Download or read book The Relationship Between College Calculus Students Understanding of Function and Their Understanding of Derivative written by Marlene Kay Pinzka and published by . This book was released on 1999 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Teaching and Learning of Calculus written by David Bressoud and published by Springer. This book was released on 2016-06-14 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.
Download or read book Analysis with Ultrasmall Numbers written by Karel Hrbacek and published by CRC Press. This book was released on 2014-12-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon–delta methods. Students can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book is suitable for a calculus course at the undergraduate or high school level or for self-study with an emphasis on nonstandard methods. The first part of the text offers material for an elementary calculus course while the second part covers more advanced calculus topics. The text provides straightforward definitions of basic concepts, enabling students to form good intuition and actually prove things by themselves. It does not require any additional "black boxes" once the initial axioms have been presented. The text also includes numerous exercises throughout and at the end of each chapter.
Download or read book The Effect of Emphasizing Multiple Representations on Calculus Student s Understanding of the Derivative Concept written by Sonja Lee Goerdt and published by . This book was released on 2007 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elementary Calculus written by H. Jerome Keisler and published by Orange Groove Books. This book was released on 2009-09-01 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Student Understanding of Function and Success in Calculus written by Daniel I. Drlik and published by . This book was released on 2015 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus. A major finding of this study is that students can be successful in a first-year calculus course without demonstrating a process level understanding of function at the beginning of the course. In general, a positive correlation between understanding of function and success in calculus was found. An item-by-item analysis of the two questionnaires revealed that students demonstrated competence, relative to their measured understanding of function, with items that are typically presented in standard mathematics courses taken prior to calculus, such as when provided a function as an algebraic rule and asked to calculate the value of the function. Also, students tended to justify decisions for solutions based on criteria not necessarily related to the definition of function. This however, appeared to have little impact on the level of success a student was able to achieve in calculus."--Boise State University ScholarWorks.
Download or read book Grade Inflation written by Valen E. Johnson and published by Springer Science & Business Media. This book was released on 2006-05-09 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grade inflation runs rampant at most colleges and universities, but faculty and administrators are seemingly unwilling to face the problem. This book explains why, exposing many of the misconceptions surrounding college grading. Based on historical research and the results of a yearlong, on-line course evaluation experiment conducted at Duke University during the 1998-1999 academic year, the effects of student grading on various educational processes, and their subsequent impact on student and faculty behavior, is examined. Principal conclusions of this investigation are that instructors' grading practices have a significant influence on end-of-course teaching evaluations, and that student expectations of grading practices play an important role in the courses that students decide to take. The latter effect has a serious impact on course enrollments in the natural sciences and mathematics, while the combination of both mean that faculty have an incentive to award high grades, and students have an incentive to choose courses with faculty who do. Grade inflation is the natural consequence of this incentive system. Material contained in this book is essential reading for anyone involved in efforts to reform our postsecondary educational system, or for those who simply wish to survive and prosper in it. Valen Johnson is a Professor of Biostatistics at the University of Michigan. Prior to accepting an appointment in Ann Arbor, he was a Professor of Statistics and Decision Sciences at Duke University, where data for this book was collected. He is a Fellow of the American Statistical Association.
Download or read book Students Qualitative Understanding of the Relationship Between the Graph of a Function and the Graphs of Its Derivatives written by John R. Stahley and published by . This book was released on 2011 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Investigation of University Students Understanding of the Fundamental Theorem of Calculus written by Julie Ellen Dent and published by . This book was released on 1995 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Learning and Understanding written by National Research Council and published by National Academies Press. This book was released on 2002-08-06 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a fresh look at programs for advanced studies for high school students in the United States, with a particular focus on the Advanced Placement and the International Baccalaureate programs, and asks how advanced studies can be significantly improved in general. It also examines two of the core issues surrounding these programs: they can have a profound impact on other components of the education system and participation in the programs has become key to admission at selective institutions of higher education. By looking at what could enhance the quality of high school advanced study programs as well as what precedes and comes after these programs, this report provides teachers, parents, curriculum developers, administrators, college science and mathematics faculty, and the educational research community with a detailed assessment that can be used to guide change within advanced study programs.
Download or read book Foundations of Differential Calculus written by Euler and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.
Download or read book Active Calculus 2018 written by Matthew Boelkins and published by Createspace Independent Publishing Platform. This book was released on 2018-08-13 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.
Download or read book The Evolution of Student Understanding of the Concept of Derivative written by Michelle J. Zandieh and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This research seeks to answer the question, "What does it mean for a student to understand the concept of derivative?" A structured way to describe an individual student's understanding of derivative is developed and applied to analyzing the evolution of that understanding for each of nine high school seniors during their year-long calculus course. The methodology is a multiple case study. Interviews, including both task-based and open-ended questions, are the primary instruments for collecting data on each student's understanding. Other data collected include tests, written questions, and classroom observations. Several theoretical frameworks contribute to the research: concept image (Tall, Vinner, and Dreyfus), process-object (Sfard; Dubinsky and colleagues), and notions of multiple representations for function, limit, and derivative. I describe the concept of derivative as three layers of process-objects: the ratio or difference quotient, the limit, and the function layers. Each layer may be observed in multiple contexts: graphical (slope), verbal description (rate of change), kinematic (e.g. velocity or acceleration), and symbolic (the symbolic difference quotient definition of derivative). A description of the connections between the various aspects of the concept of derivative comes from the work of Fischbein on paradigmatic, analogic, and diagrammatic models and the work of Lakoff on metaphor and metonymy. The major theoretical result of the dissertation is the development of a structured way of describing the concept of derivative including a diagrammatic methodology for displaying which aspects of the derivative concept a student has demonstrated. This methodology may be applied to other studies and other concepts. The major result of this study of nine students is the realization that the layers and representations of the concept of derivative do not appear to be hierarchical in that none of the nine students learn the aspects in the same order.
Download or read book Second Year Calculus written by David M. Bressoud and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.
Download or read book An Investigation of First Year Calculus Students Understanding of the Derivative written by Kathleen Gerard Snook and published by . This book was released on 1997 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Beginning Calculus Students Understanding of the Derivative written by Susan F. Pustejovsky and published by . This book was released on 1999 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
