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Mingari Scarpello, Giovanni; Ritelli, Daniele – International Journal of Mathematical Education in Science and Technology, 2019
When Johann Bernoulli published his lectures on integrals in 1742, integral calculus had become very advanced since the time of their composition in 1692. Nevertheless, these lectures are of excellent clarity and simplicity even when the book deals with major problems of Mathematical Physics. Just to pique some interest, we offer a commented…
Descriptors: Educational History, Textbooks, Mathematics Education, Calculus
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Royer, Melvin – PRIMUS, 2012
Gabriel's Horn is a solid of revolution commonly featured in calculus textbooks as a counter-intuitive example of a solid having finite volume but infinite surface area. Other examples of solids with surprising geometrical finitude relationships have also appeared in the literature. This article cites several intriguing examples (some of fractal…
Descriptors: Mathematics Education, Textbooks, Scientific Concepts, Calculus
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Chen, Zhibo – Teaching Mathematics and Its Applications: An International Journal of the IMA, 2012
A new application of logarithmic differentiation is presented, which provides an alternative elegant proof of two basic rules of differentiation: the product rule and the quotient rule. The proof can intrigue students, help promote their critical thinking and rigorous reasoning and deepen their understanding of previously encountered concepts. The…
Descriptors: Numbers, Mathematical Logic, Validity, Critical Thinking
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McGee, Daniel Lee; Moore-Russo, Deborah – International Journal of Science and Mathematics Education, 2015
In two dimensions (2D), representations associated with slopes are seen in numerous forms before representations associated with derivatives are presented. These include the slope between two points and the constant slope of a linear function of a single variable. In almost all multivariable calculus textbooks, however, the first discussion of…
Descriptors: Mathematics Instruction, Mathematical Concepts, Calculus, Semiotics
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Jones, Steven R. – Mathematics Teacher, 2013
Calculus instruction is an important topic for high school and college teachers alike. A prime target for attention is integration, which, unfortunately, students too often treat as a rote procedure. Understanding the integral better will support students' application of their mathematical knowledge to science, technology, and engineering…
Descriptors: Mathematics Instruction, Calculus, Mathematical Concepts, Teaching Methods
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Trigueros Gaisman, María; Martínez-Planell, Rafael – North American Chapter of the International Group for the Psychology of Mathematics Education, 2011
This is a study about how graphs of functions of two-variables are taught. We are interested in particular in the techniques introduced to draw and analyze these graphs. This continues previous work dedicated to students' understanding of topics of two-variable functions in multivariable calculus courses. The model of the "moments of…
Descriptors: Mathematics Instruction, Teaching Methods, Graphs, Calculus
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Capaldi, Mindy – PRIMUS, 2020
Definitions are fundamental to any mathematics classroom. We consider how definitions are presented in textbooks and instructors' lecture notes, and whether students are positioned to gain a full understanding of new terms. Four textbooks, covering precalculus, calculus, and analysis, as well as three professors' Calculus I lecture notes are…
Descriptors: Mathematics Instruction, College Mathematics, Definitions, Textbooks
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Randahl, Mira – International Journal of Mathematical Education in Science and Technology, 2012
The aim of this article is to present and discuss some results from an inquiry into mathematics textbooks authors' visions about their texts and approaches they choose when new concepts are introduced. Authors' responses are discussed in relation to results about students' difficulties with approaching calculus reported by previous research. A…
Descriptors: Mathematics, Textbooks, Postsecondary Education, Mathematical Concepts
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Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen – International Journal of Mathematical Education in Science and Technology, 2011
"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…
Descriptors: Textbooks, Mathematical Models, Physics, Problem Solving
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Wu, Yan – International Journal of Mathematical Education in Science and Technology, 2009
A closed form solution for the trigonometric integral [integral]sec[superscript 2k+1]xdx, k=0,1,2,..., is presented in this article. The result will fill the gap in another trigonometric integral [integral]sec[superscript 2m+1] x tan[superscript 2n]xdx, which is neglected by most of the calculus textbooks due to its foreseeable unorthodox solution…
Descriptors: Calculus, Mathematics Instruction, Problem Solving, Trigonometry
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Park, Jungeun; Flores, Alfinio – North American Chapter of the International Group for the Psychology of Mathematics Education, 2012
This paper explores how textbooks address two central concepts in differential calculus, derivative at a point and derivative function, make the transition from one concept to the other, and establish connections between them. We analyzed how the three most widely used calculus textbooks present these two aspects of the derivative, focusing on…
Descriptors: Calculus, Mathematics Instruction, Textbook Evaluation, Mathematical Concepts
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Hu, Chenglie – PRIMUS, 2007
This article presents a way of computing a surface integral when the vector field of the integrand is a curl field. Presented in some advanced calculus textbooks such as [1], the technique, as the author experienced, is simple and applicable. The computation is based on Stokes' theorem in 3-space calculus, and thus provides not only a means to…
Descriptors: Calculus, Mathematics Instruction, Computation, Validity
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Rodriguez, Jon-Marc G.; Bain, Kinsey; Towns, Marcy H. – International Journal of Science and Mathematics Education, 2020
In this paper, we introduce and discuss a construct called "graphical forms," an extension of Sherin's symbolic forms. In its original conceptualization, symbolic forms characterize the ideas students associate with patterns in a mathematical expression. To expand symbolic forms beyond only characterizing mathematical equations, we use…
Descriptors: Mathematical Logic, Mathematics Skills, Symbols (Mathematics), Graphs
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Brehmer, Daniel; Ryve, Andreas; Van Steenbrugge, Hendrik – Scandinavian Journal of Educational Research, 2016
The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…
Descriptors: Problem Solving, Mathematics Instruction, Textbooks, Content Analysis
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Ruby, Lawrence – Physics Teacher, 2009
In 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, and…
Descriptors: Textbooks, Educational Philosophy, Mechanics (Physics), Scientific Concepts
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