics Data System (ADS)

Pounds, Andrew

2001-05-01

This book does offer an alternative approach to physical chemistry that is particularly well suited for those who want to pursue a course of study more focused on the biological sciences. It could also be an excellent choice for schools that mainly serve preprofessional programs or for schools that have split physical chemistry tracks to independently serve the B.S. and B.A. degrees. Since the book focuses on single-variable mathematics, schools that require only one year of calculus for their chemistry degree could also think about adopting it. However, in general, the use of the text as a drop-in replacement for physical chemistry for the B.S. degree is questionable owing to its lack of focus on quantum mechanics and its implications for spectroscopy.

Implementation of Scientific Community Laboratories and Their Effect on Student Conceptual Learning, Attitudes, and Understanding of Uncertainty

NASA Astrophysics Data System (ADS)

Lark, Adam

Scientific Community Laboratories, developed by The University of Maryland, have shown initial promise as laboratories meant to emulate the practice of doing physics. These laboratories have been re-created by incorporating their design elements with the University of Toledo course structure and resources. The laboratories have been titled the Scientific Learning Community (SLC) Laboratories. A comparative study between these SLC laboratories and the University of Toledo physics department's traditional laboratories was executed during the fall 2012 semester on first semester calculus-based physics students. Three tests were executed as pre-test and post-tests to capture the change in students' concept knowledge, attitudes, and understanding of uncertainty. The Force Concept Inventory (FCI) was used to evaluate students' conceptual changes through the semester and average normalized gains were compared between both traditional and SLC laboratories. The Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS) was conducted to elucidate students' change in attitudes through the course of each laboratory. Finally, interviews regarding data analysis and uncertainty were transcribed and coded to track changes in the way students understand uncertainty and data analysis in experimental physics after their participation in both laboratory type. Students in the SLC laboratories showed a notable an increase conceptual knowledge and attitudes when compared to traditional laboratories. SLC students' understanding of uncertainty showed most improvement, diverging completely from students in the traditional laboratories, who declined throughout the semester.

Alternative theoretical method for motion of a sand-filled funnel experiment

NASA Astrophysics Data System (ADS)

Byrd, David; White, Gary

2001-11-01

In "Motion of a Sand-Filled Funnel," Peter Sullivan and Anna McLoon described how to use numerical methods and a Microsoft Excel spreadsheet to predict the motion of a variant of Atwood's machine with variable mass. They wrote for noncalculus-based physics classes, but we solve the same problem using the methods of calculus. Our method highlights the less-familiar but more accurate version of Newton's second law, ∑F =dp/dt. This can help introductory physics students understand a broader definition of Newton's second law and enhance their calculus skills. It also teaches students how to solve a variable-mass problem.

Student ability to apply the concepts of work and energy to extended systems

NASA Astrophysics Data System (ADS)

Lindsey, Beth A.; Heron, Paula R. L.; Shaffer, Peter S.

2009-11-01

We report results from an investigation of student ability to apply the concepts of work and energy to situations in which the internal structure of a system cannot be ignored, that is, the system cannot be treated as a particle. Students in introductory calculus-based physics courses were asked written and online questions after relevant instruction by lectures, textbook, and laboratory. Several difficulties were identified. Some related to student ability to calculate the work done on a system. Failure to associate work with the change in energy of a system was also widespread. The results have implications for instruction that aims for a rigorous treatment of energy concepts that is consistent with the first law of thermodynamics. The findings are guiding the development of two tutorials to supplement instruction.

Math 3320--Technical Mathematics II.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for a college pre-calculus course designed as the second course in a two-semester sequence for students in a Bachelor of Technology program. The course emphasizes applications from technology and verbal problems. Topics include trigonometric functions; identities;…

Relationships between Undergraduates' Argumentation Skills, Conceptual Quality of Problem Solutions, and Problem Solving Strategies in Introductory Physics

ERIC Educational Resources Information Center

Rebello, Carina M.

2012-01-01

This study explored the effects of alternative forms of argumentation on undergraduates' physics solutions in introductory calculus-based physics. A two-phase concurrent mixed methods design was employed to investigate relationships between undergraduates' written argumentation abilities, conceptual quality of problem solutions, as well…

Tale of Two Curricula: The Performance of 2000 Students in Introductory Electromagnetism

ERIC Educational Resources Information Center

Kohlmyer, Matthew A.; Caballero, Marcos D.; Catrambone, Richard; Chabay, Ruth W.; Ding, Lin; Haugan, Mark P.; Marr, M. Jackson; Sherwood, Bruce A.; Schatz, Michael F.

2009-01-01

The performance of over 2000 students in introductory calculus-based electromagnetism (E&M) courses at four large research universities was measured using the Brief Electricity and Magnetism Assessment (BEMA). Two different curricula were used at these universities: a traditional E&M curriculum and the Matter & Interactions (M&I)…

Gender Differences in STEM Related Advanced Placement Exams

ERIC Educational Resources Information Center

Morris, Jill B.

2013-01-01

Purpose: The purpose of this study was to examine differences between boys and girls in their performance on STEM related AP exams. Specifically, gender differences were examined for the following STEM related AP exams: Calculus AB, Calculus BC, Physics B, Physics C: Electricity and Magnetism, Physics C: Mechanics, Chemistry, and Computer Science…

A Comparative Study of Definitions on Limit and Continuity of Functions

ERIC Educational Resources Information Center

Shipman, Barbara A.

2012-01-01

Differences in definitions of limit and continuity of functions as treated in courses on calculus and in rigorous undergraduate analysis yield contradictory outcomes and unexpected language. There are results about limits in calculus that are false by the definitions of analysis, functions not continuous by one definition and continuous by…

Using Peer Instruction and I-Clickers to Enhance Student Participation in Calculus

ERIC Educational Resources Information Center

Lucas, Adam

2009-01-01

In my Calculus classes I encourage my students to actively reflect on course material, to work collaboratively, and to generate diverse solutions to questions. To facilitate this I use peer instruction (PI), a structured questioning process, and i-clickers, a radio frequency classroom response system enabling students to vote anonymously. This…

Engineering Students' Experiences of Interactive Teaching in Calculus

ERIC Educational Resources Information Center

Weurlander, Maria; Cronhjort, Mikael; Filipsson, Lars

2017-01-01

This study reports on an educational development initiative where peer instruction was used instead of traditional lectures in a calculus course for first-year engineering students. The aim of the study was to explore students' experiences of this method. Data were collected by means of an open-ended questionnaire on two occasions: early and late…

The Impact of Instructor Pedagogy on College Calculus Students' Attitude toward Mathematics

ERIC Educational Resources Information Center

Sonnert, Gerhard; Sadler, Philip M.; Sadler, Samuel M.; Bressoud, David M.

2015-01-01

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students' attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students'…

Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom

ERIC Educational Resources Information Center

de Castro, Christopher H.

2011-01-01

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

Reference Framework for Describing and Assessing Students' Understanding in First Year Calculus

ERIC Educational Resources Information Center

Kannemeyer, Larry

2005-01-01

This paper presents aspects of a study that investigates the development of an instrument, a reference framework, to analyse students' written responses to non-routine problems in a first year calculus course in order to describe the complexities of their understanding and to assess their understanding of particular mathematical concepts.…

Insights from the MAA National Study of College Calculus

ERIC Educational Resources Information Center

Bressoud, David

2015-01-01

Over the past five years, the Mathematical Association of America, with support from the National Science Foundation, has explored the teaching of mainstream Calculus 1 at the postsecondary level, where by "mainstream" we mean those courses that can be used as part of the prerequisite stream to more advanced postsecondary mathematics. We…

Bridging a Cultural Gap

ERIC Educational Resources Information Center

Leviatan, Talma

2008-01-01

There has been a broad wave of change in tertiary calculus courses in the past decade. However, the much-needed change in tertiary pre-calculus programmes--aimed at bridging the gap between high-school mathematics and tertiary mathematics--is happening at a far slower pace. Following a discussion on the nature of the gap and the objectives of a…

Multivariate Limits and Continuity: A Survey of Calculus Textbooks.

ERIC Educational Resources Information Center

Thompson, Thomas M.; Wiggins, Kenneth L.

There has been much recent discussion concerning the content of the standard calculus course for students majoring in mathematics and the sciences. Some of this discussion has focused on the available textbooks. One weakness noted in some of these books involves the definitions of limit and continuity for functions of several variables. A…

Families of linear recurrences for Catalan numbers

NASA Astrophysics Data System (ADS)

Gauthier, N.

2011-01-01

Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus and number theory.

From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

NASA Astrophysics Data System (ADS)

Reeves, Mark

2014-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

a Study of Women Engineering Students and Time to Completion of First-Year Required Courses at Texas A&M University

NASA Astrophysics Data System (ADS)

Kimball, Jorja; Cole, Bryan; Hobson, Margaret; Watson, Karan; Stanley, Christine

This paper reports findings on gender that were part of a larger study reviewing time to completion of course work that includes the first two semesters of calculus, chemistry, and physics, which are often considered the stumbling points or "barrier courses" to an engineering baccalaureate degree. Texas A&M University terms these courses core body of knowledge (CBK), and statistical analysis was conducted on two cohorts of first-year enrolling engineering students at the institution. Findings indicate that gender is statistically significantly related to completion of CBK with female engineering students completing required courses faster than males at the .01 level (p = 0.008). Statistical significance for gender and ethnicity was found between white male and white female students at the .01 level (p = 0.008). Descriptive analysis indicated that of the five majors studied (chemical, civil, computer, electrical, and mechanical engineering), women completed CBK faster than men, and African American and Hispanic women completed CBK faster than males of the same ethnicity.

Lunatics in Introductory Physics: Using Collectivized Student Moon Position Observations To Teach Basic Orbital Mechanics In Calculus Based Introductory Physics.

