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Harper, Suzanne R.; Cox, Dana C. – Mathematics Teacher, 2017

In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

Descriptors: Problem Solving, Mathematics Instruction, Student Motivation, Creativity

Freeburn, Ben; Arbaugh, Fran – Mathematics Teacher, 2017

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014, p. 10) contains eight research-informed teaching practices that have been shown to support students' mathematical thinking and learning. Two teaching practices highlighted herein are "to elicit and use evidence of students' thinking" and "support…

Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Logic, Thinking Skills

Bieda, Kristen N.; Huhn, Craig – Mathematics Teacher, 2017

Problem solving has long been a focus of research and curriculum reform (Kilpatrick 1985; Lester 1994; NCTM 1989, 2000; CCSSI 2010). The importance of problem solving is not new, but the Common Core introduced the idea of making sense of problems and persevering in solving them (CCSSI 2010, p. 6) as an aspect of problem solving. Perseverance is…

Descriptors: Mathematics Instruction, Problem Solving, Persistence, Faculty Development

McCaffrey, Tony; Matthews, Percival G. – Mathematics Teacher, 2017

In this article, the authors discuss the potential of the icon-based mathematical games, emoji math and mobile math, to promote student engagement with and understanding of algebra. They describe how these games serve as accessible entry points for algebraic thinking and that, in contrast to traditional symbolic algebra, the use of these…

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

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

Kress, Nancy Emerson – Mathematics Teacher, 2017

One of the primary expectations that the author has for her students is for them to develop greater independence when solving complex and unique mathematical problems. The story of how the author supports her students as they gain confidence and independence with complex and unique problem-solving tasks, while honoring their expectations with…

Descriptors: Mathematics Instruction, Problem Solving, Models, Teacher Student Relationship

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

Lommatsch, Christina W. – Mathematics Teacher, 2017

"Find the extreme values of the function." "At what rate is the distance between A and B increasing after 12 seconds?" Prompts like these can be heard in most first-semester calculus courses. Unfortunately, these cues also tend to prompt students' eyes to glaze over with thoughts of "When will I ever use this?" This…

Descriptors: Mathematics Instruction, Calculus, Relevance (Education), Career Choice

Madden, Sandra R.; Gonzales, Alicia C. – Mathematics Teacher, 2017

It is not every day that a former student greets a teacher with, "Your course changed my life." The authors are the professor and student of the transformative course. Alicia Gonzales wanted to understand how to work with students to co-construct an environment where persistent problem solving in a technologically rich classroom was the…

Descriptors: Problem Solving, Teacher Student Relationship, Secondary School Mathematics, Transformative Learning

Housen, Monica – Mathematics Teacher, 2017

In this article, Monica Housen describes how she uses Guess the Number of . . . , a game that develops estimation skills and persistence to provide a fun, to provide a meaningful experience for her high school students. Each week she displays objects in a clear plastic container, like those for pretzels sold in bulk. Students enter a…

Descriptors: High School Students, Mathematics Instruction, Educational Games, Teaching Methods

FitzPatrick, Daniel L.; Dominguez, Victoria S. – Mathematics Teacher, 2017

Teaching persistence and problem solving must begin with selecting a problem that can be solved mathematically, that allows for multiple methods of solving, and that generally captures the attention and curiosity of the student (Marcus and Fey 2003; NCTM 1991; Van de Walle 2003). This article shows how a STEM three-dimensional (3D) printing…

Descriptors: Problem Solving, Mathematics Instruction, STEM Education, Preservice Teacher Education

Borkovitz, Debra K.; Haferd, Thomas – Mathematics Teacher, 2017

Clock Buddies is our favorite first-day-of-class activity. It starts as a nonthreatening icebreaker activity that helps students learn one another's names, but it soon asks students to find their own strategies for solving a real-world scheduling problem. Even highly math phobic students work with others and succeed. Students gain insight from…

Descriptors: Mathematics Instruction, Mathematics Activities, Arithmetic, Problem Solving

Gerver, Robert; Santucci, Lauren; Leventhal, Hanah – Mathematics Teacher, 2017

For decades, all honors students at North Shore High School in New York were required to write a mathematics paper. In 1991, these papers were eliminated, and a new elective, "Investigations in Math Research," was added to the course catalog. Research is not an innate skill, and now, students of all ability levels who wanted the research…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Secondary School Teachers, Secondary School Students

Samuels, Jason – Mathematics Teacher, 2017

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

Descriptors: Mathematics Instruction, Calculus, Graphs, Problem Solving