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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

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

Nirode, Wayne – Mathematics Teacher, 2017

Since the 1970s, the Mathematical Association of America's (MAA) journals "Mathematics Magazine" and "College Mathematics Journal" have published "Proofs without Words" (PWWs) (Nelsen 1993). "PWWs are pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Secondary School Mathematics

Czocher, Jennifer A.; Moss, Diana L. – Mathematics Teacher, 2017

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Descriptors: Mathematical Models, Problem Solving, Mathematics Instruction, High School Students

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

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

Gonzalez, Gloriana; DeJarnette, Anna F. – Mathematics Teacher, 2013

What does problem-based instruction do for students and teachers? The open-ended geometry problem presented in this article, along with examples of students' work on the problem, illustrates how problem-based instruction can help students develop their mathematical proficiency. Recent studies have shown that students who experience problem-based…

Descriptors: Mathematical Logic, Mathematics Instruction, Geometry, Geometric Concepts

Roberts, Sally K.; Tayeh, Carla – Mathematics Teaching in the Middle School, 2010

To focus on mathematical reasoning and what makes a good argument, the authors developed an assignment that requires college students to submit a book of mathematical reasoning as an assessment during the semester. To begin, the authors looked for questions and tasks that lend themselves to developing mathematical arguments and justifications and…

Descriptors: Problem Solving, Mathematical Logic, College Students, College Mathematics

Muller, Kimberly O. – Mathematics Teacher, 2010

While serving in the U.S. Congress, Abraham Lincoln, a self-taught learner, mastered Euclid's Elements (Basler 1953). Most students today do not study mathematics for recreation. Unlike Lincoln, they need a little help in learning how to write a geometry proof. Today's technology--specifically, The Geometer's Sketchpad[R] (GSP)--can help make…

Descriptors: Secondary School Mathematics, Preservice Teachers, Mathematics Education, Geometry

Modica, Erasmo – Teaching Mathematics and Its Applications: An International Journal of the IMA, 2010

This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary…

Descriptors: Calculus, Algebra, Problem Solving, Mathematics Instruction

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2010

The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…

Descriptors: Geometry, Mathematical Logic, Validity, Mathematics Instruction

Johnson, Gwendolyn J.; Thompson, Denisse R.; Senk, Sharon L. – Mathematics Teacher, 2010

Recognizing that textbooks play a prominent role in fostering students' understanding of reasoning and proof, the authors conducted a study to examine the extent to which textbooks used in U.S. high schools provide opportunities for students to encounter proof-related reasoning and how the nature of proof-related reasoning in textbooks varies by…

Descriptors: High Schools, Textbooks, Mathematical Logic, Validity

Quinn, Anne Larson – Mathematics Teacher, 2009

Many students find proofs frustrating, and teachers struggle with how to help students write proofs. In fact, it is well documented that most students who have studied proofs in high school geometry courses do not master them and do not understand their function. And yet, according to NCTM's "Principles and Standards for School Mathematics"…

Descriptors: Mathematical Logic, Validity, Number Concepts, Teaching Methods

Chin, Cynthia E. – PRIMUS, 2007

The history of Fermat's Last Theorem, recounted in the theatrical piece "Fermat's Last Tango," is a useful vehicle for introducing students to the variety of personalities, processes, and products involved in advanced mathematical investigation. The musical's accessible, informative, and positive portrayal of mathematicians and their work is…

Descriptors: High School Students, Teaching Methods, Mathematics Instruction, Mathematical Concepts

Leadbetter, Mark – Mathematics Teaching Incorporating Micromath, 2007

In this article, the author describes a 200-year-old ladder problem that can carry learners to high levels of mathematical thinking and activity. This problem requires learners to go from a word problem to an equation to a graph and from there to a solution. As this problem of specifics is turned into a problem using variables, technology,…

Descriptors: Mathematics Instruction, Problem Solving, Mathematical Logic, Thinking Skills

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