NASA Astrophysics Data System (ADS)

Bottorff, Mark

2012-01-01

A large (74 student) calculus based physics class was required to make observations of the moon over two lunar cycles using a small telescope equipped with mechanical setting circles. The data was collectivized and then analyzed in the laboratory to determine the period of the moon and to search for evidence of the eccentricity of the moon's orbit. These results were used in conjunction with the simple pendulum experiment in which the students inferred the acceleration due to gravity. The student inferred lunar orbital period and acceleration due to gravity (augmented with the radius of the Earth) enabled the students to infer the average Earth to moon distance. Class lectures, activities, and homework on gravitation and orbits were tailored to this observational activity thereby forming a learning module. A basic physics and orbital mechanics knowledge questionnaire was administered before and after the learning module. The resulting learning gains are reported here.

Coordinating an IPLS class with a biology curriculum: NEXUS/Physics

NASA Astrophysics Data System (ADS)

Redish, Edward

2014-03-01

A multi-disciplinary team of scientists has been reinventing the Introductory Physics for Life Scientists (IPLS) course at the University of Maryland. We focus on physics that connects elements common to the curriculum for all life scientists - molecular and cellular biology - with building general scientific competencies, such as mathematical modeling, reasoning from core principles, and multi-representation translation. The prerequisites for the class include calculus, chemistry, and biology. In addition to building the basic ideas of the Newtonian framework, electric currents, and optics, our prerequisites allow us to include topics such as atomic interactions and chemical bonding, random motion and diffusion, thermodynamics (including entropy and free energy), and spectroscopy. Our chemical bonding unit helps students link the view of energy developed in traditional macroscopic physics with the idea of chemical bonding as a source of energy presented in their chemistry and biology classes. Education research has played a central role in our design, as has a strong collaboration between our Discipline-Based Education and the Biophysics Research groups. These elements permit us to combine modern pedagogy with cutting-edge insights into the physics of living systems. Supported in part by a grant from HHMI and the US NSF grant #1122818/.

BOOK REVIEW: Physics for Scientists and Engineers Third Edition

NASA Astrophysics Data System (ADS)

Giancoli, Douglas C.

2000-09-01

There are a large number of textbooks for the college and university student produced in the USA and here is one that I had not seen before even though it is now in the third edition. But it is so similar to many others. The standard version as reviewed here covers the usual topics of classical physics, namely kinematics, energy, waves and oscillations, thermodynamics, electricity and magnetism and light. Also, as is usual with the American coverage, it includes fluids, special relativity and a short chapter on quantum theory and the atom. An extended version is available covering modern physics, astrophysics and cosmology. There is also available back-up material such as instructor's manual, CD-ROM, video and other extra teaching material Full colour is used and the book is lavishly illustrated with diagrams and photographs. Calculus is used throughout the book, although this is limited to basic differentiation and integration. There is an extensive range of worked examples plus end-of-chapter questions and problems, with numerical answers given to the odd-numbered problems. The physics is illustrated with many everyday examples. The styles of course presentation and hence the styles of book used in the USA and the UK seem to be diverging. It is unlikely such a book as this would be used at A-level. This is not only because of the calculus, albeit simple, but because of the detailed coverage of classical topics. Increasingly there has been a trend in this country to be more selective in content, and yet at the same time to incorporate more modern topics such as solids, environmental and atmospheric physics, particle physics and cosmology, but described in a fairly elementary way. The book would be suitable for preliminary year and first-year university physics courses but its size and weight are daunting. I am not sure why physics described in such an encyclopaedic way is popular in the US but less so here. However, of its type this book is both attractive and comprehensive. David Lovett

A cross-national study of calculus

NASA Astrophysics Data System (ADS)

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-05-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan students showed a larger gain and normalized gain, and hence narrowed the gap. ECNU's superior performance was especially striking on the subset of problems requiring only a pre-calculus background. On those, Michigan's post-test scores were below ECNU's pre-test scores and, indeed, ECNU's higher performance on both the overall pre-test and overall post-test is attributable to its success on these problems.

Math 3310--Technical Mathematics I. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for a college pre-calculus designed as the first course in a two-semester sequence for students in a Bachelor of Technology program. The course emphasizes engineering technology applications and verbal problems. Topics include a review of elementary algebra; factoring…

Weeded Out? Gendered Responses to Failing Calculus.

PubMed

Sanabria, Tanya; Penner, Andrew

2017-06-01

Although women graduate from college at higher rates than men, they remain underrepresented in science, technology, engineering, and mathematics (STEM) fields. This study examines whether women react to failing a STEM weed-out course by switching to a non-STEM major and graduating with a bachelor's degree in a non-STEM field. While competitive courses designed to weed out potential STEM majors are often invoked in discussions around why students exit the STEM pipeline, relatively little is known about how women and men react to failing these courses. We use detailed individual-level data from the National Educational Longitudinal Study (NELS) Postsecondary Transcript Study (PETS): 1988-2000 to show that women who failed an introductory calculus course are substantially less likely to earn a bachelor's degree in STEM. In doing so, we provide evidence that weed-out course failure might help us to better understand why women are less likely to earn degrees.

Weeded Out? Gendered Responses to Failing Calculus

PubMed Central

Sanabria, Tanya; Penner, Andrew

2018-01-01

Although women graduate from college at higher rates than men, they remain underrepresented in science, technology, engineering, and mathematics (STEM) fields. This study examines whether women react to failing a STEM weed-out course by switching to a non-STEM major and graduating with a bachelor’s degree in a non-STEM field. While competitive courses designed to weed out potential STEM majors are often invoked in discussions around why students exit the STEM pipeline, relatively little is known about how women and men react to failing these courses. We use detailed individual-level data from the National Educational Longitudinal Study (NELS) Postsecondary Transcript Study (PETS): 1988–2000 to show that women who failed an introductory calculus course are substantially less likely to earn a bachelor’s degree in STEM. In doing so, we provide evidence that weed-out course failure might help us to better understand why women are less likely to earn degrees. PMID:29616148

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

PubMed

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

An investigation of student understanding of wave phenomena at a boundary as a guide to the development and assessment of instructional materials on mechanical waves

NASA Astrophysics Data System (ADS)

Kryjevskaia, Lioudmila N.

This dissertation reports on an in-depth investigation of student understanding of wave phenomena at a boundary. The research and curriculum development were conducted in the contexts of the introductory calculus-based physics course and special courses for preservice and inservice teachers. Research methods included pretests, post-tests, and informal observations and discussions with students. Several student difficulties with wave behavior at a boundary and the cause and effect relationship between wavelength, frequency, and propagation speed were identified. The results from this investigation have guided the development of two sets of instructional materials designed to address the conceptual and reasoning difficulties that were identified. The first is a sequence of tutorials intended to supplement standard lecture and laboratory instruction on mechanical waves in a traditional introductory course. The second consists of a module on mechanical waves designed for use in inquiry-oriented courses for preservice and inservice teachers. Ongoing assessment of both sets of materials indicates that they are effective in addressing many of the student difficulties that were found to be persistent. Such difficulties, when not addressed, may hinder student understanding of more advanced topics such as interference and diffraction of waves.

Student effort expectations and their learning in first-year introductory physics: A case study in Thailand

NASA Astrophysics Data System (ADS)

Wutchana, U.; Emarat, N.

2011-06-01

The Maryland Physics Expectations (MPEX) survey was designed to probe students’ expectations about their understanding of the process of learning physics and the structure of physics knowledge—cognitive expectations. This survey was administered to first-year university students in Thailand in the first semester of an introductory calculus-based physics course during academic years 2007 and 2008, to assess their expectations at the beginning of the course. The precourse MPEX results were compared and correlated with two separate measures of student learning: (1) individual students’ normalized gains from pre and post Force and Motion Conceptual Evaluation (FMCE) results, which measure students’ conceptual understanding, and (2) student’s scores on the final exam, which measure their more general problem-solving ability. The results showed a significant positive correlation between their overall MPEX score and five of the six MPEX cluster scores, with their normalized learning gains on the FMCE for both academic years. The results also showed significant positive correlations between student MPEX scores and their final exam scores for the overall MPEX score and all MPEX cluster scores except for the effort cluster. We interviewed two groups of five students each, one group with small favorable scores on the precourse MPEX effort cluster and one with high favorable scores on the precourse MPEX effort cluster, to see how the students’ learning efforts compared with their MPEX results. We concluded from the interviews that what the students think or expect about the MPEX effort involved in learning physics does not match what they actually do.

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Internet computer coaches for introductory physics problem solving

NASA Astrophysics Data System (ADS)

Xu Ryan, Qing

The ability to solve problems in a variety of contexts is becoming increasingly important in our rapidly changing technological society. Problem-solving is a complex process that is important for everyday life and crucial for learning physics. Although there is a great deal of effort to improve student problem solving skills throughout the educational system, national studies have shown that the majority of students emerge from such courses having made little progress toward developing good problem-solving skills. The Physics Education Research Group at the University of Minnesota has been developing Internet computer coaches to help students become more expert-like problem solvers. During the Fall 2011 and Spring 2013 semesters, the coaches were introduced into large sections (200+ students) of the calculus based introductory mechanics course at the University of Minnesota. This dissertation, will address the research background of the project, including the pedagogical design of the coaches and the assessment of problem solving. The methodological framework of conducting experiments will be explained. The data collected from the large-scale experimental studies will be discussed from the following aspects: the usage and usability of these coaches; the usefulness perceived by students; and the usefulness measured by final exam and problem solving rubric. It will also address the implications drawn from this study, including using this data to direct future coach design and difficulties in conducting authentic assessment of problem-solving.

Primary vaginal calculus in a middle-aged woman with mental and physical disabilities.

PubMed

Ikeda, Yuji; Oda, Katsutoshi; Matsuzawa, Naoki; Shimizu, Ken

2013-07-01

Vaginal calculi are rarely encountered and are often misdiagnosed as bladder calculi because of the difficulty in achieving an appropriate diagnosis. Most vaginal calculi result from the presence of a urethrovaginal fistula; those occurring in the absence of such fistulas are extremely rare. We present a case of a 42-year-old bedridden woman with mental and physical disabilities who had been misdiagnosed for a decade as having a bladder calculus. We removed the calculus nonsurgically and the analyzed the components. Results demonstrated the presence of a primary vaginal calculus. Vaginal calculi may occasionally occur in disabled women, but further investigation of the etiology of such calculi is required.

