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Gillette, Jane – Mathematics Teacher, 2018
Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…
Descriptors: Instructional Materials, Mathematics Education, Mathematics Skills, Problem Solving
Ghosh, Jonaki B. – Mathematics Teacher, 2018
The Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…
Descriptors: Mathematics Instruction, Teaching Methods, Puzzles, Preservice Teachers
Zhao, Manqian; Lapuk, Karen – Mathematics Teacher, 2019
According to the National Center for Education Statistics (2016), the number of public school students in the United States who were English learners (ELs) was estimated at 4.5 million. However, in 2005, the national standardized testing scores (Fry 2007) show that about 51 percent of eighth-grade EL students were behind other students in reading…
Descriptors: Mathematics Education, Mathematics Instruction, English Language Learners, Mathematics Teachers
Clinch, Adam – Mathematics Teacher, 2018
One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…
Descriptors: Mathematics Instruction, Algebra, Teaching Methods, Problem Solving
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
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
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
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
Hardy, Michael D. – Mathematics Teacher, 2014
Unit conversion need not be boring. If students see that the skill is necessary, both their motivation to learn and their appreciation of the process can be enhanced. As a result, students become actively engaged and construct understanding and computational skills that they will retain over time. The activity described here makes use of scale…
Descriptors: Mathematics Instruction, Motor Vehicles, Mathematics Skills, Teaching Methods
Bossé, Michael J.; Lynch-Davis, Kathleen; Adu-Gyamfi, Kwaku; Chandler, Kayla – Mathematics Teacher, 2016
Assessment and instruction are interwoven in mathematically rich formative assessment tasks, so employing these tasks in the classrooms is an exciting and time-efficient opportunity. To provide a window into how these tasks work in the classroom, this article analyzes summaries of student work on such a task and considers several students'…
Descriptors: Mathematics Instruction, Formative Evaluation, Student Evaluation, Problem Solving
Eddy, Colleen M.; Pratt, Sarah S.; Green, Cheyenne N. – Mathematics Teacher, 2018
Have you ever considered how technology could facilitate reasoning and sense making of systems of linear inequalities? In this article, the authors share how to use Google® Maps® and Desmos to achieve this and provide students with opportunities to access mathematics as they build a more formalized understanding. Using an inquiry-based approach,…
Descriptors: Maps, Mathematics Instruction, Mathematical Concepts, Inquiry
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
Mulcahy, Colm; Goetz, Albert – Mathematics Teacher, 2014
This article begins with three brain teasers, and the answers, provided at the end of the article, may prove surprising. Figuring out why they are correct leads the reader to delightful "aha" moments. The kinds of "aha!" moments that result from solving these challenges for yourself were held in high estimation by the person…
Descriptors: Mathematics Instruction, Teaching Methods, Problem Solving, Student Motivation
Shaw, Doug J.; Miller, Catherine M. – Mathematics Teacher, 2015
Since 1950, the Prisoner's Dilemma has intrigued economists and amused fans of mathematics. It presents a situation in which two players acting to their own advantage do not do as well together as two players whose actions oppose their individual interests--hence, the dilemma. Variations of the Prisoner's Dilemma have appeared in diverse…
Descriptors: Game Theory, Mathematics Education, Mathematics Activities, Mathematical Logic
Watanabe, Maika; Evans, Laura – Mathematics Teacher, 2015
This article discusses assessments that can be used to help encourage a collaborative classroom community, in which students help one another learn mathematics. The authors describe participation quizzes and explanation quizzes as assessment tools that encourage students to work together, share specific questions on challenging mathematics…
Descriptors: Cooperative Learning, Mathematics Instruction, Student Evaluation, Mathematics Tests