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Cetner, Michelle – Mathematics Teacher, 2015

When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…

Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Algebra

Cupillari, Antonella – Mathematics Teacher, 2015

Practical problems that use mathematical concepts are among the highlights of any mathematics class, for better and for worse. Teachers are thrilled to show applications of new theoretical ideas, whereas most students dread "word problems." This article presents a sequence of three activities designed to get students to think about…

Descriptors: Mathematical Concepts, Word Problems (Mathematics), Mathematics Activities, Geometric Concepts

Ponce, Gregorio A.; Tuba, Imre – Mathematics Teacher, 2015

New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

Descriptors: Equations (Mathematics), Instructional Innovation, Teaching Methods, Creative Teaching

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

Garofalo, Joe; Trinter, Christine P.; Swartz, Barbara A. – Mathematics Teacher, 2015

One method of proof is to provide a logical argument that demonstrates the existence of a mathematical object (e.g., a number) that can be used to prove or disprove a conjecture or statement. Some such proofs result in the actual identification of such an object, whereas others just demonstrate that such an object exists. These types of proofs are…

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

Nebesniak, Amy L.; Burgoa, A. Aaron – Mathematics Teacher, 2015

As teachers working with students in entry-level algebra classes, authors Amy Nebesniak and A. Aaron Burgoa realized that their instruction was a major factor in how their students viewed mathematics. They often presented students with abstract formulas that seemed to appear out of thin air. One instance occurred while they were teaching students…

Descriptors: Mathematics Instruction, Algebra, Equations (Mathematics), Mathematical Formulas

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

Perham, Arnold E.; Perham, Faustine L. – Mathematics Teacher, 2015

The Transcontinental Railroad began laying track east from Sacramento, California, in 1863 and west from Omaha, Nebraska, in 1865; the two lines eventually met in Promontory Summit, Utah, in 1869. One of the train towns, Ogallala, Nebraska, consisted of only a section house and water tank alongside newly laid track. Over the next few years, train…

Descriptors: Mathematics Instruction, Interdisciplinary Approach, United States History, Transportation

Conner, Kimberly – Mathematics Teacher, 2015

This article is based on the author's experiences as a second-year teacher at a small private school teaching all sections of Geometry and Algebra 2. Working with the same students in both courses, the author was aware of each one's levels of retention and execution of Algebra 1 concepts before the beginning of the year. The author often noticed…

Descriptors: Algebra, Private Schools, Geometry, Mathematics Skills

DeJarnette, Anna F.; Rosado Lausell, Sahid L.; González, Gloriana – Mathematics Teacher, 2015

How can geometry teachers design great tasks that allow students to make connections among interrelated concepts and expand their geometric reasoning skills? Many curricular materials provide problems for students to apply a single geometric concept. However, these problems do not always promote reasoning opportunities for students, because…

Descriptors: Geometry, Geometric Concepts, Task Analysis, Mathematics Activities

Cargile, Lori A. – Mathematics Teacher, 2015

Khan Academy, the free Web-based tutorial program, landed on the education landscape in about 2011, when it was featured on the popular weekly news show "60 Minutes." The program is now used worldwide by more than 10 million learners each month and is used in more than 29,000 classrooms in 216 countries. Are classroom teachers using the…

Descriptors: Web Based Instruction, Tutorial Programs, Teaching Methods, Mathematics Instruction

Hsiao, Joy – Mathematics Teacher, 2015

Paper folding, or origami in Japanese, is a traditional craft that has been enjoyed by both children and adults for hundreds of years. Mathematicians have long studied the mathematics of paper folding. They use square papers to construct mathematical shapes (for example, folding an equilateral triangle from a square paper or trisecting an angle),…

Descriptors: Handicrafts, Geometric Concepts, Geometry, Problem Solving

Keazer, Lindsay M.; Menon, Rahul S. – Mathematics Teacher, 2015

This article argues that the practices of reasoning and sense making are critical for developing students' mathematical literacy. Seven mathematics teachers collaborated throughout a school year to discuss the ideas proposed in Reasoning and Sense Making (NCTM 2009) and put them into practice through action research. Conducting action research,…

Descriptors: Mathematics Instruction, Mathematics Teachers, Mathematical Logic, Teacher Collaboration

Russo, Mark F. – Mathematics Teacher, 2015

During the author's career, he has taught many students who loved and excelled at mathematics, as well as students who underachieved and displayed a strong aversion for the subject. Year after year he tried new approaches to reach this latter group, but year after year the results were mostly the same. Helping students understand the content was…

Descriptors: Mathematics Instruction, High School Students, Secondary School Mathematics, Student Interests

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