A Preliminary Study of the Effectiveness of Different Recitation Teaching Methods

NASA Astrophysics Data System (ADS)

Endorf, Robert J.; Koenig, Kathleen M.; Braun, Gregory A.

2006-02-01

We present preliminary results from a comparative study of student understanding for students who attended recitation classes which used different teaching methods. Student volunteers from our introductory calculus-based physics course attended a special recitation class that was taught using one of four different teaching methods. A total of 272 students were divided into approximately equal groups for each method. Students in each class were taught the same topic, "Changes in energy and momentum," from Tutorials in Introductory Physics. The different teaching methods varied in the amount of student and teacher engagement. Student understanding was evaluated through pretests and posttests given at the recitation class. Our results demonstrate the importance of the instructor's role in teaching recitation classes. The most effective teaching method was for students working in cooperative learning groups with the instructors questioning the groups using Socratic dialogue. These results provide guidance and evidence for the teaching methods which should be emphasized in training future teachers and faculty members.

Verification of causal influences of reasoning skills and epistemology on physics conceptual learning

NASA Astrophysics Data System (ADS)

Ding, Lin

2014-12-01

This study seeks to test the causal influences of reasoning skills and epistemologies on student conceptual learning in physics. A causal model, integrating multiple variables that were investigated separately in the prior literature, is proposed and tested through path analysis. These variables include student preinstructional reasoning skills measured by the Classroom Test of Scientific Reasoning, pre- and postepistemological views measured by the Colorado Learning Attitudes about Science Survey, and pre- and postperformance on Newtonian concepts measured by the Force Concept Inventory. Students from a traditionally taught calculus-based introductory mechanics course at a research university participated in the study. Results largely support the postulated causal model and reveal strong influences of reasoning skills and preinstructional epistemology on student conceptual learning gains. Interestingly enough, postinstructional epistemology does not appear to have a significant influence on student learning gains. Moreover, pre- and postinstructional epistemology, although barely different from each other on average, have little causal connection between them.

Gravitational Wave Detection in the Introductory Lab

NASA Astrophysics Data System (ADS)

Burko, Lior M.

2017-01-01

Great physics breakthroughs are rarely included in the introductory physics course. General relativity and binary black hole coalescence are no different, and can be included in the introductory course only in a very limited sense. However, we can design activities that directly involve the detection of GW150914, the designation of the Gravitation Wave signal detected on September 14, 2015, thereby engage the students in this exciting discovery directly. The activities naturally do not include the construction of a detector or the detection of gravitational waves. Instead, we design it to include analysis of the data from GW150914, which includes some interesting analysis activities for students of the introductory course. The same activities can be assigned either as a laboratory exercise or as a computational project for the same population of students. The analysis tools used here are simple and available to the intended student population. It does not include the sophisticated analysis tools, which were used by LIGO to carefully analyze the detected signal. However, these simple tools are sufficient to allow the student to get important results. We have successfully assigned this lab project for students of the introductory course with calculus at Georgia Gwinnett College.

Using isomorphic problems to learn introductory physics

NASA Astrophysics Data System (ADS)

Lin, Shih-Yin; Singh, Chandralekha

2011-12-01

In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem) which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. We found that most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.

A Cognitive Model of College Mathematics Placement

DTIC Science & Technology

1989-08-01

study focused on the precalculus -- calculus placement decision. The Cognitive model uses novel, or analysis level, placement test items in an attempt to...relative to the requirements of a precalculus course. Placement test scores may be partitioned to give analysis and non-analysis subtest scores which can...67 5.1.1 1989 Intercorrelations ....................................................................... 67 5.1.2 1989 Precalculus -Calculus

Calculus in Your Career: Putting the "Relate" Back in Related Rates

ERIC Educational Resources Information Center

Lommatsch, Christina W.

2017-01-01

"Find the extreme values of the function." "At what rate is the distance between A and B increasing after 12 seconds?" Prompts like these can be heard in most first-semester calculus courses. Unfortunately, these cues also tend to prompt students' eyes to glaze over with thoughts of "When will I ever use this?" This…

The Effect of Graphing Calculators on Student Achievement in College Algebra and Pre-Calculus Mathematics Courses

ERIC Educational Resources Information Center

Hatem, Neil

2010-01-01

This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…

Students' Conceptual Understanding of a Function and Its Derivative in an Experimental Calculus Course

ERIC Educational Resources Information Center

Habre, Samer; Abboud, May

2006-01-01

Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its…

The Hawaii Teleschool: An Evaluation of Distance Learning for Advanced Placement Calculus Instruction in "Paradise."

ERIC Educational Resources Information Center

Barker, Bruce O.; Bannon, James

This paper describes the Hawaii Interactive Television System (HITS) program and provides an evaluation of the first year of broadcasts for the advanced placement (AP) calculus course. HITS allows two-way video-audio interaction among origination sites, but the configuration used by the Department of Education for its Teleschool program is the…

Anticipating Mathematics Performance: A Cross-Validation Comparison of AID3 and Regression. AIR 1988 Annual Forum Paper.

ERIC Educational Resources Information Center

Bloom, Allan M.; And Others

In response to the increasing importance of student performance in required classes, research was conducted to compare two prediction procedures, linear modeling using multiple regression and nonlinear modeling using AID3. Performance in the first college math course (College Mathematics, Calculus, or Business Calculus Matrices) was the dependent…

Sharks, Minnows, and Wheelbarrows: Calculus Modeling Projects

ERIC Educational Resources Information Center

Smith, Michael D.

2011-01-01

The purpose of this article is to present two very active applied modeling projects that were successfully implemented in a first semester calculus course at Hollins University. The first project uses a logistic equation to model the spread of a new disease such as swine flu. The second project is a human take on the popular article "Do Dogs Know…

What Do Croatian Pre-Service Teachers Remember from Their Calculus Course?

ERIC Educational Resources Information Center

Jukic, Ljerka; Brückler, Franka Miriam

2014-01-01

This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two pre-service mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of…

Recommendations for the Undergraduate Mathematics Program for Students in the Life Sciences. An Interim Report.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

This report considers the mathematics required by life science students (those with majors in agriculture and renewable resources, all branches of biology, and medicine) who have successfully completed the usual pre-calculus courses. A core is proposed, to include one year of calculus, some linear algebra, and some probability and statistics.…

Parametric Surfaces Competition: Using Technology to Foster Creativity

ERIC Educational Resources Information Center

Kaur, Manmohan; Wangler, Thomas

2014-01-01

Although most calculus students are comfortable with the Cartesian equations of curves and surfaces, they struggle with the concept of parameters. A multivariable calculus course is really the time to nail this concept down, once and for all, since it provides an easy way to represent many beautiful and useful surfaces, and graph them using a…

Designing a Telescope Mirror for Second-Semester Calculus Students

ERIC Educational Resources Information Center

Marchand, Richard J.; Rogers, Robert R.; Parker, Andrew T.

2006-01-01

The purpose of this article is to present an interdisciplinary project, developed as a collaborative effort by the authors, involving the design of a telescope mirror as it was given to second semester calculus students. The goals of the project are to provide an applied setting for the topics typically covered in this type of course including the…

Productive and Ineffective Efforts: How Student Effort in High School Mathematics Relates to College Calculus Success

ERIC Educational Resources Information Center

Barnett, M.D.; Sonnert, G.; Sadler, P.M.

2014-01-01

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the…

A physically based connection between fractional calculus and fractal geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

Modeling student success in engineering education

NASA Astrophysics Data System (ADS)

Jin, Qu

In order for the United States to maintain its global competitiveness, the long-term success of our engineering students in specific courses, programs, and colleges is now, more than ever, an extremely high priority. Numerous studies have focused on factors that impact student success, namely academic performance, retention, and/or graduation. However, there are only a limited number of works that have systematically developed models to investigate important factors and to predict student success in engineering. Therefore, this research presents three separate but highly connected investigations to address this gap. The first investigation involves explaining and predicting engineering students' success in Calculus I courses using statistical models. The participants were more than 4000 first-year engineering students (cohort years 2004 - 2008) who enrolled in Calculus I courses during the first semester in a large Midwestern university. Predictions from statistical models were proposed to be used to place engineering students into calculus courses. The success rates were improved by 12% in Calculus IA using predictions from models developed over traditional placement method. The results showed that these statistical models provided a more accurate calculus placement method than traditional placement methods and help improve success rates in those courses. In the second investigation, multi-outcome and single-outcome neural network models were designed to understand and to predict first-year retention and first-year GPA of engineering students. The participants were more than 3000 first year engineering students (cohort years 2004 - 2005) enrolled in a large Midwestern university. The independent variables include both high school academic performance factors and affective factors measured prior to entry. The prediction performances of the multi-outcome and single-outcome models were comparable. The ability to predict cumulative GPA at the end of an engineering student's first year of college was about a half of a grade point for both models. The predictors of retention and cumulative GPA while being similar differ in that high school academic metrics play a more important role in predicting cumulative GPA with the affective measures playing a more important role in predicting retention. In the last investigation, multi-outcome neural network models were used to understand and to predict engineering students' retention, GPA, and graduation from entry to departure. The participants were more than 4000 engineering students (cohort years 2004 - 2006) enrolled in a large Midwestern university. Different patterns of important predictors were identified for GPA, retention, and graduation. Overall, this research explores the feasibility of using modeling to enhance a student's educational experience in engineering. Student success modeling was used to identify the most important cognitive and affective predictors for a student's first calculus course retention, GPA, and graduation. The results suggest that the statistical modeling methods have great potential to assist decision making and help ensure student success in engineering education.

