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Teuscher, Dawn; Palsky, Kylie; Palfreyman, Charlie Y. – Mathematics Teacher, 2018

The goal of this article is to raise questions that will promote discussions among secondary mathematics teachers about the concept of inverse functions and how to motivate a more conceptual understanding of them in their classrooms. The authors share data to answer the following questions: (1) What meanings of inverse functions do high school…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Mathematical Concepts, Teaching Methods

Nabb, Keith; Hofacker, Erick B.; Ernie, Kathryn T.; Ahrendt, Susan – Mathematics Teacher, 2018

This article highlights three of the eight Mathematics Teaching Practices (MTP) published in the National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" (2014): (1) facilitating meaningful mathematical discourse (MTP 4); (2) posing purposeful questions (MTP 5); and (3)…

Descriptors: Mathematics Instruction, Teaching Methods, Active Learning, Calculus

Davis, Anna A.; Joswick, Candace – Mathematics Teacher, 2018

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600…

Descriptors: Mathematics Instruction, Computer Graphics, Computer Simulation, Teaching Methods

Popelka, Susan R.; Langlois, Joshua – Mathematics Teacher, 2018

"Flatland: A Romance of Many Dimensions" is an 1884 novella written by English schoolmaster Edwin Abbott. He describes what it would be like to live in a two-dimensional (2D) world--Flatland. It is fascinating reading that underscores the challenge of teaching three-dimensional (3D) mathematics using 2D tools. Real-world applications of…

Descriptors: High School Students, Secondary School Mathematics, Calculus, Computer Uses in Education

Adams, Caleb L. – Mathematics Teacher, 2018

Polynomials with rational roots and extrema may be difficult to create. Although techniques for solving cubic polynomials exist, students struggle with solutions that are in a complicated format. Presented in this article is a way instructors may wish to introduce the topics of roots and critical numbers of polynomial functions in calculus. In a…

Descriptors: Mathematics Instruction, Calculus, Mathematical Concepts, Concept Formation

Wagner, Jennifer; Sharp, Janet – Mathematics Teacher, 2017

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

Descriptors: Calculus, Mathematics Instruction, Mathematical Concepts, Concept Formation

Kress, Nancy Emerson – Mathematics Teacher, 2017

One of the primary expectations that the author has for her students is for them to develop greater independence when solving complex and unique mathematical problems. The story of how the author supports her students as they gain confidence and independence with complex and unique problem-solving tasks, while honoring their expectations with…

Descriptors: Mathematics Instruction, Problem Solving, Models, Teacher Student Relationship

Lommatsch, Christina W. – Mathematics Teacher, 2017

"Find the extreme values of the function." "At what rate is the distance between A and B increasing after 12 seconds?" Prompts like these can be heard in most first-semester calculus courses. Unfortunately, these cues also tend to prompt students' eyes to glaze over with thoughts of "When will I ever use this?" This…

Descriptors: Mathematics Instruction, Calculus, Relevance (Education), Career Choice

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

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

Gunter, Devon – Mathematics Teacher, 2016

It is no easy feat to engage young people with abstract material as well as push them to greater depths of understanding. Add in the extra pressures of curriculum expectations and standards and the problem is exacerbated. Projects designed around standards and having multiple entry points clearly offer students the best opportunity to engage with…

Descriptors: Algebra, Calculus, Student Projects, Motion

Stephens, Greg – Mathematics Teacher, 2016

Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

Descriptors: Mathematics Instruction, Equations (Mathematics), Technology Uses in Education, Educational Technology

Ferguson, Sarah – Mathematics Teacher, 2016

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

Descriptors: Advanced Placement Programs, Calculus, Mathematics Instruction, Learning Activities

Yang, Yajun; Gordon, Sheldon P. – Mathematics Teacher, 2014

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

Descriptors: Mathematical Formulas, Calculus, Algebra, Mathematical Concepts

Nabb, Keith – Mathematics Teacher, 2013

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

Descriptors: Calculus, Introductory Courses, Mathematics Instruction, Algebra

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