A problem-based learning activity focusing on the human impact on the environment and the importance of sustainable development is presented. The activity revolves around a mysterious island where the civilization is on the blink of extinction, prompting students to investigate how human behavior, ecosystems, resources, and natural balance…

In this article, the author describes strategies to support students in conjecturing in ways that promote their agency. Conjecturing involves justifying (i.e., a practice that promotes epistemic agency and engages students in mathematical reasoning to defend their claims; Bieda & Staples, 2020) by which a conjecture becomes proven, modified,…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

A Common Core expectation of high school mathematics students is to analyze functions using different representations. One type of function to be analyzed is piecewise-defined functions. The author has found most approaches to the study of piecewise functions to be abstract, disconnected from any context, and difficult for students to understand.…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

This article details a high school classroom activity in which algebra tiles are used to help students gain a conceptual understanding of completing the square. The activity utilises the eight elements of effective mathematics education suggested in the National Council of Teacher of Mathematics' (NCTM's) "Principles to action: Ensuring…

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…

Recognizing the challenges that students face when they may lack background and experiential knowledge with regard to coins is important so that teachers can address this during instruction. Exposure to coins is one of the basic necessities to learning about the coins, but that is just the initial part of the learning sequence. Unless students are…

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach…

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…

Educators across the nation are now well under way in implementing the Common Core State Standards (CCSS; National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010) for mathematics. The emerging literature regarding CCSS mathematics instruction for students with disabilities urges…

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

Statistics standards found in the Common Core (CCSSI 2010) and other state standards require considerable instructional time and focus for students to develop the depth and breadth of understanding necessary. In this article, the authors offer an approach to teaching a statistics unit that combines student choice with authentic and sustained…

Long before the release of the Common Core State Standards (CCSSI 2010), the Mathematical Tug-of-War was engaging students in the type of reasoning and problem solving described by the Standards for Mathematical Practice (SMP). In this updated version of a Marilyn Burns task, students use algebraic reasoning to determine the outcome of a contest…

In "The Critical Advantage," noted scholar and early childhood expert William T. Gormley, Jr. takes a wide ranging look at the important role of critical thinking in preparing students for college, careers, and civic life. Drawing on research from psychology, philosophy, business, political science, neuroscience, and other disciplines,…