Clickers don't always help: Classroom context and goals can mitigate clicker effects on student learning

NASA Astrophysics Data System (ADS)

Shapiro, Amy; O'Rielly, Grant; Sims-Knight, Judith

2014-03-01

Clickers are commonly used in large-enrollment introductory courses in order to encourage attendance, increase student engagement and improve learning. We report the results from a highly controlled study of factual and conceptual clicker questions in calculus-based introductory physics courses, on students' performance on the factual and conceptual exam questions they targeted. We found that clicker questions did not enhance student performance on either type of exam question. The use of factual clicker questions actually decreased student performance on conceptual exam questions, however. Directing students' attention to surface features of the course content may distract them from the important underlying concepts. The conceptual clicker questions were likely ineffective because the practice students got on homework questions had a stronger effect than the single question posed in class. Interestingly, the same studies in general education biology and psychology courses show a strong, positive effect of clickers on student learning. This study suggest that the usefulness of clickers should be weighed in the context of other course activities and goals. Secondary analyses will explore the effect of students' GPA, motivation and study strategies on the results. This work was supported by the Institute of Education Sciences, US Dept. of Education, through Grant R305A100625 to UMass Dartmouth. The opinions expressed are those of the authors and do not represent views of the Institute or the US Dept. of Education.

A Study of Novice Instructors' Questioning Techniques and Classroom Discourse Surrounding Those Questions

ERIC Educational Resources Information Center

Roach, Kitty Lane

2015-01-01

The goals of this dissertation were to examine how novice calculus teachers used questions in their classrooms, how those questions and their use might change after video case-based course coordination, and what evidence of influence on student learning might be seen in undergraduate student achievement. This research focused on one way to elicit…

Triangles with Integer Side Lengths and Rational Internal Radius P and External Radius R

ERIC Educational Resources Information Center

Zelator, Konstantine

2005-01-01

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

Experiences in Evaluating Outcomes in Tool-Based, Competence Building Education in Dynamical Systems Using Symbolic Computer Algebra

ERIC Educational Resources Information Center

Perram, John W.; Andersen, Morten; Ellekilde, Lars-Peter; Hjorth, Poul G.

2004-01-01

This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large…

Suggested Courseware for the Non-Calculus Physics Student: Measurement, Vectors, and One-Dimensional Motion.

ERIC Educational Resources Information Center

Mahoney, Joyce; And Others

1988-01-01

Evaluates 16 commercially available courseware packages covering topics for introductory physics. Discusses the price, sub-topics, program type, interaction, time, calculus required, graphics, and comments of each program. Recommends two packages in measurement and vectors, and one-dimensional motion respectively. (YP)

Restructuring Introductory Physics by Adapting an Active Learning Studio Model

ERIC Educational Resources Information Center

Gatch, Delena

2010-01-01

Despite efforts to engage students in the traditional lecture environment, faculty in Georgia Southern University's Physics Department became dissatisfied with lecture as the primary means of instruction. During the fall semester of 2006, our department began adapting the studio model to suit the needs of introductory calculus-based physics…

Three Different Teaching Approaches in Pre-Calculus Bridging Mathematics

ERIC Educational Resources Information Center

Miller-Reilly, Barbara

2007-01-01

During the past decade three different bridging mathematics courses have been offered at the University of Auckland. A case study approach was used to investigate the effectiveness of these courses: two larger courses and one individual study programme. A different teaching approach, by committed experienced teachers, was used in each course. The…

Representing Targets of Measurement within Evidence-Centered Design

ERIC Educational Resources Information Center

Ewing, Maureen; Packman, Sheryl; Hamen, Cynthia; Thurber, Allison Clark

2010-01-01

In the last few years, the Advanced Placement (AP) Program[R] has used evidence-centered assessment design (ECD) to articulate the knowledge, skills, and abilities to be taught in the course and measured on the summative exam for four science courses, three history courses, and six world language courses; its application to calculus and English…

Inquiry experiences as a lecture supplement for preservice elementary teachers and general education students

NASA Astrophysics Data System (ADS)

Marshall, Jill A.; Dorward, James T.

2000-07-01

The study reported here was designed to substantiate the findings of previous research on the use of inquiry-based laboratory activities in introductory college physics courses. The authors sought to determine whether limited use of inquiry activities as a supplement to a traditional lecture and demonstration curriculum would improve student achievement in introductory classes for preservice teachers and general education students. Achievement was measured by responses to problems designed to test conceptual understanding as well as overall course grades. We analyzed the effect on selected student outcome measures in a preliminary study in which some students engaged in inquiry activities and others did not, and interviewed students about their perceptions of the inquiry activities. In the preliminary study, preservice elementary teachers and female students showed significantly higher achievement after engaging such activities, but only on exam questions relating directly to the material covered in the exercises. In a second study we used a common exam problem to compare the performance of students who had engaged in a revised version of the inquiry activities with the performance of students in algebra and calculus-based classes. The students who had engaged in inquiry investigations significantly outperformed the other students.

Using contests to ``spice up'' workshop physics

NASA Astrophysics Data System (ADS)

Duffy, M. G.; Warden, J. A.

1997-03-01

Once or twice each semester we give the students in our calculus-based Workshop Physics (1) course a problem dressed up as a contest. To "win," a team must correctly predict the outcome of a unique event and test that prediction within a single fifty minute class period. Successful teams win a home-cooked meal or other prize unrelated to course grade. We design a contest to focus cooperative effort, yet it also serves in ways like a problem session, review, or exam, but with no grade pressure. As illustrated by the sample contests exhibited on the poster, you can adjust the difficulty of these exercises to get a variety of different success rates. While this is hardly a novel idea, we provide it as a reminder that it is useful to step out of the normal homework, quiz, exam mode once in a while. Pedagogical goals include: • Fast, intensive review, like an exam but without the pass/fail stress. • Puts a premium on cooperative effort and promotes teamwork. • Serves as a morale booster, an antidote to "midterm blues." Student teams are given a chance to predict the outcome of a unique event and to test that prediction within a single fifty-minute class. The task chosen requires at least two careful measurements and subsequent analysis.

Teaching assistant-student interactions in a modified SCALE-UP classroom

NASA Astrophysics Data System (ADS)

DeBeck, George; Demaree, Dedra

2012-02-01

In the spring term of 2010, Oregon State University (OSU) began using a SCALE-UP style classroom in the instruction of the introductory calculus-based physics series. Instruction in this classroom was conducted in weekly two-hour sessions facilitated by the primary professor and either two graduate teaching assistants (GTAs) or a graduate teaching assistant and an undergraduate learning assistant (LA). During the course of instruction, two of the eight tables in the room were audio and video recorded. We examine the practices of the GTAs in interacting with the students through both qualitative and quantitative analyses of these recordings. Quantitatively, significant differences are seen between the most experienced GTA and the rest. A major difference in confidence is also observed in the qualitative analysis of this GTA compared to a less experienced GTA.

Introductory Life Science Mathematics and Quantitative Neuroscience Courses

ERIC Educational Resources Information Center

Duffus, Dwight; Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an…

Math 3011--College Algebra and Trigonometry. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…

What works with worked examples: Extending self-explanation and analogical comparison to synthesis problems

NASA Astrophysics Data System (ADS)

Badeau, Ryan; White, Daniel R.; Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.

2017-12-01

The ability to solve physics problems that require multiple concepts from across the physics curriculum—"synthesis" problems—is often a goal of physics instruction. Three experiments were designed to evaluate the effectiveness of two instructional methods employing worked examples on student performance with synthesis problems; these instructional techniques, analogical comparison and self-explanation, have previously been studied primarily in the context of single-concept problems. Across three experiments with students from introductory calculus-based physics courses, both self-explanation and certain kinds of analogical comparison of worked examples significantly improved student performance on a target synthesis problem, with distinct improvements in recognition of the relevant concepts. More specifically, analogical comparison significantly improved student performance when the comparisons were invoked between worked synthesis examples. In contrast, similar comparisons between corresponding pairs of worked single-concept examples did not significantly improve performance. On a more complicated synthesis problem, self-explanation was significantly more effective than analogical comparison, potentially due to differences in how successfully students encoded the full structure of the worked examples. Finally, we find that the two techniques can be combined for additional benefit, with the trade-off of slightly more time on task.

Learning in a Physics Classroom Community: Physics Learning Identity Construct Development, Measurement and Validation

NASA Astrophysics Data System (ADS)

Li, Sissi L.

At the university level, introductory science courses usually have high student to teacher ratios which increases the challenge to meaningfully connect with students. Various curricula have been developed in physics education to actively engage students in learning through social interactions with peers and instructors in class. This learning environment demands not only conceptual understanding but also learning to be a scientist. However, the success of student learning is typically measured in test performance and course grades while assessment of student development as science learners is largely ignored. This dissertation addresses this issue with the development of an instrument towards a measure of physics learning identity (PLI) which is used to guide and complement case studies through student interviews and in class observations. Using the conceptual framework based on Etienne Wenger's communities of practice (1998), I examine the relationship between science learning and learning identity from a situated perspective in the context of a large enrollment science class as a community of practice. This conceptual framework emphasizes the central role of identity in the practices negotiated in the classroom community and in the way students figure out their trajectory as members. Using this framework, I seek to understand how the changes in student learning identity are supported by active engagement based instruction. In turn, this understanding can better facilitate the building of a productive learning community and provide a measure for achievement of the curricular learning goals in active engagement strategies. Based on the conceptual framework, I developed and validated an instrument for measuring physics learning identity in terms of student learning preferences, self-efficacy for learning physics, and self-image as a physics learner. The instrument was pilot tested with a population of Oregon State University students taking calculus based introductory physics. The responses were analyzed using principal component exploratory factor analysis. The emergent factors were analyzed to create reliable subscales to measure PLI in terms of physics learning self-efficacy and social expectations about learning. Using these subscales, I present a case study of a student who performed well in the course but resisted the identity learning goals of the curriculum. These findings are used to support the factors that emerged from the statistical analysis and suggest a potential model of the relationships between the factors describing science learning and learning identity in large enrollment college science classes. This study offers an instrument with which to measure aspects of physics learning identity and insights on how PLI might develop in a classroom community of practice.

