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Edwards, Thomas G.; Chelst, Kenneth R. – Mathematics Teacher, 2019
While tutoring his granddaughter in second-year algebra recently, the second author lamented that every textbook he could find expresses the quadratic formula as probably the most common form of the formula. What troubled him is that this form hides the meaning of the various components of the equation. Indeed, the meaning was obscured by the…
Descriptors: Mathematics Instruction, Mathematical Formulas, Algebra, Teaching Methods
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Rebholz, Joachim A. – Mathematics Teacher, 2017
Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…
Descriptors: Mathematics Instruction, High School Students, Secondary School Mathematics, Graphs
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Kirwan, J. Vince – Mathematics Teacher, 2017
Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…
Descriptors: Visualization, Mathematics Instruction, Teaching Methods, Algebra
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Richardson, Janessa; Bachman, Rachel M. – Mathematics Teacher, 2017
This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…
Descriptors: Preservice Teachers, Mathematics Instruction, Mathematical Concepts, Mathematical Logic
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Johnson, Heather Lynn; Hornbein, Peter; Azeem, Sumbal – Mathematics Teacher, 2016
The authors provide a dynamic Ferris wheel computer activity that teachers can use as an instructional tool to help students investigate functions. They use a student's work to illustrate how students can use relationships between quantities to further their thinking about functions.
Descriptors: Mathematics Instruction, Teaching Methods, Educational Technology, Computer Uses in Education
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Anhalt, Cynthia Oropesa; Cortez, Ricardo – Mathematics Teacher, 2015
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Descriptors: Mathematics Instruction, Mathematical Models, Teaching Methods, Mathematical Concepts
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Kurz, Terri L.; Garcia, Jorge – Mathematics Teacher, 2015
Since the 1950s, the understanding of how the base 10 system works has been encouraged through alternative base systems (Price 1995; Woodward 2004). If high school students are given opportunities to learn other base systems and analyze what they denote, we believe that they will better understand the structure of base 10 and its operations…
Descriptors: Mathematics Instruction, Mathematical Concepts, Teaching Methods, Grade 8
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Wendt, Ted; Murphy, Kevin – Mathematics Teacher, 2015
According to a 2012 study from the Program for International Student Assessment, twenty-nine out of sixty-five participating nations and other jurisdictions outperformed the United States in mathematics by a statistically significant margin (up from twenty-three in 2009) (Heitin 2013). To improve students' mathematical understanding, the authors…
Descriptors: Mathematics Instruction, Mathematics Achievement, Common Core State Standards, Mathematics Skills
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Fonger, Nicole L. – Mathematics Teacher, 2014
How can the key concept of equivalent expressions be addressed so that students strengthen their representational fluency with symbols, graphs, and numbers? How can research inform the synergistic use of both paper-and-pencil analysis and computer algebra systems (CAS) in a classroom learning environment? These and other related questions have…
Descriptors: Mathematics Instruction, Mathematical Concepts, Computer Uses in Education, Algebra
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Viro, Julia – Mathematics Teacher, 2014
Constructing viable arguments and reasoning abstractly is an essential part of the Common Core State Standards for Mathematics (CCSSI 2010). This article discusses the scenarios in which a mathematical task is impossible to accomplish, as well as how to approach impossible scenarios in the classroom. The concept of proof is introduced as the…
Descriptors: Mathematics Instruction, Mathematical Concepts, Validity, Mathematical Logic
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Hillen, Amy F.; Malik, LuAnn – Mathematics Teacher, 2013
Card sorting has the potential to provide opportunities for exploration of a variety of topics and levels. In a card-sorting task, each participant is presented with a set of cards--each of which depicts a relationship--and is asked to sort the cards into categories that make sense to him or her. The concept of function is critical to…
Descriptors: Mathematics Instruction, Mathematical Concepts, Faculty Development, Secondary School Teachers
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Allen, Kasi C. – Mathematics Teacher, 2013
Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…
Descriptors: Algebra, Mathematics Instruction, High School Students, Secondary School Mathematics
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Zelkowski, Jeremy S. – Mathematics Teacher, 2013
Principles and Standards for School Mathematics (NCTM 2000) states, "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." The focus on reasoning and sense making with technology in the lesson presented in this article will enable students to do more…
Descriptors: Mathematics Instruction, Educational Technology, Mathematical Concepts, Teaching Methods
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Fernandez, Eileen; Geist, Kristi A. – Mathematics Teacher, 2011
Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy. The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population,…
Descriptors: Textbooks, Calculus, Mathematics Instruction, Mathematical Concepts
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Ellis, Mark W.; Bryson, Janet L. – Mathematics Teacher, 2011
The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…
Descriptors: Mathematics Instruction, Equations (Mathematics), Teaching Methods, Secondary School Mathematics
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