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Khalili, Parviz; Vasiliu, Daniel – International Journal of Mathematical Education in Science and Technology, 2010

In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.

Descriptors: Calculus, Mathematics Education, Mathematical Logic, Validity

Kay, Robin; Kletskin, Ilona – Computers & Education, 2012

Problem-based video podcasts provide short, web-based, audio-visual explanations of how to solve specific procedural problems in subject areas such as mathematics or science. A series of 59 problem-based video podcasts covering five key areas (operations with functions, solving equations, linear functions, exponential and logarithmic functions,…

Descriptors: Video Technology, Higher Education, Mathematics Education, Calculus

Bowers, Diana; Foley, Virginia P. – Journal of Academic Administration in Higher Education, 2018

The purpose of this study was to determine if there was a significant relationship between students who entered a Tennessee university for the first time in the fall of 2014 who had earned either Advanced Placement (AP) or dual enrollment credit and their college readiness and 1-year college retention. College readiness was defined by students'…

Descriptors: Advanced Placement, Dual Enrollment, College Readiness, School Holding Power

Pavao, H. Germano; Capelas de Oliveira, E. – International Journal of Mathematical Education in Science and Technology, 2008

We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)

Descriptors: Trigonometry, Calculus, Mathematics Instruction, Computation

Andreescu, Titu; Cordeiro, Kathy; Andreescu, Alina – John Wiley & Sons, Inc, 2019

Professionals throughout the education system are recognizing that standardized testing is holding students back. Schools tend to view children as "outcomes" rather than as "individuals" who require guidance on thinking critically and creatively. "Awesome Math" focuses on team-based problem solving to teach discrete…

Descriptors: Mathematics Instruction, Teaching Methods, Problem Based Learning, Problem Solving

Kawash, Jalal – Journal of Computers in Mathematics and Science Teaching, 2004

The Structured Query Language (SQL) forms a substantial component of introductory database courses and is supported by almost every commercial database product. One disadvantage of SQL is that it does not provide a universal quantification construct. Queries that have twisted universal and existential quantifiers can be stunning for students,…

Descriptors: Databases, Database Design, Calculus, Translation

Peer reviewed

Henderson, Ronald W.; Landesman, Edward M. – Journal of Educational Technology Systems, 1989

Reports on the design considerations involved in the development of a series of interactive videodisc modules in pre-calculus mathematics. Topics discussed include math deficiencies and anxieties at the college level; videodisc and microcomputer technology; instructional design; learning theories; and the results of two field tests in secondary…

Descriptors: Calculus, Field Tests, Higher Education, Instructional Design

Nagle, Courtney Rose – ProQuest LLC, 2012

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

Descriptors: Mathematics Education, Calculus, Mathematical Concepts, High School Students

Sullivan, Patrick – ProQuest LLC, 2013

The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus…

Descriptors: Secondary School Mathematics, Algebra, High School Students, Symbols (Mathematics)

Heckler, Andrew F.; Bogdan, Abigail M. – Physical Review Physics Education Research, 2018

A critical component of scientific reasoning is the consideration of alternative explanations. Recognizing that decades of cognitive psychology research have demonstrated that relative cognitive accessibility, or "what comes to mind," strongly affects how people reason in a given context, we articulate a simple "cognitive…

Descriptors: Science Process Skills, Abstract Reasoning, Thinking Skills, Physics

Glaister, P. – Mathematics and Computer Education, 2004

This article shows how Pythagorean triples can be generated naturally from a class of infinite series whose sums are zero, making surprising and interesting connections between different areas mathematics. This material can be suitable for use by teachers and students at various levels, but the simplest forms of the ideas may be best understood at…

Descriptors: Mathematical Concepts, Mathematics Instruction, Geometry

Williamson, S. Gill – 1987

This textbook was designed for a first course in differential and integral calculus, and is directed toward students in engineering, the sciences, mathematics, and computer science. Its major goal is to bring students to a level of technical competence and intuitive understanding of calculus that is adequate for applying the subject to real world…

Descriptors: Algorithms, Calculus, College Mathematics, Functions (Mathematics)

Chen, Hongwei – International Journal of Mathematical Education in Science & Technology, 2006

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

Descriptors: Calculus, Mathematical Logic, Validity, Equations (Mathematics)

Glaister, P. – Mathematics and Computer Education, 2005

In this paper, the author gives a further simple generalization of a power series evaluation of an integral using Taylor series to derive the result. The author encourages readers to consider numerical methods to evaluate the integrals and sums. Such methods are suitable for use in courses in advanced calculus and numerical analysis.

Descriptors: Calculus, Computation, Mathematical Concepts, Generalization

Donovan, William; Wurman, Ze'ev – Pioneer Institute for Public Policy Research, 2019

This paper looks at the popularity of after-school mathematics by focusing on the Kumon and Russian School of Mathematics models. In 1954, Toru Kumon, a high school math teacher in Japan, designed a series of math worksheets to help improve the test scores of his son Takeshi, a second grader. Toru's goal was to teach Takeshi how to learn…

Descriptors: Foreign Countries, After School Programs, Mathematics Instruction, Teaching Methods