The Mathematical Courses of Pedro Padilla and Etienne Bezout: Teaching Calculus in Eighteenth-Century Spain and France

ERIC Educational Resources Information Center

Blanco, Monica

2013-01-01

The aim of this paper is to provide a cross-national comparative analysis of the introduction of calculus in Spanish and French military educational institutions through the works of Pedro Padilla y Arcos (1724-1807?) and Etienne Bezout (1730-1783), respectively. Both authors developed their educational work in the context of military schools and…

Placement Model for First-Time Freshmen in Calculus I (Math 131): University of Northern Colorado

ERIC Educational Resources Information Center

Heiny, Robert L.; Heiny, Erik L.; Raymond, Karen

2017-01-01

Two approaches, Linear Discriminant Analysis, and Logistic Regression are used and compared to predict success or failure for first-time freshmen in the first calculus course at a medium-sized public, 4-year institution prior to Fall registration. The predictor variables are high school GPA, the number, and GPA's of college prep mathematics…

An Exploratory Study of the Diagnostic Teaching of Heuristic Problem Solving Strategies in Calculus.

ERIC Educational Resources Information Center

Lucas, John Frank

The aims of the study were to explore the effects of teaching heuristics in a calculus course and to generate hypotheses about related changes in heuristic usage and problem solving performance. Thirty college students in two classes participated and a Solomon four-group research design was used. Students from one group in each class were…

Airfoil Design in Multivariable Calculus: Tying It All Together

ERIC Educational Resources Information Center

Laverty, Rich; Povich, Timothy; Williams, Tasha

2005-01-01

Near the conclusion of their final term in the calculus sequence at The United States Military Academy, cadets are given a week long group project. At the end of the week, the project is briefed to their instructors, classmates, and superior officers. From a teaching perspective, the goal is to encapsulate as much of the course as possible in one…

A Mixed Methods Explanatory Study of the Failure/Drop Rate for Freshman STEM Calculus Students

ERIC Educational Resources Information Center

Worthley, Mary

2013-01-01

In a national context of high failure rates in freshman calculus courses, the purpose of this study was to understand who is struggling, and why. High failure rates are especially alarming given a local environment where students have access to a variety of academic, and personal, assistance. The sample consists of students at Colorado State…

The Relevance of Mathematics: Leaders and Teachers as Gatekeeper for Queensland Senior Calculus Mathematics

ERIC Educational Resources Information Center

Easey, Michael; Gleeson, Jim

2016-01-01

The aim of the larger study, of which this paper is a part, is to investigate the decline in Year 10 male students' participation in senior calculus mathematics courses at an independent boys' school located in metropolitan Queensland. This paper draws on Sealey and Noyes's (2010) relevance framework to conduct document analysis and interviews…

A Mixed-Methods Explanatory Study of the Failure Rate for Freshman STEM Calculus Students

ERIC Educational Resources Information Center

Worthley, Mary R.; Gloeckner, Gene W.; Kennedy, Paul A.

2016-01-01

In this study we aimed to understand who was struggling in freshman calculus courses, and why. Concentrating on the Fall sections of the class, the best predictors for success (R[superscript 2] = 0.4) were placement test results, the student's own appraisal of the quality of mathematics teaching they received in high school, and the Motivated…

Students' Ways of Thinking about Two-Variable Functions and Rate of Change in Space

ERIC Educational Resources Information Center

Weber, Eric David

2012-01-01

This dissertation describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet…

Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

ERIC Educational Resources Information Center

Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy

2006-01-01

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…

Fundamentals of Physics, 6th Edition Enhanced Problems Version

NASA Astrophysics Data System (ADS)

Halliday, David; Resnick, Robert; Walker, Jearl

2002-04-01

No other text on the market today can match the success of Halliday, Resnick and Walker's Fundamentals of Physics. This text continues to outperform the competition year after year, and the new edition will be no exception. Intended for Calculus-based Physics courses, the 6th edition of this extraordinary text is a major redesign of the best-selling 5th edition, which still maintains many of the elements that led to its enormous success. Jearl Walker adds his unique style to this edition with the addition of new problems designed to capture, and keep, students' attention. Nearly all changes are based on suggestions from instructors and students using the 5th edition, from reviewer comments, and from research done on the process of learning. The primary goal of this text is to provide students with a solid understanding of fundamental physics concepts, and to help them apply this conceptual understanding to quantitative problem solving. The principal goal of Halliday-Resnick-Walker is to provide instructors with a tool by which they can teach students how to effectively read scientific material and successfully reason through scientific questions. To sharpen this tool, the Enhanced Problems Version of the sixth edition of Fundamentals of Physics contains over 1000 new, high-quality problems that require thought and reasoning rather than simplistic plugging of data into formulas.

TIMSS Advanced 2015 and Advanced Placement Calculus & Physics. A Framework Analysis. Research in Review 2016-1

ERIC Educational Resources Information Center

Lazzaro, Christopher; Jones, Lee; Webb, David C.; Grover, Ryan; Di Giacomo, F. Tony; Marino, Katherine Adele

2016-01-01

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

Engaging Students in a Large-Enrollment Physics Class Using an Academically Focused Social Media Platform

NASA Astrophysics Data System (ADS)

Gavrin, Andy; Lindell, Rebecca

2017-03-01

There are many reasons for an instructor to consider using social media, particularly in a large introductory course. Improved communications can lessen the sense of isolation some students feel in large classes, and students may be more likely to respond to faculty announce-ments in a form that is familiar and comfortable. Furthermore, many students currently establish social media sites for their classes, without the knowledge or participation of their instructors. Such "shadow" sites can be useful, but they can also become distributors of misinformation, or venues for inappropriate or disruptive discussions. CourseNetworking (CN) is a social media platform designed for the academic environment. It combines many features common among learning management systems (LMS's) with an interface that looks and feels more like Facebook than a typical academic system. We have recently begun using CN as a means to engage students in an introductory calculus-based mechanics class, with enrollments of 150-200 students per semester. This article presents basic features of CN, and details our initial experiences and observations.

Bridging a cultural gap

NASA Astrophysics Data System (ADS)

Leviatan, Talma

2008-09-01

There has been a broad wave of change in tertiary calculus courses in the past decade. However, the much-needed change in tertiary pre-calculus programmes—aimed at bridging the gap between high-school mathematics and tertiary mathematics—is happening at a far slower pace. Following a discussion on the nature of the gap and the objectives of a potential bridging programme, this paper aims at demonstrating that the gap can be bridged, by presenting an ongoing modular bridging programme especially designed for the diverse types of student populations in teachers training colleges. We also present here some innovative teaching and assessment methods that were judged essential for the success of these programmes—focusing mainly on the "Questionnaire Based Instruction Method". Finally we suggest directions of follow up and research.

The relativistic gravity train

NASA Astrophysics Data System (ADS)

Seel, Max

2018-05-01

The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solutions have been discussed. Here relativistic corrections are presented. It is discussed how the corrections affect the time to fall through Earth, the Sun, a white dwarf, a neutron star, and—the ultimate limit—the difference in time measured by a moving, a stationary and the fiducial observer at infinity if the density of the sphere approaches the density of a black hole. The relativistic gravity train can serve as a problem with approximate and exact analytic solutions and as numerical exercise in any introductory course on relativity.

Learning, Retention, and Forgetting of Newton's Third Law throughout University Physics

ERIC Educational Resources Information Center

Sayre, Eleanor C.; Franklin, Scott V.; Dymek, Stephanie; Clark, Jessica; Sun, Yifei

2012-01-01

We present data from a between-student study on student response to questions on Newton's third law given in two introductory calculus-based physics classes (Mechanics and Electromagnetism) at a large northeastern university. Construction of a response curve reveals subtle dynamics in student learning not capturable by pretesting and post-testing.…

Suggested Courseware for the Non-Calculus Physics Student: Projectile Motion, Circular Motion, Rotational Dynamics, and Statics.

ERIC Educational Resources Information Center

Mahoney, Joyce; And Others

1988-01-01

Evaluates 10 courseware packages covering topics for introductory physics. Discusses the price; sub-topics; program type; interaction; possible hardware; time; calculus required; graphics; and comments on each program. Recommends two packages in projectile and circular motion, and three packages in statics and rotational dynamics. (YP)

A Team Taught Interdisciplinary Approach To Physics and Calculus Education.

ERIC Educational Resources Information Center

Johnson, David B.

The Special Intensive Program for Scientists and Engineers (SIPSE) at Diablo Valley College in California replaces the traditional engineering calculus and physics sequences with a single sequence that combines the two subjects into an integrated whole. The project report provides an overview of SIPSE, a section that traces the project from…

First-Year University Physics Students' Knowledge about Direct Current Circuits: Probing Improvement in Understanding as a Function of Teaching and Learning Interventions

ERIC Educational Resources Information Center

Newman, Richard; van der Ventel, Brandon; Hanekom, Crischelle

2017-01-01

Probing university students' understanding of direct-current (DC) resistive circuits is still a field of active physics education research. We report here on a study we conducted of this understanding, where the cohort consisted of students in a large-enrollment first-year physics module. This is a non-calculus based physics module for students in…

CIMAC: A Coordinated Introduction to Calculus and Mechanics

NASA Astrophysics Data System (ADS)

Fathe, Laurie; Quinn, Jennifer; McDonald, Michael A.

