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Robert J. Fisher – Chemical Engineering Education, 2025
Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…
Descriptors: Chemical Engineering, Mathematics, Problem Solving, Skill Development
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Dae S. Hong – School Science and Mathematics, 2024
This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.
Descriptors: Educational Opportunities, Calculus, Instructional Materials, Teaching Methods
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Aguiar, C. E.; Barroso, M. F.; Dias, P. M. C.; Francisquini, M. F. B. – Physics Education, 2022
Difficulties presented by students on the concept of instantaneous velocity are well known. This is in part due to instantaneous speed being often defined in terms of the notion of mathematical limit, which may not be clear to many students in introductory physics courses. In this work we present a complementary teaching proposal that can help…
Descriptors: Physics, Scientific Concepts, Difficulty Level, Mathematics
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Kondratieva, Margo; Winsløw, Carl – International Journal of Research in Undergraduate Mathematics Education, 2018
We present a theoretical approach to the problem of the transition from Calculus to Analysis within the undergraduate mathematics curriculum. First, we formulate this problem using the anthropological theory of the didactic, in particular the notion of praxeology, along with a possible solution related to Klein's "Plan B": here,…
Descriptors: Mathematics Instruction, Teaching Methods, Calculus, Computation
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Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2018
This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around…
Descriptors: Mathematics Instruction, Calculus, Problem Solving, Case Studies
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Madrazo, Anthony Loria; Dio, Ryan Villareas – Journal on Mathematics Education, 2020
The transition of the educational system in the Philippines vastly affects basic and higher education. A mismatch of pre-requisite Mathematics learning competencies from the basic education level occurred when the student reached higher education. This descriptive-developmental method of the study utilized the developed contextualized learning…
Descriptors: Calculus, Mathematics Instruction, Geometry, Independent Study
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Soares, A.; dos Santos, A. L. – International Journal of Mathematical Education in Science and Technology, 2017
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…
Descriptors: Introductory Courses, Mathematics Instruction, Calculus, Mathematical Logic
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Caglayan, Gunhan – International Journal of Mathematical Education in Science and Technology, 2016
The purpose of this article is to offer teaching ideas in the treatment of the definite integral concept and the Riemann sums in a technology-supported environment. Specifically, the article offers teaching ideas and activities for classroom for the numerical methods of approximating a definite integral via left- and right-hand Riemann sums, along…
Descriptors: Teaching Methods, Technology Integration, Mathematics, Mathematics Education
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Dickman, Benjamin – Mathematics Teacher, 2016
Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…
Descriptors: Problem Solving, Mathematics Instruction, Calculus, Fractions
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Johnson, Estrella; Ellis, Jessica; Rasmussen, Chris – International Journal of Mathematical Education in Science and Technology, 2016
This paper is based on a large-scale empirical study designed to investigate Calculus I programmes across the United States to better understand the relationship between instructors' concerns about coverage, instructional practices, and the nature of the material covered. We found that there was no association between instructors feeling pressured…
Descriptors: College Mathematics, Mathematics, Mathematics Instruction, Calculus
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Zandieh, Michelle; Wawro, Megan; Rasmussen, Chris – PRIMUS, 2017
In this paper we address practical questions such as: How do symbols appear and evolve in an inquiry-oriented classroom? How can an instructor connect students with traditional notation and vocabulary without undermining their sense of ownership of the material? We tender an example from linear algebra that highlights the roles of the instructor…
Descriptors: Algebra, Mathematics, Mathematics Instruction, Mathematics Education
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López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael – International Journal of Mathematical Education in Science and Technology, 2016
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
Descriptors: Equations (Mathematics), Semi Structured Interviews, Undergraduate Students, Calculus
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Duzhin, Fedor; Gustafsson, Anders – Education Sciences, 2018
Course instructors need to assess the efficacy of their teaching methods, but experiments in education are seldom politically, administratively, or ethically feasible. Quasi-experimental tools, on the other hand, are often problematic, as they are typically too complicated to be of widespread use to educators and may suffer from selection bias…
Descriptors: Self Evaluation (Individuals), Artificial Intelligence, College Faculty, Instructional Effectiveness
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Kissane, Barry – Australian Senior Mathematics Journal, 2016
Two decades ago, in an award-winning paper, Dan Kennedy (1995) likened learning mathematics to climbing a tree, for which there was only one way to climb: up a large and solid trunk. In the limited time that is available, many students give up the climb, impede others, fall off the trunk, or fail to climb the tree sufficiently well. In the case of…
Descriptors: Technology Integration, Mathematics, Mathematics Education, Comparative Analysis
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Liang, Senfeng – International Journal of Research in Education and Science, 2016
Although the mathematics community has long accepted the concept of limit as the foundation of modern Calculus, the concept of limit itself has been marginalized in undergraduate Calculus education. In this paper, I analyze the strategy of conceptual conflict to teach the concept of limit with the aid of an online tool--Desmos graphing calculator.…
Descriptors: Graphing Calculators, Mathematics, Mathematics Instruction, Mathematical Concepts
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