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Showing 1 to 15 of 108 results Save | Export
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Gabriel Gianni Cantanelli; Barbara A. Shipman – PRIMUS, 2024
Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Visual Aids
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Jungeun Park; Jason Martin; Michael Oehrtman; Douglas Rizzolo – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
Our study explores teaching practices that aim to promote students' learning to define an analytical object. A Calculus II instructor conducted a teaching experiment (TE) in which 11 students reinvented a formal definition of a limit over five class periods with the instructor's guidance. During the TE, the instructor's teaching practices were…
Descriptors: Mathematics Teachers, Mathematics Instruction, Teaching Methods, Calculus
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Dae S. Hong; Jae Ki Lee – International Journal of Mathematical Education in Science and Technology, 2024
This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…
Descriptors: College Mathematics, Calculus, College Faculty, Teaching Methods
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Irma E. Stevens – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
Researchers have recommended using tasks that support students in reasoning covariationally to build productive meanings for graphs, rates of change, exponential growth, and more. However, not many recent studies have been done to identify how students reason when engaging in covariational reasoning tasks in undergraduate precalculus courses. In…
Descriptors: Undergraduate Students, College Mathematics, Calculus, Graphs
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Saba Gerami – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
In this study, I present how eight U.S. college calculus instructors with different patterns of inquiry practices used instructional situations to frame instructional tasks for introducing derivatives graphically to students. During four interviews, the instructors proposed up to eight tasks for introducing derivatives physically, graphically,…
Descriptors: College Mathematics, Mathematics Instruction, Teaching Methods, Undergraduate Students
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Soosloff, Elisa; Huey, Maryann; Alexander, Daniel S. – PRIMUS, 2023
In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…
Descriptors: Mathematics Instruction, Visual Aids, Prior Learning, Teaching Methods
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Smith, Joseph R.; Snapp, Bart; Madar, Savva; Brown, Jonathan R.; Fowler, Jim; Andersen, Maeve; Porter, Christopher D.; Orban, Chris – PRIMUS, 2023
We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google…
Descriptors: STEM Education, Telecommunications, Handheld Devices, Computer Simulation
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Hoban, Richard A. – International Journal of Mathematical Education in Science and Technology, 2021
Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope;…
Descriptors: Mathematical Concepts, Concept Formation, Mathematics Instruction, College Freshmen
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David, Erika J.; Hah Roh, Kyeong; Sellers, Morgan E. – PRIMUS, 2020
This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Students, Calculus
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David, Erika; Rah, Kyeong Hah; Sellers, Morgan – North American Chapter of the International Group for the Psychology of Mathematics Education, 2018
The purpose of this study is to examine the characteristics of students' thinking about graphs while evaluating statements from Calculus. We conducted clinical interviews in which undergraduate students evaluated mathematical statements using graphs to explain their reasoning. We report our classification of students' thinking about aspects of…
Descriptors: Calculus, Undergraduate Students, Mathematics Instruction, College Mathematics
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Mirin, Alison – North American Chapter of the International Group for the Psychology of Mathematics Education, 2018
This study focuses on students' understanding of multiple representations of functions. It examines student responses to a task in which calculus students are asked to evaluate the derivative at a point of the cubing function when represented piecewise. Results suggest that attending to the graph of the piecewise function does not improve…
Descriptors: Mathematics Instruction, Calculus, College Mathematics, Mathematical Concepts
Frank, Kristin Marianna – ProQuest LLC, 2017
Researchers have documented the importance of seeing a graph as an emergent trace of how two quantities' values vary simultaneously in order to reason about the graph in terms of quantitative relationships. If a student does not see a graph as a representation of how quantities change together then the student is limited to reasoning about…
Descriptors: Logical Thinking, Graphs, Calculus, College Students
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Samuels, Jason – Mathematics Teacher, 2017
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…
Descriptors: Mathematics Instruction, Calculus, Graphs, Problem Solving
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Ekici, Celil; Gard, Andrew – PRIMUS, 2017
In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…
Descriptors: Mathematics Instruction, Teaching Methods, Calculus, Mathematical Formulas
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Bakri, Syah Runniza Ahmad; Liew, Chin Ying; Chen, Chee Khium; Tuh, Moi Hua; Ling, Siew Ching – Asian Journal of University Education, 2020
Sketching the graph of mathematical functions using derivatives is a challenging task for undergraduate students who enrol for the first level of calculus course. Before graph plotting, students are required to perform a thorough function analysis using the concepts learned in differentiation. They are then expected to solicit the results obtained…
Descriptors: Calculus, Mathematics Instruction, College Mathematics, Undergraduate Students
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