1997-04-01

CIMAC, new course incorporating Mechanics, Precalculus, and Calculus, targets the growing number of motivated but underprepared students who wish to pursue a major in science or mathematics. Team-taught by a Physicist and a Mathematician, CIMAC, a new course incorporating Mechanics, Precalculus, and Calculus, targets the growing number of motivated but underprepared students who wish to pursue a major in science or mathematics. Team-taught by a Physicist and a Mathematician, the class contains specific content while exploiting the substantial commonality of these subjects. CIMAC also addresses variety of non-content areas, including supplementing basic mathematics and communication skills, accommodating various learning styles, and building student confidence. Specific approaches include class formats; gateway exams; group assignments; emphasis on writing and reading; use of computers and graphing calculators for comprehension, data acquisition, analysis, and modeling; student-led help sessions; and use of the Web http://www.oxy.edu/ departments/math/cimac/ This talk highlights the development of the course and teaching insights and innovations which have arisen from it, and addresses benefits and difficulties of coordinating material and team teaching across disciplinary lines. Finally, it presents data on student success and retention.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Definite Integral Automatic Analysis Mechanism Research and Development Using the "Find the Area by Integration" Unit as an Example

ERIC Educational Resources Information Center

Ting, Mu Yu

2017-01-01

Using the capabilities of expert knowledge structures, the researcher prepared test questions on the university calculus topic of "finding the area by integration." The quiz is divided into two types of multiple choice items (one out of four and one out of many). After the calculus course was taught and tested, the results revealed that…

Predicting College Math Success: Do High School Performance and Gender Matter? Evidence from Sultan Qaboos University in Oman

ERIC Educational Resources Information Center

Islam, M. Mazharul; Al-Ghassani, Asma

2015-01-01

The objective of this study was to evaluate the performance of students of college of Science of Sultan Qaboos University (SQU) in Calculus I course, and examine the predictive validity of student's high school performance and gender for Calculus I success. The data for the study was extracted from students' database maintained by the Deanship of…

Local (L, [epsilon])-Approximation of a Function of Single Variable: An Alternative Way to Define Limit

ERIC Educational Resources Information Center

Bokhari, M. A.; Yushau, B.

2006-01-01

At the start of a freshman calculus course, many students conceive the classical definition of limit as the most problematic part of calculus. They not only find it difficult to understand, but also consider it of no use while solving most of the limit problems and therefore, skip it. This paper reformulates the rigorous definition of limit, which…

The Solid Earth

NASA Astrophysics Data System (ADS)

Fowler, C. M. R.

2004-12-01

The second edition of this acclaimed textbook has been brought fully up-to-date to reflect the latest advances in geophysical research. It is designed for students in introductory geophysics courses who have a general background in the physical sciences, including introductory calculus. New to this edition are a section of color plates and separate sections on the earth's mantle and core. The book also contains an extensive glossary of terms, and includes numerous exercises for which solutions are available to instructors from solutions@cambridge.org. First Edition Hb (1990): 0-521-37025-6 First Edition Pb (1990): 0-521-38590-3

Non-Zero Net Force and Constant Velocity: A Study in Mazur's Peer Instruction

NASA Astrophysics Data System (ADS)

Newburgh, Ronald

2009-10-01

A problem addressed infrequently in beginning physics courses is that of a moving body with changing mass. Elementary texts often have footnotes referring to jet planes and rockets but rarely do they go further. This omission is understandable because calculations with variable mass generally require the tools of calculus. This paper presents a changing mass problem that can be treated on an elementary level, thereby leading to an understanding of the role of changing mass on Newton's second law. It also illustrates Mazur's technique of Peer Instruction, a technique that demands active student participation.

The Solid Earth

NASA Astrophysics Data System (ADS)

Fowler, C. M. R.

2005-02-01

The second edition of this acclaimed textbook has been brought fully up-to-date to reflect the latest advances in geophysical research. It is designed for students in introductory geophysics courses who have a general background in the physical sciences, including introductory calculus. New to this edition are a section of color plates and separate sections on the earth's mantle and core. The book also contains an extensive glossary of terms, and includes numerous exercises for which solutions are available to instructors from solutions@cambridge.org. First Edition Hb (1990): 0-521-37025-6 First Edition Pb (1990): 0-521-38590-3

An Algebra-Based Introductory Computational Neuroscience Course with Lab.

PubMed

Fink, Christian G

2017-01-01

A course in computational neuroscience has been developed at Ohio Wesleyan University which requires no previous experience with calculus or computer programming, and which exposes students to theoretical models of neural information processing and techniques for analyzing neural data. The exploration of theoretical models of neural processes is conducted in the classroom portion of the course, while data analysis techniques are covered in lab. Students learn to program in MATLAB and are offered the opportunity to conclude the course with a final project in which they explore a topic of their choice within computational neuroscience. Results from a questionnaire administered at the beginning and end of the course indicate significant gains in student facility with core concepts in computational neuroscience, as well as with analysis techniques applied to neural data.

Comparing the Impact of Traditional and Modeling College Algebra Courses on Student Performance in Survey of Calculus

ERIC Educational Resources Information Center

West, Jerry G.

2013-01-01

Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…

Profile of American Youth: Demographic Influences on ASVAB (Armed Services Vocational Aptitude Battery) Test Performance

DTIC Science & Technology

1984-02-01

completed courses in calcm1lus, precalculus , trigonometry, geometry and computer programming. As a matter of fact, of the twelve courses covered in the...had studied the course-- precalculus /calculus and trigonometry. The NAEP survey also collected data from the 13-year-olds regarding the number of years

Moore and Less!

ERIC Educational Resources Information Center

Asghari, Amir

2012-01-01

This article is the story of a very non-standard, absolutely student-centered multivariable calculus course. The course advocates the so-called problem method in which the problems used are a bridge between what the learners know and what they are about to know. The main feature of the course is a unique conceptual story that runs through the…

Improving Critical Skills Using Wikis and CGPS in a Physics Classroom

ERIC Educational Resources Information Center

Mohottala, H. E.

2016-01-01

We report the combined use of Wikispaces (wikis) and collaborative group problem solving (CGPS) sessions conducted in introductory-level calculus-based physics classes. As a part of this new teaching tool, some essay-type problems were posted on the wiki page on a weekly basis and students were encouraged to participate in problem solving without…

Graduate student training and creating new physics labs for biology students, killing two birds with one stone.

NASA Astrophysics Data System (ADS)

Jones, Barbara

2001-03-01

At UCSD biology majors are required to take 3 quarters of a calculus based physics course. This is taught in a standard format large lecture class partly by faculty and partly by freeway flyers. We are working with physics graduate students who are also participating in our PFPF (Preparing Future Physics Faculty) program to write, review, and teach new weekly labs for these biology students. This provides an experience for the grad student that is both rewarding to them and useful to the department. The grad students participate in curriculum development, they observe the students behaviour in the labs, and assess the effectiveness of different lab formats. The labs are intended to provide an interactive, hands on experience with a wide variety of equipment which is mostly both simple and inexpensive. Both students and grads find the labs to be engaging and fun. Based on group discussions the labs are modified to try to try to create the best teaching environment. The biology students benefit from the improvements both in the quality of the labs they do, and from the enthusiasm of the TAs who take an active interest in their learning. The ability to make significant changes to the material taught maintains the interest of the grad students and helps to make the labs a stable and robust environment.

On Solving Linear Recurrences

ERIC Educational Resources Information Center

Dobbs, David E.

2013-01-01

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

Figures and First Years: Examining first-year Calculus I student ability to incorporate figures into technical reports

NASA Astrophysics Data System (ADS)

Antonacci, Nathan; Rogers, Michael; Pfaff, Thomas

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures into technical reports. Students were handed guidelines as part of their Multidisciplinary Sustainability Education Module meant to aid them in crafting effective figures. Figure-specific questionnaires were added in the class to gain insight into the quantitative literacy skills students possessed both before starting their course and after its completion. Reviews of the figures in 78 technical reports written by 106 students showed repeated failure to refer to figures in discussion sections and use them in evidence-based arguments. Analysis of quantitative literacy skills revealed that the students could both read and interpret figures, suggesting that issues with literacy were not the main contributor to the sub-par graphs.

Impacts of a Summer Bridge Program in Engineering on Student Retention and Graduation

ERIC Educational Resources Information Center

Cançado, Luciana; Reisel, John R.; Walker, Cindy M.

2018-01-01

A summer bridge program was developed in an engineering program to advance the preparation of incoming freshmen students, particularly with respect to their math course placement. The program was intended to raise the initial math course placement of students who otherwise would begin their engineering studies in courses below Calculus I. One…

Introductory life science mathematics and quantitative neuroscience courses.

PubMed

Duffus, Dwight; Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses.

Using Time-on-Task Measurements to Understand Student Performance in a Physics Class: A Ten-Year Study

NASA Astrophysics Data System (ADS)

Stewart, John

2015-04-01

The amount of time spent on out-of-class activities such as working homework, reading, and studying for examinations is presented for 10 years of an introductory, calculus-based physics class at a large public university. While the class underwent significant change in the 10 years studied, the amount of time invested by students in weeks not containing an in-semester examination was constant and did not vary with the length of the reading or homework assignments. The amount of time spent preparing for examinations did change as the course was modified. The time spent on class assignments, both reading and homework, did not scale linearly with the length of the assignment. The time invested in both reading and homework per length of the assignment decreased as the assignments became longer. The class average time invested in examination preparation did change with the average performance on previous examinations in the same class, with more time spent in preparation for lower previous examination scores (R2 = 0 . 70).

Conditional Independence in Applied Probability.

ERIC Educational Resources Information Center

Pfeiffer, Paul E.

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

NASA Astrophysics Data System (ADS)

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter

2018-05-01

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students' development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.

Examining End-of-Chapter Problems across Editions of an Introductory Calculus-Based Physics Textbook

ERIC Educational Resources Information Center

Xiao, Bin

2016-01-01

End-Of-Chapter (EOC) problems have been part of many physics education studies. Typically, only problems "localized" as relevant to a single chapter were used. This work examines how well this type of problem represents all EOC problems and whether EOC problems found in leading textbooks have changed over the past several decades. To…

Internal ballistics of a pneumatic potato cannon

NASA Astrophysics Data System (ADS)

Mungan, Carl E.

2009-05-01

Basic laws of thermodynamics and mechanics are used to analyse an air gun. Such devices are often employed in outdoor physics demonstrations to launch potatoes using compressed gas that is here assumed to expand reversibly and adiabatically. Reasonable agreement is found with reported muzzle speeds for such homebuilt cannons. The treatment is accessible to undergraduate students who have taken calculus-based introductory physics.

A Collection of Numbers Whose Proof of Irrationality Is Like that of the Number "e"

ERIC Educational Resources Information Center

Osler, Thomas J.; Stugard, Nicholas

2006-01-01

In some elementary courses, it is shown that square root of 2 is irrational. It is also shown that the roots like square root of 3, cube root of 2, etc., are irrational. Much less often, it is shown that the number "e," the base of the natural logarithm, is irrational, even though a proof is available that uses only elementary calculus. In this…

Incorporating Writing in an Integrated Calculus, Linear Algebra, and Differential Equations Sequence.

