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Purvinis, Elaine M.; Fagan, Joshua B. – Mathematics Teacher, 2019

In first- and second-year algebra classrooms, the all-too-familiar whine of "when are we ever going to use this in real life?" challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect…

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

Ichinose, Cherie Lynn; Martinez-Cruz, Armando M. – Mathematics Teacher, 2018

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…

Descriptors: Mathematics Instruction, Teaching Methods, Problem Solving, Common Core State Standards

Angotti, Robin L.; Mudzimiri, Rejoice – Mathematics Teacher, 2018

Mathematical modeling, a key strand in mathematics, engages students in rich, authentic, exciting, and culturally relevant problems and connects abstract mathematics to the surrounding world. In this, article, the authors describe a modeling activity that can be used when teaching linear equations. Modeling problems, in general, are typically high…

Descriptors: Mathematics Instruction, Mathematical Models, Relevance (Education), Problem Solving

Coomes, Jacqueline – Mathematics Teacher, 2018

It is critical for mathematics tasks to provide students with the opportunity to engage actively in reasoning, sense making, and problem solving so that they develop a deep understanding of mathematics. Learning mathematics while solving a problem can be like entering a dark room with a single small light. The objects are in the shadows, difficult…

Descriptors: Mathematics Instruction, Problem Solving, Mathematical Concepts, Concept Formation

Murray, Natasha T. K. – Mathematics Teacher, 2018

How can we make sense of what we learned today?" This is a question the author commonly poses to her algebra students in an effort to have them think about the connections between the new concept they are learning and concepts they have previously learned. For students who have a strong, expansive understanding of previously learned topics,…

Descriptors: Mathematical Concepts, Number Concepts, Algebra, Mathematics Instruction

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

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

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

Taff, Jason – Mathematics Teacher, 2017

In this article, Jason Taff shares an approach that he presented to advanced seventh-grade prealgebra students. He begins by summarizing some of the shortcomings of equating the order of operations concept with the PEMDAS (often rendered mnemonically as "Please Excuse My Dear Aunt Sally") procedure with the hope of helping teachers at…

Descriptors: Grade 7, Algebra, Mathematics Instruction, Mnemonics

Dougherty, Barbara J.; Bush, Sarah B.; Karp, Karen S. – Mathematics Teacher, 2017

The perpetuation of mathematical rules that expire (Karp, Bush, and Dougherty 2014; 2015), or rules that are taught in previous grades that no longer hold true, suggests that many secondary students harbor misconceptions from their elementary and middle-grades mathematics experiences as they progress to mathematics classes that are more…

Descriptors: Mathematics Instruction, Secondary School Mathematics, High Schools, Standards

Goldenberg, E. Paul; Carter, Cynthia J. – Mathematics Teacher, 2017

A first-year algebra student's curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics. In this article, the authors, math teachers in Massachusetts, examine how to solve for factorials of negative numbers and discuss how they taught…

Descriptors: Algebra, Secondary School Mathematics, Numbers, Mathematics Teachers

Turton, Roger – Mathematics Teacher, 2016

"Mathematical Lens" uses photographs as a springboard for mathematical inquiry and appears in every issue of "Mathematics Teacher." Recently while dismantling an old wooden post-and-rail fence, Roger Turton noticed something very interesting when he piled up the posts and rails together in the shape of a prism. The total number…

Descriptors: Mathematics, Mathematics Instruction, Teaching Methods, Photography

Lancaster, Ron – Mathematics Teacher, 2016

Can you solve the following Problem? There are 200 fish in an aquarium, and 99 percent of them are guppies. How many guppies must be removed to reduce the tank's guppy population to 98 percent? The key to this problem is to work backward by using the data given in figure 2 to determine the surface area of the top of the aquarium; then determine…

Descriptors: Mathematics Instruction, Problem Solving, Word Problems (Mathematics), Equations (Mathematics)

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

Goetz, Albert – Mathematics Teacher, 2016

"Media Clips" appears in every issue of "Mathematics Teacher," offering readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. Based on "In All the Light We Cannot See" (2014), by Anthony Doerr, this article provides a brief trigonometry problem that was solved by…

Descriptors: Mathematics Instruction, Trigonometry, Problem Solving, Equations (Mathematics)