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…

Historically, individuals with intellectual disabilities (ID) were limited in the amount of assets that they could earn. However, the enactment of the Achieving a Better Life Experience (ABLE) Act in 2014 provided for significant increases in the amount of earnings and savings allowable. Many of these individuals are capable of saving money and…

The oxidation of iron is an important reaction due to its high economic impact. In this laboratory exploration, the total order of this reaction was determined using commercially available handwarmer packets that rely on the iron-oxygen reaction to generate heat. The active ingredient in the handwarmer packet is iron, which interacts with…

A Number Talk is a brief activity (10-15 minutes in length) that is designed to support students' mathematical sense making and promote flexible thinking. During a Number Talk, students engage in mental computations. Number Talks help students do the following: (1) Develop number sense focused on making sense of quantity and mathematical…

COVID-19, the most severe global pandemic since the Spanish flu that followed World War I, threatens nearly every country, from global powers to developing nations. This threat presents a concurrent challenge for educational systems. With schools closed during the pandemic, students and teachers have had to stay at home worldwide. This shift has…

Research in science, technology, engineering, mathematics (STEM) education suggests development of STEM competency requires effective learning environments, including the use of varied representations (e.g., visual, symbolic) and opportunities for students to make connections among them. Although such practices have been advocated in the teaching…

Developing students' strengths while teaching the content required by national and state standards in science, technology, engineering, and mathematics (STEM) is challenging for classroom teachers. In the Cultivating Diverse Talent in STEM (CDTIS) project, the assessment results found in strength-based reports gave teachers the tools needed to…

We share ideas for preparing for and enacting high-cognitive demand tasks in ways that support students in articulating and justifying their ideas. We offer strategies for developing and posing several types of purposeful questions: (1) eliciting thinking, (2) generating ideas, (3) clarifying explanations, and (4) justifying claims.

Gifted adolescents may identify as "gamers" who create avatars to navigate video games and cell phone apps. Avatars provide a unique venue through which gifted teens can explore the issues of self and identity in a critical time of their development. The purpose of this article is to (a) provide an overview of what avatars are, (b)…

Purpose: This paper aims to investigate design principles for transforming existing making communities of practice within public libraries into online knowledge-building communities to support youths, families with young children and adult members' making and tinkering during COVID-19. Design/methodology/approach: Building upon C4P and connected…

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…

Hubka's theory of technical systems (TTS) is briefly outlined. It describes commonalities in all engineering devices, whatever their physical principles of action. This theory is based on a general transformation system (TrfS), which can be used to show engineering in the contexts of society, economics and historic developments. The life cycle of…

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…

This brief "Math for Real" article introduces Ohanna, a seventh grader who lives in New York City and regularly takes the bus to get around the city. Ohanna pays $2.50 per bus ride when using her MetroCard. She earns a 5% bonus when she refills the card with a minimum of $5.00. For example, if she adds $10.00 on her MetroCard, her…