ERIC Educational Resources Information Center

Kelly, Susan E.; LeDocq, Rebecca Lewin

2001-01-01

Describes the specific courses in a sequence along with how the writing has been implemented in each course. Provides ideas for how to efficiently handle the additional paper load so students receive the necessary feedback while keeping the grading time reasonable. (Author/ASK)

Introductory Life Science Mathematics and Quantitative Neuroscience Courses

PubMed Central

Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses. PMID:20810971

The impact of instructor pedagogy on college calculus students' attitude toward mathematics

NASA Astrophysics Data System (ADS)

Sonnert, Gerhard; Sadler, Philip M.; Sadler, Samuel M.; Bressoud, David M.

2015-04-01

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students' attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students' attitudes toward mathematics during a 'mainstream' calculus course while controlling for student backgrounds. The attitude measure combines students' self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted 'good teaching' practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational 'technology' (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students' attitudes towards mathematics. (3) 'Ambitious teaching' (e.g. group work, word problems, 'flipped' reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional 'good teaching' practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do not appear to have a reliable, positive impact on student attitudes toward mathematics.

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

Improving Student Success in Calculus: A Comparison of Four College Calculus Classes

NASA Astrophysics Data System (ADS)

Bagley, Spencer Franklin

The quality of education in science, technology, engineering, and mathematics (STEM) fields is an issue of particular educational and economic importance, and Calculus I is a linchpin course in STEM major tracks. A national study is currently being conducted examining the characteristics of successful programs in college calculus (CSPCC, 2012). In work related to the CSPCC program, this study examines the effects on student outcomes of four different teaching strategies used at a single institution. The four classes were a traditional lecture, a lecture with discussion, a lecture incorporating both discussion and technology, and an inverted model. This dissertation was guided by three questions: (1) What impact do these four instructional approaches have on students' persistence, beliefs about mathematics, and conceptual and procedural achievement in calculus? (2) How do students at the local institution compare to students in the national database? And (3) How do the similarities and differences in opportunities for learning presented in the four classes contribute to the similarities and differences in student outcomes? Quantitative analysis of surveys and exams revealed few statistically significant differences in outcomes, and students in the inverted classroom often had poorer outcomes than those in other classes. Students in the technology-enhanced class scored higher on conceptual items on the final exam than those in other classes. Comparing to the national database, local students had similar switching rates but less expert-like attitudes and beliefs about mathematics than the national average. Qualitative analysis of focus group interviews, classroom observations, and student course evaluations showed that several implementation issues, some the result of pragmatic constraints, others the result of design choice, weakened affordances provided by innovative features and shrunk the differences between classes. There were substantial differences between the inverted classroom in this study and successful implementations in the literature. I identified a set of departures that forms a list of best practices for inverting classrooms. Students in all classes felt that prior calculus experience was a prerequisite for their current calculus class, and that class sessions felt rushed. These concerns implicate the constraints imposed by the curriculum shared by the four classes.

The role of a posteriori mathematics in physics

NASA Astrophysics Data System (ADS)

MacKinnon, Edward

2018-05-01

The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.

Geometric calculus-based postulates for the derivation and extension of the Maxwell equations

NASA Astrophysics Data System (ADS)

McClellan, Gene E.

2012-09-01

Clifford analysis, particularly application of the geometric algebra of three-dimensional physical space and its associated geometric calculus, enables a compact formulation of Maxwell's electromagnetic (EM) equations from a set of physically relevant and mathematically pleasing postulates. This formulation results in a natural extension of the Maxwell equations yielding wave solutions in addition to the usual EM waves. These additional solutions do not contradict experiment and have three properties in common with the apparent properties of dark energy. These three properties are that the wave solutions 1) propagate at the speed of light, 2) do not interact with ordinary electric charges or currents, and 3) possess retrograde momentum. By retrograde momentum, we mean that the momentum carried by such a wave is directed oppositely to the direction of energy transport. A "gas" of such waves generates negative pressure.

Integration of CAI into a Freshmen Liberal Arts Math Course in the Community College.

ERIC Educational Resources Information Center

McCall, Michael B.; Holton, Jean L.

1982-01-01

Discusses four computer-assisted-instruction programs used in a college-level mathematics course to introduce computer literacy and improve mathematical skills. The BASIC programs include polynomial functions, trigonometric functions, matrix algebra, and differential calculus. Each program discusses mathematics theory and introduces programming…

Chaos: A Mathematical Introduction

NASA Astrophysics Data System (ADS)

Banks, John; Dragan, Valentina; Jones, Arthur

2003-06-01

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.

Who Takes College Algebra?

ERIC Educational Resources Information Center

Herriott, Scott R.; Dunbar, Steven R.

2009-01-01

The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…

Maximum Pre-Angiogenic Tumor Size

ERIC Educational Resources Information Center

Erickson, Amy H. Lin

2010-01-01

This material has been used twice as an out-of-class project in a mathematical modeling class, the first elective course for mathematics majors. The only prerequisites for this course were differential and integral calculus, but all students had been exposed to differential equations, and the project was assigned during discussions about solving…

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1998-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Initialization, conceptualization, and application in the generalized (fractional) calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2007-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Factors Associated with Success in College Calculus II

ERIC Educational Resources Information Center

Rosasco, Margaret E.

2013-01-01

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

Solving a problem by using what you know: a physicist looks at a problem in ecology

NASA Astrophysics Data System (ADS)

Greenler, Robert

2015-08-01

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap physics (e.g. chemistry, engineering, geology) but also true in any endeavour where mathematical modelling may contribute insight to the solution of problems (e.g. timing of traffic lights, efficient ways to seat passengers on airplanes, whether it is better to walk or run in a rain shower). The second idea concerns an approach to problem solving. Before some people try to solve a problem, they think they first must learn everything that is known about the subject. However, sometimes an effective approach is to declare, ‘I’m going to solve this problem with what I know now!’ I see a relationship between this approach and the idea of back-of-the-envelope calculations, which many of us appreciate. Of course there are limitations to this method, but I believe that such an aggressive approach to a problem—uninfluenced by the methods everyone else has used—can be productive. This paper describes such an approach to a real-world problem, using only what is known by the teacher of the introductory, calculus-based physics course. The intent of this paper is to encourage students and teachers of physics to look for unconventional areas, outside of physics, where they might use the techniques they have learned to solve problems

The Vector Calculus Gap: Mathematics (Does Not Equal) Physics.

ERIC Educational Resources Information Center

Dray, Tevian; Manogue, Corinne A.

1999-01-01

Discusses some of the differences between the ways mathematicians and physicists view vector calculus and the gap between the way this material is traditionally taught by mathematicians and the way physicists use it. Suggests some ways to narrow the gap. (Author/ASK)

Spontaneous uretero-sigmoid fistula secondary to calculus

PubMed Central

Marzouk, Ines; Moussa, Makram; Saadallah, Lotfi; Bouchoucha, Sami; Hendaoui, Lotfi

2016-01-01

A 25-year-old man was referred to the urology department after a subacute history of left back pain, burning micturition associated with pneumaturia and fecaluria. Ultrasonography was performed showing hydronephrosis, and plain film radiography demonstrated a long vertical left pelvic calculi. Uro-computed tomography (CT) combined with a water enema CT showed a 10 cm long calculus with the cranial extremity fistulating the sigmoidal wall. Surgical treatment included left nephroureterectomy and sigmoidectomy with a colorectal anastomosis. Postoperative course was uneventful. PMID:28096928

An analysis of science content and representations in introductory college physics textbooks and multimodal learning resources

NASA Astrophysics Data System (ADS)

Donnelly, Suzanne M.

This study features a comparative descriptive analysis of the physics content and representations surrounding the first law of thermodynamics as presented in four widely used introductory college physics textbooks representing each of four physics textbook categories (calculus-based, algebra/trigonometry-based, conceptual, and technical/applied). Introducing and employing a newly developed theoretical framework, multimodal generative learning theory (MGLT), an analysis of the multimodal characteristics of textbook and multimedia representations of physics principles was conducted. The modal affordances of textbook representations were identified, characterized, and compared across the four physics textbook categories in the context of their support of problem-solving. Keywords: college science, science textbooks, multimodal learning theory, thermodynamics, representations

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

How Do Freshman Engineering Students Reflect an Online Calculus Course?

ERIC Educational Resources Information Center

Boz, Burcak; Adnan, Muge

2017-01-01

Improved access to technology has led to an increase in the number of online courses and degree programs in higher education. Despite continuous progress, little attention is paid to "understanding" students prior to implementation of learning and teaching processes. Being a valuable input for design of online learning environments and…

Predicting the Health of a Natural Water System

ERIC Educational Resources Information Center

Graves, Gregory H.

2010-01-01

This project was developed as an interdisciplinary application of the optimization of a single-variable function. It was used in a freshman-level single-variable calculus course. After the first month of the course, students had been exposed to the concepts of the derivative as a rate of change, average and instantaneous velocities, derivatives of…

Flipping a College Calculus Course: A Case Study

ERIC Educational Resources Information Center

Sahin, Alpaslan; Cavlazoglu, Baki; Zeytuncu, Yunus E.

2015-01-01

As online videos have become more easily available and more attractive to the new generation of students, and as new student-learning approaches tend to have more technology integration, the flipped classroom model has become very popular. The purpose of this study was to understand college students' views on flipped courses and investigate how…

Calculus of Elementary Functions, Part II. Teacher's Commentary. Revised Edition.

