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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

Nabbout-Cheiban, Marie; Fisher, Forest; Edwards, Michael Todd – Mathematics Teacher, 2017

The Common Core State Standards for Mathematics envisions data analysis as a key component of K-grade 12 mathematics instruction with statistics introduced in the early grades. Nonetheless, deficiencies in statistical learning persist throughout elementary school and beyond. Too often, mathematics teachers lack the statistical knowledge for…

Descriptors: Mathematics Instruction, Technology Uses in Education, Educational Technology, Statistics

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

Quintanilla, John A. – Mathematics Teacher, 2017

Exploration with spreadsheets and reliance on previous skills can lead students to determine the line of best fit. To perform linear regression on a set of data, students in Algebra 2 (or, in principle, Algebra 1) do not have to settle for using the mysterious "black box" of their graphing calculators (or other classroom technologies).…

Descriptors: Algebra, Mathematics Instruction, Regression (Statistics), Spreadsheets

Wanko, Jeffrey J. – Mathematics Teacher, 2017

Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

Descriptors: Mathematics Instruction, Teaching Methods, Puzzles, Logical Thinking

Goldenberg, E. Paul; Carter, Cynthia J.; Mark, June; Nikula, Johannah; Spencer, Deborah B. – Mathematics Teacher, 2017

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

Descriptors: Mathematics Education, Mathematics Instruction, Common Core State Standards, Mathematics Skills

Lo, Chung Kwan – Mathematics Teacher, 2017

There is a growing interest in using a flipped classroom format in day-to-day teaching. Direct computer-based individual instruction outside the classroom and interactive group learning activities inside the classroom are the two essential components of the flipped classroom model. By watching instructional videos, students can work through some…

Descriptors: Action Research, Video Technology, Teaching Methods, Grade 8

Paoletti, Teo; Monahan, Ceire; Vishnubhotla, Madhavi – Mathematics Teacher, 2017

GeoGebra is a free tool that has the potential to change both how and what is taught in mathematics. GeoGebra allows teachers and students to explore various mathematical ideas either through the full applet (https://www.geogebra.org/graphing) or by sharing applets via GeoGebra's Materials site (https://www.geogebra. org/materials/). It has many…

Descriptors: Computer Oriented Programs, Mathematics Instruction, Learner Engagement, Geometry

Rapke, Tina – Mathematics Teacher, 2017

Many studies have claimed that traditional testing actually promotes students' use of superficial approaches to learning. When preparing to take tests, students typically memorize and cram rather than understanding the material and gaining new perspectives. This article describes how the author recast traditional tests by having students take a…

Descriptors: Mathematics Instruction, Mathematics Tests, Formative Evaluation, Summative Evaluation

Lee, Younhee; Lim, Woong – Mathematics Teacher, 2017

Understanding how one representation connects to another and how the essential ideas in that relationship are generalized can result in a mathematical theorem or a formula. In this article, the authors demonstrate this process by connecting a vector cross product in algebraic form to a geometric representation and applying a key mathematical idea…

Descriptors: Mathematics Education, Geometric Concepts, Algebra, Mathematical Formulas

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

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

McGraw, Rebecca – Mathematics Teacher, 2017

The task shared in this article provides geometry students with opportunities to recall and use basic geometry vocabulary, extend their knowledge of area relationships, and create area formulas. It is characterized by reasoning and sense making (NCTM 2009) and the "Construct viable arguments and critique the reasoning of others"…

Descriptors: Mathematics Education, Geometric Concepts, Mathematical Formulas, Mathematics Skills

McCulloch, Allison W.; Whitehead, Ashley; Lovett, Jennifer N.; Whitley, Blake – Mathematics Teacher, 2017

Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

Descriptors: Mathematics Instruction, Audio Equipment, Textbooks, Word Problems (Mathematics)

Shriver, Janet; Willard, Teri; McDaniel, Mandy – Mathematics Teacher, 2017

In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…

Descriptors: Mathematics Instruction, Learning Activities, Algebra, Models