ERIC Educational Resources Information Center

Herriot, Sarah T.; And Others

This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This teacher's guide is for Part II of the course. It is designed to follow Part I of the text. The guide contains background information, suggested instructional…

Calculus of Elementary Functions, Part I. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Herriot, Sarah T.; And Others

This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This text, Part I, contains the first five chapters of the course and two appendices. Chapters included are: (1) Polynomial Functions; (2) The Derivative of a Polynomial…

Using the Scientific Method to Motivate Biology Students to Study Precalculus

ERIC Educational Resources Information Center

Fulton, James P.; Sabatino, Linda

2008-01-01

During the last two years we have developed a precalculus course customized around biology by using the scientific method as a framework to engage and motivate biology students. Historically, the precalculus and calculus courses required for the Suffolk County Community College biology curriculum were designed using examples from the physical…

A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

ERIC Educational Resources Information Center

Wilson, Jason; Lawman, Joshua; Murphy, Rachael; Nelson, Marissa

2011-01-01

This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…

Excellence in Physics Education Award Talk: Curriculum Development for Active Learning using Real Time Graphing and Data Collection Tools

NASA Astrophysics Data System (ADS)

Laws, Priscilla

2010-02-01

In June 1986 Ronald Thornton (at the Tufts University Center for Science and Mathematics Teaching) and Priscilla Laws (at Dickinson College) applied independently for grants to develop curricular materials based on both the outcomes of Physics Education Research and the use of Microcomputer Based Laboratory Tools (MBL) developed by Robert Tinker, Ron Thornton and others at Technical Education Research Centers (TERC). Thornton proposed to develop a series of Tools for Scientific Thinking (TST) laboratory exercises to address known learning difficulties using carefully sequenced MBL observations. These TST laboratories were to be beta tested at several types of institutions. Laws proposed to develop a Workshop Physics Activity Guide for a 2 semester calculus-based introductory course sequence centering on MBL-based guided inquiry. Workshop Physics was to be designed to replace traditional lectures and separate labs in relatively small classes and was to be tested at Dickinson College. In September 1986 a project officer at the Fund for Post-Secondary Education (FIPSE) awarded grants to Laws and Thornton provided that they would collaborate. David Sokoloff (at the University of Oregon) joined Thornton to develop and test the TST laboratories. This talk will describe the 23 year collaboration between Thornton, Laws, and Sokoloff that led to the development of a suite of Activity Based Physics curricular materials, new apparatus and enhanced computer tools for real time graphing, data collection and mathematical modeling. The Suite includes TST Labs, the Workshop Physics Activity Guide, RealTime Physics Laboratory Modules, and a series of Interactive Lecture Demonstrations. A textbook and a guide to using the Suite were also developed. The vital importance of obtaining continued grant support, doing continuous research on student learning, collaborating with instructors at other institutions, and forging relationships with vendors and publishers will be described. )

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Presenting the Straddle Lemma in an introductory Real Analysis course

NASA Astrophysics Data System (ADS)

Soares, A.; Santos, A. L. dos

2017-04-01

In this article, we revisit the concept of strong differentiability of real functions of one variable, underlying the concept of differentiability. Our discussion is guided by the Straddle Lemma, which plays a key role in this context. The proofs of the results presented are designed to meet a young audience in mathematics, typical of students in a first course of Real Analysis or an honors-level Calculus course.

A huge bladder calculus causing acute renal failure.

PubMed

Komeya, Mitsuru; Sahoda, Tamami; Sugiura, Shinpei; Sawada, Takuto; Kitami, Kazuo

2013-02-01

A 81-year-old male was referred to our emergency outpatient unit due to acute renal failure. The level of serum creatinine was 276 μmol/l. A CT scan showed bilateral hydronephroureter, large bladder stone (7 cm × 6 cm × 6 cm) and bladder wall thickness. He was diagnosed as post renal failure due to bilateral hydronephroureter. Large bladder stone is thought to be the cause of bilateral hydronephroureter and renal failure. To improve renal failure, we performed open cystolithotomy and urethral catheterization. Three days after the surgery, the level of serum creatinine decreased to 224 μmol/l. He was discharged from our hospital with uneventful course. Bladder calculus is thought to be a rare cause of renal failure. We summarize the characteristics of bladder calculus causing renal failure. We should keep that long-term pyuria and urinary symptom, and repeated urinary tract infection can cause huge bladder calculus and renal failure in mind.

Numerical Weather Prediction Models on Linux Boxes as tools in meteorological education in Hungary

NASA Astrophysics Data System (ADS)

Gyongyosi, A. Z.; Andre, K.; Salavec, P.; Horanyi, A.; Szepszo, G.; Mille, M.; Tasnadi, P.; Weidiger, T.

2012-04-01

Education of Meteorologist in Hungary - according to the Bologna Process - has three stages: BSc, MSc and PhD, and students graduating at each stage get the respective degree (BSc, MSc and PhD). The three year long base BSc course in Meteorology can be chosen by undergraduate students in the fields of Geosciences, Environmental Sciences and Physics. BasicsFundamentals in Mathematics (Calculus), Physics (General and Theoretical) Physics and Informatics are emphasized during their elementary education. The two year long MSc course - in which about 15 to 25 students are admitted each year - can be studied only at our the Eötvös Loránd uUniversity in the our country. Our aim is to give a basic education in all fields of Meteorology. Main topics are: Climatology, Atmospheric Physics, Atmospheric Chemistry, Dynamic and Synoptic Meteorology, Numerical Weather Prediction, modeling Modeling of surfaceSurface-atmosphere Iinteractions and Cclimate change. Education is performed in two branches: Climate Researcher and Forecaster. Education of Meteorologist in Hungary - according to the Bologna Process - has three stages: BSc, MSc and PhD, and students graduating at each stage get the respective degree. The three year long BSc course in Meteorology can be chosen by undergraduate students in the fields of Geosciences, Environmental Sciences and Physics. Fundamentals in Mathematics (Calculus), (General and Theoretical) Physics and Informatics are emphasized during their elementary education. The two year long MSc course - in which about 15 to 25 students are admitted each year - can be studied only at the Eötvös Loránd University in our country. Our aim is to give a basic education in all fields of Meteorology: Climatology, Atmospheric Physics, Atmospheric Chemistry, Dynamic and Synoptic Meteorology, Numerical Weather Prediction, Modeling of Surface-atmosphere Interactions and Climate change. Education is performed in two branches: Climate Researcher and Forecaster. Numerical modeling became a common tool in the daily practice of weather experts forecasters due to the i) increasing user demands for weather data by the costumers, ii) the growth in computer resources, iii) numerical weather prediction systems available for integration on affordable, off the shelf computers and iv) available input data (from ECMWF or NCEP) for model integrations. Beside learning the theoretical basis, since the last year. Students in their MSc or BSc Thesis Research or in Student's Research ProjectsStudent's Research Projects h have the opportunity to run numerical models and to analyze the outputs for different purposes including wind energy estimation, simulation of the dynamics of a polar low, and subtropical cyclones, analysis of the isentropic potential vorticity field, examination of coupled atmospheric dispersion models, etc. A special course in the application of numerical modeling has been held (is being announced for the upcoming semester) (is being announced for the upcoming semester) for our students in order to improve their skills on this field. Several numerical model (NRIPR ETA and WRF) systems have been adapted in the University and integrated WRF have been tested and used for the geographical region of the Carpathian Basin (NRIPR, ETA and WRF). Recently ALADIN/CHAPEAU the academic version of the ARPEGE ALADIN cy33t1 meso-scale numerical weather prediction model system (which is the operational forecasting tool of our National Weather Service) has been installed at our Institute. ALADIN is the operational forecasting model of the Hungarian Meteorological Service and developed in the framework of the international ALADIN co-operation. Our main objectives are i) the analysis of different typical weather situations, ii) fine tuning of parameterization schemes and the iii) comparison of the ALADIN/CHAPEAU and WRF model outputs based on case studies. The necessary hardware and software innovations has have been done. In the presentation the computer resources needed for the integration of both WRF and ALADIN/CHAPEAU models will be briefly described. The software developments performed for the evaluation and comparison of the different modeling systems will be demonstrated. The main objectives of the education program on the practical numerical weather modeling will be introduced, as well as its detailed thematics and the structure of the labs.

Colloquium: Fractional calculus view of complexity: A tutorial

NASA Astrophysics Data System (ADS)

West, Bruce J.

2014-10-01

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Fractional vector calculus for fractional advection dispersion

NASA Astrophysics Data System (ADS)

Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

2006-07-01

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

A Simple Acronym for Doing Calculus: CAL

ERIC Educational Resources Information Center

Hathaway, Richard J.

2008-01-01

An acronym is presented that provides students a potentially useful, unifying view of the major topics covered in an elementary calculus sequence. The acronym (CAL) is based on viewing the calculus procedure for solving a calculus problem P* in three steps: (1) recognizing that the problem cannot be solved using simple (non-calculus) techniques;…

Bridging the Vector Calculus Gap

NASA Astrophysics Data System (ADS)

Dray, Tevian; Manogue, Corinne

2003-05-01

As with Britain and America, mathematicians and physicists are separated from each other by a common language. In a nutshell, mathematics is about functions, but physics is about things. For the last several years, we have led an NSF-supported effort to "bridge the vector calculus gap" between mathematics and physics. The unifying theme we have discovered is to emphasize geometric reasoning, not (just) algebraic computation. In this talk, we will illustrate the language differences between mathematicians and physicists, and how we are trying reconcile them in the classroom. For further information about the project go to: http://www.physics.orst.edu/bridge

Assessing Peer Leader Skill Acquisition and Group Dynamics in a First-Year Calculus Course

ERIC Educational Resources Information Center

Glover, Rebecca; Hammond, Nicholas B.; Smith, Justin; Guerra, Dalyana

2018-01-01

Peer-led team learning (PLTL), specifically the model known as 'Workshops', has been shown to contribute positively and significantly to student success in STEM courses across subjects (Gosser et al., 2001). Our research adds to the SOTL literature describing the effectiveness of Workshops by reporting on the changes in student leaders. We examine…

An Evaluation of the Supplemental Instruction Programme in a First Year Calculus Course

ERIC Educational Resources Information Center

Fayowski, V.; MacMillan, P. D.

2008-01-01

Supplemental Instruction (SI) incorporates collaborative learning in small, peer-led, group settings in order to integrate instruction in learning and reasoning skills with course content. Several meta-analyses speak to the efficacy of SI but fail to address selection bias due to ability/motivation and gender. In this study, SI was paired with a…